Abstract
The pion light-cone distribution amplitude (LCDA) is a central non-perturbative object of interest for high-energy exclusive processes in quantum chromodynamics. In this article, the second Mellin moment of the pion LCDA is determined as a proof-of-concept calculation for the first numerical implementation of the heavy-quark operator product expansion (HOPE) method. The resulting value for the second Mellin moment, determined in quenched QCD at a pion mass of $m_\pi=550$ MeV at a factorization scale of 2 GeV is $ \langle \xi^2 \rangle = 0.210 \pm 0.013\text{ (stat.)} \pm 0.034\text{ (sys.)}$. This result is compatible with those from previous determinations of this quantity.
Highlights
The pion light-cone distribution amplitude (LCDA) plays an important role in parton physics
It is central to a description of a range of exclusive processes in high energy quantum chromodynamics [1]
Numerical implementation of the heavy-quark OPE (HOPE) strategy, this calculation bears the character of a feasibility study, which investigates the relatively well-known second Mellin moment
Summary
The pion light-cone distribution amplitude (LCDA) plays an important role in parton physics. In the light-cone gauge, φπðξ; μÞ can be interpreted as the probability amplitude for the pion to transition to the state of a quark and an antiquark that carry ð1 þ ξÞ=2 and ð1 − ξÞ=2 fractions of the pion momentum, respectively [1] This LCDA plays an important role in understanding exclusive processes in QCD [1,2], in addition to being a crucial ingredient for extracting information regarding the Cabibbo-. It relies on investigating the OPE analysis for hadronic amplitudes in Euclidean space with the insertion of two local quark bilinears that contain a fictitious, valence heavy quark For this reason, this approach is termed the heavy-quark OPE (HOPE) method. Numerical implementation of the HOPE strategy, this calculation bears the character of a feasibility study, which investigates the relatively well-known second Mellin moment This allows a better quantification of the efficacy of the method.
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