### Abstract

Original language | English |
---|---|

Journal | arXiv.org |

Publication status | Published - 31 Mar 2016 |

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### Bibliographical note

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

- hep-ph

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*arXiv.org*.

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

Research output: Contribution to Journal › Article › Academic › peer-review

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 -