Determination of γ and−2βsfrom charmless two-body decays of beauty mesons

Abstract

Determination of γ and −2β s from charmless two-body decays of beauty mesons .LHCb Collaboration a r t i c l e i n f o a b s t r a c tUsing the latest LHCb measurements of time-dependent CP violation in the B 0 s → K + K − decay, a U-spin relation between the decay amplitudes of B 0 s → K + K − and B 0 → π + π − decay processes allows constraints to be placed on the angle γ of the unitarity triangle and on the B 0 s mixing phase −2β s .Results from an extended approach, which uses additional inputs on B 0 → π 0 π 0 and B + → π + π 0 decays from other experiments and exploits isospin symmetry, are also presented. The dependence of the results on the maximum allowed amount of U-spin breaking is studied. At 68% probability, the value γ = (63.5 +7.2 −6.7 ) • modulo 180 • is determined. In an alternative analysis, the value −2β s = −0.12 +0.14 −0.16 rad is found. In both measurements, the uncertainties due to U-spin breaking effects up to 50% are included. decays are related by the U-spin symmetry of strong interactions. This symmetry, related to the exchange of d and s quarks in the decay diagrams, can be exploited to determine the unknown hadronic factors. A more sophisticated analysis has also been proposed [13], where it is suggested to combine the U-spin analysis of B 0 → π + π − and B 0 s → K + K − decays with the isospin analysis of B 0 → π + π − , B 0 → π 0 π 0 and B + → π + π 0 decays [14], in order to achieve a more robust determination of γ with respect to U-spin breaking effects. The B 0, can also be determined with either analysis approach. An analysis based on Bayesian statistics, aimed at determining probability density functions (PDFs) for γ and −2β s , is presented in this Letter. This uses the latest LHCb measurements of time-dependent CP violation in the B 0 s → K + K − decay, exploiting U-spin symmetry with the B 0 → π + π − decay. An extended analysis, including measurements on B 0 → π 0 π 0 and B + → π + π 0 decays from other experiments, is also performed. The Letter is organized as follows. First, the theoretical formalism needed to describe CP violation is introduced in Section 2, including the SM parameterization of the decay amplitudes of the various decays.

Universal Unitarity Triangle 2016 and the tension between $$\Delta M_{s,d}$$ Δ M s , d and $$\varepsilon _K$$ ε K in CMFV models

“…We observe significant tensions both between the results in S 1 and S 2 and also between them and the inclusive tree-level determination of |V ub |. On the other hand the exclusive determination of |V ub | accompanied by the inclusive one for |V cb | gives |V ub |/|V cb | = 0.0850± 0.0026, very close to the result in (21). However the separate values of |V ub | and |V cb | in (22) and (23) used to obtain this result are not compatible with our findings in S 1 , implying problems with ∆M s,d as we will see below.…”

“…• The precise relation between |V ub | and |V cb | obtained by us in (21) provides another test of CMFV. See Fig.…”

Summary of Working Group 4 : mixing and mixing-related $CP$ violation in the $B$ system

“…These can be interpreted 1 in a combined U-spin analysis [15] as either measurements of γ or φ s . Because the combined U-spin analysis is much less sensitive to U-spin breaking [16] when interpreted as a measurement of φ s , this is therefore the currently preferred way to interpret the measurements of these CP observables.…”

Selection of LHCb results from Run I

“…Since both tree and loop diagrams contribute to the amplitudes, the number of unknowns exceeds the number of observables and assumptions are thus needed. Both isopin symmetry [24], relating B ± → π ± π 0 and B 0 → π 0 π 0 , and U-spin symmetry [25], relating B 0 → π + π − and B 0 s → K + K − , are used to constrain the number of unknowns. Non-factorizable and U-spin breaking effects are considered as perturbing factors to amplitude ratios.…”