Small-x asymptotics of the quark helicity distribution: Analytic results
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. These evolution equations form a set of coupled integro-differential equations, which previously could only be solved numerical...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2017-09-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269317305087 |
| _version_ | 1818480471040851968 |
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| author | Yuri V. Kovchegov Daniel Pitonyak Matthew D. Sievert |
| author_facet | Yuri V. Kovchegov Daniel Pitonyak Matthew D. Sievert |
| author_sort | Yuri V. Kovchegov |
| collection | DOAJ |
| description | 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. 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 ΔqS(x,Q2)∼(1x)αh with αh=43αsNc2π, in excellent agreement with the numerical estimate αh≈2.31αsNc2π 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. |
| first_indexed | 2024-12-10T11:24:07Z |
| format | Article |
| id | doaj.art-493298ef38f9415aba0662dbe35b126a |
| institution | Directory Open Access Journal |
| issn | 0370-2693 1873-2445 |
| language | English |
| last_indexed | 2024-12-10T11:24:07Z |
| publishDate | 2017-09-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Physics Letters B |
| spelling | doaj.art-493298ef38f9415aba0662dbe35b126a2022-12-22T01:50:48ZengElsevierPhysics Letters B0370-26931873-24452017-09-01772C13614010.1016/j.physletb.2017.06.032Small-x asymptotics of the quark helicity distribution: Analytic resultsYuri V. Kovchegov0Daniel Pitonyak1Matthew D. Sievert2Department of Physics, The Ohio State University, Columbus, OH 43210, USADivision of Science, Penn State University-Berks, Reading, PA 19610, USATheoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USAIn 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. 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 ΔqS(x,Q2)∼(1x)αh with αh=43αsNc2π, in excellent agreement with the numerical estimate αh≈2.31αsNc2π 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.http://www.sciencedirect.com/science/article/pii/S0370269317305087 |
| spellingShingle | Yuri V. Kovchegov Daniel Pitonyak Matthew D. Sievert Small-x asymptotics of the quark helicity distribution: Analytic results Physics Letters B |
| title | Small-x asymptotics of the quark helicity distribution: Analytic results |
| title_full | Small-x asymptotics of the quark helicity distribution: Analytic results |
| title_fullStr | Small-x asymptotics of the quark helicity distribution: Analytic results |
| title_full_unstemmed | Small-x asymptotics of the quark helicity distribution: Analytic results |
| title_short | Small-x asymptotics of the quark helicity distribution: Analytic results |
| title_sort | small x asymptotics of the quark helicity distribution analytic results |
| url | http://www.sciencedirect.com/science/article/pii/S0370269317305087 |
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