Chiral extrapolation of the strangeness changing scalar Kπ form factor

Abstract

We perform a chiral extrapolation of lattice data on the scalar Kπ form factor and the ratio of the kaon and pion decay constants within Chiral Perturbation Theory to two loops. We determine the value of the scalar form factor at zero momentum transfer, at the Callan-Treiman point and at its soft kaon analog as well as its slope. Results are in good agreement with their determination from experiment using the standard couplings of quarks to the W boson. The slope is however rather large. A study of the convergence of the chiral expansion is also performed.

Chiral dynamics with strange quarks in the light of recent lattice simulations

“…The decay constant in the N f = 3 chiral limit is found to be rather low, in agreement with other recent works [26,44]. The pattern of N f = 3 chiral symmetry breaking (with low quark condensate and decay constant) is reflected by the values obtained for the lowenergy constants L 4 and L 6 , which are both positive and do not show any sign of Zweig suppression.…”

“…However, one has to determine how large the NNLO term f 4 can be with such a prescription, and consequently how well the chiral series for f + converges. If F 0 is significantly lower than F π as indicated not only by our fit, but by other recent estimates [26,44], the convergence is expected to be rather slow, forcing us to treat the NLO contribution to f + (0) more carefully. We advocated that correlators of vector and axial currents yields observables with good convergence properties, selecting F π F K f 0 (0).…”

“…In the case where F 0 is small compared to F π , as hinted at by lattice simulations and NNLO fits of chiral series [26,44], F 2 π F π V (t) is expected to exhibit a better convergence than F π V (t) in our framework according to eqs. (2.16)-(2.17).…”

“…Second, lattice simulations [RBC/UKQCD [4][5][6], PACS-CS [3]] have encountered difficulties in their fits of NLO N f = 3 chiral expansions. Let us remark that the inclusion of NNLO terms for K ℓ3 form factors and F K /F π to fits of the RBC/UKQCD data seems to solve convergence issues for these particular quantities assuming no Zweig-rule violation in the scalar sector [44]: a good χ 2 is obtained with a rather good convergence of the chiral series with NNLO terms of the expected size (this work did not discuss F π itself, for which the problems of convergence seem the most acute [4,14]). …”

Approximating chiral $${SU}(3)$$ S U ( 3 ) amplitudes

“…The separately scale-dependent contributions of O( p 6 ) are given for the usual renormalisation scale μ = 770 MeV. The entries for 'numerical results' were provided by Bernard and Passemar [10].…”