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Consider the difference where we have set 623 = 1/4. We search for energy and path length ranges where this difference is large. We expect the energy range to be range of resonance, from the first term. This is nearly true. The fourth term, which has a negative sign, is zero when the phase (1.27632L/E) ~ nm. Hence the above difference is likely to be large for those energies which are in the resonance energy range and for which the phase condition is satisfied.

Figure 12 Consider the difference where we have set 623 = 1/4. We search for energy and path length ranges where this difference is large. We expect the energy range to be range of resonance, from the first term. This is nearly true. The fourth term, which has a negative sign, is zero when the phase (1.27632L/E) ~ nm. Hence the above difference is likely to be large for those energies which are in the resonance energy range and for which the phase condition is satisfied.

Related Figures (152)

Figure 2.1: Neutrino spectrum from different sources as a function of energy
Figure 2.1: Neutrino spectrum from different sources as a function of energy
Figure 2.2: Schematic illustration of the status of masses and mixing of neutrino eigenstates. The flavour content is indicated by different shading; the vy. contribution shown in the third mass eigenstate is an upper bound. The direct or normal mass hierarchy is assumed here; in the case of the inverted hierarchy, the v3 state would be the lightest. The mass squared differences as obtained from the data are also shown.
Figure 2.2: Schematic illustration of the status of masses and mixing of neutrino eigenstates. The flavour content is indicated by different shading; the vy. contribution shown in the third mass eigenstate is an upper bound. The direct or normal mass hierarchy is assumed here; in the case of the inverted hierarchy, the v3 state would be the lightest. The mass squared differences as obtained from the data are also shown.
Table 2.1: On-going and planned large scale neutrino experiments [43]. If approved shortly, ICAL at the proposed INO laboratory is expected to be operational by 2010-11.
Table 2.1: On-going and planned large scale neutrino experiments [43]. If approved shortly, ICAL at the proposed INO laboratory is expected to be operational by 2010-11.
Table 3.1: Best-fit values and 30 intervals for three flavour neutrino oscillation parame- ters from global data including solar, atmospheric, reactor (KamLAND and CHOOZ) and accelerator (K2K) experiments [53].
Table 3.1: Best-fit values and 30 intervals for three flavour neutrino oscillation parame- ters from global data including solar, atmospheric, reactor (KamLAND and CHOOZ) and accelerator (K2K) experiments [53].
Figure 3.1: The allowed neutrino parameter space allowed from solar, atmospheric, reactor and accelerator experiments [29, 30].
Figure 3.1: The allowed neutrino parameter space allowed from solar, atmospheric, reactor and accelerator experiments [29, 30].
Figure 3.2: The current neutrino parameter space relevant to atmospheric neutrino oscilla- tions. Figure from Ref. [28].
Figure 3.2: The current neutrino parameter space relevant to atmospheric neutrino oscilla- tions. Figure from Ref. [28].
The atmospheric neutrino physics program possible with a magnetised iron tracking calorime- ter is substantial. It is possible to observe a clear signal of oscillation by observing one full oscillation period so that the precision of the parameters, 632 and 023, can be improved to 10%. A broad range in both path length L (see Fig. 3.3) and energy, E, and indeed in theit ratio, L/E, possible with atmospheric neutrinos, offers the opportunity to probe a large range of d32. Among the physics capabilities, in addition, are the sensitivity to matter effects
The atmospheric neutrino physics program possible with a magnetised iron tracking calorime- ter is substantial. It is possible to observe a clear signal of oscillation by observing one full oscillation period so that the precision of the parameters, 632 and 023, can be improved to 10%. A broad range in both path length L (see Fig. 3.3) and energy, E, and indeed in theit ratio, L/E, possible with atmospheric neutrinos, offers the opportunity to probe a large range of d32. Among the physics capabilities, in addition, are the sensitivity to matter effects
Table 3.2: Precision for |53;| and sin? 623 at 30 for the true values 63; = 2 x 1073 eV’, sin? 023 = 0.5 for 5 years exposure. Table reproduced from [39] with information added on ICAL/INO. Note that the table refers to the older NOvA proposal; the revised March 2005 “totally active’ NOvA detector is expected to be competitive with T2K. where Pmax aNd Pmin are the maximum and minimum allowed values of the parameter p, at a given confidence level, and po is the best-fit value. The precision on 639 and sin? 693 is currently set by the Super-K and K2K data and is shown at 3a level in Table 3.2.
Table 3.2: Precision for |53;| and sin? 623 at 30 for the true values 63; = 2 x 1073 eV’, sin? 023 = 0.5 for 5 years exposure. Table reproduced from [39] with information added on ICAL/INO. Note that the table refers to the older NOvA proposal; the revised March 2005 “totally active’ NOvA detector is expected to be competitive with T2K. where Pmax aNd Pmin are the maximum and minimum allowed values of the parameter p, at a given confidence level, and po is the best-fit value. The precision on 639 and sin? 693 is currently set by the Super-K and K2K data and is shown at 3a level in Table 3.2.
Figure 3.6: The relative error on 63) and sin? 493 as a function of the input value of 639 at the 2c level. The figure is adapted from Ref [39]. As in Table 3.2, the curve for NOvA corresponds to the older proposal. The precision with the revised March 2005 “totally active” NOVA is expected to be comparable to that from T2K. The errors for a 5 year exposure at ICAL have been overlaid. The achievable precision from future running or proposed experiments is also listed, along with the precision from ICAL. All numbers correspond to 5 years exposure of the detector [39]. It is seen that ICAL will be marginally better than the MINOS experiment. Of course in all cases, the precision will improve with exposure. Moreover, this precision is strongly sensitive to the central values of these parameters. This dependence is shown in Fig. 3.6 at the 20 level. Again, it is seen that the advantages of ICAL will be fully exploited if 639 is at the lower end of the allowed range.
Figure 3.6: The relative error on 63) and sin? 493 as a function of the input value of 639 at the 2c level. The figure is adapted from Ref [39]. As in Table 3.2, the curve for NOvA corresponds to the older proposal. The precision with the revised March 2005 “totally active” NOVA is expected to be comparable to that from T2K. The errors for a 5 year exposure at ICAL have been overlaid. The achievable precision from future running or proposed experiments is also listed, along with the precision from ICAL. All numbers correspond to 5 years exposure of the detector [39]. It is seen that ICAL will be marginally better than the MINOS experiment. Of course in all cases, the precision will improve with exposure. Moreover, this precision is strongly sensitive to the central values of these parameters. This dependence is shown in Fig. 3.6 at the 20 level. Again, it is seen that the advantages of ICAL will be fully exploited if 639 is at the lower end of the allowed range.
Figure 3.7: The muon survival probability in vacuum and in matter for both signs of d39 plotted against the neutrino energy for different values of baseline lengths, L (in km). The oscillation parameters used in all the plots are : 632 = 2 x 10~eV? and sin? 2623 = 1.
Figure 3.7: The muon survival probability in vacuum and in matter for both signs of d39 plotted against the neutrino energy for different values of baseline lengths, L (in km). The oscillation parameters used in all the plots are : 632 = 2 x 10~eV? and sin? 2623 = 1.
Figure 3.8: The total event rate for muons and anti-muons in matter and in vacuum plottec against L for the restricted choice of L and E range.
Figure 3.8: The total event rate for muons and anti-muons in matter and in vacuum plottec against L for the restricted choice of L and E range.
Figure 3.9: Left: The total event rate for muons and anti-muons in matter and in vacuum plotted against log,,(L/F) for the restricted choice of L and E range. Right: The muon survival probability P/j, and the anti-muon survival probability P?; in matter and in vacuum Pi, plotted against log,)(L/E) for positive sign of 632.
Figure 3.9: Left: The total event rate for muons and anti-muons in matter and in vacuum plotted against log,,(L/F) for the restricted choice of L and E range. Right: The muon survival probability P/j, and the anti-muon survival probability P?; in matter and in vacuum Pi, plotted against log,)(L/E) for positive sign of 632.
Table 3.3: Significance of the asymmetry for different exposures in kton-years for resolution widths 0, in E and L (see Eq. 3.24) of 15%. Asymmetries are shown for typical values of $13 = 7,9, 11, 13°; the CHOOZ bound limits this angle to 6,3 < 14.9°.
Table 3.3: Significance of the asymmetry for different exposures in kton-years for resolution widths 0, in E and L (see Eq. 3.24) of 15%. Asymmetries are shown for typical values of $13 = 7,9, 11, 13°; the CHOOZ bound limits this angle to 6,3 < 14.9°.
Table 3.4: Same as Table 3.3 for resolution widths 0) in E and L (see Eq. 3.24) of 10%
Table 3.4: Same as Table 3.3 for resolution widths 0) in E and L (see Eq. 3.24) of 10%
Figure 3.12: The difference Uy /Dy — U4/D, for various bins of F and |c¢|.
Figure 3.12: The difference Uy /Dy — U4/D, for various bins of F and |c¢|.
Figure 3.13: Sensitivity to octant ambiguity resolution in terms of 413
Figure 3.13: Sensitivity to octant ambiguity resolution in terms of 413
Figure 3.14: Variation of the ratio of the rates for up-coming and down-going neutrinos, integrated from E = 5-10 GeV, in bins of logj) Z (km)/E (GeV) = 0.1. The variation with Am? is shown in the three panels, where results for a Am? over the currently allowed lo range, via., Am? = (2.1,2.4,2.7) x 10~% eV? are shown. The two histograms in each panel correspond to 623 = 40° (upper) and 50° (lower). The value of 013 is kept fixed at 9°. Statistical error bars corresponding to an exposure of 1000 kton-years are also shown.
