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Title: Small-x asymptotics of the quark helicity distribution: Analytic results

Abstract

In this Letter, we analytically solve the evolution equations for the small-x asymptotic behavior of the (flavor singlet) quark helicity distribution in the large- N c limit. Here, these evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerically. This approximate numerical solution, however, revealed simplifying properties of the small-x asymptotics, which we exploit here to obtain an analytic solution.

Authors:
ORCiD logo [1];  [2]; ORCiD logo [3]
  1. The Ohio State Univ., Columbus, OH (United States)
  2. Penn State Univ.-Berks, Reading, PA (United States)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC). Nuclear Physics (NP) (SC-26); USDOE
OSTI Identifier:
1364064
Report Number(s):
LA-UR-17-22988
Journal ID: ISSN 0370-2693
Grant/Contract Number:
AC52-06NA25396; SC0004286; 2012LANL7033; 20160183ER
Resource Type:
Journal Article: Published Article
Journal Name:
Physics Letters. Section B
Additional Journal Information:
Journal Volume: 772; Journal Issue: C; Journal ID: ISSN 0370-2693
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Atomic and Nuclear Physics

Citation Formats

Kovchegov, Yuri V., Pitonyak, Daniel, and Sievert, Matthew D.. Small-x asymptotics of the quark helicity distribution: Analytic results. United States: N. p., 2017. Web. doi:10.1016/j.physletb.2017.06.032.
Kovchegov, Yuri V., Pitonyak, Daniel, & Sievert, Matthew D.. Small-x asymptotics of the quark helicity distribution: Analytic results. United States. doi:10.1016/j.physletb.2017.06.032.
Kovchegov, Yuri V., Pitonyak, Daniel, and Sievert, Matthew D.. 2017. "Small-x asymptotics of the quark helicity distribution: Analytic results". United States. doi:10.1016/j.physletb.2017.06.032.
@article{osti_1364064,
title = {Small-x asymptotics of the quark helicity distribution: Analytic results},
author = {Kovchegov, Yuri V. and Pitonyak, Daniel and Sievert, Matthew D.},
abstractNote = {In this Letter, we analytically solve the evolution equations for the small-x asymptotic behavior of the (flavor singlet) quark helicity distribution in the large- Nc limit. Here, these evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerically. This approximate numerical solution, however, revealed simplifying properties of the small-x asymptotics, which we exploit here to obtain an analytic solution.},
doi = {10.1016/j.physletb.2017.06.032},
journal = {Physics Letters. Section B},
number = C,
volume = 772,
place = {United States},
year = 2017,
month = 6
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record at 10.1016/j.physletb.2017.06.032

Citation Metrics:
Cited by: 2works
Citation information provided by
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  • In this Letter, we analytically solve the evolution equations for the small-x asymptotic behavior of the (flavor singlet) quark helicity distribution in the large- N c limit. Here, these evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerically. This approximate numerical solution, however, revealed simplifying properties of the small-x asymptotics, which we exploit here to obtain an analytic solution.
  • We construct a numerical solution of the small-x evolution equations derived in our recent work for the (anti)quark transverse momentum dependent helicity TMDs and parton distribution functions (PDFs) as well as the g 1 structure function. We focus on the case of large N c, where one finds a closed set of equations. Employing the extracted intercept, we are able to predict directly from theory the behavior of the quark helicity PDFs at small x, which should have important phenomenological consequences. Finally, we also give an estimate of how much of the proton’s spin carried by the quarks may bemore » at small x and what impact this has on the spin puzzle.« less
  • Here, we determine the small-x asymptotics of the gluon helicity distribution in a proton at leading order in perturbative QCD at large N c. To achieve this, we begin by evaluating the dipole gluon helicity TMD at small x. In the process we obtain an interesting new result: in contrast to the unpolarized dipole gluon TMD case, the operator governing the small-x behavior of the dipole gluon helicity TMD is different from the operator corresponding to the polarized dipole scattering amplitude (used in our previous work to determine the small-x asymptotics of the quark helicity distribution).
  • We use a novel method to calculate analytically the QCD instanton prefactor due to a quark field carrying a small-mass parameter m. In the SU(2) instanton background of size {rho}, the spinor effective action {gamma}{sup F} (in the minimal subtraction scheme), which gives rise to the prefactor exp(-{gamma}{sup F}), is shown to have the small-m{rho} behavior {gamma}{sup F}=-ln(m/{mu})-ln({mu}{rho})/3 -2{alpha}(1/2)-(m{rho}){sup 2} {l_brace}ln(m{rho}/2)+{gamma}+1/2{r_brace} -2(m{rho}){sup 4}{l_brace}-ln{sup 2}(m{rho})/4 +ln(m{rho})(1/2-{gamma}+ln2)/2 +C{r_brace}+O((m{rho}){sup 6}), where {gamma}=0.577 216..., {alpha}(1/2)=0.145 873..., and our numerically evaluated value for the constant C is C=-0.382 727.... A good agreement between this form and the numerically exact calculation is found if (m{rho}) <more » or approx. 0.8.« less