Special lattice coffee: Lattice Weak Matrix Elements and Unitarity Triangles

by Amarjit Soni

Friday 28 Apr 2023, 09:00 → 11:00 Europe/Zurich

4/2-037 - TH meeting room (CERN)

Lattice calculations of matrix elements relevant for weak decays were initiated in the early 80’s. The original focus was K to 2 pi decays  with the tantalizing targets being  the Delta I=1/2 rule and calculation of indirect and  direct CP violation monitored respectively by the parameters epsilon and epsilon’. These earliest attempts could make scant progress in numerical estimates as they were severely hampered by the use of naïve Wilson fermions which badly break chiral symmetry especially at rather coarse couplings that were then available due to the extremely limited  computing power. However, because chiral symmetry was much less of a concern in heavy-light physics that served as a motivation for calculating pseudoscalar decay constants, semi-leptonic form-factors, B, Bs mixing-parameters and their related ratio, \xi. These led us  to identify the observables from B, Bs physics that were needed for constructing the Standard Unitarity Triangle (SUT).   By 2007-08  the lattice community along with input of  the experimental data from the two asymmetric  B-factories  made significant progress  in constraining the SUT that it clearly showed that the single phase in the SM- CKM matrix  is sufficient to account for indirect CP asymmetry of O(10^-3) seen in KL-> 2 pi as well as O(1) CP violation seen in B-decays   thereby confirming the KM mechanism of CP violation.  

Progress in the original target of K=> 2 pi physics resumed after the 1st successful lattice simulations of Domain Wall Quarks (DWQ) in 96-97. The Lellouch-Lusher idea of using finite volume correlation functions for constructing infinite volume K to pi pi matrix elements is also crucial in this regard. At present, within  RBC-UKQCD two independent methods for obtaining K to 2 pi matrix elements for Re and Im A0 and A2 and for epsilon’ have emerged.   Not only this helps by  addition of yet another constraint on the SUT, more importantly, it plays a crucial role in the construction of the K-Unitarity Triangle.