Figure 3.14: Variation of the ratio of the rates for up-coming and down-going neutrinos, integrated from E = 5-10 GeV, in bins of logj) Z (km)/E (GeV) = 0.1. The variation with Am? is shown in the three panels, where results for a Am? over the currently allowed lo range, via., Am? = (2.1,2.4,2.7) x 10~% eV? are shown. The two histograms in each panel correspond to 623 = 40° (upper) and 50° (lower). The value of 013 is kept fixed at 9°. Statistical error bars corresponding to an exposure of 1000 kton-years are also shown.
Figure 3.15: As in Fig. 3.14, for 6:3; = 9°, including finite detector resolutions. Above: smearing in F and @ by Gaussian resolutions with widths og/E = 0.15 and og = 5°, and Below: smearing in F and L by Gaussian resolutions with widths og/E = 0,/L = 0.15. We now go on to study the effect of finite detector resolutions on the extraction of oscillation parameters. We generate contours of allowed parameter space for an input data of up/down neutrino and anti-neutrino event rates in fixed L/F bins for a set of input values for (013, Am?, 623) and focus, as before, on the octant resolution. The other parameters,
Figure 3.15: As in Fig. 3.14, for 6:3; = 9°, including finite detector resolutions. Above: smearing in F and @ by Gaussian resolutions with widths og/E = 0.15 and og = 5°, and Below: smearing in F and L by Gaussian resolutions with widths og/E = 0,/L = 0.15. We now go on to study the effect of finite detector resolutions on the extraction of oscillation parameters. We generate contours of allowed parameter space for an input data of up/down neutrino and anti-neutrino event rates in fixed L/F bins for a set of input values for (013, Am?, 623) and focus, as before, on the octant resolution. The other parameters,
Figure 3.16: Allowed parameter space from neutrino and anti-neutrino up/down event rates for an exposure of 1000 kton-years and input parameter values (623, 013) = (39°, 7°) for fixed Am? = 2.4 x 1073 eV”. The 99% CL contours are shown for an ideal detector (dashed lines) and for a detector with finite Gaussian resolutions of widths 15% in EF and L. An island of input allowed parameter space near the “wrong octant” solution, 023 = 7/2 — 633°" = 51°, marked with a a cross, is seen. 69, and 9, have been fixed at their best-fit values, and we have used 6 = 0. We find that atmospheric neutrino (and anti-neutrino) data accumulated over 1000 kton-years is sufficient to distinguish a non-maximal solution from a maximal solution as well as the octant of 423 for 613 > 8° and 693 < 39° or 623 > 51°. The inclusion of finite detector resolution severely degrades the errors on the parameters. For instance, the error on Am? is twice as large as that with an ideal detector. This is shown for two values of 613, 013 = 7°,8°, for 623 = 39° (sin? 023 = 0.4) and Am? = 2.4 x 107% eV? in Figs. 3.16 and 3.17 respectively.
Figure 3.16: Allowed parameter space from neutrino and anti-neutrino up/down event rates for an exposure of 1000 kton-years and input parameter values (623, 013) = (39°, 7°) for fixed Am? = 2.4 x 1073 eV”. The 99% CL contours are shown for an ideal detector (dashed lines) and for a detector with finite Gaussian resolutions of widths 15% in EF and L. An island of input allowed parameter space near the “wrong octant” solution, 023 = 7/2 — 633°" = 51°, marked with a a cross, is seen. 69, and 9, have been fixed at their best-fit values, and we have used 6 = 0. We find that atmospheric neutrino (and anti-neutrino) data accumulated over 1000 kton-years is sufficient to distinguish a non-maximal solution from a maximal solution as well as the octant of 423 for 613 > 8° and 693 < 39° or 623 > 51°. The inclusion of finite detector resolution severely degrades the errors on the parameters. For instance, the error on Am? is twice as large as that with an ideal detector. This is shown for two values of 613, 013 = 7°,8°, for 623 = 39° (sin? 023 = 0.4) and Am? = 2.4 x 107% eV? in Figs. 3.16 and 3.17 respectively.
to the octant of 623. That is, 0:3 = 7° (sin? 6,3 = 0.015) remains the limit at which matter effects are substantial enough to determine the octant of the (23) mixing angle (as also the mass ordering of the (23) mass eigenstates, as discussed in Ref. |60]), even on including finite resolution functions, while the actual value of the (23) angle which simultaneously allows maximality and octant discrimination at 99% CL level moves marginally from 423 = 40° in the absence of finite resolution effects, to 623 = 39° (sin? 23 ~ 0.4) at the lower limit of 6,3. We note that the situation is not as clean when the true value of 43 lies in the second octant. The muon survival probability in this case is not as well separated from that for max- imal 03, unlike when 63 is in the first octant. Hence, while results for octant discrimination will be symmetric with the case when 693 is in the first octant, the issue of maximality may not be so easily settled. For example, with other parameters as before, and using 623 = 51°, which is the octant mirror of #23 = 39°, the “data” discriminate between the right and wrong octant at 99% CL, but cannot discriminate the true value of 623 from maximality. By going farther away from maximality, for example, at 023 = 52.5°, we once again have maximality discrimination. Tee eee ee th ee cee
to the octant of 623. That is, 0:3 = 7° (sin? 6,3 = 0.015) remains the limit at which matter effects are substantial enough to determine the octant of the (23) mixing angle (as also the mass ordering of the (23) mass eigenstates, as discussed in Ref. |60]), even on including finite resolution functions, while the actual value of the (23) angle which simultaneously allows maximality and octant discrimination at 99% CL level moves marginally from 423 = 40° in the absence of finite resolution effects, to 623 = 39° (sin? 23 ~ 0.4) at the lower limit of 6,3. We note that the situation is not as clean when the true value of 43 lies in the second octant. The muon survival probability in this case is not as well separated from that for max- imal 03, unlike when 63 is in the first octant. Hence, while results for octant discrimination will be symmetric with the case when 693 is in the first octant, the issue of maximality may not be so easily settled. For example, with other parameters as before, and using 623 = 51°, which is the octant mirror of #23 = 39°, the “data” discriminate between the right and wrong octant at 99% CL, but cannot discriminate the true value of 623 from maximality. By going farther away from maximality, for example, at 023 = 52.5°, we once again have maximality discrimination. Tee eee ee th ee cee
where 632 and 6b are the differences between the eigenvalues of the matrices m? and b, re- spectively. Note that db has units of energy (GeV). We assume equal masses for neutrinos and anti-neutrinos. For simplicity we have assumed that the two mixing angles that diago- nalize the matrices m? and b are equal (i.e. Am = 6 = 6). In addition, the additional phase that arises due to the two different unitary matrices needed to diagonalize the 63. and db matrices® is set to zero. The difference between P,,,, and Pyz is given by
where 632 and 6b are the differences between the eigenvalues of the matrices m? and b, re- spectively. Note that db has units of energy (GeV). We assume equal masses for neutrinos and anti-neutrinos. For simplicity we have assumed that the two mixing angles that diago- nalize the matrices m? and b are equal (i.e. Am = 6 = 6). In addition, the additional phase that arises due to the two different unitary matrices needed to diagonalize the 63. and db matrices® is set to zero. The difference between P,,,, and Pyz is given by
Figure 3.19: The ratio of total (up+down) muon to anti-muon events plotted against log,o( for different values of db (in GeV). The oscillation parameters used in all the plots 632 2x 10-%eV? and sin? 2653 = 1.
Figure 3.19: The ratio of total (up+down) muon to anti-muon events plotted against log,o( for different values of db (in GeV). The oscillation parameters used in all the plots 632 2x 10-%eV? and sin? 2653 = 1.
4A similar asymmetry has also been studied in the context of the ordinary matter effects in [60 Based on the above observations, we identify the following asymmetry’:
4A similar asymmetry has also been studied in the context of the ordinary matter effects in [60 Based on the above observations, we identify the following asymmetry’:
Figure 3.22: Base lengths (km) from the proposed neutrino factories to the two proposed INO sites in India: Left half shows the base lengths to the site at PUSHEP whereas the right-half shows the base lengths to the site at Rammam. The densities of the layers that the neutrinos pass through are also indicated.
Figure 3.22: Base lengths (km) from the proposed neutrino factories to the two proposed INO sites in India: Left half shows the base lengths to the site at PUSHEP whereas the right-half shows the base lengths to the site at Rammam. The densities of the layers that the neutrinos pass through are also indicated.
Figure 3.23: The sin #3 reach for detector exposures of 32 kton-year, 50 kton-year and 100 kton-year for an entry-level neutrino factory configuration with 1 = 20 GeV for the JHF-Rammam and the JHF-PUSHI EP baseline. The lower panels show the change in reach if the storage muon energy is increased to 50 GeV, keeping the number of decays per year the same, i.e, 10!°/year; there is substantial improvement in the reach in the case of the JHF-Rammam baseline.
Figure 3.23: The sin #3 reach for detector exposures of 32 kton-year, 50 kton-year and 100 kton-year for an entry-level neutrino factory configuration with 1 = 20 GeV for the JHF-Rammam and the JHF-PUSHI EP baseline. The lower panels show the change in reach if the storage muon energy is increased to 50 GeV, keeping the number of decays per year the same, i.e, 10!°/year; there is substantial improvement in the reach in the case of the JHF-Rammam baseline.
via this method. Note that the event-rate peaks nicely for neutrinos in the 10-20 GeV range for the currently allowed and favoured range of values of 632 from atmospheric neutrino data. Figure 3.24: The number of wrong-sign muon events as a function of E,/632 (GeV/eV?) for the Fermilab—-PUSHEP baseline. The dip to the left of the distribution is due to a minimum of the oscillation probability.
via this method. Note that the event-rate peaks nicely for neutrinos in the 10-20 GeV range for the currently allowed and favoured range of values of 632 from atmospheric neutrino data. Figure 3.24: The number of wrong-sign muon events as a function of E,/632 (GeV/eV?) for the Fermilab—-PUSHEP baseline. The dip to the left of the distribution is due to a minimum of the oscillation probability.
