We discuss Yukawa-enhanced contributions from Z-mediated new physics to down-type quark ∆F = 2 pr... more We discuss Yukawa-enhanced contributions from Z-mediated new physics to down-type quark ∆F = 2 processes in the framework of the standard model gaugeinvariant effective theory (SMEFT). Besides the renormalization group (RG) mixing of the Z-mediating ψ 2 H 2 D operators into ∆F = 2 operators, we include at the electroweak scale one-loop (NLO) matching corrections consistently, necessary for the removal of the matching scale dependence. We point out that the right-handed Z-mediated interactions generate through Yukawa RG mixing ∆F = 2 left-right operators, which are further enhanced through QCD RG effects and chirally enhanced hadronic matrix elements. We investigate the impact of these new effects on the known correlations between ∆F = 2 and ∆F = 1 transitions in the SMEFT framework and point out qualitative differences to previous parameterizations of Z-mediated new physics that arise for the left-handed case. We illustrate how specific models fit into our model-independent framework by using four models with vector-like quarks. We carry out model-independent analyses of scenarios with purely left-handed and purely right-handed new-physics Z couplings for each of the three sectors s → d, b → s and b → d. Specifically we discuss the correlations between ε /ε, ε K , K L → µ + µ − K + → π + νν and K L → π 0 νν in the Kaon sector, and φ s , B s → µ + µ − and B → K (*) (µ + µ − , νν) in the b → s sector and B d → µ + µ − in the b → d sector.
We discuss those composite models of quarks and leptons with an SU(lt3 metacolor group and preons... more We discuss those composite models of quarks and leptons with an SU(lt3 metacolor group and preons in the complex, anomaly-free, and asymptotically free representations, which do not have spectators with SU(3) @ SU(2) @ U(1) quantum numbers. We find that many of these models can be ruled out independently of the way the chiral (metaflavor) symmetries are realized and the bound states are constructed. The remaining models contain a large number of preons-100 or more.
We present a complete calculation of leading and next-to-leading QCD corrections to the QCD facto... more We present a complete calculation of leading and next-to-leading QCD corrections to the QCD factors rl2K and ~2B, relevant for the CP-violating e-parameter and BOB ° mixing in the presence of a heavy top quark. We demonstrate explicitly that the resulting r/2's are gauge as well as renormalization prescription independent. We also show that they do not depend on the infrared structure of the theory. We emphasize that these results only follow after correct factorization of short and long distance contributions, which has not been done properly in many recent QCD analyses present in the literature. We stress however that r/2(x t) with x t = m~/M w depends sensitively on the definition of the top quark mass and only the product O2(xt)S(xt) (S(x t) being the function resulting from the lowest order box diagram) is free from this dependence. For m t = mt(Mw) the corresponding rt2's decrease strongly with mr, whereas for mr* = ~t(mt) they show only a weak m*-dependence: 0.58 >/rl~ K >/0.56 and 0.88 >/~*u/> 0.84 for 60 GeV ~< m* ~< 300 GeV and A~s= 200 MeV. A critical discussion of the existing literature on QCD calculations in the presence of a large m t is presented.
Proceedings of 11th International Workshop on the CKM Unitarity Triangle — PoS(CKM2021)
The persistent tensions between inclusive and exclusive determinations of |V cb | and |V ub | wea... more The persistent tensions between inclusive and exclusive determinations of |V cb | and |V ub | weaken the power of theoretically clean rare K and B decays in the search for new physics (NP). We demonstrate how this uncertainty can be practically removed by considering within the SM suitable ratios of various branching ratios. This includes the branching ratios for K
We review several aspects of K-Physics: i) Main targets of the field, ii) The theoretical framewo... more We review several aspects of K-Physics: i) Main targets of the field, ii) The theoretical framework for K-decays, iii) Standard analysis of the unitarity triangle, iv) ε ′ /ε, v) Rare and CP violating K-decays, vi) Comparision of the potentials of K → πνν and CP-B asymmetries. vii) Some aspects of the physics beyond the Standard Model.
We present an effective Lagrangian formalism for the calculation of flavour changing neutral and ... more We present an effective Lagrangian formalism for the calculation of flavour changing neutral and charged scalar currents in weak decays including SU (2)×U (1) symmetry breaking effects and the effects of the electroweak couplings g 1 and g 2. We apply this formalism to the MSSM with large tan β with the CKM matrix as the only source of flavour violation, heavy supersymmetric particles and light Higgs bosons. We give analytic formulae for the neutral and charged Higgs boson couplings to quarks including large tan β resummed corrections in the SU (2) × U (1) limit and demonstrate that these formulae can only be used for a semi-quantitative analysis. In particular they overestimate the effects of large tan β resummed corrections. We give also improved analytic formulae that reproduce the numerical results of the full approach within 5 − 10%. We present for the first time the predictions for the branching ratios B 0 s,d → µ + µ − and the B 0 d,s −B 0 d,s mass differences ∆M d,s that include simultaneously the resummed large tan β corrections, SU (2) × U (1) breaking effects and the effects of the electroweak couplings. We perform an anatomy of the correlation between the increase of the rates of the decays B 0 s,d → µ + µ − and the suppression of ∆M s , that for large tan β are caused by the enhanced flavour changing neutral Higgs couplings to down quarks. We take into account the constraint from B → X s γ clarifying some points in the calculation of the large tan β enhanced corrections to this decay.
