Testing m_u = 0 on the lattice

Abstract

A massless up quark is an intriguing possible solution to the strong CP problem. We discuss how lattice computations can be used in conjunction with chiral perturbation theory to address the consistency of m u = 0 with the observed hadron spectrum and interactions. It is not necessary to simulate very light quarks-three flavor partially quenched computations with comparable sea and valence quark masses on the order of the strange quark mass could suffice.

Effective chiral Lagrangians and lattice QCD

“…(2.4). As pointed out in [7] a choice for α 7 and α 8 which is compatible with m u = 0 is given by 6) which is quite different from the corresponding numbers listed in eq. (2.2).…”

Chiral perturbation theory for the Wilson lattice action

“…(9), (10).m q compensates for the large O(1/a) shift in the quark masses, but it also contains positive powers of a. This is not a problem -redefinitions of the mass parameter of this sort only lead to changes in the W i 's.…”

“…The low-energy behavior of these theories is described by PQ χPT [7], which has the same unknown low-energy constants as χPT for ordinary QCD [8]. Thus, PQ simulations provide additional mass parameters that can be used to probe the theory in a larger parameter space, and gain better statistics in determining the GL coefficients [9,10]. It is of clear practical value to consider the generalization of WχPT to the PQ case.…”

Up Quark Mass in Lattice QCD with Three Light Dynamical Quarks and Implications for StrongCPInvariance

“…Because the valence and sea quark mass dependence of the Lagrangian of pqChPT is explicit and full QCD is within the parameter space of pqQCD (m V = m S ), the values obtained for the GL coefficients in a pqQCD calculation are the exact values for the coefficients in full QCD [7,8]. Furthermore, independent variation of valence and sea quark masses allows additional lever arms in the determination the the coefficients.…”