Kaon and pion parton distributions
Zhu-Fang Cui, Minghui Ding, Fei Gao, Khépani Raya, Daniele Binosi, Lei Chang, Craig D. Roberts, J. Rodrı́guez-Quintero, Sebastian M. Schmidt
Abstract
Abstract Beginning with results for the leading-twist two-particle distribution amplitudes of $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> - and K -mesons, each of which exhibits dilation driven by the mechanism responsible for the emergence of hadronic mass, we develop parameter-free predictions for the pointwise behaviour of all $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> and K distribution functions (DFs), including glue and sea. The large- x behaviour of each DF meets expectations based on quantum chromodynamics; the valence-quark distributions match extractions from available data, including the pion case when threshold resummation effects are included; and at $$\zeta _5=5.2\,$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ζ</mml:mi> <mml:mn>5</mml:mn> </mml:msub> <mml:mo>=</mml:mo> <mml:mn>5.2</mml:mn> <mml:mspace/> </mml:mrow> </mml:math> GeV, the scale of existing measurements, the light-front momentum of these hadrons is shared as follows: $$\langle x_{\mathrm{valence}} \rangle ^\pi = 0.41(4)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>valence</mml:mi> </mml:msub> <mml:mo>⟩</mml:mo> </mml:mrow> <mml:mi>π</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.41</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>4</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , $$\langle x_{\mathrm{glue}} \rangle ^\pi = 0.45(2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>glue</mml:mi> </mml:msub> <mml:mo>⟩</mml:mo> </mml:mrow> <mml:mi>π</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.45</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , $$\langle x_{\mathrm{sea}} \rangle ^\pi = 0.14(2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>sea</mml:mi> </mml:msub> <mml:mo>⟩</mml:mo> </mml:mrow> <mml:mi>π</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.14</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> ; and $$\langle x_{\mathrm{valence}} \rangle ^K = 0.42(3)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>valence</mml:mi> </mml:msub> <mml:mo>⟩</mml:mo> </mml:mrow> <mml:mi>K</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.42</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , $$\langle x_{\mathrm{glue}} \rangle ^K = 0.44(2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>glue</mml:mi> </mml:msub> <mml:mo>⟩</mml:mo> </mml:mrow> <mml:mi>K</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.44</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , $$\langle x_{\mathrm{sea}} \rangle ^K = 0.14(2)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mo>⟨</mml:mo> <mml:msub> <mml:mi>x</mml:mi> <mml:mi>sea</mml:mi> </mml:msub> <mml:mo>⟩</mml:mo> </mml:mrow> <mml:mi>K</mml:mi> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.14</mml:mn> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . The kaon’s glue and sea distributions are similar to those in the pion, although the inclusion of mass-dependent splitting functions introduces some differences on the valence-quark domain. This study should stimulate improved analyses of existing data and motivate new experiments sensitive to all $$\pi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>π</mml:mi> </mml:math> and K DFs. With little known empirically about the structure of the Standard Model’s (pseudo-) Nambu-Goldstone modes and analyses of existing, limited data being controversial, it is likely that new generation experiments at upgraded and anticipated facilities will provide the information needed to resolve the puzzles and complete the picture of these complex bound states.