The $B\to\pi K$ decays with significant electroweak penguin contributions show a puzzling pattern... more The $B\to\pi K$ decays with significant electroweak penguin contributions show a puzzling pattern. We explore this "$B\to\pi K$ puzzle" through a systematic strategy. The starting point, which is essentially unaffected by electroweak penguins, is the determination of the angle $\gamma$ of the unitarity triangle through the CP-violating $B^0_d\to\pi^+\pi^-$, $B^0_d\to\pi^-K^+$ asymmetries, yielding $\gamma=(73.9^{+5.8}_{-6.5})^\circ$, and the extraction of hadronic parameters through the measured $B\to\pi\pi$ branching ratios. Using arguments related to the SU(3) flavour symmetry, we convert the hadronic $B\to\pi\pi$ parameters into their $B\to\pi K$ counterparts, allowing us to predict the $B\to\pi K$ observables in the Standard Model. We find agreement with the data for those quantities that are only marginally affected by electroweak penguins, while this is not the case for the observables with sizeable electroweak penguin contributions. Since we may also perform a coupl...
Flavour SU(3) symmetry of strong interactions and certain dynamical assumptions have been used in... more Flavour SU(3) symmetry of strong interactions and certain dynamical assumptions have been used in a series of recent publications to extract weak CKM phases from B-decays into {ππ, πK, KK} final states. We point out that irrespectively of SU(3)-breaking effects the presence of QCD-penguin contributions with internal u-and c-quarks precludes a clean determination of the angle β in the unitarity triangle by using the branching ratios only. This difficulty can be overcome by measuring in addition the ratio x d /x s of B 0 d −B 0 d to B 0 s −B 0 s mixings. * Supported by the German Bundesministerium für Forschung und Technologie under contract 06 TM 732 and by the CEC science project SC1-CT91-0729.
We update our 1993 analysis of the CP violating ratio ε ′ /ε in view of the changes in several in... more We update our 1993 analysis of the CP violating ratio ε ′ /ε in view of the changes in several input parameters, in particular the improved value of the top quark mass. We also investigate the strange quark mass m s dependence of ε ′ /ε in view of rather low values found in the most recent lattice calculations. A simple scanning of the input parameters within one standard deviation gives the ranges: −1.2 • 10 −4 ≤ ε ′ /ε ≤ 16.0 • 10 −4 and 0 ≤ ε ′ /ε ≤ 43.0 • 10 −4 for m s (m c) = 150 ± 20 MeV and m s (m c) = 100 ± 20 MeV respectively. If the experimentally measured numbers and the theoretical input parameters are used with Gaussian errors, we find ε ′ /ε = (3.6 ± 3.4) • 10 −4 and ε ′ /ε = (10.4 ± 8.3) • 10 −4 respectively. We also give results for ImV * ts V td. Analyzing the dependence of ε ′ /ε on various parameters we find that only for m s (m c) ≤ 100 MeV and a conspiration of other input parameters, values for ε ′ /ε as large as (2 − 4) • 10 −3 and consistent with the NA31 result can be obtained. † Supported by the German Bundesministerium für Bildung und Forschung under contract 06 TM 743 and DFG Project Li 519/2-1.
The main aspects of the 1IN approach to non-leptonic weak interactions developed in collaboration... more The main aspects of the 1IN approach to non-leptonic weak interactions developed in collaboration with Bardeen and G&ard are reviewed in detail. The results for the hadronic matrix elements relevant for K ~ 7rlr decays, K °-ff0 mixing and CP violation in the K-system are presented. The implications of these results for the AI-1/2 rule in K-+ lnr decays and the CP violating parameters e and e~ are discussed in detail. It is pointed out that the mass of the top quark (ms) should not be too large for the standard model to be able to fit the recent NA31 data for E~/c. An upper bound for mt is found as a function of various non-perturbative parameters. Typically mt< 90 Geg is required. Implications of the B °-/~0 mixing for ~/E and the value of ms are discussed.
