B → K and D → K form factors from fully relativistic lattice QCD

We present the result of lattice QCD calculation of the scalar, vector and tensor form factors for the B → K ℓ + ℓ − decay, across the full physical range of momentum transfer. We use the highly improved staggered quark (HISQ) formalism for all valence quarks on eight ensembles of gluon-field configurations generated by the MILC collaboration. These include four flavors of HISQ quarks in the sea, with three ensembles having the light u / d quarks at physical masses. In the first fully relativistic calculation of these form factors, we use the heavy-HISQ method. This allows us to determine the form factors as a function of heavy-quark mass from the c to the b , and so we also obtain new results for the D → K tensor form factor. The advantage of the relativistic formalism is that we can match the lattice weak currents to their continuum counterparts much more accurately than in previous calculations; our scalar and vector currents are renormalized fully nonperturbatively and we use a well-matched intermediate momentum-subtraction scheme for our tensor current. Our scalar and vector B → K form factors have uncertainties of less than 4% across the entire physical q 2 range and the uncertainty in our tensor form factor is less than 7%. Our heavy-HISQ method allows us to map out the dependence on heavy-quark mass of the form factors and we can also see the impact of changing spectator quark mass by comparing to earlier HPQCD results for the same quark weak transition but for heavier mesons

Standard Model predictions for B → Kℓ+ℓ−, B → Kℓ−1ℓ+2 and B → Kv¯v using form factors from Nf = 2 + 1 + 1 lattice QCD

We use HPQCD’s recent lattice QCD determination of B → K scalar, vector and tensor form factors to determine Standard Model differential branching fractions for B → K ℓ + ℓ − , B → K ℓ + 1 ℓ − 2 and B → K ν ¯ ν . These form factors are calculated across the full q 2 range of the decay and have smaller uncertainties than previous work, particularly at low q 2 . For B → K ℓ + ℓ − we find the Standard Model branching fraction in the q 2 region below the squared J / ψ mass to exceed the LHCb results, with tensions as high as 4.7 σ for B + → K + μ + μ − . For the high q 2 region we see 3 σ tensions. The tensions are much reduced by applying shifts to Wilson coefficients C 9 and C 10 in the effective weak Hamiltonian, moving them away from their Standard Model values consistent with those indicated by other B phenomenology. We also update results for lepton-flavor ratios R μ e and R τ μ and the “flat term,” F ℓ H in the differential branching fraction for ℓ ∈ { e , μ , τ } . Our results for the form-factor dependent contributions needed for searches for lepton-flavor violating decays B → K ℓ − 1 ℓ + 2 achieve uncertainties of 7%. We also compute the branching fraction B ( B → K ν ¯ ν ) with an uncertainty below 10%, for comparison with future experimental results

Toward accurate form factors for B-to-light meson decay from lattice QCD

We present the results of a lattice QCD calculation of the scalar and vector form factors for the unphysical B s → η s decay, over the full physical range of q 2 . This is a useful testing ground both for lattice QCD and for our wider understanding of the behavior of form factors. Calculations were performed using the highly improved staggered quark (HISQ) action on N f = 2 + 1 + 1 gluon ensembles generated by the MILC Collaboration with an improved gluon action and HISQ sea quarks. We use three lattice spacings and a range of heavy quark masses from that of charm to bottom, all in the HISQ formalism. This permits an extrapolation in the heavy quark mass and lattice spacing to the physical point and nonperturbative renormalization of the vector matrix element on the lattice. We find results in good agreement with previous work using nonrelativistic QCD b quarks and with reduced errors at low q 2 , supporting the effectiveness of our heavy HISQ technique as a method for calculating form factors involving heavy quarks. A comparison with results for other decays related by SU(3) flavor symmetry shows that the impact of changing the light daughter quark is substantial but changing the spectator quark has very little effect. We also map out form factor shape parameters as a function of heavy quark mass and compare to heavy quark effective theory expectations for mass scaling at low and high recoil. This work represents an important step in the progression from previous work on heavy-to-heavy decays ( b → c ) to the numerically more challenging heavy-to-light decays

Improved Vcs determination using precise lattice QCD form factors for D → Kℓν

We provide a 0.8%-accurate determination of V c s from combining experimental results for the differential rate of D → K semileptonic decays with precise form factors that we determine from lattice QCD. This is the first time that V c s has been determined with an accuracy that allows its difference from 1 to be seen. Our lattice QCD calculation uses the Highly Improved Staggered Quark (HISQ) action for all valence quarks on gluon field configurations generated by the MILC collaboration that include the effect of u , d , s and c HISQ quarks in the sea. We use eight gluon field ensembles with five values of the lattice spacing ranging from 0.15 fm to 0.045 fm and include results with physical u / d quarks for the first time. Our calculated form factors cover the full q 2 range of the physical decay process and enable a Standard Model test of the shape of the differential decay rate as well as the determination of V c s from a correlated weighted average over q 2 bins. We obtain | V c s | = 0.9663 ( 53 ) latt ( 39 ) exp ( 19 ) η E W ( 40 ) EM , where the uncertainties come from lattice QCD, experiment, short-distance electroweak and electromagnetic corrections, respectively. This last uncertainty, neglected for D → K ℓ ν hitherto, now needs attention if the uncertainty on V c s is to be reduced further. We also determine V c s values in good agreement using the measured total branching fraction and the rates extrapolated to q 2 = 0 . Our form factors enable tests of lepton flavour universality violation. We find the ratio of branching fractions for D 0 → K − with μ and e in the final state to be R μ / e = 0.9779 ( 2 ) latt ( 50 ) E M in the Standard Model, with the uncertainty dominated by that from electromagnetic corrections