Determination of low-energy constants of Wilson chiral perturbation theory

Abstract

By matching Wilson twisted mass lattice QCD determinations of pseudoscalar meson masses to Wilson Chiral Perturbation Theory we determine the low-energy constants W 6 , W 8 and their linear combination c 2 . We explore the dependence of these low-energy constants on the choice of the lattice action and on the number of dynamical flavours.

The kaon mass in 2+1+1 flavor twisted mass Wilson ChPT

“…between the LECs in the 2-flavor and 3-flavor theories, making the leading analytic m s dependence of f (2) explicit. After this absorption we have completely undone the expansion in the strange quark mass and end up with ChPT for the two light quark flavors only.…”

“…The chiral log with the kaon mass is proportional to the LEC combination W 78 = 2W 7 +W 8 . Estimates for W 8 exist [2] but to date nothing is known about the size of W 7 . In contrast, the prefactor of the chiral log involving the neutral pion mass is proportional to 2W 6 +W 8 , which is nothing but the pion mass splitting.…”

“…On the right hand side we may use the measured values in [2,17] for the various quantities involved. The results ∆M K /M K (for µ = 1GeV) are listed in table 2.…”

“…However, the splitting is rather large at the nonzero lattice spacings in the simulations. Table 1 summarizes data published in [2] for ensembles at three different lattice spacings, ranging from approximately 0.09fm (A lattices) to 0.06fm (D lattices). The neutral pion is significantly lighter than the charged one, with a mass that can be half the mass of the charged one for the coarsest lattices.…”

Baryon chiral perturbation theory with Wilson fermions up to $${\mathcal {O}}(a^2)$$ O ( a 2 ) and discretization effects of latest $$n_f=2+1$$ n f = 2 + 1 LQCD octet baryon masses

“…The EFT for the anisotropic Wilson lattice action has been formulated up to O(a 2 ) [52] as well. In this context, it is interesting to note that recently several attempts have been made to determine the unknown LECs of the WChPT [53][54][55][56][57].…”