We calculate the effective hamiltonians for~,1B= 1 and iS = 1 decays including next-to-leading QC... more We calculate the effective hamiltonians for~,1B= 1 and iS = 1 decays including next-to-leading QCD corrections. In particular we present the two-loop 6>< 6 anomalous dimension matrices describing the mixing of current-current and QCD penguin operators calculated in the dimensional regularization scheme with anticommuting y~and in the 't Hooft-Veltman scheme. The renormalization scheme dependences and their cancellation for physical quantities are discussed in detail. We point out that beyond the leading order, matching between coefficients and hadronic matrix elements of local operators both in the renormalization scale ji and in the renormalization scheme for the operators has to be made. The next-to-leading corrections enhance substantially the Wilson coefficients of QCD penguin operators and these effects are stronger than the ones found for current-current operators. Consequently, the contributions of QCD penguins to B-decays, the iI = 1/2 rule and '/E are enlarged. For~s I GeV and t~300 MeV. these effects amount to 20-30%. In particular we emphasize that for p. < I GeV the next-to-leading corrections to the coefficients of penguin operators arc large, reaching 40% for p. 0.8 GeV. For such low values of p. the renormalization group improved perturbation theory cannot be trusted any longer. Moreover the results are very sensitive functions of I Correspondence to: A.J. Buras. Physik Department der TU Miinchen, James-Franck-Strasse. DW-8046 Garching, Germany. * Supported by the German Bundesministerium für Forschung and Technologie, contract 06 TM 761.
... 3a). This 380 AJ Buras, J.-M. G rard / 1 / N expansion for kaons dsds K' K Ko sdsd (a) (... more ... 3a). This 380 AJ Buras, J.-M. G rard / 1 / N expansion for kaons dsds K' K Ko sdsd (a) (b) Fig. 2. (a) Leading (- N), (b) non-leading (- 1) box diagram contributions to K - K transition due to HS -Z defined in eq. (3.33). dsds K'AO 0 (DK' K' K' sdsd (a) (b) Fig. ...
Many experimentally accessible quantities are related to the angles and sides of the Unitarity Tr... more Many experimentally accessible quantities are related to the angles and sides of the Unitarity Triangle (UT) and their measurement can hence put constraints on the UT plane coordinates (ρ̄, η̄). The main experimental and theoretical inputs to the UT Analysis performed by the UTfit collaboration are summarized in tables 1 and 2, respectively. The choice of lattice QCD quantities used in UTfit is motivated in 2. The relation between ρ̄ and η̄ and the measured quantities is discussed for example in 1.
We present a model independent analysis of new-physics contributions to the rare decays K + → π +... more We present a model independent analysis of new-physics contributions to the rare decays K + → π + νν and K L → π 0 νν. We parameterize the effects of new physics in these decays by two parameters: r K and the phase θ K , with r K = 1 and θ K = 0 in the Standard Model. We show how these parameters can be extracted from future data together with the relevant CKM parameters, in particular the angle β of the unitarity triangle. To this end CP asymmetries in B → ψK S and B → π + π − as well as the ratio |V ub /V cb | have to be also considered. This analysis offers simultaneously some insight in a possible violation of a "golden relation" between K → πνν decays and the CP asymmetry in B → ψK S in the Standard Model pointed out some time ago. We illustrate these ideas by considering a general class of supersymmetric models. We find that in the "constrained" MSSM, in which θ K = 0, the measurements of Br(K + → π + νν) and Br(K L → π 0 νν) directly determine the angle β. Moreover, the "golden relation" remains unaffected. On the other hand, in general SUSY models with unbroken R-parity the present experimental constraints still allow for substantial deviations from r K = 1 and θ K = 0. Typically 0.5 < r K < 1.3 and −25 0 < θ K < 25 0. Consequently, in these models the violation of the "golden relation" is possible and values for Br(K + → π + νν) and Br(K L → π 0 νν) departing from the Standard Model expectations by factors 2-3 cannot be excluded. Simultaneously, the extraction of the "true" angle β from K → πνν is not possible without additional information from other decays. Our conclusions differ in certain aspects from the ones reached in previous analyses. In particular, we stress the possible importance of left-right flavour-violating mass insertions that were not considered before.
