DIFFRACTION 2002: Interpretation of the New Diffractive Phenomena in Quantum Chromodynamics and in the S-Matrix Theory, 2003
We analyze the consequences of t-channel unitarity for photon cross sections and show what assump... more We analyze the consequences of t-channel unitarity for photon cross sections and show what assumptions are necessary to allow for the existence of new singularities at Q 2 = 0 for the γp and γγ total cross sections. For virtual photons, such singularities can in general be present, but we show that, apart from the perturbative singularity associated with γ * γ * → qq, no new ingredient is needed to reproduce the data from LEP and HERA, in the Regge region. * on leave from Bogolyubov Institute for Theoretical Physics, Kiev.
The recent high-energy QCD equations including the effects of fluctuations are solved numerically... more The recent high-energy QCD equations including the effects of fluctuations are solved numerically. We discuss their asymptotic properties and compare them with the corresponding behaviour without fluctuations as well as with the statistical-physics model obtained in the saddle point approximation. The potential consequences on phenomenology, particularly on geometric scaling violations, are drawn.
We propose a stochastic particle model in (1+1)-dimensions, with one dimension corresponding to r... more We propose a stochastic particle model in (1+1)-dimensions, with one dimension corresponding to ra- pidity and the other one to the transverse size of a dipole in QCD, which mimics high-energy evolution and scattering in QCD in the presence of both saturation and particle-number fluctuations, and hence of Pomeron loops. The model evolves via non-linear particle splitting, with a non-local
In a previous publication, we have established a collinearly-improved version of the Balitsky-Kov... more In a previous publication, we have established a collinearly-improved version of the Balitsky-Kovchegov (BK) equation, which resums to all orders the radiative corrections enhanced by large double transverse logarithms. Here, we study the relevance of this equation as a tool for phenomenology, by confronting it to the HERA data. To that aim, we first improve the perturbative accuracy of our resummation, by including two classes of single-logarithmic corrections: those generated by the first non-singular terms in the DGLAP splitting functions and those expressing the one-loop running of the QCD coupling. The equation thus obtained includes all the next-to-leading order corrections to the BK equation which are enhanced by (single or double) collinear logarithms. We then use numerical solutions to this equation to fit the HERA data for the electron-proton reduced cross-section at small Bjorken x. We obtain good quality fits for physically acceptable initial conditions. Our best fit, which shows a good stability up to virtualities as large as Q 2 = 400 GeV 2 for the exchanged photon, uses as an initial condition the running-coupling version of the McLerran-Venugopalan model, with the QCD coupling running according to the smallest dipole prescription.
We show how one can obtain geometric scaling properties from the Balitsky-Kovchegov (BK) equation... more We show how one can obtain geometric scaling properties from the Balitsky-Kovchegov (BK) equation. We start by explaining how, this property arises for the b-independent BK equation. We show that it is possible to extend this model to the full BK equation including momentum transfer. The saturation scale behaves like max(q,Q_T) where q is the momentum transfer and Q_T a
We discuss new physical phenomena expected in particle production in hadron-hadron collisions at ... more We discuss new physical phenomena expected in particle production in hadron-hadron collisions at high energy, as a consequence of Pomeron loop effects in the evolution equations for the Color Glass Condensate. We focus on gluon production in asymmetric, 'dilute-dense', collisions : a dilute projectile scatters off a dense hadronic target, whose gluon distribution is highly evolved. This situation is representative for particle production in proton-proton collisions at forward rapidities (say, at LHC) and admits a dipole factorization similar to that of deep inelastic scattering (DIS). We show that at sufficiently large forward rapidities, where the Pomeron loop effects become important in the evolution of the target wavefunction, gluon production is dominated by 'black spots' (saturated gluon configurations) up to very large values of the transverse momentum, well above the average saturation momentum in the target. In this regime, the produced gluon spectrum exhibits diffusive scaling, so like DIS at sufficiently high energy.
... Author(s): JT DE SANTANA AMARAL High Energy Physics Phenomenology Group, GFPAE, Instituto de ... more ... Author(s): JT DE SANTANA AMARAL High Energy Physics Phenomenology Group, GFPAE, Instituto de Física, Universidade ... Imperial College Press | Global Publishing | Asia-Pacific Biotech News | Innovation Magazine | Asia Pacific Mathematics Newsletter Labcreations Co ...
