Flavor Physics with Heavy Baryons and Resonances Using Lattice QCD

Abstract

Flavor-changing transitions play an important role in the search for new physics beyond the Standard Model (SM). In order to compare experimental results with SM theoretical predictions we must calculate hadronic matrix elements in Quantum Chromodynamics (QCD). In order to perform such calculations we use formulations of QCD on a Euclidean space-time mesh. Having a discretized Euclidean QCD action allows us to use Monte Carlo methods to generate the field configurations we use to evaluate the path integral numerically. In this thesis, we present results on the lattice calculation of matrix elements for decay processes with negative parity baryons in the final state, Λb → Λ(1520)ℓ+ℓ- , Λb → Λc (2595)ℓ-ν, and Λb → Λc(2625)ℓ-ν , which are under investigation by LHCb and can provide new information on current tensions seen in mesonic b → sμ+μ- and b → cτ-ν transitions. We also present preliminary results on form factor calculations for the process Λc → Λ(1520)ℓ+ν which can be measured by the BESIII and Belle II experiments. One of the most important contributors to the tensions in mesonic b → sμ+μ- transitions is B → K*(892)μ+μ- . The theoretical calculations used for B →K*(892)μ+μ- were performed assuming the K*(892) is a stable hadron; however, in reality this state is unstable under the strong force. In order to do a proper treatment, one has to calculate the B → Kπ matrix elements and the finite volume effects of the lattice have to be accounted for using the Briceño-Hansen-Walker-Loud (BHWL) formalism. For that, we will need to first calculate the Kπ scattering amplitudes from multi-hadron spectra on the lattice. We have done these calculations and present results here. Another similar process of interest is B → ρ(→ ππ)ℓ-ν, which would help understand better the tensions between exclusive and inclusive determinations of |Vub |. For that reason, we also present results on the necessary ππ (JPC = 1−− , I = 1, I3 = 1) scattering amplitude obtained from the lattice. The task of extracting the B → ρ(→ ππ)ℓ-ν and B → K*(892)(→ Kπ)μ+μ- transition matrix elements from the three-point functions is still in progress. However, we have completed this step for a simpler 1 → 2 process, πγ → ρ(→ ππ), that will help us pave the way for the proper treatment of B → ρ(→ ππ)ℓ-ν and B → K*(892)(→ Kπ)μ+μ- using BHWL.