Figure 3.25: The number of wrong-sign muon events as a function of 632 for the three baselines from JHF, demonstrating the sign discriminating capability which arises as a result of matter effects. Event rates are computed for an entry-level configuration with a 32 kton- year exposure, beam energy of 20 GeV and 10!" decays per year.
Figure 3.25: The number of wrong-sign muon events as a function of 632 for the three baselines from JHF, demonstrating the sign discriminating capability which arises as a result of matter effects. Event rates are computed for an entry-level configuration with a 32 kton- year exposure, beam energy of 20 GeV and 10!" decays per year.
Figure 3.26: The same as Fig. 3.25, but for an upgraded neutrino factory configuration with a 50 kton-year exposure, 10?! decays per year and a beam energy of 50 GeV.
Figure 3.26: The same as Fig. 3.25, but for an upgraded neutrino factory configuration with a 50 kton-year exposure, 10?! decays per year and a beam energy of 50 GeV.
Figure 3.27: The ratio of wrong-sign muon events for equal-time runs of opposite sign muons and 6 = +7/2 (dashed curves) and 6 = 0 (data points, with statistical error bars) in the storage ring, versus base-length. All plots correspond to 10?! yz decays per year. The top row shows the results for sin@,;3 = 0.1 (sin? 26;3 = 0.04) and 10?! decays per year, with beam energies of 20 GeV in one case and 50 GeV in the other. The bottom row shows the results when sin 613 = 0.03 (sin? 2613 = 0.0036). The positions of the data points reflect the base-lengths for detector locations at Beijing, Rammam and PUSHEP in order of increasing leneth.
Figure 3.27: The ratio of wrong-sign muon events for equal-time runs of opposite sign muons and 6 = +7/2 (dashed curves) and 6 = 0 (data points, with statistical error bars) in the storage ring, versus base-length. All plots correspond to 10?! yz decays per year. The top row shows the results for sin@,;3 = 0.1 (sin? 26;3 = 0.04) and 10?! decays per year, with beam energies of 20 GeV in one case and 50 GeV in the other. The bottom row shows the results when sin 613 = 0.03 (sin? 2613 = 0.0036). The positions of the data points reflect the base-lengths for detector locations at Beijing, Rammam and PUSHEP in order of increasing leneth.
Figure 3.28: The same as Fig. 3.27, but for baselines corresponding to Fermilab—-PUSHEP and Fermilab—Rammam along with the same rati All other parameters are indicated in the plots. os for JHF to the two proposed Indian sites. The data points with the sharp line through them are for 6 = 0. The other lines are for 6 = 4 tn /2.
Figure 3.28: The same as Fig. 3.27, but for baselines corresponding to Fermilab—-PUSHEP and Fermilab—Rammam along with the same rati All other parameters are indicated in the plots. os for JHF to the two proposed Indian sites. The data points with the sharp line through them are for 6 = 0. The other lines are for 6 = 4 tn /2.
In vacuum we have
In vacuum we have
Figure 3.30: The flavour composition of mass eigenstates in vacuum (A = 0) and in matter at resonance (A = A,.,). The vacuum parameters used are sin?2023 = 1.0 and sin?20,3 = 0.1.
Figure 3.30: The flavour composition of mass eigenstates in vacuum (A = 0) and in matter at resonance (A = A,.,). The vacuum parameters used are sin?2023 = 1.0 and sin?20,3 = 0.1.
at neutrino factories. Typical baselines from existing and proposed neutrino factories to two the possible sites for INO include L ~ 7000 km (PUSHEP-CERN and Rammam-—CERN). Also baselines ZL ~ 10500 km are possible for (PUSHEP-Fermilab and Rammam-Fermilab) and these are well within the range of baselines where these effects are large and observable [63]. Figure 3.31: P,,, as a function of the neutrino energy, EF (GeV) for different values of 43 and 631 = 0.002 eV?.
at neutrino factories. Typical baselines from existing and proposed neutrino factories to two the possible sites for INO include L ~ 7000 km (PUSHEP-CERN and Rammam-—CERN). Also baselines ZL ~ 10500 km are possible for (PUSHEP-Fermilab and Rammam-Fermilab) and these are well within the range of baselines where these effects are large and observable [63]. Figure 3.31: P,,, as a function of the neutrino energy, EF (GeV) for different values of 43 and 631 = 0.002 eV?.
Figure 3.32: P,,, plotted against the neutrino energy, E(in GeV) for different values of 613. Here 63, = 0.002 eV?.
Figure 3.32: P,,, plotted against the neutrino energy, E(in GeV) for different values of 613. Here 63, = 0.002 eV?.
Figure 4.1: All-particle energy spectrum; results from various experiments. Figure repro- duced from Ref. [89].
Figure 4.1: All-particle energy spectrum; results from various experiments. Figure repro- duced from Ref. [89].
The calculations which follow are performed for a 50 kton iron calorimeter. Our prototype is based on the suggested design for ICAL at INO. We note that a muon with energy E,, = 100 TeV generates approximately 40 cascades, each of energy greater than Ey = 10 GeV and 10 cascades with energy in excess of 100 GeV. By counting the cascades for several choices of thresholds for a traversing muon, a reliable estimate of its energy may be obtained. Fig. 4.2 shows the average number of cascades above a threshold energy Eo produced by a muon entering the detector with energy E,, and T’ = 1000 radiation lengths. Three different choices of Eo = 1, 10,100 GeV are used. Figure 4.2: Average number of cascades above a threshold Eg vs. muon energy. The three lines correspond to Ey = 1 GeV (solid), Eg = 10 GeV (dotted) and Ey = 100 GeV(dashed), with T’ = 1000 radiation lengths.
The calculations which follow are performed for a 50 kton iron calorimeter. Our prototype is based on the suggested design for ICAL at INO. We note that a muon with energy E,, = 100 TeV generates approximately 40 cascades, each of energy greater than Ey = 10 GeV and 10 cascades with energy in excess of 100 GeV. By counting the cascades for several choices of thresholds for a traversing muon, a reliable estimate of its energy may be obtained. Fig. 4.2 shows the average number of cascades above a threshold energy Eo produced by a muon entering the detector with energy E,, and T’ = 1000 radiation lengths. Three different choices of Eo = 1, 10,100 GeV are used. Figure 4.2: Average number of cascades above a threshold Eg vs. muon energy. The three lines correspond to Ey = 1 GeV (solid), Eg = 10 GeV (dotted) and Ey = 100 GeV(dashed), with T’ = 1000 radiation lengths.
Table 4.1: PRS parameters for the prompt muon and anti-muon fluxes. m, is the mass of the charm quark. The second column refers to the different parametrisations of the parton distribution.
Table 4.1: PRS parameters for the prompt muon and anti-muon fluxes. m, is the mass of the charm quark. The second column refers to the different parametrisations of the parton distribution.
Figure 4.3: Degraded muon energy, /,, vs. surface muon energy, £7 after passing a depth of 3.5 x 10°g/cm?, corresponding to the proposed INO location.
Figure 4.3: Degraded muon energy, /,, vs. surface muon energy, £7 after passing a depth of 3.5 x 10°g/cm?, corresponding to the proposed INO location.
Figure 4.4: Left: (Es°x Flux) vs. surface muon energy E* for total TIG flux (solid), conventional (dotted), TIG prompt (short dashed), and prompt fluxes corresponding to PRS1 (short spaced dots), PRS2 (large dashed) and PRS3 (large spaced dots). Right: (E? x Flux) vs. energy of muon entering the underground detector E,,, (for the flux models listed on the left) after passing through the rock distance of 3.5 x 10°gm/cm?. where « = Logio(E/GeV), with a,b,c and d as in Table.4.1. In | surface rbove Fig. 4.4 (left panel) we show the conventional (TIG) and prompt (TIG and PRS) muon fluxes. We note that depending on the flux model, the prompt fluxes rise the conventional flux for (surface) muon energies between 200 TeV and 1000 TeV. In terms of (degraded) muons entering the detector, we see from Fig. 4.3 and Fig. 4.4 tight panel) that this corresponds to measured muon energies of several tens of TeV and several will he hundreds of TeV. Thus, we note that underground muon measurements in this range p reduce the present uncertainties in deducing the charm contributions to muon and veutrino fluxes. Our calculations below provide a quantitative estimate of the potential o! chese measurements to accomplish this.
Figure 4.4: Left: (Es°x Flux) vs. surface muon energy E* for total TIG flux (solid), conventional (dotted), TIG prompt (short dashed), and prompt fluxes corresponding to PRS1 (short spaced dots), PRS2 (large dashed) and PRS3 (large spaced dots). Right: (E? x Flux) vs. energy of muon entering the underground detector E,,, (for the flux models listed on the left) after passing through the rock distance of 3.5 x 10°gm/cm?. where « = Logio(E/GeV), with a,b,c and d as in Table.4.1. In | surface rbove Fig. 4.4 (left panel) we show the conventional (TIG) and prompt (TIG and PRS) muon fluxes. We note that depending on the flux model, the prompt fluxes rise the conventional flux for (surface) muon energies between 200 TeV and 1000 TeV. In terms of (degraded) muons entering the detector, we see from Fig. 4.3 and Fig. 4.4 tight panel) that this corresponds to measured muon energies of several tens of TeV and several will he hundreds of TeV. Thus, we note that underground muon measurements in this range p reduce the present uncertainties in deducing the charm contributions to muon and veutrino fluxes. Our calculations below provide a quantitative estimate of the potential o! chese measurements to accomplish this.