This Report summarizes the proceedings of the 2013 Les Houches workshop on Physics at TeV Collide... more This Report summarizes the proceedings of the 2013 Les Houches workshop on Physics at TeV Colliders. Session 1 dealt primarily with (1) the techniques for calculating standard model multi-leg NLO and NNLO QCD and NLO EW cross sections and (2) the comparison of those cross sections with LHC data from Run 1, and projections for future measurements in Run 2.
Within the framework of a (1+1)-dimensional model which mimics evolution and scattering in QCD at... more Within the framework of a (1+1)-dimensional model which mimics evolution and scattering in QCD at high energy, we study the influence of the running of the coupling on the high-energy dynamics with Pomeron loops. We find that the particle number fluctuations are strongly suppressed by the running of the coupling, by at least one order of magnitude as compared to the case of a fixed coupling, for all the rapidities that we have investigated, up to Y = 200. This reflects the slowing down of the evolution by running coupling effects, in particular, the large rapidity evolution which is required for the formation of the saturation front via diffusion. We conclude that, for all energies of interest, processes like deep inelastic scattering or forward particle production can be reliably studied within the framework of a mean-field approximation (like the Balitsky-Kovchegov equation) which includes running coupling effects.
The measurement of the proton structure function at HERA is often seen as a hint for the observat... more The measurement of the proton structure function at HERA is often seen as a hint for the observation of saturation in high-energy QCD e.g. through the observation of geometric scaling. Accordingly, the dipole picture provides a powerful framework in which the QCD-based saturation models can be confronted to the data. In this paper, we give a parametrisation of proton structure function which is directly constrained by the dynamics of QCD in its high-energy limit and fully includes the heavy quark effects. We obtain a good agreement with the available data. Furthermore, to the contrary of various models in the literature, we do not observe a significant decrease of the saturation momentum due to the heavy quark inclusion. * on leave from the PTF group of the University of Liège. † Electronic address: [email protected]
The area of a jet is a measure of its susceptibility to radiation, like pileup or underlying even... more The area of a jet is a measure of its susceptibility to radiation, like pileup or underlying event (UE), that on average, in the jet's neighbourhood, is uniform in rapidity and azimuth. In this article we establish a theoretical grounding for the discussion of jet areas, introducing two main definitions, passive and active areas, which respectively characterise the sensitivity to pointlike or diffuse pileup and UE radiation. We investigate the properties of jet areas for three standard jet algorithms, k t , Cambridge/Aachen and SISCone. Passive areas for single-particle jets are equal to the naive geometrical expectation πR 2 , but acquire an anomalous dimension at higher orders in the coupling, calculated here at leading order. The more physically relevant active areas differ from πR 2 even for single-particle jets, substantially so in the case of the cone algorithms like SISCone with a Tevatron Run-II split-merge procedure. We compare our results with direct measures of areas in parton-shower Monte Carlo simulations and find good agreement with the main features of the analytical predictions. We furthermore justify the use of jet areas to subtract the contamination from pileup.
Using consistent truncations of the BFKL kernel, we derive analytical traveling-wave solutions of... more Using consistent truncations of the BFKL kernel, we derive analytical traveling-wave solutions of the Balitsky-Kovchegov saturation equation for both fixed and running coupling. A universal parametrization of the "interior" of the wave front is obtained and compares well with numerical simulations of the original Balitsky-Kovchegov equation, even at non-asymptotic energies. Using this universal parametrization, we find evidence for a traveling-wave pattern of the dipole amplitude determined from the gluon distribution extracted from deep inelastic scattering data.
We study the asymptotic solutions of a version of the Balitsky-Kovchegov evolution with discrete ... more We study the asymptotic solutions of a version of the Balitsky-Kovchegov evolution with discrete steps in rapidity. We derive a closed iterative equation in momentum space. We show that it possesses traveling-wave solutions and extract their properties. We find no evidence for chaotic behaviour due to discretization. PACS numbers: 11.10.Lm, 12.40.Ee, 24.85.+p ‡ on leave from the fundamental theoretical physics group of the University of Liège. ¶ URA 2306, unité de recherche associée au CNRS.