Motivated by the recent findings that the ratio ε /ε in the Standard Model (SM) appears to be sig... more Motivated by the recent findings that the ratio ε /ε in the Standard Model (SM) appears to be significantly below the data we investigate whether the necessary enhancement of ε /ε can be obtained in 331 models, based on the gauge group SU(3) C × SU(3) L × U(1) X . In these models new physics (NP) contributions to ε /ε and other flavour observables are dominated by tree-level exchanges of a Z with non-negligible contributions from tree-level Z exchanges generated through the Z -Z mixing. NP contributions to ε /ε in these models are governed by the electroweak penguin operator Q 8 for which the hadronic matrix element is already rather well known so that our analysis of NP contributions is subject to much smaller theoretical uncertainties than within the SM. In particular strong cancelations between different contributions do not take place. The size of NP effects depends not only on M Z but in particular on a parameter β, which distinguishes between various 331 models. Also a parameter tan β present in the Z -Z mixing plays a role. We perform the analysis in seven 331 models characterized by different β, tan β and fermion representations under the gauge group that have been selected in our earlier analysis on the basis of electroweak precision data. Imposing the constraints from ∆F = 2 transitions we find that only three of these models can provide a significant positive shift in ε /ε up to 6 × 10 -4 for M Z = 3 TeV. Two of them allow simultaneously a supression of the rate for B s → µ + µ -by 20% thereby bringing the theory closer to the data without any significant impact on the Wilson coefficient C 9 . The third model provides simultaneous shift ∆C 9 = -0.6, softening the anomalies in B → K * µ + µ -, without any significant impact on B s → µ + µ -. NP effects in rare K decays, in particular in K + → π + ν ν, turn out to be small. This is also the case of B → K(K * )ν ν. Both predictions could be challenged by NA62 experiment and Belle II in this decade. The special flavour structure of 331 models implies that even for M Z = 30 TeV a shift of ε /ε up to 8 × 10 -4 and a significant shift in ε K can be obtained, while the effects in other flavour observables are small. In this manner ε /ε and ε K appear to be unique flavour observables in these models which provide the possibility of accessing masses of M Z far beyond the LHC reach.
The experimental value for the isospin amplitude Re(A_2) in K->pi pi decays has been successfu... more The experimental value for the isospin amplitude Re(A_2) in K->pi pi decays has been successfully explained within the Standard Model, both within large N approach to QCD and by QCD lattice calculations. On the other hand in both approaches the theoretical values of Re(A_0) are by at least 30% below the data so that the Delta I=1/2 rule in K->pi pi decays is not fully explained. While this deficit could be the result of present theoretical uncertainties in both approaches, it cannot be excluded that the missing piece in Re(A_0) comes from New Physics. We demonstrate that this deficit can be significantly softened by tree-level FCNC transitions mediated by a heavy colourless Z' gauge boson with particularly chosen flavour violating couplings assuring negligible NP contributions to Re(A_2) and significantly enhancing the contribution of the leading QCD penguin operator Q_6 to Re(A_0). A large fraction of the missing piece in the Delta I=1/2 rule can be explained in this mann...
We make the simple observation that there exists a universal unitarity triangle for all models, l... more We make the simple observation that there exists a universal unitarity triangle for all models, like the SM, the Two Higgs Doublet Models I and II and the MSSM with minimal flavour violation, that do not have any new operators beyond those present in the SM and in which all flavour changing transitions are governed by the CKM matrix with no new phases beyond the CKM phase. This universal triangle can be determined in the near future from the ratio (∆M) d /(∆M) s and sin 2β measured first through the CP asymmetry in B 0 d → ψK S and later in K → πνν decays. Also suitable ratios of the branching ratios for B → X d,s νν and B d,s → µ + µ − and the angle γ measured by means of CP asymmetries in B decays can be used for this determination. Comparison of this universal triangle with the nonuniversal triangles extracted in each model using ε, (∆M) d and various branching ratios for rare decays will allow to find out in a transparent manner which of these models, if any, is singled out by experiment. A virtue of the universal triangle is that it allows to separate the determination of the CKM parameters from the determination of new parameters present in the extensions of the SM considered here.
In the past decade, one of the major challenges of particle physics has been to gain an in-depth ... more In the past decade, one of the major challenges of particle physics has been to gain an in-depth understanding of the role of quark flavor. In this time frame, measurements and the theoretical interpretation of their results have advanced tremendously. A much broader understanding of flavor particles has been achieved, apart from their masses and quantum numbers, there now exist detailed measurements of the characteristics of their interactions allowing stringent tests of Standard Model predictions. Among the most interesting phenomena of flavor physics is the violation of the CP symmetry that has been subtle and difficult to explore. In the past, observations of CP violation were confined to neutral K mesons, but since the early 1990s, a large number of CP-violating processes have been studied in detail in neutral B mesons. In parallel, measurements of the couplings of the heavy quarks and the dynamics for their decays in large samples of K, D, and B mesons have been greatly improved in accuracy and the results are being used as probes in the search for deviations from the Standard Model. In the near future, there will be a transition from the current to a new generation of experiments, thus a review of the status of quark flavor physics is timely. This report is the result of the work of the physicists attending the 5 th CKM workshop, hosted by the University of Rome "La Sapienza", September 9-13, 2008. It summarizes the results of the current generation of experiments that is about to be completed and it confronts these results with the theoretical understanding of the field which has greatly improved in the past decade.