Figure 4.5: Left: Number of muons entering the 50 kton detector in 5 years per solid angle vs. muon energy. Energy losses in the surrounding rock are taken into account. Depth of the detector is assumed to be 3.5 x 10°g/cm?. Right: Number of cascades above a threshold Eo = 10 GeV per solid angle in 5 years of exposure time for a 50 kton iron detector, for various flux models described in the text. Here E,, is the energy of the muon entering the detector, assuming it traversed a depth of rock corresponding to 3.5 x 10°gm/cm?.
Figure 4.5: Left: Number of muons entering the 50 kton detector in 5 years per solid angle vs. muon energy. Energy losses in the surrounding rock are taken into account. Depth of the detector is assumed to be 3.5 x 10°g/cm?. Right: Number of cascades above a threshold Eo = 10 GeV per solid angle in 5 years of exposure time for a 50 kton iron detector, for various flux models described in the text. Here E,, is the energy of the muon entering the detector, assuming it traversed a depth of rock corresponding to 3.5 x 10°gm/cm?.
EE . << EEE Figure 4.6: Multi- track (Kolar) events recorded in KGF neutrino-detectors.
EE . << EEE Figure 4.6: Multi- track (Kolar) events recorded in KGF neutrino-detectors.
Fe A Re ce Bae! © The iron structure for this detector will be self supporting with the layer above resting on the layer immediately below using iron spacers located every 2 m along the X-direction. The details are shown in Fig. 5.2. This will create 2 m wide roads along the Y-direction for the insertion of RPC trays. There will be a total of 8 roads per module in a layer. The iron plates will be magnetised with a field of about ~1.3 Tesla. The total mass of the detector will be around 50 kton.
Fe A Re ce Bae! © The iron structure for this detector will be self supporting with the layer above resting on the layer immediately below using iron spacers located every 2 m along the X-direction. The details are shown in Fig. 5.2. This will create 2 m wide roads along the Y-direction for the insertion of RPC trays. There will be a total of 8 roads per module in a layer. The iron plates will be magnetised with a field of about ~1.3 Tesla. The total mass of the detector will be around 50 kton.
Figure 5.3: Sketch of a typical glass RPC unit.
Figure 5.3: Sketch of a typical glass RPC unit.
Figure 5.4: Proposed readout scheme for the ICAL detector.
Figure 5.4: Proposed readout scheme for the ICAL detector.
to look for required patterns of hits in the detector and initiate data recording if any of the interesting predefined hit patterns occur inside the detector. For instance, a trigger may be generated when certain hit patterns such as 2 or 3 hit layers out of 5 consecutive layers occur. This will ensure the trigger generation of nearly all the relevant atmospheric neutrino events. Programmability is the key requirement of this sub-system so that different physics motivated data recording plans may be supported during the course of experiment. A commercial FPGA device based design is best suited for this purpose.
to look for required patterns of hits in the detector and initiate data recording if any of the interesting predefined hit patterns occur inside the detector. For instance, a trigger may be generated when certain hit patterns such as 2 or 3 hit layers out of 5 consecutive layers occur. This will ensure the trigger generation of nearly all the relevant atmospheric neutrino events. Programmability is the key requirement of this sub-system so that different physics motivated data recording plans may be supported during the course of experiment. A commercial FPGA device based design is best suited for this purpose.
Figure 5.5: Schematic of steel structural supports for ICAL. The design capacity of the mechanical structure of the ICAL detector has been worked out in detail and is described in Appendix C. The study assumes a detector with 140 layers of 6 cm steel plates stacked vertically, with 48 m x 16 m plates in plane and spaced with a 2.5 cm gap in between. 9.3 Current status of detector R & D
Figure 5.5: Schematic of steel structural supports for ICAL. The design capacity of the mechanical structure of the ICAL detector has been worked out in detail and is described in Appendix C. The study assumes a detector with 140 layers of 6 cm steel plates stacked vertically, with 48 m x 16 m plates in plane and spaced with a 2.5 cm gap in between. 9.3 Current status of detector R & D
Figure 5.6: Schematic view of the first gas mixing unit and control system at TIFR.
Figure 5.6: Schematic view of the first gas mixing unit and control system at TIFR.
Figure 5.7: Front view of the 4-component gas mixing unit with 16 output channels.
Figure 5.7: Front view of the 4-component gas mixing unit with 16 output channels.
Figure 5.9: Photograph of the RPC test area at TIFR.
Figure 5.9: Photograph of the RPC test area at TIFR.
Figure 5.10: Schematic of cosmic ray telescope and muon trigger timing sequence. Fig. 5.11 shows plots of the RPC efficiency as a function of high voltage applied between the glass electrodes for different gas mixtures. Plateau efficiencies of over 90% have been obtained for all the gas mixtures beyond 8.5 kV.
Figure 5.10: Schematic of cosmic ray telescope and muon trigger timing sequence. Fig. 5.11 shows plots of the RPC efficiency as a function of high voltage applied between the glass electrodes for different gas mixtures. Plateau efficiencies of over 90% have been obtained for all the gas mixtures beyond 8.5 kV.
Figure 5.11: Efficiency plot of RPC as a function of applied voltage for various gas mixtures.
Figure 5.11: Efficiency plot of RPC as a function of applied voltage for various gas mixtures.
Figure 5.12: Typical timing resolution (7) of an RPC as a function of applied voltage.
Figure 5.12: Typical timing resolution (7) of an RPC as a function of applied voltage.
Figure 5.13: Typical mean charge (in arb. units) as a function of applied HV across an RPC.
Figure 5.13: Typical mean charge (in arb. units) as a function of applied HV across an RPC.
Figure 5.14: Typical noise rate plot of the RPC.
Figure 5.14: Typical noise rate plot of the RPC.
Figure 5.16: Muon tracking setup using RPC stack.
Figure 5.16: Muon tracking setup using RPC stack.
Figure 5.17: Close-up view of the stack of 10 RPCs mounted in a rack.
Figure 5.17: Close-up view of the stack of 10 RPCs mounted in a rack.
Figure 5.18: Some interesting tracks recorded in the detector. Fig. 5.18 shows some interesting cosmic ray muon induced tracks recorded using the above setup. Muons arriving at different angles could be captured simply by relocating the telescope window. This has demonstrated that indeed these prototype chambers are capable of effectively tracking cosmic ray muons.
Figure 5.18: Some interesting tracks recorded in the detector. Fig. 5.18 shows some interesting cosmic ray muon induced tracks recorded using the above setup. Muons arriving at different angles could be captured simply by relocating the telescope window. This has demonstrated that indeed these prototype chambers are capable of effectively tracking cosmic ray muons.
Figure 5.20: Schematic of the read-out electronics for the 1 m* prototype detector. A schematic of the readout electronics for the prototype detector is shown in Fig. 5.20. There will be one front-end board per signal plane per layer of the detector. Detector signa conditioners, translators, Boolean latches, multiplexers for event data and monitoring and trigger system as well as timing measurement primitives are some of the major components that reside on the front-end board. Event data from either signal planes of a layer are mixed and routed to the back-end on high-speed serial links. The CAMAC back-end is driven by a Linux host and will house the master trigger generator, TDC, scaler, real-time clock and other front-end control modules.
Figure 5.20: Schematic of the read-out electronics for the 1 m* prototype detector. A schematic of the readout electronics for the prototype detector is shown in Fig. 5.20. There will be one front-end board per signal plane per layer of the detector. Detector signa conditioners, translators, Boolean latches, multiplexers for event data and monitoring and trigger system as well as timing measurement primitives are some of the major components that reside on the front-end board. Event data from either signal planes of a layer are mixed and routed to the back-end on high-speed serial links. The CAMAC back-end is driven by a Linux host and will house the master trigger generator, TDC, scaler, real-time clock and other front-end control modules.
Figure 5.21: Top: ICAL magnet (three modules) showing the coil slots and the iron plate arrangement. Bottom: one module of the magnet with the coil inserted. Field uniformity can be judged by the colour pattern. that the faulty elements can be easily replaced with the least effort. This amounts to minimising the distance that needs to be accessed to reach the faulty detector.
Figure 5.21: Top: ICAL magnet (three modules) showing the coil slots and the iron plate arrangement. Bottom: one module of the magnet with the coil inserted. Field uniformity can be judged by the colour pattern. that the faulty elements can be easily replaced with the least effort. This amounts to minimising the distance that needs to be accessed to reach the faulty detector.
A coil with 40,000 amp-turns is needed for producing a field of 1.3 T in one module. The calculated magnetic field lines in a typical layer of the horizontal plates are plotted in Fig. 5.22. The arrows show the reversal of the field on the two sides of the coils. The variation of the field along the z-axis is shown in Fig. 5.23. Over the entire set of plates the variation is within 0.3%, the field varying by less than 0.15% over a height of + 5 m from the centre. The variation of the field in y- and x- directions is shown in Fig. 5.23 and Fig 5.24 respectively. The field is quite uniform in the x-direction, varying by less than 0.25% but in the y-direction it starts falling beyond the length of the coil slot (+ 4 m). Figure 5.22: Field lines in a horizontal (x-y) plane of any of the iron plates, the arrows denote the field direction.
A coil with 40,000 amp-turns is needed for producing a field of 1.3 T in one module. The calculated magnetic field lines in a typical layer of the horizontal plates are plotted in Fig. 5.22. The arrows show the reversal of the field on the two sides of the coils. The variation of the field along the z-axis is shown in Fig. 5.23. Over the entire set of plates the variation is within 0.3%, the field varying by less than 0.15% over a height of + 5 m from the centre. The variation of the field in y- and x- directions is shown in Fig. 5.23 and Fig 5.24 respectively. The field is quite uniform in the x-direction, varying by less than 0.25% but in the y-direction it starts falling beyond the length of the coil slot (+ 4 m). Figure 5.22: Field lines in a horizontal (x-y) plane of any of the iron plates, the arrows denote the field direction.
