Lattice QCD calculations of Kl3 and pion form factors using partially twisted boundary conditions

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Description/Abstract

This thesis presents results of lattice QCD computations of the K → π semi-leptonic (Kl3) and pion electromagnetic form factors using partially twisted boundary conditions. These form factors parameterize low-energynon-perturbative strong interaction effects and cannot therefore be calculated in perturbative QCD. The pion electromagnetic form factor provides information on its charge distribution. The Kl3 form factor at zero momentum transfer (q2 = 0) can be used in the determination of the |Vus| element of the CKM matrix. An accurate determination of these form factors is therefore important. Using partially twisted boundary conditions we calculate the Kl3 form factor directly at q2 = 0, removing the need for the q2 interpolation required in previous lattice QCD simulations, thus eliminating one source of systematic error in this calculation. We also use partially twisted boundary conditions to calculate the pion form factor at values of q2 close to q2 = 0 allowing for a direct evaluation of the charge radius of the pion. The simulations are performed on an ensemble of the RBC/UKQCD collaboration’s gauge configurations with Domain Wall Fermions and the Iwasaki gauge action with an inverse lattice spacing of 1.73(3) GeV at light quark masses corresponding to a pion mass of 330 MeV. We calculate the form factors at these simulated quark masses and then use chiral perturbation theory to extrapolate our results to physical light quark masses. We find for the charge radius of the physical pion fir2π fi = 0.418(31) fm2, in agreement with the experimentally determined result. For the value of the Kl3 form factor, fKπ + (q2), at q2 = 0 and physical quark masses we find fKπ + (0) = 0.960(+5 −6). This result is then used to determine a value for |Vus|. Together with a recent determination of |Vud| we find that the current results are consistent with unitarity of the CKM matrix