We discuss Yukawa-enhanced contributions from Z-mediated new physics to down-type quark ∆F = 2 pr... more We discuss Yukawa-enhanced contributions from Z-mediated new physics to down-type quark ∆F = 2 processes in the framework of the standard model gaugeinvariant effective theory (SMEFT). Besides the renormalization group (RG) mixing of the Z-mediating ψ 2 H 2 D operators into ∆F = 2 operators, we include at the electroweak scale one-loop (NLO) matching corrections consistently, necessary for the removal of the matching scale dependence. We point out that the right-handed Z-mediated interactions generate through Yukawa RG mixing ∆F = 2 left-right operators, which are further enhanced through QCD RG effects and chirally enhanced hadronic matrix elements. We investigate the impact of these new effects on the known correlations between ∆F = 2 and ∆F = 1 transitions in the SMEFT framework and point out qualitative differences to previous parameterizations of Z-mediated new physics that arise for the left-handed case. We illustrate how specific models fit into our model-independent framework by using four models with vector-like quarks. We carry out model-independent analyses of scenarios with purely left-handed and purely right-handed new-physics Z couplings for each of the three sectors s → d, b → s and b → d. Specifically we discuss the correlations between ε /ε, ε K , K L → µ + µ − K + → π + νν and K L → π 0 νν in the Kaon sector, and φ s , B s → µ + µ − and B → K (*) (µ + µ − , νν) in the b → s sector and B d → µ + µ − in the b → d sector.
We discuss those composite models of quarks and leptons with an SU(lt3 metacolor group and preons... more We discuss those composite models of quarks and leptons with an SU(lt3 metacolor group and preons in the complex, anomaly-free, and asymptotically free representations, which do not have spectators with SU(3) @ SU(2) @ U(1) quantum numbers. We find that many of these models can be ruled out independently of the way the chiral (metaflavor) symmetries are realized and the bound states are constructed. The remaining models contain a large number of preons-100 or more.
We present a complete calculation of leading and next-to-leading QCD corrections to the QCD facto... more We present a complete calculation of leading and next-to-leading QCD corrections to the QCD factors rl2K and ~2B, relevant for the CP-violating e-parameter and BOB ° mixing in the presence of a heavy top quark. We demonstrate explicitly that the resulting r/2's are gauge as well as renormalization prescription independent. We also show that they do not depend on the infrared structure of the theory. We emphasize that these results only follow after correct factorization of short and long distance contributions, which has not been done properly in many recent QCD analyses present in the literature. We stress however that r/2(x t) with x t = m~/M w depends sensitively on the definition of the top quark mass and only the product O2(xt)S(xt) (S(x t) being the function resulting from the lowest order box diagram) is free from this dependence. For m t = mt(Mw) the corresponding rt2's decrease strongly with mr, whereas for mr* = ~t(mt) they show only a weak m*-dependence: 0.58 >/rl~ K >/0.56 and 0.88 >/~*u/> 0.84 for 60 GeV ~< m* ~< 300 GeV and A~s= 200 MeV. A critical discussion of the existing literature on QCD calculations in the presence of a large m t is presented.
Proceedings of 11th International Workshop on the CKM Unitarity Triangle — PoS(CKM2021)
The persistent tensions between inclusive and exclusive determinations of |V cb | and |V ub | wea... more The persistent tensions between inclusive and exclusive determinations of |V cb | and |V ub | weaken the power of theoretically clean rare K and B decays in the search for new physics (NP). We demonstrate how this uncertainty can be practically removed by considering within the SM suitable ratios of various branching ratios. This includes the branching ratios for K
We review several aspects of K-Physics: i) Main targets of the field, ii) The theoretical framewo... more We review several aspects of K-Physics: i) Main targets of the field, ii) The theoretical framework for K-decays, iii) Standard analysis of the unitarity triangle, iv) ε ′ /ε, v) Rare and CP violating K-decays, vi) Comparision of the potentials of K → πνν and CP-B asymmetries. vii) Some aspects of the physics beyond the Standard Model.
We present an effective Lagrangian formalism for the calculation of flavour changing neutral and ... more We present an effective Lagrangian formalism for the calculation of flavour changing neutral and charged scalar currents in weak decays including SU (2)×U (1) symmetry breaking effects and the effects of the electroweak couplings g 1 and g 2. We apply this formalism to the MSSM with large tan β with the CKM matrix as the only source of flavour violation, heavy supersymmetric particles and light Higgs bosons. We give analytic formulae for the neutral and charged Higgs boson couplings to quarks including large tan β resummed corrections in the SU (2) × U (1) limit and demonstrate that these formulae can only be used for a semi-quantitative analysis. In particular they overestimate the effects of large tan β resummed corrections. We give also improved analytic formulae that reproduce the numerical results of the full approach within 5 − 10%. We present for the first time the predictions for the branching ratios B 0 s,d → µ + µ − and the B 0 d,s −B 0 d,s mass differences ∆M d,s that include simultaneously the resummed large tan β corrections, SU (2) × U (1) breaking effects and the effects of the electroweak couplings. We perform an anatomy of the correlation between the increase of the rates of the decays B 0 s,d → µ + µ − and the suppression of ∆M s , that for large tan β are caused by the enhanced flavour changing neutral Higgs couplings to down quarks. We take into account the constraint from B → X s γ clarifying some points in the calculation of the large tan β enhanced corrections to this decay.
