K→π form factors with reduced model dependence

Abstract

Using partially twisted boundary conditions we compute the K → π semi-leptonic form factors in the range of momentum transfers 0 q 2 ≤ q 2 max = (mK −mπ) 2 in lattice QCD with N f = 2+1 dynamical flavours. In this way we are able to determine f Kπ + (0) without any interpolation in the momentum transfer, thus eliminating one source of systematic error. This study confirms our earlier phenomenological ansatz for the strange quark mass dependence of the scalar form factor. We identify and estimate potentially significant NNLO effects in the chiral expansion that guides the extrapolation of the data to the physical point. Our main result is f Kπ + (0) = 0.9599(34)( +31 −43 )(14), where the first error is statistical, the second error is due to the uncertainties in the chiral extrapolation of the lattice data and the last error is an estimate of potential discretisation effects.

Pseudoscalar meson electromagnetic form factor at high Q2 from full lattice QCD

“…electric charge radius. Lattice QCD calculations of the π form factor at small values of Q 2 [5][6][7][8][9][10][11][12] give a theoretical determination that agrees well with experiment.…”

Topological susceptibility on the lattice and the three-flavour quark condensate

“…In this context, it is interesting to consider the topological susceptibility as a way to extract the quark condensate, taking into account the possibility that it is not the order parameter triggering three-flavour chiral symmetry breaking. Indeed various analyses of lattice results [15,[37][38][39][40][41][42] suggest an overall good agreement between lattice simulations and χPT concerning chiral series obtained as an expansion in m u and m d only (N f = 2 χPT), but significant disagreements concerning the chiral expansions in powers of m u , m d , m s (N f = 3 χPT). In some cases, small values of the N f = 3 quark condensate and pseudoscalar decay constant fail to saturate the LO chiral expansions.…”

Two-Baryon Systems with Twisted Boundary Conditions

“…They provide a means with which to select the phase space of particles in a given finite volume, beyond that allowed by periodic or anti-periodic boundary conditions. In LQCD calculations, TBCs have been used to resolve the threshold region required in the evaluation of transition matrix elements without requiring large lattice volumes [21][22][23][24][25][26][27][28]82]. They can also be used in calculations of elastic 2 → 2 processes by providing a better sampling of CM kinematics in a single volume, allowing for better constraints on scattering parameters [57][58][59][60].…”

“…An arbitrary momentum can be selected for a (non-interacting) hadron by a judicious choice of the twist angles of its valence quarks, p = 2π L n + φ L , where φ is the sum of the twists of the valence quarks, again with 0 < φ i < 2π, and n is an integer triplet. TBCs have been shown to be useful in LQCD calculations of the low-momentum transfer behavior of form factors required in determining hadron radii and moments, circumventing the need for large-volume lattices [21][22][23][24][25][26][27][28]. They have also been speculated to be helpful in calculations of K → ππ decays by bringing the initial and final FV states closer in energy [29,30].…”