Figure 5.23: Left: Variation of field strength in z-direction, between horizontal plates. The value of NI is given in Amp.turn. Note the expanded scale. Right: Variation of field in direction parallel to the coil slots.
Figure 5.23: Left: Variation of field strength in z-direction, between horizontal plates. The value of NI is given in Amp.turn. Note the expanded scale. Right: Variation of field in direction parallel to the coil slots.
Figure 5.26: Calculated and measured field within the gap of the 1:100 prototypes.
Figure 5.26: Calculated and measured field within the gap of the 1:100 prototypes.
Figure 5.27: Field uniformity in between the two coil slots. Field when there is 4 gap in a plate {dividing it along x-axis
Figure 5.27: Field uniformity in between the two coil slots. Field when there is 4 gap in a plate {dividing it along x-axis
Figure 5.28: Overall view of the prototype magnet with the magnetised plates and the coil inserted. The z-axis is in the vertical direction.
Figure 5.28: Overall view of the prototype magnet with the magnetised plates and the coil inserted. The z-axis is in the vertical direction.
Figure 5.29: Field lines in the prototype magnet.
Figure 5.29: Field lines in the prototype magnet.
Table 5.3: Specifications of the magnet steel and the coil for one module ~*~ ellie A design based on the above considerations has been completed. Fig. 5.29 shows the jeld lines indicating the field direction. The colour scheme suggests the level of uniformity of the field. Fig. 5.30 shows the field component along the direction of the slots. The field iniformity is acceptable over a length of about 1 m. Fig. 5.30 shows that the field is very iniform in the middle of the detectors and has the same direction in a length of 1.2 m. The eld, of course, has opposite directions on the two sides of the coil slots. Since this is outside che working area of the detector, this reversal of direction does not matter.
Table 5.3: Specifications of the magnet steel and the coil for one module ~*~ ellie A design based on the above considerations has been completed. Fig. 5.29 shows the jeld lines indicating the field direction. The colour scheme suggests the level of uniformity of the field. Fig. 5.30 shows the field component along the direction of the slots. The field iniformity is acceptable over a length of about 1 m. Fig. 5.30 shows that the field is very iniform in the middle of the detectors and has the same direction in a length of 1.2 m. The eld, of course, has opposite directions on the two sides of the coil slots. Since this is outside che working area of the detector, this reversal of direction does not matter.
Table 5.4: Physical parameters of the prototype magnet.
Table 5.4: Physical parameters of the prototype magnet.
Figure 5.30: Left: Field in the prototype magnet in a direction parallel to the coil slots. Right: Field in the x-direction; the direction is reversed only outside the coils.
Figure 5.30: Left: Field in the prototype magnet in a direction parallel to the coil slots. Right: Field in the x-direction; the direction is reversed only outside the coils.
Figure 5.31: Arrangement of C-section (left) and T-section (right) of the prototype magnet.
Figure 5.31: Arrangement of C-section (left) and T-section (right) of the prototype magnet.
Figure 6.1: View of a unit cell of the simulated ICAL detector. The outermost layers are 3 cm of iron, with the sensitive detector (of gas, glass, G10 and copper from the centre out) symmetrically placed in a central 2.5 cm air gap. The detector is simulated as 140 unit cells, with top and bottom edge layers of 3 cm iron each.
Figure 6.1: View of a unit cell of the simulated ICAL detector. The outermost layers are 3 cm of iron, with the sensitive detector (of gas, glass, G10 and copper from the centre out) symmetrically placed in a central 2.5 cm air gap. The detector is simulated as 140 unit cells, with top and bottom edge layers of 3 cm iron each.
1 The atmospheric neutrino flux Figure 6.2: The HONDA atmospheric muon neutrino flux, E d?¢/(dlog E dcos6,) where the flux @ is defined to be the number of neutrinos per square cm per steradian per second, averaged over bins of cos 6, of size 0.1 and bins of logy) E(MeV) of 0.02, shown as a function of the zenith angle at different energies, EF, in GeV. The flux is clearly dropping very fast with energy, as can be seen by following the different curves for the same zenith angle bin. Muon anti-neutrinos and electron neutrinos and anti-neutrinos exhibit a similar behaviour.
1 The atmospheric neutrino flux Figure 6.2: The HONDA atmospheric muon neutrino flux, E d?¢/(dlog E dcos6,) where the flux @ is defined to be the number of neutrinos per square cm per steradian per second, averaged over bins of cos 6, of size 0.1 and bins of logy) E(MeV) of 0.02, shown as a function of the zenith angle at different energies, EF, in GeV. The flux is clearly dropping very fast with energy, as can be seen by following the different curves for the same zenith angle bin. Muon anti-neutrinos and electron neutrinos and anti-neutrinos exhibit a similar behaviour.
Figure 6.3: Number of events in GeV bins from 5 years’ CC atmospheric muon neutrinc interactions. The distributions both for the original neutrino and the generated muon, ir the absence of oscillations, are shown.
Figure 6.3: Number of events in GeV bins from 5 years’ CC atmospheric muon neutrinc interactions. The distributions both for the original neutrino and the generated muon, ir the absence of oscillations, are shown.
Figure 6.4: The figure shows the events distribution as a function of the fraction of neutrino energy carried by the muon. The data is a 5 years CC muon neutrino sample, without oscillations. Clearly most events fall in a region with small (£, — E,,)/E,, indicating that the muon carries a substantial fraction of the neutrino energy in most events. Here FE, and E,,, refer to the energies of the neutrino and muon respectively.
Figure 6.4: The figure shows the events distribution as a function of the fraction of neutrino energy carried by the muon. The data is a 5 years CC muon neutrino sample, without oscillations. Clearly most events fall in a region with small (£, — E,,)/E,, indicating that the muon carries a substantial fraction of the neutrino energy in most events. Here FE, and E,,, refer to the energies of the neutrino and muon respectively.
VS YZ Figure 6.5: Zenith angle distribution of CC v, events is shown by plotting the events rates per bin as a function of cos@, where 0, is the neutrino zenith angle. The bin size is 0.1. NUANCE labels “up-going” events as those with cos@, > 0. These events are depleted when (2-flavour) oscillations are turned on, where oscillation parameters 632, 023 = 2 x 1073 eV2. 45° have been used.
VS YZ Figure 6.5: Zenith angle distribution of CC v, events is shown by plotting the events rates per bin as a function of cos@, where 0, is the neutrino zenith angle. The bin size is 0.1. NUANCE labels “up-going” events as those with cos@, > 0. These events are depleted when (2-flavour) oscillations are turned on, where oscillation parameters 632, 023 = 2 x 1073 eV2. 45° have been used.
Figure 6.6: The same as Fig. 6.5 for the zenith angle distribution of the muons
Figure 6.6: The same as Fig. 6.5 for the zenith angle distribution of the muons
Figure 6.7: Distribution of events in bins of 9 degrees as a function of the relative angle @,,, between the incident neutrino and the produced muon in the CC interaction.
Figure 6.7: Distribution of events in bins of 9 degrees as a function of the relative angle @,,, between the incident neutrino and the produced muon in the CC interaction.
Figure 6.8: The variations of effective path-length (left) and number of hits (right) with energy for fixed 6 (= 40°) in ICAL-H for muons (without and with a magnetic field of 1 T in the z direction).
Figure 6.8: The variations of effective path-length (left) and number of hits (right) with energy for fixed 6 (= 40°) in ICAL-H for muons (without and with a magnetic field of 1 T in the z direction).
Figure 6.9: Distributions for the total energy for muons using fitting Algorithm I. The incident momenta are given in the KINE statement, which lists, in order, particle id (here muon), (x,y,z) in cm of the production point, and (p,,p,,p-) in GeV. ror FC events. Fig. 6.9 shows a few typical results obtained by using Algorithm I. Herein the distribution of the muon total energy (and the corresponding fits) as obtained by fitting the initial part of the track to a curve to determine the radius of curvature at the production point is shown using a large number of muon triggers with constant B, = 1 T and p; = py = pz = 1, 3, 5, 7 GeV. The energies obtained for the different data sets are E = 1.73 + 0.23 (1.74) GeV, 9.42 J E 0.61 (5.20) GeV, 8.94 t 0.85 (8.66) GeV, and 11.69 4 t 0.95 (12.12) GeV respectively, where the numbers in brackets are the incident energies. We refer to this as Analysis Set 1.
Figure 6.9: Distributions for the total energy for muons using fitting Algorithm I. The incident momenta are given in the KINE statement, which lists, in order, particle id (here muon), (x,y,z) in cm of the production point, and (p,,p,,p-) in GeV. ror FC events. Fig. 6.9 shows a few typical results obtained by using Algorithm I. Herein the distribution of the muon total energy (and the corresponding fits) as obtained by fitting the initial part of the track to a curve to determine the radius of curvature at the production point is shown using a large number of muon triggers with constant B, = 1 T and p; = py = pz = 1, 3, 5, 7 GeV. The energies obtained for the different data sets are E = 1.73 + 0.23 (1.74) GeV, 9.42 J E 0.61 (5.20) GeV, 8.94 t 0.85 (8.66) GeV, and 11.69 4 t 0.95 (12.12) GeV respectively, where the numbers in brackets are the incident energies. We refer to this as Analysis Set 1.
Figure 6.10: Sample fits to transverse tracks with momenta p, = py = 2,5,7,10 Ge\ respectively. This technique was implemented in Analysis Set 2 for p,; = py = 2,3,4,5, 7,10 GeV. Sample fits to the trajectory for p, = py = 2,5, 7,10 GeV are shown in Fig. 6.10. The corresponding expected and determined values of Rp are shown in Table 6.1. Both methods are found to be reliable.
