The asymptotic behaviour of parton distributions at small and large $x$

Richard D. Ball, Emanuele R. Nocera, Juan Rojo

Abstract

It has been argued from the earliest days of quantum chromodynamics (QCD) that at asymptotically small values of $x$ the parton distribution functions (PDFs) of the proton behave as $x^\alpha$, where the values of $\alpha$ can be deduced from Regge theory, while at asymptotically large values of $x$ the PDFs behave as $(1-x)^\beta$, where the values of $\beta$ can be deduced from the Brodsky-Farrar quark counting rules. We critically examine these claims by extracting the exponents $\alpha$ and $\beta$ from various global fits of parton distributions, analysing their scale dependence, and comparing their values to the naive expectations. We find that for valence distributions both Regge theory and counting rules are confirmed, at least within uncertainties, while for sea quarks and gluons the results are less conclusive. We also compare results from various PDF fits for the structure function ratio $F_2^n/F_2^p$ at large $x$, and caution against unrealistic uncertainty estimates due to overconstrained parametrisations.
Original language English arXiv.org Published - 31 Mar 2016

Fingerprint

partons
distribution functions
counting
quarks
gluons
quantum chromodynamics
exponents
valence
protons
estimates

Bibliographical note

20 pages, 9 figures, this version matches the version accepted for publication in EPJC

• hep-ph

Cite this

@article{e3d70c0b0d024b0eb6097dd489b45a91,
title = "The asymptotic behaviour of parton distributions at small and large $x$",
abstract = "It has been argued from the earliest days of quantum chromodynamics (QCD) that at asymptotically small values of $x$ the parton distribution functions (PDFs) of the proton behave as $x^\alpha$, where the values of $\alpha$ can be deduced from Regge theory, while at asymptotically large values of $x$ the PDFs behave as $(1-x)^\beta$, where the values of $\beta$ can be deduced from the Brodsky-Farrar quark counting rules. We critically examine these claims by extracting the exponents $\alpha$ and $\beta$ from various global fits of parton distributions, analysing their scale dependence, and comparing their values to the naive expectations. We find that for valence distributions both Regge theory and counting rules are confirmed, at least within uncertainties, while for sea quarks and gluons the results are less conclusive. We also compare results from various PDF fits for the structure function ratio $F_2^n/F_2^p$ at large $x$, and caution against unrealistic uncertainty estimates due to overconstrained parametrisations.",
keywords = "hep-ph",
author = "Ball, {Richard D.} and Nocera, {Emanuele R.} and Juan Rojo",
note = "20 pages, 9 figures, this version matches the version accepted for publication in EPJC",
year = "2016",
month = "3",
day = "31",
language = "English",
journal = "arXiv.org",
issn = "2331-8422",

}

The asymptotic behaviour of parton distributions at small and large $x$. / Ball, Richard D.; Nocera, Emanuele R.; Rojo, Juan.

In: arXiv.org, 31.03.2016.

TY - JOUR

T1 - The asymptotic behaviour of parton distributions at small and large $x$

AU - Ball, Richard D.

AU - Nocera, Emanuele R.

AU - Rojo, Juan

N1 - 20 pages, 9 figures, this version matches the version accepted for publication in EPJC

PY - 2016/3/31

Y1 - 2016/3/31

N2 - It has been argued from the earliest days of quantum chromodynamics (QCD) that at asymptotically small values of $x$ the parton distribution functions (PDFs) of the proton behave as $x^\alpha$, where the values of $\alpha$ can be deduced from Regge theory, while at asymptotically large values of $x$ the PDFs behave as $(1-x)^\beta$, where the values of $\beta$ can be deduced from the Brodsky-Farrar quark counting rules. We critically examine these claims by extracting the exponents $\alpha$ and $\beta$ from various global fits of parton distributions, analysing their scale dependence, and comparing their values to the naive expectations. We find that for valence distributions both Regge theory and counting rules are confirmed, at least within uncertainties, while for sea quarks and gluons the results are less conclusive. We also compare results from various PDF fits for the structure function ratio $F_2^n/F_2^p$ at large $x$, and caution against unrealistic uncertainty estimates due to overconstrained parametrisations.

AB - It has been argued from the earliest days of quantum chromodynamics (QCD) that at asymptotically small values of $x$ the parton distribution functions (PDFs) of the proton behave as $x^\alpha$, where the values of $\alpha$ can be deduced from Regge theory, while at asymptotically large values of $x$ the PDFs behave as $(1-x)^\beta$, where the values of $\beta$ can be deduced from the Brodsky-Farrar quark counting rules. We critically examine these claims by extracting the exponents $\alpha$ and $\beta$ from various global fits of parton distributions, analysing their scale dependence, and comparing their values to the naive expectations. We find that for valence distributions both Regge theory and counting rules are confirmed, at least within uncertainties, while for sea quarks and gluons the results are less conclusive. We also compare results from various PDF fits for the structure function ratio $F_2^n/F_2^p$ at large $x$, and caution against unrealistic uncertainty estimates due to overconstrained parametrisations.

KW - hep-ph

UR - https://arxiv.org/abs/1604.00024

M3 - Article

JO - arXiv.org

JF - arXiv.org

SN - 2331-8422

ER -