The isospin asymmetries of B → Kµ + µ − and B → K * µ + µ − decays and the partial branching fractions of the B 0 → K 0 µ + µ − , B + → K + µ + µ − and B + → K * + µ + µ − decays are measured as functions of the dimuon mass squared, q 2 . The data used correspond to an integrated luminosity of 3 fb −1 from proton-proton collisions collected with the LHCb detector at centre-of-mass energies of 7 TeV and 8 TeV in 2011 and 2012, respectively. The isospin asymmetries are both consistent with the Standard Model expectations. The three measured branching fractions favour lower values than their respective theoretical predictions, however they are all individually consistent with the Standard Model.

A large-scale implementation of the complete active space self-consistent field (CASSCF) method is presented. The active space is described using the variational two-electron reduced-density-matrix (v2RDM) approach, and the algorithm is applicable to much larger active spaces than can be treated using configuration-interaction-driven methods. Density fitting or Cholesky decomposition approximations to the electron repulsion integral tensor allow for the simultaneous optimization of large numbers of external orbitals. We have tested the implementation by evaluating singlet-triplet energy gaps in the linear polyacene series and two dinitrene biradical compounds. For the acene series, we report computations that involve active spaces consisting of as many as 50 electrons in 50 orbitals and the simultaneous optimization of 1892 orbitals. For the dinitrene compounds, we find that the singlet-triplet gaps obtained from v2RDM-driven CASSCF with partial three-electron N-representability conditions agree with those obtained from configuration-interaction-driven approaches to within one-third of 1 kcal mol(-1). When enforcing only the two-electron N-representability conditions, v2RDM-driven CASSCF yields less accurate singlet-triplet energy gaps in these systems, but the quality of the results is still far superior to those obtained from standard single-reference approaches.

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.

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