Empirical Determination of the Pion Mass Distribution
Yin-Zhen Xu, Khépani Raya, Zhu-Fang Cui, Craig D. Roberts, J. Rodrı́guez-Quintero
Abstract
Existing pion+nucleus Drell-Yan and electron+pion scattering data are used to develop ensembles of model-independent representations of the pion generalized parton distribution (GPD). Therewith, one arrives at a data-driven prediction for the pion mass distribution form factor, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>θ</mml:mi> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> </mml:msubsup> </mml:mrow> </mml:math> . Compared with the pion elastic electromagnetic form factor, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>θ</mml:mi> <mml:mn>2</mml:mn> <mml:mi>π</mml:mi> </mml:msubsup> </mml:mrow> </mml:math> is harder: the ratio of the radii derived from these two form factors is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:msubsup> <mml:mi>r</mml:mi> <mml:mi>π</mml:mi> <mml:mrow> <mml:msub> <mml:mi>θ</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:msubsup> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>r</mml:mi> <mml:mi>π</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>0.79</mml:mn> <mml:mo stretchy="false">(</mml:mo> <mml:mn>3</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> . Our data-driven predictions for the pion GPD, related form factors and distributions should serve as valuable constraints on theories of pion structure.