Valence-quark distribution functions in the kaon and pion

Abstract

We describe expressions for pion and kaon dressed-quark distribution functions that incorporate contributions from gluons which bind quarks into these mesons and hence overcome a flaw of the commonly used handbag approximation. The distributions therewith obtained are purely valence in character, ensuring that dressed-quarks carry all a meson's momentum at a characteristic hadronic scale and vanishing as $(1-x)^2$ when Bjorken-$x\to 1$. Comparing such distributions within the pion and kaon, it is apparent that the size of SU(3)-flavour symmetry breaking in meson parton distribution functions is modulated by the flavour dependence of dynamical chiral symmetry breaking. Corrections to these leading-order formulae may be divided into two classes, responsible for shifting dressed-quark momentum into glue and sea-quarks. Working with available empirical information, we build an algebraic framework that is capable of expressing the principal impact of both classes of corrections. This enables a realistic comparison with experiment which allows us to identify and highlight basic features of measurable pion and kaon valence-quark distributions. We find that whereas roughly two-thirds of the pion's light-front momentum is carried by valence dressed-quarks at a characteristic hadronic scale, this fraction rises to 95% in the kaon; evolving distributions with these features to a scale typical of available Drell-Yan data produces a kaon-to-pion ratio of u-quark distributions that is in agreement with the single existing data set; and predict a u-quark distribution within the pion that agrees with a modern reappraisal of $\pi N$ Drell-Yan data. Precise new data are essential in order to validate this reappraisal and because a single modest-quality measurement of the kaon-to-pion ratio cannot be considered definitive.Comment: 10 pages, 3 figures. arXiv admin note: text overlap with arXiv:1406.545

Pion and kaon parton distribution functions from basis light front quantization and QCD evolution

“…Furthermore, the various valence, gluon, and sea contributions to the first moment of the pion at 4 GeV 2 are {0.489, 0.398, 0.113}, respectively, which agree with the results from BSE model 26 {0.48(3), 0.41(2), 0.11(2)}. We further find our results agree well with other results [21][22][23][24][25][26] .…”

Flavor dependence of the pion and kaon form factors and parton distribution functions

“…[83]. However, the x dependence differs from much of the data in the valence region, the reason for this discrepancy is not clear, however it may lie with the absence of momentum dependence in standard NJL BetheSalpeter vertices [14,17,84], or with the data itself. We note however the correspondence that u K + /u π + < 1 as x → 1 and that Fig.…”

“…There have been numerous studies of hadron PDFs and form factors within quark models of various degrees of sophistication and success, for example, see Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32], respectively.…”

Distribution amplitudes of radially-excitedπandKmesons

“…Moreover, here, as in so many other cases [12,[71][72][73][74], it is the flavour-dependence of DCSB that determines the strength of SU (3)-flavour breaking, not the current-quark mass-difference generated by the Higgs mechanism.…”