NLO Q²-evolution of the nucleon's transversity distribution h₁(x, Q²)

الأصل · EN

We present a calculation of the two-loop anomalous dimension for the transversity distribution h₁(x,Q²), γʰ⁽¹⁾ₙ, in the MS scheme of the dimensional regularization. Because of the chiral-odd nature, h₁ does not mix with the gluon distributions, and thus our result is the same for the flavor-singlet and nonsinglet distributions. At small n (moment of h₁), γʰ⁽¹⁾ₙ is significantly larger than γᶠ,ᵍ⁽¹⁾ₙ (the anomalous dimension for the nonsinglet f₁ and g₁), but approaches γᶠ,ᵍ⁽¹⁾ₙ very quickly at large n, keeping the relation γʰ⁽¹⁾ₙ > γᶠ,ᵍ⁽¹⁾ₙ. This feature is in parallel to the relation between the one-loop anomalous dimension for f₁ (g₁) and h₁. We also show that this difference in the anomalous dimension between h₁ and g₁ leads to a drastic difference in the Q²-evolution of those distributions in the small x region.