Consistency constraints on ms from QCD dispersion relations and chiral perturbation theory in Kℓ3 decays

Abstract

We use both old and new theoretical developments in QCD dispersion relation constraints on the scalar form factor in the decay K → πℓν ℓ to obtain constraints on the strange quark mass. The perturbative QCD side of the calculation incorporates up to four-loop corrections, while the hadronic side uses a recently developed parameterization constructed explicitly to satisfy the dispersive constraints. Using chiral perturbation theory (χPT) as a model for soon-to-be measured data, we find a series of lower bounds on m s increasing with the accuracy to which one believes χPT to represent the full QCD result.11.55. Fv, 13.20.Eb, 12.15.Ff, 12.39.Fe Typeset using REVT E X * lebed@jlab.org † Permanent address:

Improving the phenomenology ofKl3form factors with analyticity and unitarity

“…To answer these questions one needs an estimate of the higher-order terms neglected in usual parameterizations. As discussed in previous works, for instance [36], [38], [53], the technique of unitarity bounds allows one to find a model-independent estimate of the theoretical error produced by the truncation of the Taylor expansion.…”

“…Standard mathematical techniques then allow one to correlate the values of the form factor or its derivative at different points. For the Kπ form factors, the method was applied in [35][36][37][38][39][40][41]. The latest applications [40,41] led, in particular, to stringent constraints on the shape of the scalar form factor at low energies.…”

Light quark masses from scalar sum rules

“…QCD sum rules [4][5][6][7] have been applied to various channels containing strange quantum numbers, in particular the scalar channel that will be the subject of this work [8][9][10][11][12][13][14][15], the pseudoscalar channel [16], the Cabibbo suppressed τ -decay width [17][18][19][20][21][22][23], as well as the total e + e − cross section [24][25][26][27]. Also lower bounds on the strange mass have been determined in the framework of QCD sum rules [16,[28][29][30][31]. In addition, lattice QCD simulations for various hadronic quantities have been used to extract the strange quark mass.…”

Vusandmsfrom HadronicτDecays

“…It is also on the borderline of being compatible with lower bounds on m s from sum rules [16,[45][46][47][48]. Finally, we have performed a simultaneous fit of V us and m s to the five moments 0; 0 to 4; 0.…”