Using all available data on the deep-inelastic cross-sections at HERA at x ≤ 10 −2 , we look for ... more Using all available data on the deep-inelastic cross-sections at HERA at x ≤ 10 −2 , we look for geometric scaling of the form σ γ * p (τ ) where the scaling variable τ behaves alternatively like log Q 2 − λY, as in the original definition, or log Q 2 −λ √ Y , which is suggested by the asymptotic properties of the Balitsky-Kovchegov (BK) equation with running QCD coupling constant. A "Quality Factor" (QF) is defined, quantifying the phenomenological validity of the scaling and the uncertainty on the intercept λ. Both choices have a good QF, showing that the second choice is as valid as the first one, predicted for fixed coupling constant. A comparison between the QCD asymptotic predictions and data is made and the QF analysis shows that the agreement can be reached, provided going beyond leading logarithmic accuracy for the BK equation.
It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An... more It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation scales formed with all the events is distributed according to a probability law whose cumulants have been recently computed. In this work, we obtain the probability distribution from the cumulants. We prove that it can be considered as Gaussian over a large domain that we specify and our results are confirmed by numerical simulations.
Jet shapes have the potential to play a role in many LHC analyses, for example in quark-gluon dis... more Jet shapes have the potential to play a role in many LHC analyses, for example in quark-gluon discrimination or jet substructure analyses for hadronic decays of boosted heavy objects. Most shapes, however, are significantly affected by pileup. We introduce a general method to correct for pileup effects in shapes, which acts event-by-event and jet-by-jet, and accounts also for hadron masses. It involves a numerical determination, for each jet, of a given shape's susceptibility to pileup. Together with existing techniques for determining the level of pileup, this then enables an extrapolation to zero pileup. The method can be used for a wide range of jet shapes and we show its successful application in the context of quark/gluon discrimination and top-tagging.
We reproduce the DIS measurements of the proton structure function at high energy from the dipole... more We reproduce the DIS measurements of the proton structure function at high energy from the dipole model in momentum space. To model the dipole-proton forward scattering amplitude, we use the knowledge of asymptotic solutions of the Balitsky-Kovchegov equation, describing high-energy QCD in the presence of saturation effects. We compare our results with the previous analysis in coordinate space and discuss possible extensions of our approach. § On leave from the fundamental theoretical physics group of the University of Liège * Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected] ¶ Electronic address: [email protected]
DIFFRACTION 2002: Interpretation of the New Diffractive Phenomena in Quantum Chromodynamics and in the S-Matrix Theory, 2003
We analyze the consequences of t-channel unitarity for photon cross sections and show what assump... more We analyze the consequences of t-channel unitarity for photon cross sections and show what assumptions are necessary to allow for the existence of new singularities at Q 2 = 0 for the γp and γγ total cross sections. For virtual photons, such singularities can in general be present, but we show that, apart from the perturbative singularity associated with γ * γ * → qq, no new ingredient is needed to reproduce the data from LEP and HERA, in the Regge region. * on leave from Bogolyubov Institute for Theoretical Physics, Kiev.
The recent high-energy QCD equations including the effects of fluctuations are solved numerically... more The recent high-energy QCD equations including the effects of fluctuations are solved numerically. We discuss their asymptotic properties and compare them with the corresponding behaviour without fluctuations as well as with the statistical-physics model obtained in the saddle point approximation. The potential consequences on phenomenology, particularly on geometric scaling violations, are drawn.
We propose a stochastic particle model in (1+1)-dimensions, with one dimension corresponding to r... more We propose a stochastic particle model in (1+1)-dimensions, with one dimension corresponding to ra- pidity and the other one to the transverse size of a dipole in QCD, which mimics high-energy evolution and scattering in QCD in the presence of both saturation and particle-number fluctuations, and hence of Pomeron loops. The model evolves via non-linear particle splitting, with a non-local
In a previous publication, we have established a collinearly-improved version of the Balitsky-Kov... more In a previous publication, we have established a collinearly-improved version of the Balitsky-Kovchegov (BK) equation, which resums to all orders the radiative corrections enhanced by large double transverse logarithms. Here, we study the relevance of this equation as a tool for phenomenology, by confronting it to the HERA data. To that aim, we first improve the perturbative accuracy of our resummation, by including two classes of single-logarithmic corrections: those generated by the first non-singular terms in the DGLAP splitting functions and those expressing the one-loop running of the QCD coupling. The equation thus obtained includes all the next-to-leading order corrections to the BK equation which are enhanced by (single or double) collinear logarithms. We then use numerical solutions to this equation to fit the HERA data for the electron-proton reduced cross-section at small Bjorken x. We obtain good quality fits for physically acceptable initial conditions. Our best fit, which shows a good stability up to virtualities as large as Q 2 = 400 GeV 2 for the exchanged photon, uses as an initial condition the running-coupling version of the McLerran-Venugopalan model, with the QCD coupling running according to the smallest dipole prescription.
