Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD

Gunnar S Bali,Simon Bürger,Michael Gruber,Piotr Korcyl,Vladimir M Braun,Fabian Hutzler,Meinulf Göckeler,Andreas Schäfer,Philipp Wein,André Sternbeck

doi:10.1007/jhep08(2019)065

Abstract

We present the first lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes with full control of all errors: {a}_2^{pi }={0.101}_{-24}^{+24} for the pion; {a}_1^K={0.0533}_{-35}^{+34} and {a}_2^K={0.090}_{-20}^{+19} for the kaon. The calculation is carried out on 35 different CLS ensembles with Nf = 2 + 1 flavors of dynamical Wilson-clover fermions. These cover a multitude of pion and kaon mass combinations (including the physical point) and 5 different lattice spacings down to a = 0.039 fm. The momentum smearing technique and a new operator basis are employed to reduce statistical fluctuations and to improve the overlap with the ground states. The results are obtained from a combined chiral and continuum limit extrapolation that includes three separate trajectories in the quark mass plane.

Highlights

Theoretical attempts to predict the shape of the pion LCDA φπ(x, μ2) as a function of the longitudinal momentum fraction x at a scale μ have a long history
We present the first lattice determination of the two lowest Gegenbauer moments of the leading-twist pion and kaon light-cone distribution amplitudes with full control of all errors: aπ2 = 0.101+−2244 for the pion; aK1 = 0.0533+−3345 and aK2 = 0.090+−1290 for the kaon
The discussion was shaped for many years by the famous paper by Chernyak and Zhitnitsky (CZ) [8] who calculated the second moment in x of the pion LCDA using QCD sum rules [9] and found a number much larger than the result expected at asymptotically large scales

Summary

Introduction

Theoretical attempts to predict the shape of the pion LCDA φπ(x, μ2) as a function of the longitudinal momentum fraction x at a scale μ have a long history. The discussion was shaped for many years by the famous paper by Chernyak and Zhitnitsky (CZ) [8] who calculated the second moment in x of the pion LCDA using QCD sum rules [9] and found a number much larger than the result expected at asymptotically large scales. The validity of collinear factorization in hard exclusive reactions at relatively low momentum transfer was questioned [11, 12] and the role of a competing “soft” or “end-point” mechanism was emphasized In particular it was shown [12, 13] that the data on the pion form factor at Q2 ∼ 1–3 GeV2 could be described by the soft contribution alone, without any “hard”. The paradigm “asymptotic-like LCDA versus CZ-like LCDA” continues to be the preferred language of many model studies

Methods

Findings

Discussion

Conclusion