Combined analysis of the unitarity triangle and CP violation in the Standard Model

Abstract

We perform a combined analysis of the unitarity triangle and of the CP violating parameter ε ′ /ε using the most recent determination of the relevant experimental data and, whenever possible, hadronic matrix elements from lattice QCD. We discuss the rôle of the main non-perturbative parameters and make a comparison with other recent analyses. We use lattice results for the matrix element of Q 8 obtained without reference to the strange quark mass. Since a reliable lattice determination of the matrix element of Q 6 is still missing, the theoretical predictions for ε ′ /ε suffer from large uncertainties. By evaluating this matrix element with the vacuum-saturation approximation, we typically find as central value ε ′ /ε = (4 ÷ 7) × 10 −4 . We conclude that the experimental data suggest large deviation of the value of the matrix element of Q 6 from the vacuum-saturation approximation, possibly due to penguin contractions.

Framework for maximum likelihood analysis of neutronβdecay observables to resolve the limits of theV−Alaw

“…To our knowledge ours is the first study of the quantitative ability to falsify the SM and particularly the V − A law, after the manner of Refs. [1][2][3][4][5][6][7], in the context of neutron beta decay observables.…”

“…Having reviewed the formalism for neutron β decay, the starting point for our maximum likelihood analysis of neutron β decay observables is the frequentist Rfit framework of the CKMfitter Group [1,2]; in future work we will explore the other analysis schemes outlined by the CKMfitter Group [1,2] and the UTFit Collaboration [3][4][5][6][7], such as Bayesian analyses. We review CKMfitter's Rfit analysis in sufficient detail to provide sufficient context for the discussion of our global fit.…”

“…Inspired by the pioneering global fits of the CKM matrix developed by the CKMfitter Group [1,2] and the UTFit Collaboration [3][4][5][6][7] for the interpretation of flavorphysics results from the B factories and the Tevatron, we outline the prospects for the elucidation of physics beyond the standard model (BSM) via a global fit of neutron β decay observables, including the lifetime and the energy-dependence of the angular correlation coefficients. Our global fit, which we term nFitter, employs a maximum likelihood statistical framework which accounts for both experimental and theoretical uncertainties, with the latter arising primarily from the poorly known weak hadronic second-class currents.…”

ε′/ε and rare K and B decays in the MSSM

“…In our opinion the issue of the size of FSI in the evaluation of ε ′ /ε is still an open question. An interesting recent proposal in [18], if realized, could put Reference ε ′ /ε [10 −4 ] Munich [5] 9.2 +6.8 −4.0 (MC) Munich [5] 1.4 → 32.7 (S) Rome [6,9] 8.1 +10.3 −9.5 (MC) Rome [6,9] −13.0 → 37.0 (S) Trieste [10] 22 ± 8 (MC) Trieste [10] 9 → 48 (S) Dortmund [11] 6.8 → 63.9 (S) Montpellier [7] 24.2 ± 8.0 Granada-Lund [8] 34 ± 18 Dubna-DESY [14] −3.2 → 3.3 (S) Taipei [12] 7 → 16 Barcelona-Valencia [13] 17 ± 6 Table 1: Results for ε ′ /ε in the SM in units of 10 −4 .…”

BK in the chiral limit within the 1/Nc expansion

“…Among these "refinements" one has most notably the inclusion of higher order terms in the chiral expansion. These are crucial in order to be able to make a meaningful comparison with the values favoured by lattice QCD determinations [22] as well as by recent phenomenological analysis [23,24].…”