# 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- limit. 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 find that the small-x power-law tail of the quark helicity distribution scales as with , in excellent agreement with the numerical estimate obtained previously. We then verify this solution by cross-checking the predicted scaling behavior of the auxiliary “neighbor dipole amplitude” against the numerics, again finding excellent agreement.

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States); The Ohio State University, Columbus, OH

- Sponsoring Org.:
- USDOE Office of Science (SC). Nuclear Physics (NP) (SC-26); USDOE Office of Science (SC), Nuclear Physics (NP)

- OSTI Identifier:
- 1364064

- Alternate Identifier(s):
- OSTI ID: 1369207; OSTI ID: 1604437

- Report Number(s):
- LA-UR-17-22988

Journal ID: ISSN 0370-2693; S0370269317305087; PII: S0370269317305087

- Grant/Contract Number:
- AC52-06NA25396; 2012LANL7033; 20160183ER; SC0004286

- Resource Type:
- Published Article

- Journal Name:
- Physics Letters B

- Additional Journal Information:
- Journal Name: Physics Letters B Journal Volume: 772 Journal Issue: C; Journal ID: ISSN 0370-2693

- Publisher:
- Elsevier

- Country of Publication:
- Netherlands

- 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. Netherlands: N. p., 2017.
Web. https://doi.org/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. Netherlands. https://doi.org/10.1016/j.physletb.2017.06.032
```

```
Kovchegov, Yuri V., Pitonyak, Daniel, and Sievert, Matthew D.. Fri .
"Small- x asymptotics of the quark helicity distribution: Analytic results". Netherlands. https://doi.org/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- limit. 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 find that the small-x power-law tail of the quark helicity distribution scales as with , in excellent agreement with the numerical estimate obtained previously. We then verify this solution by cross-checking the predicted scaling behavior of the auxiliary “neighbor dipole amplitude” against the numerics, again finding excellent agreement.},

doi = {10.1016/j.physletb.2017.06.032},

journal = {Physics Letters B},

number = C,

volume = 772,

place = {Netherlands},

year = {2017},

month = {9}

}

https://doi.org/10.1016/j.physletb.2017.06.032

*Citation information provided by*

Web of Science

Web of Science

Works referenced in this record:

##
Unitarization of the BFKL Pomeron on a nucleus

journal, March 2000

- Kovchegov, Yuri V.
- Physical Review D, Vol. 61, Issue 7

##
Baryon stopping and valence quark distribution at small x

journal, January 2004

- Itakura, Kazunori; Kovchegov, Yuri V.; McLerran, Larry
- Nuclear Physics A, Vol. 730, Issue 1-2

##
Double logarithmic asymptotics and regge singularities of quark amplitudes with flavour exchange

journal, March 1983

- Kirschner, R.; Lipatov, L. N.
- Nuclear Physics B, Vol. 213, Issue 1

##
Flavor singlet contribution to the structure functiong 1 at small-x

journal, December 1996

- Bartels, J.; Ermolaev, B. I.; Ryskin, M. G.
- Zeitschrift für Physik C: Particles and Fields, Vol. 72, Issue 4

##
Small- $x$ Asymptotics of the Quark Helicity Distribution

journal, January 2017

- Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
- Physical Review Letters, Vol. 118, Issue 5

##
Small- *x* ${F}_{2}$ structure function of a nucleus including multiple Pomeron exchanges

journal, June 1999

- Kovchegov, Yuri V.
- Physical Review D, Vol. 60, Issue 3

##
Studying the perturbative Reggeon

journal, January 2000

- Griffiths, S.; Ross, D. A.
- The European Physical Journal C, Vol. 12, Issue 2

##
The renormalization group equation for the color glass condensate

journal, June 2001

- Iancu, Edmond; Leonidov, Andrei; McLerran, Larry
- Physics Letters B, Vol. 510, Issue 1-4

##
Helicity evolution at small $x$ : Flavor singlet and nonsinglet observables

journal, January 2017

- Kovchegov, Yuri V.; Pitonyak, Daniel; Sievert, Matthew D.
- Physical Review D, Vol. 95, Issue 1

##
Nonlinear gluon evolution in the color glass condensate: I

journal, September 2001

- Iancu, Edmond; Leonidov, Andrei; McLerran, Larry
- Nuclear Physics A, Vol. 692, Issue 3-4

##
Reggeon interactions in perturbative QCD

journal, September 1995

- Kirschner, R.
- Zeitschrift für Physik C Particles and Fields, Vol. 65, Issue 3

##
Factorization and high-energy effective action

journal, June 1999

- Balitsky, Ian
- Physical Review D, Vol. 60, Issue 1

##
Regge asymptotics of scattering with flavour exchange in QCD

journal, September 1995

- Kirschner, R.
- Zeitschrift für Physik C Particles and Fields, Vol. 67, Issue 3

##
Resumming double logarithms in the QCD evolution of color dipoles

journal, May 2015

- Iancu, E.; Madrigal, J. D.; Mueller, A. H.
- Physics Letters B, Vol. 744

##
Operator expansion for high-energy scattering

journal, March 1996

- Balitsky, I.
- Nuclear Physics B, Vol. 463, Issue 1

##
Regge asymptotics of scattering amplitudes in the logarithmic approximation of QCD

journal, March 1986

- Kirschner, R.
- Zeitschrift für Physik C Particles and Fields, Vol. 31, Issue 1

Works referencing / citing this record:

##
Sub-eikonal corrections to scattering amplitudes at high energy

journal, January 2019

- Chirilli, Giovanni Antonio
- Journal of High Energy Physics, Vol. 2019, Issue 1

##
Helicity-dependent generalization of the JIMWLK evolution

journal, December 2019

- Cougoulic, Florian; Kovchegov, Yuri V.
- Physical Review D, Vol. 100, Issue 11

##
First Simultaneous Extraction of Spin-Dependent Parton Distributions and Fragmentation Functions from a Global QCD Analysis

journal, September 2017

- Ethier, J. J.; Sato, N.; Melnitchouk, W.
- Physical Review Letters, Vol. 119, Issue 13

##
Non-eikonal corrections to multi-particle production in the color glass condensate

journal, July 2019

- Agostini, Pedro; Altinoluk, Tolga; Armesto, Néstor
- The European Physical Journal C, Vol. 79, Issue 7