Figure 6.10: Sample fits to transverse tracks with momenta p, = py = 2,5,7,10 Ge\ respectively. This technique was implemented in Analysis Set 2 for p,; = py = 2,3,4,5, 7,10 GeV. Sample fits to the trajectory for p, = py = 2,5, 7,10 GeV are shown in Fig. 6.10. The corresponding expected and determined values of Rp are shown in Table 6.1. Both methods are found to be reliable.
Figure 6.11: Zenith angle distributions for muons. The incident momenta are given in the KINE statement. See Fig. 6.9 for details.
Figure 6.11: Zenith angle distributions for muons. The incident momenta are given in the KINE statement. See Fig. 6.9 for details.
Table 6.2: Charge identification efficiency for simulated 5-year atmospheric neutrino data samples.
Table 6.2: Charge identification efficiency for simulated 5-year atmospheric neutrino data samples.
‘igure 6.12: The frequency distribution of hits for fixed pion energies of E, = 1,5, 10,1 xeV, with 1000 random events per sample. The ICAL detector is not very sensitive to individual hadrons. Indeed, it appears that such a detector cannot distinguish different hadrons such as kK and 7. Many atmospheric neutrino CC events of interest have substantial multi-pion events; all the hadrons produced in a single such event are calibrated using hit multiplicity. That is, the total hits (that are rejected as being part of the muon track) are calibrated to the total energy of the hadrons in the event. There is also no directional information in this approach. Hence, while calibrating, care has been taken to average the simulated tracks over all possible directions. FRc: ceca ewe woe: eens: wl mews eel Bhs axles: olf Phe ecm coetd&bo acucapasd women Jl Sececonk Bcomun DB: fF119
‘igure 6.12: The frequency distribution of hits for fixed pion energies of E, = 1,5, 10,1 xeV, with 1000 random events per sample. The ICAL detector is not very sensitive to individual hadrons. Indeed, it appears that such a detector cannot distinguish different hadrons such as kK and 7. Many atmospheric neutrino CC events of interest have substantial multi-pion events; all the hadrons produced in a single such event are calibrated using hit multiplicity. That is, the total hits (that are rejected as being part of the muon track) are calibrated to the total energy of the hadrons in the event. There is also no directional information in this approach. Hence, while calibrating, care has been taken to average the simulated tracks over all possible directions. FRc: ceca ewe woe: eens: wl mews eel Bhs axles: olf Phe ecm coetd&bo acucapasd women Jl Sececonk Bcomun DB: fF119
Figure 6.13: Left: The average number of hits as a function of pion energy for 1000 random events per sample of constant energy events. The smooth curve is a best fit to the data. Right: Variation of the width of the Gaussian distribution, 7 as a function of the energy. Plotted is the ratio 0/E as a function of E}, along with best fit curve.
Figure 6.13: Left: The average number of hits as a function of pion energy for 1000 random events per sample of constant energy events. The smooth curve is a best fit to the data. Right: Variation of the width of the Gaussian distribution, 7 as a function of the energy. Plotted is the ratio 0/E as a function of E}, along with best fit curve.
events (say between zenith angles 70° and 110°), all the events with L/E below 200 Km/GeV are lost. So in practice we consider only the high energy events at near horizon. This cut can be relaxed gradually as we move away from the horizon. Based on these ideas, numerical study is done to arrive at the cuts for our analysis. Fig. 6.14 gives the selected/rejected region in the E-(L/F) domain. Figure 6.14: Region of acceptance for the choice of cut for FC events.
events (say between zenith angles 70° and 110°), all the events with L/E below 200 Km/GeV are lost. So in practice we consider only the high energy events at near horizon. This cut can be relaxed gradually as we move away from the horizon. Based on these ideas, numerical study is done to arrive at the cuts for our analysis. Fig. 6.14 gives the selected/rejected region in the E-(L/F) domain. Figure 6.14: Region of acceptance for the choice of cut for FC events.
Figure 6.15: Typical resolution functions for energy F and path-length L of fully contained neutrino events. With these cuts, the total energy resolution is obtained. Although the resolutions used in the analysis were generated in small bins in both E and L/F, a typical energy resolution is shown in Fig. 6.15. The muon direction was reconstructed and a corresponding typical resolution in path length L is also shown in the same figure. This results in a resolution in the variable L/E as shown in Fig. 6.16.
Figure 6.15: Typical resolution functions for energy F and path-length L of fully contained neutrino events. With these cuts, the total energy resolution is obtained. Although the resolutions used in the analysis were generated in small bins in both E and L/F, a typical energy resolution is shown in Fig. 6.15. The muon direction was reconstructed and a corresponding typical resolution in path length L is also shown in the same figure. This results in a resolution in the variable L/E as shown in Fig. 6.16.
The number of events that survive the cuts is shown in Table 6.3. Table 6.3: Efficiency of ICAL for 3, 6, 10, 15, and 20 year data samples for both FC and (FC + PC) events, after applying cuts as described in the text. analysed as before. This is because the programs using the track-curvature algorithm have not been fully optimised. In particular, reasonable results have been obtained for partially contained events where the tracks have at most 20 hits. Hence only such events have been included in the analysis.
The number of events that survive the cuts is shown in Table 6.3. Table 6.3: Efficiency of ICAL for 3, 6, 10, 15, and 20 year data samples for both FC and (FC + PC) events, after applying cuts as described in the text. analysed as before. This is because the programs using the track-curvature algorithm have not been fully optimised. In particular, reasonable results have been obtained for partially contained events where the tracks have at most 20 hits. Hence only such events have been included in the analysis.
Figure 6.16: Typical resolution functions in L/F for fully contained neutrino events.
Figure 6.16: Typical resolution functions in L/F for fully contained neutrino events.
Figure 6.17: The up/down ratio as a function of L/E obtained from GEANT simulated data of a 6 year NUANCE data sample with oscillation parameters 632, 023 = 2 x 107~° eV?, 45°. The allowed oscillation parameter space is shown on the right, where the 90% CL and 99% CL regions and best-fit value are shown.
Figure 6.17: The up/down ratio as a function of L/E obtained from GEANT simulated data of a 6 year NUANCE data sample with oscillation parameters 632, 023 = 2 x 107~° eV?, 45°. The allowed oscillation parameter space is shown on the right, where the 90% CL and 99% CL regions and best-fit value are shown.
Figure 6.18: As in Fig. 6.17, but for a combined sample of FC and PC events. The resulting up/down events ratio is shown in Fig. 6.18, with the allowed oscillation parameter space. The best-fit point corresponds to 632 = 2.04 x 107° eV? and sin? 2023 = 1.0 for the same input values of 2.00 x 1073 eV? and 1.0 respectively. It may be seen that the allowed parameter space is somewhat larger than with the pure FC sample. This is a clear indication that the PC events analysis needs to be further optimised. PC events crucially add to the statistics in the low L/E bins. Thus an improved analysis in this sector is necessary to improve upon the obtained precision of the parameters.
Figure 6.18: As in Fig. 6.17, but for a combined sample of FC and PC events. The resulting up/down events ratio is shown in Fig. 6.18, with the allowed oscillation parameter space. The best-fit point corresponds to 632 = 2.04 x 107° eV? and sin? 2023 = 1.0 for the same input values of 2.00 x 1073 eV? and 1.0 respectively. It may be seen that the allowed parameter space is somewhat larger than with the pure FC sample. This is a clear indication that the PC events analysis needs to be further optimised. PC events crucially add to the statistics in the low L/E bins. Thus an improved analysis in this sector is necessary to improve upon the obtained precision of the parameters.
Figure 6.19: The allowed oscillation parameter space obtained from this analysis overlaid with the corresponding contours (at 90% (dashed lines) and 99% C.L. (solid lines)) obtained from the Super-Kamiokande Collaboration using both zenith angle (contours narrow in 623) and L/F (contours narrow in Am?) analyses [201].
Figure 6.19: The allowed oscillation parameter space obtained from this analysis overlaid with the corresponding contours (at 90% (dashed lines) and 99% C.L. (solid lines)) obtained from the Super-Kamiokande Collaboration using both zenith angle (contours narrow in 623) and L/F (contours narrow in Am?) analyses [201].
Figure 6.20: Precision in 632 and sin? 623 with FC events, as a function of exposure.
Figure 6.20: Precision in 632 and sin? 623 with FC events, as a function of exposure.
Figure 6.21: Precision in 532 and sin? 623 with FC+PC events, as a function of exposure.
Figure 6.21: Precision in 532 and sin? 623 with FC+PC events, as a function of exposure.
Figure 6.22: Flux of neutrinos at depths X in km w.e. below ground, as indicated. The twe values correspond roughly to vertical depths at PUSHEP and Rammam.
Figure 6.22: Flux of neutrinos at depths X in km w.e. below ground, as indicated. The twe values correspond roughly to vertical depths at PUSHEP and Rammam.
Figure 6.23: Integrated flux per hour of muons at constant depths X in km w.e. below ground, in energy bins of 20 GeV (E), > 1 GeV). The two sets of curves correspond roughly to vertical depths at PUSHEP and Rammam. The contributions from the top aperture (32 m xX 16 m) and the total from the top and four sides of ICAL are separately shown.
Figure 6.23: Integrated flux per hour of muons at constant depths X in km w.e. below ground, in energy bins of 20 GeV (E), > 1 GeV). The two sets of curves correspond roughly to vertical depths at PUSHEP and Rammam. The contributions from the top aperture (32 m xX 16 m) and the total from the top and four sides of ICAL are separately shown.
Figure 6.24: As in Fig. 6.23, at triangulated depths X in km w.e. below ground. For more details, see the text.
