Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD
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Springer
Received: March 26, Revised: June 7, Accepted: June 30, Published: August 12,
2019 2019 2019 2019
Gunnar S. Bali,a,b Vladimir M. Braun,a Simon B¨ urger,a Meinulf G¨ ockeler,a Michael Gruber,a Fabian Hutzler,a Piotr Korcyl,c Andreas Sch¨ afer,a Andr´ e Sternbeckd a and Philipp Wein on behalf of the RQCD collaboration a
Institut f¨ ur Theoretische Physik, Universit¨ at Regensburg, 93040 Regensburg, Germany b Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India c Marian Smoluchowski Institute of Physics, Jagiellonian University, ul. Lojasiewicza 11, 30-348 Krak´ ow, Poland d Theoretisch-Physikalisches Institut, Friedrich-Schiller-Universit¨ at Jena, 07743 Jena, Germany
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] 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 +34 +19 K K of all errors: aπ2 = 0.101+24 −24 for the pion; a1 = 0.0533−35 and a2 = 0.090−20 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. Keywords: Lattice QCD, Nonperturbative Effects, Kaon Physics ArXiv ePrint: 1903.08038
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP08(2019)065
JHEP08(2019)065
Light-cone distribution amplitudes of pseudoscalar mesons from lattice QCD
Contents 1 Introduction
1
2 General formalism 2.1 Continuum definitions 2.2 Lattice definitions 2.3 Renormalization procedure
4 4 5 7 10 10 11 12 14
4 Extrapolation strategy and error budget 4.1 A game of ones 4.2 Extrapolation of the second LCDA moments 4.3 Extrapolation of the first LCDA moment 4.4 Summary of the results
15 15 16 18 18
5 Discussion
20
A Lattice ensembles and supplementary figures
25
1
Introduction
Hadron light-cone distribution amplitudes (LCDAs) have been introduced four decades ago [1–7] in the context of the QCD description of hard exclusive reactions. The LCDAs are scale-dependent nonperturbative functions that can be interpreted as quantum-mechanical amplitudes. Within this article we will use the term “LCDAs” synonymous with the leading-twist LCDAs. The latter describe the distribution of the longitudinal momentum amongst the quarks in the leading Fock state contribution of a hadron wave function at
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