The $B\to\pi K$ decays with significant electroweak penguin contributions show a puzzling pattern... more The $B\to\pi K$ decays with significant electroweak penguin contributions show a puzzling pattern. We explore this "$B\to\pi K$ puzzle" through a systematic strategy. The starting point, which is essentially unaffected by electroweak penguins, is the determination of the angle $\gamma$ of the unitarity triangle through the CP-violating $B^0_d\to\pi^+\pi^-$, $B^0_d\to\pi^-K^+$ asymmetries, yielding $\gamma=(73.9^{+5.8}_{-6.5})^\circ$, and the extraction of hadronic parameters through the measured $B\to\pi\pi$ branching ratios. Using arguments related to the SU(3) flavour symmetry, we convert the hadronic $B\to\pi\pi$ parameters into their $B\to\pi K$ counterparts, allowing us to predict the $B\to\pi K$ observables in the Standard Model. We find agreement with the data for those quantities that are only marginally affected by electroweak penguins, while this is not the case for the observables with sizeable electroweak penguin contributions. Since we may also perform a coupl...
Flavour SU(3) symmetry of strong interactions and certain dynamical assumptions have been used in... more Flavour SU(3) symmetry of strong interactions and certain dynamical assumptions have been used in a series of recent publications to extract weak CKM phases from B-decays into {ππ, πK, KK} final states. We point out that irrespectively of SU(3)-breaking effects the presence of QCD-penguin contributions with internal u-and c-quarks precludes a clean determination of the angle β in the unitarity triangle by using the branching ratios only. This difficulty can be overcome by measuring in addition the ratio x d /x s of B 0 d −B 0 d to B 0 s −B 0 s mixings. * Supported by the German Bundesministerium für Forschung und Technologie under contract 06 TM 732 and by the CEC science project SC1-CT91-0729.
We update our 1993 analysis of the CP violating ratio ε ′ /ε in view of the changes in several in... more We update our 1993 analysis of the CP violating ratio ε ′ /ε in view of the changes in several input parameters, in particular the improved value of the top quark mass. We also investigate the strange quark mass m s dependence of ε ′ /ε in view of rather low values found in the most recent lattice calculations. A simple scanning of the input parameters within one standard deviation gives the ranges: −1.2 • 10 −4 ≤ ε ′ /ε ≤ 16.0 • 10 −4 and 0 ≤ ε ′ /ε ≤ 43.0 • 10 −4 for m s (m c) = 150 ± 20 MeV and m s (m c) = 100 ± 20 MeV respectively. If the experimentally measured numbers and the theoretical input parameters are used with Gaussian errors, we find ε ′ /ε = (3.6 ± 3.4) • 10 −4 and ε ′ /ε = (10.4 ± 8.3) • 10 −4 respectively. We also give results for ImV * ts V td. Analyzing the dependence of ε ′ /ε on various parameters we find that only for m s (m c) ≤ 100 MeV and a conspiration of other input parameters, values for ε ′ /ε as large as (2 − 4) • 10 −3 and consistent with the NA31 result can be obtained. † Supported by the German Bundesministerium für Bildung und Forschung under contract 06 TM 743 and DFG Project Li 519/2-1.
The main aspects of the 1IN approach to non-leptonic weak interactions developed in collaboration... more The main aspects of the 1IN approach to non-leptonic weak interactions developed in collaboration with Bardeen and G&ard are reviewed in detail. The results for the hadronic matrix elements relevant for K ~ 7rlr decays, K °-ff0 mixing and CP violation in the K-system are presented. The implications of these results for the AI-1/2 rule in K-+ lnr decays and the CP violating parameters e and e~ are discussed in detail. It is pointed out that the mass of the top quark (ms) should not be too large for the standard model to be able to fit the recent NA31 data for E~/c. An upper bound for mt is found as a function of various non-perturbative parameters. Typically mt< 90 Geg is required. Implications of the B °-/~0 mixing for ~/E and the value of ms are discussed.