Figure 6.24: As in Fig. 6.23, at triangulated depths X in km w.e. below ground. For more details, see the text.
Figure 6.25: Cosmic ray muon events for one hour exposure at ICAL/PUSHEP. Shown are the “vertices”, that is, the points of entry of the muons into the detector.
Figure 6.25: Cosmic ray muon events for one hour exposure at ICAL/PUSHEP. Shown are the “vertices”, that is, the points of entry of the muons into the detector.
Figure 6.28: Tracks in ICAL of high energy muons vertically passing through the detector. The z-axis indicates a transverse direction while the y-axis is the vertical direction and is labelled by the layer number. The energy of the muons in TeV is indicated next to the tracks.
Figure 6.28: Tracks in ICAL of high energy muons vertically passing through the detector. The z-axis indicates a transverse direction while the y-axis is the vertical direction and is labelled by the layer number. The energy of the muons in TeV is indicated next to the tracks.
Figure 6.29: Number of hits normalised to the vertical detector height versus the incident muon energy. The x-axis scale begins at 10 TeV and 7’ corresponds to a distance of 477 radiation lengths. Linear behaviour is noticed up to E,, ~ 100 TeV. | estimates are of the order of 50%; see text for details. Errors on the energy
Figure 6.29: Number of hits normalised to the vertical detector height versus the incident muon energy. The x-axis scale begins at 10 TeV and 7’ corresponds to a distance of 477 radiation lengths. Linear behaviour is noticed up to E,, ~ 100 TeV. | estimates are of the order of 50%; see text for details. Errors on the energy
Figure 6.30: Number of hits per layer shown over the track length of vertical muons with en- ergies E' = 10,100, 1000 TeV. Cascades are clearly seen as peaks in the number of hits/layer. Larger cascades are more energetic.
Figure 6.30: Number of hits per layer shown over the track length of vertical muons with en- ergies E' = 10,100, 1000 TeV. Cascades are clearly seen as peaks in the number of hits/layer. Larger cascades are more energetic.
The underground cavern that houses the generators is 20 meters wide, 39 meters high and 70 meters long, so its dimensions are similar to the requirement of INO for locating the iron calorimeter detector. The transformers are located in a smaller cavern and there are a few more caverns of smaller size. The proposed INO tunnel portal is to be located close to the existing portal of the PUSHEP access tunnel. The proposed laboratory cavern will be located under the 2207 m peak, about a km away from the PUSHEP caverns; however, the entire area is composed of similar (monolithic) charnockite rock. The prior existence of a number of tunnels and caverns is important and useful for future forecasting. In fact, a number of geological features such as shears, dykes and joints in the INO tunnel/cavern area have been mapped from both surface projections and from the existing PUSHEP tunnels. The site is also conveniently located in seismic zone-2, which implies a minimum seismic activity zone in India. A panoramic view of the peak directly above the projected site is shown in Fig. 7.2. located in a cavern 500 m underground, accessed by a 1.5 km long tunnel. The intake and tail-race tunnels as well as the transformer are all housed underground as well. In all, nearly 13 km of tunnels have been constructed for this project. Fig. 7.1 gives a panoramic view of the PUSHEP site.
The underground cavern that houses the generators is 20 meters wide, 39 meters high and 70 meters long, so its dimensions are similar to the requirement of INO for locating the iron calorimeter detector. The transformers are located in a smaller cavern and there are a few more caverns of smaller size. The proposed INO tunnel portal is to be located close to the existing portal of the PUSHEP access tunnel. The proposed laboratory cavern will be located under the 2207 m peak, about a km away from the PUSHEP caverns; however, the entire area is composed of similar (monolithic) charnockite rock. The prior existence of a number of tunnels and caverns is important and useful for future forecasting. In fact, a number of geological features such as shears, dykes and joints in the INO tunnel/cavern area have been mapped from both surface projections and from the existing PUSHEP tunnels. The site is also conveniently located in seismic zone-2, which implies a minimum seismic activity zone in India. A panoramic view of the peak directly above the projected site is shown in Fig. 7.2. located in a cavern 500 m underground, accessed by a 1.5 km long tunnel. The intake and tail-race tunnels as well as the transformer are all housed underground as well. In all, nearly 13 km of tunnels have been constructed for this project. Fig. 7.1 gives a panoramic view of the PUSHEP site.
Figure 7.2: Panoramic view of the mountain peak (2207 meters) at PUSHEP. The laboratory cavern will be located directly under the this peak.
Figure 7.2: Panoramic view of the mountain peak (2207 meters) at PUSHEP. The laboratory cavern will be located directly under the this peak.
Figure 7.3: INO tunnel portal location at Rammam Site.
Figure 7.3: INO tunnel portal location at Rammam Site.
Figure 7.4: Panoramic view of the Rammam river valley.
Figure 7.4: Panoramic view of the Rammam river valley.
Figure 7.5: Atmospheric muon background as a function of depth. The best locations for INO correspond to backgrounds as in Gran Sasso or better.
Figure 7.5: Atmospheric muon background as a function of depth. The best locations for INO correspond to backgrounds as in Gran Sasso or better.
Figure 7.6: A schematic of the two-way single tunnel shown in cross-section. Single tunnel approach Single tunnel approach is cost effective. Further saving may be effected by having single lane traffic with space for emergency vehicle parking and turnarounds every few hundred meters. Emergency exit may be provided by a pedestrian walkway separated by concrete wall from the traffic lane. Fresh air through ventilation ducts flows through the pedestrian tunnel w hich may also contain the exhaust ducts, electrical wiring, water mains and other such facilities that extend up to laboratory cavern. Fire proof doors between the traffic lane and the pedestrian walkway may be provided where the vehicular turnarounds are located. Similar design requirements may be used for a wider tunnel allowing two lane traffic along with a pedestrian walkway containing all the ducts.
Figure 7.6: A schematic of the two-way single tunnel shown in cross-section. Single tunnel approach Single tunnel approach is cost effective. Further saving may be effected by having single lane traffic with space for emergency vehicle parking and turnarounds every few hundred meters. Emergency exit may be provided by a pedestrian walkway separated by concrete wall from the traffic lane. Fresh air through ventilation ducts flows through the pedestrian tunnel w hich may also contain the exhaust ducts, electrical wiring, water mains and other such facilities that extend up to laboratory cavern. Fire proof doors between the traffic lane and the pedestrian walkway may be provided where the vehicular turnarounds are located. Similar design requirements may be used for a wider tunnel allowing two lane traffic along with a pedestrian walkway containing all the ducts.
Figure 7.7: An artist illustration of the Laboratory Cavern Complex
Figure 7.7: An artist illustration of the Laboratory Cavern Complex
Figure 7.8: Top view of the laboratory cavern with a single detector module
Figure 7.8: Top view of the laboratory cavern with a single detector module
Table 8.1: Estimated cost of INO underground laboratory at the two possible sites in PUSHEP and Rammam. It is to be noted that the higher cost of construction at Rammam is due to the length of the main access tunnel which is more than twice the length of the tunnel at PUSHEP. In addition there is an adit of 2 km at Rammam due to the long length of the tunnel. This additional cost will allow for more depth at Rammam compared to that at PUSHEP. If on the other hand we restrict the depth at Rammam to that of PUSHEP then the cost of tunnel construction at both places may be comparable. The site at Rammam also provides an opportunity of stopping at some desired depth for the proposed experiment and extending it later for future ones.
Table 8.1: Estimated cost of INO underground laboratory at the two possible sites in PUSHEP and Rammam. It is to be noted that the higher cost of construction at Rammam is due to the length of the main access tunnel which is more than twice the length of the tunnel at PUSHEP. In addition there is an adit of 2 km at Rammam due to the long length of the tunnel. This additional cost will allow for more depth at Rammam compared to that at PUSHEP. If on the other hand we restrict the depth at Rammam to that of PUSHEP then the cost of tunnel construction at both places may be comparable. The site at Rammam also provides an opportunity of stopping at some desired depth for the proposed experiment and extending it later for future ones.
The cost factors are listed in detail in Table 8.2: We give an estimate for a 50 kton module of the ICAL detector which is an optimum target mass required for the detector. However, based on the physics needs and the goals outlined in the chapter 3 on physics issues, the final detector mass may go up to 100 ktons. The cost of the detector will go up proportionately. The laboratory construction cost outlined above, however, will remain the same. The cavern design already takes into account a possible expansion of ICAL up to three times the present design. Th ok fe be pee ob e Dt debetd ee ToL. 2 9.
The cost factors are listed in detail in Table 8.2: We give an estimate for a 50 kton module of the ICAL detector which is an optimum target mass required for the detector. However, based on the physics needs and the goals outlined in the chapter 3 on physics issues, the final detector mass may go up to 100 ktons. The cost of the detector will go up proportionately. The laboratory construction cost outlined above, however, will remain the same. The cavern design already takes into account a possible expansion of ICAL up to three times the present design. Th ok fe be pee ob e Dt debetd ee ToL. 2 9.
At the pre-construction stage, the engineering group, along with technical advisors, will make precise the design requirements and cost-estimates, drawing time schedules, calling for tenders and contracting work. This group will also be responsible for executing plans as per time and cost schedules, and providing emergency solutions under unforeseen conditions at the construction stage. Apart from these INO may also employ research consultants and other such advisors as needed. Some of these groups may be wound up once the specific tasks are completed like the excavation group and design group. The Running stage involves a clear management philosophy to achieve desired goals by combining a clear line of command and accountability. A single managing entity with an administrative structure and broad involvement of NCG and the scientific community is a good starting point. The Research group under an Associate Director, and a full fledged administrative set up, will come into existence once the construction phase is over. In Fig. 9.3 we show a sketch of the proposed administrative set up. We have so far discussed the local interaction among various groups within INO. However, an extremely important aspect of the proposal is the INO-industry interface. The scale on which INO is conceived is huge and the role of industry—be it in the construction of the laboratory, equipping the laboratory, building the massive steel structure for ICAL, electronics components, etc.,—is going to be a crucial aspect.