We show how one can obtain geometric scaling properties from the Balitsky-Kovchegov (BK) equation... more We show how one can obtain geometric scaling properties from the Balitsky-Kovchegov (BK) equation. We start by explaining how, this property arises for the b-independent BK equation. We show that it is possible to extend this model to the full BK equation including momentum transfer. The saturation scale behaves like max(q,Q_T) where q is the momentum transfer and Q_T a
We discuss new physical phenomena expected in particle production in hadron-hadron collisions at ... more We discuss new physical phenomena expected in particle production in hadron-hadron collisions at high energy, as a consequence of Pomeron loop effects in the evolution equations for the Color Glass Condensate. We focus on gluon production in asymmetric, 'dilute-dense', collisions : a dilute projectile scatters off a dense hadronic target, whose gluon distribution is highly evolved. This situation is representative for particle production in proton-proton collisions at forward rapidities (say, at LHC) and admits a dipole factorization similar to that of deep inelastic scattering (DIS). We show that at sufficiently large forward rapidities, where the Pomeron loop effects become important in the evolution of the target wavefunction, gluon production is dominated by 'black spots' (saturated gluon configurations) up to very large values of the transverse momentum, well above the average saturation momentum in the target. In this regime, the produced gluon spectrum exhibits diffusive scaling, so like DIS at sufficiently high energy.
... Author(s): JT DE SANTANA AMARAL High Energy Physics Phenomenology Group, GFPAE, Instituto de ... more ... Author(s): JT DE SANTANA AMARAL High Energy Physics Phenomenology Group, GFPAE, Instituto de Física, Universidade ... Imperial College Press | Global Publishing | Asia-Pacific Biotech News | Innovation Magazine | Asia Pacific Mathematics Newsletter Labcreations Co ...
This Report summarizes the proceedings of the 2013 Les Houches workshop on Physics at TeV Collide... more This Report summarizes the proceedings of the 2013 Les Houches workshop on Physics at TeV Colliders. Session 1 dealt primarily with (1) the techniques for calculating standard model multi-leg NLO and NNLO QCD and NLO EW cross sections and (2) the comparison of those cross sections with LHC data from Run 1, and projections for future measurements in Run 2.
Within the framework of a (1+1)-dimensional model which mimics evolution and scattering in QCD at... more Within the framework of a (1+1)-dimensional model which mimics evolution and scattering in QCD at high energy, we study the influence of the running of the coupling on the high-energy dynamics with Pomeron loops. We find that the particle number fluctuations are strongly suppressed by the running of the coupling, by at least one order of magnitude as compared to the case of a fixed coupling, for all the rapidities that we have investigated, up to Y = 200. This reflects the slowing down of the evolution by running coupling effects, in particular, the large rapidity evolution which is required for the formation of the saturation front via diffusion. We conclude that, for all energies of interest, processes like deep inelastic scattering or forward particle production can be reliably studied within the framework of a mean-field approximation (like the Balitsky-Kovchegov equation) which includes running coupling effects.
The measurement of the proton structure function at HERA is often seen as a hint for the observat... more The measurement of the proton structure function at HERA is often seen as a hint for the observation of saturation in high-energy QCD e.g. through the observation of geometric scaling. Accordingly, the dipole picture provides a powerful framework in which the QCD-based saturation models can be confronted to the data. In this paper, we give a parametrisation of proton structure function which is directly constrained by the dynamics of QCD in its high-energy limit and fully includes the heavy quark effects. We obtain a good agreement with the available data. Furthermore, to the contrary of various models in the literature, we do not observe a significant decrease of the saturation momentum due to the heavy quark inclusion. * on leave from the PTF group of the University of Liège. † Electronic address: [email protected]
The area of a jet is a measure of its susceptibility to radiation, like pileup or underlying even... more The area of a jet is a measure of its susceptibility to radiation, like pileup or underlying event (UE), that on average, in the jet's neighbourhood, is uniform in rapidity and azimuth. In this article we establish a theoretical grounding for the discussion of jet areas, introducing two main definitions, passive and active areas, which respectively characterise the sensitivity to pointlike or diffuse pileup and UE radiation. We investigate the properties of jet areas for three standard jet algorithms, k t , Cambridge/Aachen and SISCone. Passive areas for single-particle jets are equal to the naive geometrical expectation πR 2 , but acquire an anomalous dimension at higher orders in the coupling, calculated here at leading order. The more physically relevant active areas differ from πR 2 even for single-particle jets, substantially so in the case of the cone algorithms like SISCone with a Tevatron Run-II split-merge procedure. We compare our results with direct measures of areas in parton-shower Monte Carlo simulations and find good agreement with the main features of the analytical predictions. We furthermore justify the use of jet areas to subtract the contamination from pileup.