We calculate the effective hamiltonians for~,1B= 1 and iS = 1 decays including next-to-leading QC... more We calculate the effective hamiltonians for~,1B= 1 and iS = 1 decays including next-to-leading QCD corrections. In particular we present the two-loop 6>< 6 anomalous dimension matrices describing the mixing of current-current and QCD penguin operators calculated in the dimensional regularization scheme with anticommuting y~and in the 't Hooft-Veltman scheme. The renormalization scheme dependences and their cancellation for physical quantities are discussed in detail. We point out that beyond the leading order, matching between coefficients and hadronic matrix elements of local operators both in the renormalization scale ji and in the renormalization scheme for the operators has to be made. The next-to-leading corrections enhance substantially the Wilson coefficients of QCD penguin operators and these effects are stronger than the ones found for current-current operators. Consequently, the contributions of QCD penguins to B-decays, the iI = 1/2 rule and '/E are enlarged. For~s I GeV and t~300 MeV. these effects amount to 20-30%. In particular we emphasize that for p. < I GeV the next-to-leading corrections to the coefficients of penguin operators arc large, reaching 40% for p. 0.8 GeV. For such low values of p. the renormalization group improved perturbation theory cannot be trusted any longer. Moreover the results are very sensitive functions of I Correspondence to: A.J. Buras. Physik Department der TU Miinchen, James-Franck-Strasse. DW-8046 Garching, Germany. * Supported by the German Bundesministerium für Forschung and Technologie, contract 06 TM 761.
... 3a). This 380 AJ Buras, J.-M. G rard / 1 / N expansion for kaons dsds K' K Ko sdsd (a) (... more ... 3a). This 380 AJ Buras, J.-M. G rard / 1 / N expansion for kaons dsds K' K Ko sdsd (a) (b) Fig. 2. (a) Leading (- N), (b) non-leading (- 1) box diagram contributions to K - K transition due to HS -Z defined in eq. (3.33). dsds K'AO 0 (DK' K' K' sdsd (a) (b) Fig. ...
Many experimentally accessible quantities are related to the angles and sides of the Unitarity Tr... more Many experimentally accessible quantities are related to the angles and sides of the Unitarity Triangle (UT) and their measurement can hence put constraints on the UT plane coordinates (ρ̄, η̄). The main experimental and theoretical inputs to the UT Analysis performed by the UTfit collaboration are summarized in tables 1 and 2, respectively. The choice of lattice QCD quantities used in UTfit is motivated in 2. The relation between ρ̄ and η̄ and the measured quantities is discussed for example in 1.
We present a model independent analysis of new-physics contributions to the rare decays K + → π +... more We present a model independent analysis of new-physics contributions to the rare decays K + → π + νν and K L → π 0 νν. We parameterize the effects of new physics in these decays by two parameters: r K and the phase θ K , with r K = 1 and θ K = 0 in the Standard Model. We show how these parameters can be extracted from future data together with the relevant CKM parameters, in particular the angle β of the unitarity triangle. To this end CP asymmetries in B → ψK S and B → π + π − as well as the ratio |V ub /V cb | have to be also considered. This analysis offers simultaneously some insight in a possible violation of a "golden relation" between K → πνν decays and the CP asymmetry in B → ψK S in the Standard Model pointed out some time ago. We illustrate these ideas by considering a general class of supersymmetric models. We find that in the "constrained" MSSM, in which θ K = 0, the measurements of Br(K + → π + νν) and Br(K L → π 0 νν) directly determine the angle β. Moreover, the "golden relation" remains unaffected. On the other hand, in general SUSY models with unbroken R-parity the present experimental constraints still allow for substantial deviations from r K = 1 and θ K = 0. Typically 0.5 < r K < 1.3 and −25 0 < θ K < 25 0. Consequently, in these models the violation of the "golden relation" is possible and values for Br(K + → π + νν) and Br(K L → π 0 νν) departing from the Standard Model expectations by factors 2-3 cannot be excluded. Simultaneously, the extraction of the "true" angle β from K → πνν is not possible without additional information from other decays. Our conclusions differ in certain aspects from the ones reached in previous analyses. In particular, we stress the possible importance of left-right flavour-violating mass insertions that were not considered before.
