Judd Harrison

𝐵 meson decays to unstable hadrons, which subsequently decay to multiple stable hadrons, are a crucial component of new physics searches in the heavy flavour sector. For example, the rare decay 𝐵 → 𝐾*( → 𝐾𝜋)𝓁𝜈, which is particularly sensitive to new physics effects, currently exhibits tension at the level of ≈ 3𝜎 with the Standard Model. However, accurately including the effects of the unstable resonances in theory calculations is challenging. In lattice QCD this can be handled using the Lellouch-Luscher formalism, which uses energy shifts and matrix elements extracted from correlation functions in a finite volume to determine the scattering phases and matrix elements in an infinite volume.

In this project HPQCD has developed the tools needed to study these decays using the Lellouch-Luscher formalism in conjunction with the highly improved staggered quark (HISQ) action, which we have first applied to the related weak decay 𝑫 → 𝐾*( → 𝐾𝜋)𝓁𝜈 . Our results for the energies and scattering phases are shown in the left plot of figure 1 for our 𝑎 = 0.15 fm, 𝑀_𝜋 = 216MaV, 𝑁_𝑓=2+1+1 ensemble.

The matrix elements describing the decay can be fully parameterised using form factors, which we extract from three-point correlation functions and translate to the infinite volume using the scattering phases. In the right plot of figure 1, the form factor 𝐴  is shown as a function of momentum transfer, 𝑞², and 𝐾𝜋 centre of mass energy, 𝐸*. The use of HISQ, which is particularly well-suited to studies of 𝐵 mesons, is a significant technical development, with wide ranging implications for future studies of 𝐵 meson decays to multiple hadrons.

We are currently processing data for two additional HISQ  𝑁_𝑓=2+1+1 ensembles, one with 𝑎 = 0.15fm and  MeV, as well as one with  fm and physically light pions. This will enable a full physical-continuum extrapolation in the near future.