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 |
| Published: |
Elsevier
2017-09-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269317305087 |
| Summary: | 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. |
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| ISSN: | 0370-2693 1873-2445 |