Using consistent truncations of the BFKL kernel, we derive analytical traveling-wave solutions of... more Using consistent truncations of the BFKL kernel, we derive analytical traveling-wave solutions of the Balitsky-Kovchegov saturation equation for both fixed and running coupling. A universal parametrization of the "interior" of the wave front is obtained and compares well with numerical simulations of the original Balitsky-Kovchegov equation, even at non-asymptotic energies. Using this universal parametrization, we find evidence for a traveling-wave pattern of the dipole amplitude determined from the gluon distribution extracted from deep inelastic scattering data.
We study the asymptotic solutions of a version of the Balitsky-Kovchegov evolution with discrete ... more We study the asymptotic solutions of a version of the Balitsky-Kovchegov evolution with discrete steps in rapidity. We derive a closed iterative equation in momentum space. We show that it possesses traveling-wave solutions and extract their properties. We find no evidence for chaotic behaviour due to discretization. PACS numbers: 11.10.Lm, 12.40.Ee, 24.85.+p ‡ on leave from the fundamental theoretical physics group of the University of Liège. ¶ URA 2306, unité de recherche associée au CNRS.
Using all available data on the deep-inelastic cross-sections at HERA at x ≤ 10 −2 , we look for ... more Using all available data on the deep-inelastic cross-sections at HERA at x ≤ 10 −2 , we look for geometric scaling of the form σ γ * p (τ ) where the scaling variable τ behaves alternatively like log Q 2 − λY, as in the original definition, or log Q 2 −λ √ Y , which is suggested by the asymptotic properties of the Balitsky-Kovchegov (BK) equation with running QCD coupling constant. A "Quality Factor" (QF) is defined, quantifying the phenomenological validity of the scaling and the uncertainty on the intercept λ. Both choices have a good QF, showing that the second choice is as valid as the first one, predicted for fixed coupling constant. A comparison between the QCD asymptotic predictions and data is made and the QF analysis shows that the agreement can be reached, provided going beyond leading logarithmic accuracy for the BK equation.
It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An... more It was recently noticed that high-energy scattering processes in QCD have a stochastic nature. An event-by-event scattering amplitude is characterised by a saturation scale which is a random variable. The statistical ensemble of saturation scales formed with all the events is distributed according to a probability law whose cumulants have been recently computed. In this work, we obtain the probability distribution from the cumulants. We prove that it can be considered as Gaussian over a large domain that we specify and our results are confirmed by numerical simulations.
Jet shapes have the potential to play a role in many LHC analyses, for example in quark-gluon dis... more Jet shapes have the potential to play a role in many LHC analyses, for example in quark-gluon discrimination or jet substructure analyses for hadronic decays of boosted heavy objects. Most shapes, however, are significantly affected by pileup. We introduce a general method to correct for pileup effects in shapes, which acts event-by-event and jet-by-jet, and accounts also for hadron masses. It involves a numerical determination, for each jet, of a given shape's susceptibility to pileup. Together with existing techniques for determining the level of pileup, this then enables an extrapolation to zero pileup. The method can be used for a wide range of jet shapes and we show its successful application in the context of quark/gluon discrimination and top-tagging.
We reproduce the DIS measurements of the proton structure function at high energy from the dipole... more We reproduce the DIS measurements of the proton structure function at high energy from the dipole model in momentum space. To model the dipole-proton forward scattering amplitude, we use the knowledge of asymptotic solutions of the Balitsky-Kovchegov equation, describing high-energy QCD in the presence of saturation effects. We compare our results with the previous analysis in coordinate space and discuss possible extensions of our approach. § On leave from the fundamental theoretical physics group of the University of Liège * Electronic address: [email protected] † Electronic address: [email protected] ‡ Electronic address: [email protected] ¶ Electronic address: [email protected]
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Papers by G. Soyez