At the pre-construction stage, the engineering group, along with technical advisors, will make precise the design requirements and cost-estimates, drawing time schedules, calling for tenders and contracting work. This group will also be responsible for executing plans as per time and cost schedules, and providing emergency solutions under unforeseen conditions at the construction stage. Apart from these INO may also employ research consultants and other such advisors as needed. Some of these groups may be wound up once the specific tasks are completed like the excavation group and design group. The Running stage involves a clear management philosophy to achieve desired goals by combining a clear line of command and accountability. A single managing entity with an administrative structure and broad involvement of NCG and the scientific community is a good starting point. The Research group under an Associate Director, and a full fledged administrative set up, will come into existence once the construction phase is over. In Fig. 9.3 we show a sketch of the proposed administrative set up. We have so far discussed the local interaction among various groups within INO. However, an extremely important aspect of the proposal is the INO-industry interface. The scale on which INO is conceived is huge and the role of industry—be it in the construction of the laboratory, equipping the laboratory, building the massive steel structure for ICAL, electronics components, etc.,—is going to be a crucial aspect.
Figure 9.4: The proposed research group organisation at INO.
Figure 9.4: The proposed research group organisation at INO.
Figure 9.5: Anticipated wide-area interaction at INO and its wider impact. will generate a feed-back loop as shown in Fig. 9.5.
Figure 9.5: Anticipated wide-area interaction at INO and its wider impact. will generate a feed-back loop as shown in Fig. 9.5.
Figure A-1: The Gifford shaft at KGF Champion Reef Mine provided access to various levels of the KGF underground laboratory. Historically, the Indian initiative in cosmic ray and neutrino Physics experiments goes back several decades. In fact the first atmospheric neutrino induced muon events were recorded at the Kolar Gold Fields (KGF) underground laboratory nearly thirty five years ago. The KGF experiments spanned several decades involving a systematic study of cosmic ray muons and neutrinos, and other exotic processes at great depths underground. The experience gained here makes it possible to mount a large scale experiment proposed in this report.
Figure A-1: The Gifford shaft at KGF Champion Reef Mine provided access to various levels of the KGF underground laboratory. Historically, the Indian initiative in cosmic ray and neutrino Physics experiments goes back several decades. In fact the first atmospheric neutrino induced muon events were recorded at the Kolar Gold Fields (KGF) underground laboratory nearly thirty five years ago. The KGF experiments spanned several decades involving a systematic study of cosmic ray muons and neutrinos, and other exotic processes at great depths underground. The experience gained here makes it possible to mount a large scale experiment proposed in this report.
Figure A-2: Neutrino Detectors at the depth of 2.3 Km at KGF.
Figure A-2: Neutrino Detectors at the depth of 2.3 Km at KGF.
Figure A-3: An expanded view of a section of Thlescope 2 in which : an inelastic collision ir rock of an upward moving neutrino was recorded. The black dots are the fired NFT’s.
Figure A-3: An expanded view of a section of Thlescope 2 in which : an inelastic collision ir rock of an upward moving neutrino was recorded. The black dots are the fired NFT’s.
Figure A-5: Multi-track (Kolar) events recorded in KGF neutrino-detectors.
Figure A-5: Multi-track (Kolar) events recorded in KGF neutrino-detectors.
physics measurements relevant to solar neutrino physics have been performed at Variable Energy Cyclotron Centre, Kolkata and at the “Be radioactive ion beam facility at the Nuclear Science Centre, New Delhi.
physics measurements relevant to solar neutrino physics have been performed at Variable Energy Cyclotron Centre, Kolkata and at the “Be radioactive ion beam facility at the Nuclear Science Centre, New Delhi.
[he quarks have fractional charge and interact primarily through the colour force though hey experience all other basic interactions. Their binding through the colour interaction s what gives rise to the proton, the neutron, nuclei and all other hadrons. The charged eptons do not interact via the colour force, but experience the other three forces of nature, lectromagnetic, weak and gravity. The other building blocks of SM are the gauge bosons hat mediate the various interactions, namely, the gluons, the photons and the W*+ and the 7 boson. The ”Standard Model” (SM) of particle physics is a description of the way particles of matter interact. The SM has twelve building blocks of matter, six leptons and six quarks, and their antiparticles.
[he quarks have fractional charge and interact primarily through the colour force though hey experience all other basic interactions. Their binding through the colour interaction s what gives rise to the proton, the neutron, nuclei and all other hadrons. The charged eptons do not interact via the colour force, but experience the other three forces of nature, lectromagnetic, weak and gravity. The other building blocks of SM are the gauge bosons hat mediate the various interactions, namely, the gluons, the photons and the W*+ and the 7 boson. The ”Standard Model” (SM) of particle physics is a description of the way particles of matter interact. The SM has twelve building blocks of matter, six leptons and six quarks, and their antiparticles.
Figure C-1: Schematic of steel structural supports for ICAL where each plate is taken to be 4 m wide.
Figure C-1: Schematic of steel structural supports for ICAL where each plate is taken to be 4 m wide.
Figure C-2: Bending deformation of glass and steel.
Figure C-2: Bending deformation of glass and steel.
Figure C-3: Bearing width of the concrete floor. Permissible bearing strength for M30 grade concrete
Figure C-3: Bearing width of the concrete floor. Permissible bearing strength for M30 grade concrete
Some field tests may be needed to confirm the bearing strength of concrete. Figure C-4: Schematic view of ICAL including structural supports. 6. Bearing stress on rock:
Some field tests may be needed to confirm the bearing strength of concrete. Figure C-4: Schematic view of ICAL including structural supports. 6. Bearing stress on rock:
Figure D-1: Boosted spectrum of neutrinos (solid line) and anti-neutrinos (broken line) at the far detector assuming no oscillation. The flux is given in units of yr~-'m~?7MeV~?. The fluxes and cross sections
Figure D-1: Boosted spectrum of neutrinos (solid line) and anti-neutrinos (broken line) at the far detector assuming no oscillation. The flux is given in units of yr~-'m~?7MeV~?. The fluxes and cross sections
Figure D-2: The number of events as a function of 0;3 for v (left) and v (right) for a 5-year run. Here, 632 is chosen positive (negative) for v (v). Note the insensitivity to the CP phase }. Precision measurement of 613 The current bound on 6,3 from the global oscillation analysis is sin? 6,3; < 0.05 (3c) [52, 191]. It is seen from Fig. D-2 that for a five-year exposure, ICAL will record a substantial number of events even for sin? 6,3 as small as 0.0003. Results are presented for two limiting choices of the CP phase 6. The CERN to INO distance is near the ‘magic baseline’ (~ 7000 Km) where matter effects are largest and the effect of the CP phase almost negligible. This makes it possible to evade the ‘#;3; — 6 degeneracy’ problem which plagues experiments at other baselines. For mass-squared differences and mixing parameters we use the values from Ref. [192] ?. We follow the convention 6,; = m? —m;. In this calculation, we have assumed an uncertainty of 2% in the knowledge of the number of ions in the storage ring. We have included a 10% fluctuation in the cross section. The statistical error has been added to the above in quadrature. We have neglected nuclear effects. For the baselines under consideration, the neutrino beam passes through the mantle of the earth where to a good approximation the density can be considered to be constant. The plots presented here are obtained by numerically solving the full 3-flavour neutrino propagation equation based on the framework of Barger et al. [193]. mga: ene 1 aes . ite “ Pa (res: + 1 n
Figure D-2: The number of events as a function of 0;3 for v (left) and v (right) for a 5-year run. Here, 632 is chosen positive (negative) for v (v). Note the insensitivity to the CP phase }. Precision measurement of 613 The current bound on 6,3 from the global oscillation analysis is sin? 6,3; < 0.05 (3c) [52, 191]. It is seen from Fig. D-2 that for a five-year exposure, ICAL will record a substantial number of events even for sin? 6,3 as small as 0.0003. Results are presented for two limiting choices of the CP phase 6. The CERN to INO distance is near the ‘magic baseline’ (~ 7000 Km) where matter effects are largest and the effect of the CP phase almost negligible. This makes it possible to evade the ‘#;3; — 6 degeneracy’ problem which plagues experiments at other baselines. For mass-squared differences and mixing parameters we use the values from Ref. [192] ?. We follow the convention 6,; = m? —m;. In this calculation, we have assumed an uncertainty of 2% in the knowledge of the number of ions in the storage ring. We have included a 10% fluctuation in the cross section. The statistical error has been added to the above in quadrature. We have neglected nuclear effects. For the baselines under consideration, the neutrino beam passes through the mantle of the earth where to a good approximation the density can be considered to be constant. The plots presented here are obtained by numerically solving the full 3-flavour neutrino propagation equation based on the framework of Barger et al. [193]. mga: ene 1 aes . ite “ Pa (res: + 1 n
Figure D-3: The 30 uncertainty in the measurement of 013 for v (left) and v (right) from a 5-year run.
Figure D-3: The 30 uncertainty in the measurement of 013 for v (left) and v (right) from a 5-year run.
Sma tis aan ee Pine phen ae Figure G-1: Approximate longitudinal section of the mountain above the Rohtang tunnel.
Sma tis aan ee Pine phen ae Figure G-1: Approximate longitudinal section of the mountain above the Rohtang tunnel.
Figure G-3: The descent from Rohtang Pass in to Chandra river valley, visible in the back- ground. (Photo courtesy: David Clarke)
Figure G-3: The descent from Rohtang Pass in to Chandra river valley, visible in the back- ground. (Photo courtesy: David Clarke)