Motivated by the recent findings that the ratio ε /ε in the Standard Model (SM) appears to be sig... more Motivated by the recent findings that the ratio ε /ε in the Standard Model (SM) appears to be significantly below the data we investigate whether the necessary enhancement of ε /ε can be obtained in 331 models, based on the gauge group SU(3) C × SU(3) L × U(1) X . In these models new physics (NP) contributions to ε /ε and other flavour observables are dominated by tree-level exchanges of a Z with non-negligible contributions from tree-level Z exchanges generated through the Z -Z mixing. NP contributions to ε /ε in these models are governed by the electroweak penguin operator Q 8 for which the hadronic matrix element is already rather well known so that our analysis of NP contributions is subject to much smaller theoretical uncertainties than within the SM. In particular strong cancelations between different contributions do not take place. The size of NP effects depends not only on M Z but in particular on a parameter β, which distinguishes between various 331 models. Also a parameter tan β present in the Z -Z mixing plays a role. We perform the analysis in seven 331 models characterized by different β, tan β and fermion representations under the gauge group that have been selected in our earlier analysis on the basis of electroweak precision data. Imposing the constraints from ∆F = 2 transitions we find that only three of these models can provide a significant positive shift in ε /ε up to 6 × 10 -4 for M Z = 3 TeV. Two of them allow simultaneously a supression of the rate for B s → µ + µ -by 20% thereby bringing the theory closer to the data without any significant impact on the Wilson coefficient C 9 . The third model provides simultaneous shift ∆C 9 = -0.6, softening the anomalies in B → K * µ + µ -, without any significant impact on B s → µ + µ -. NP effects in rare K decays, in particular in K + → π + ν ν, turn out to be small. This is also the case of B → K(K * )ν ν. Both predictions could be challenged by NA62 experiment and Belle II in this decade. The special flavour structure of 331 models implies that even for M Z = 30 TeV a shift of ε /ε up to 8 × 10 -4 and a significant shift in ε K can be obtained, while the effects in other flavour observables are small. In this manner ε /ε and ε K appear to be unique flavour observables in these models which provide the possibility of accessing masses of M Z far beyond the LHC reach.
The experimental value for the isospin amplitude Re(A_2) in K->pi pi decays has been successfu... more The experimental value for the isospin amplitude Re(A_2) in K->pi pi decays has been successfully explained within the Standard Model, both within large N approach to QCD and by QCD lattice calculations. On the other hand in both approaches the theoretical values of Re(A_0) are by at least 30% below the data so that the Delta I=1/2 rule in K->pi pi decays is not fully explained. While this deficit could be the result of present theoretical uncertainties in both approaches, it cannot be excluded that the missing piece in Re(A_0) comes from New Physics. We demonstrate that this deficit can be significantly softened by tree-level FCNC transitions mediated by a heavy colourless Z' gauge boson with particularly chosen flavour violating couplings assuring negligible NP contributions to Re(A_2) and significantly enhancing the contribution of the leading QCD penguin operator Q_6 to Re(A_0). A large fraction of the missing piece in the Delta I=1/2 rule can be explained in this mann...
We make the simple observation that there exists a universal unitarity triangle for all models, l... more We make the simple observation that there exists a universal unitarity triangle for all models, like the SM, the Two Higgs Doublet Models I and II and the MSSM with minimal flavour violation, that do not have any new operators beyond those present in the SM and in which all flavour changing transitions are governed by the CKM matrix with no new phases beyond the CKM phase. This universal triangle can be determined in the near future from the ratio (∆M) d /(∆M) s and sin 2β measured first through the CP asymmetry in B 0 d → ψK S and later in K → πνν decays. Also suitable ratios of the branching ratios for B → X d,s νν and B d,s → µ + µ − and the angle γ measured by means of CP asymmetries in B decays can be used for this determination. Comparison of this universal triangle with the nonuniversal triangles extracted in each model using ε, (∆M) d and various branching ratios for rare decays will allow to find out in a transparent manner which of these models, if any, is singled out by experiment. A virtue of the universal triangle is that it allows to separate the determination of the CKM parameters from the determination of new parameters present in the extensions of the SM considered here.
In the past decade, one of the major challenges of particle physics has been to gain an in-depth ... more In the past decade, one of the major challenges of particle physics has been to gain an in-depth understanding of the role of quark flavor. In this time frame, measurements and the theoretical interpretation of their results have advanced tremendously. A much broader understanding of flavor particles has been achieved, apart from their masses and quantum numbers, there now exist detailed measurements of the characteristics of their interactions allowing stringent tests of Standard Model predictions. Among the most interesting phenomena of flavor physics is the violation of the CP symmetry that has been subtle and difficult to explore. In the past, observations of CP violation were confined to neutral K mesons, but since the early 1990s, a large number of CP-violating processes have been studied in detail in neutral B mesons. In parallel, measurements of the couplings of the heavy quarks and the dynamics for their decays in large samples of K, D, and B mesons have been greatly improved in accuracy and the results are being used as probes in the search for deviations from the Standard Model. In the near future, there will be a transition from the current to a new generation of experiments, thus a review of the status of quark flavor physics is timely. This report is the result of the work of the physicists attending the 5 th CKM workshop, hosted by the University of Rome "La Sapienza", September 9-13, 2008. It summarizes the results of the current generation of experiments that is about to be completed and it confronts these results with the theoretical understanding of the field which has greatly improved in the past decade.
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Papers by A. Buras