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Next-to-leading order Q^2-evolution of the transversity distribution h_1(x, Q^2)
High Energy Physics - Phenomenology · Submitted 1 Jul 1997
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim At small n (moment of h_1), $\gamma^{h(1)}_n$ is significantly larger than $\gamma^{f(1)}_n$ (the anomalous dimension for the nonsinglet f_1), but approaches $\gamma^{f(1)}_n$ very quickly at large n, keeping the relation $\gamma^{h(1)}_n > \gamma^{f(1)}_n$.
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The abstract, sentence by sentence
We present a calculation of the two-loop anomalous dimension for the transversity distribution h_1(x,Q^2), $\gamma^{h(1)}_n$, in the MS scheme of the dimensional regularization. Due to the chiral-odd nature, h_1 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 h_1), $\gamma^{h(1)}_n$ is significantly larger than $\gamma^{f(1)}_n$ (the anomalous dimension for the nonsinglet f_1), but approaches $\gamma^{f(1)}_n$ very quickly at large n, keeping the relation $\gamma^{h(1)}_n > \gamma^{f(1)}_n$. This feature is in parallel to the relation between the one-loop anomalous dimension for f_1 and h_1.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a calculation of the two-loop anomalous dimension for the transversity distribution h_1(x,Q^2), $\gamma^{h(1)}_n$, in the MS scheme of the dimensional regularization. | contribution 0.98 | 0.96 | 0.24 | asserted 1.00 |
| s1 | Due to the chiral-odd nature, h_1 does not mix with the gluon distributions, and thus our result is the same for the flavor-singlet and nonsinglet distributions. | interpretation 0.57 | 0.48 | 0.11 | asserted 1.00 |
| s2 | At small n (moment of h_1), $\gamma^{h(1)}_n$ is significantly larger than $\gamma^{f(1)}_n$ (the anomalous dimension for the nonsinglet f_1), but approaches $\gamma^{f(1)}_n$ very quickly at large n, keeping the relation $\gamma^{h(1)}_n > \gamma^{f(1)}_n$. | result 0.99 | 0.88 | 0.56 | asserted 1.00 |
| s3 | This feature is in parallel to the relation between the one-loop anomalous dimension for f_1 and h_1. | interpretation 0.91 | 0.25 | 0.09 | asserted 1.00 |
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The paper
Original abstract
We present a calculation of the two-loop anomalous dimension for the transversity distribution h_1(x,Q^2), $\gamma^{h(1)}_n$, in the MS scheme of the dimensional regularization. Due to the chiral-odd nature, h_1 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 h_1), $\gamma^{h(1)}_n$ is significantly larger than $\gamma^{f(1)}_n$ (the anomalous dimension for the nonsinglet f_1), but approaches $\gamma^{f(1)}_n$ very quickly at large n, keeping the relation $\gamma^{h(1)}_n > \gamma^{f(1)}_n$. This feature is in parallel to the relation between the one-loop anomalous dimension for f_1 and h_1.
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References
How the literature uses it
15 arXiv papers cite this in 30 sentences
Papers citing it · 18 sentences without a confident label
Compares with it 4 papers
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As result, we obtain [equation] which should be compared with the two-loop anomalous dimension of transversity operator, calculated in Refs. [ref] : [equation] The difference is only in the last term.
Three loop anomalous dimension of the non-singlet transversity operator in QCD · Reconstruction · 0.99
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[equation] which is in perfect agreement with the results of Refs. [ref] .
Three-loop evolution kernel for transversity operator · Two-loop evolution kernel · 0.99
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We agree with the results given in [ref] and confirm the $T_F$-contributions for the moments $N=1$ to 8 given in Refs. [ref] .
2- and 3-Loop Heavy Flavor Corrections to Transversity · Anomalous Dimensions · 1.00
Cites it as background 7 papers
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The evolution of transversity distribution is very well known [ref] while the evolution of the twist-3 fragmentation function involves multiparton correlation functions [ref] , as a common feature of higher-twist correlation functions.
Extraction of Quark Transversity Distribution and Collins Fragmentation Functions with QCD Evolution · Introduction · 0.87
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While the diagonal elements of the ADM simply correspond to the forward anomalous dimensions, which are well-known from the study of inclusive processes [ref] , the off-diagonal elements only appear for exclusive processes and require a separate calculation.
Off-forward anomalous dimensions in the leading-$n_f$ limit · Introduction · 0.96
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The scaling violations of the transversity distribution were explored in leading-, [ref] [The small $x$ limit of the LO anomalous dimension was calculated in [ref] .], and next-to-leading order, [ref] .
$O(\alpha_s^2)$ and $O(\alpha_s^3)$ Heavy Flavor Contributions to Transversity at $Q^2 \gg m^2$ · Introduction · 0.91
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