High-energy operator product expansion at sub-eikonal level

Chirilli, Giovanni Antonio

doi:10.1007/jhep06(2021)096

Cited by 34 publications

(15 citation statements)

References 55 publications

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“…The small-x asymptotics of helicity PDFs obtained in [6][7][8] disagreed with that obtained in [29,30]: while the origin of this discrepancy is still a largely open problem, possible reasons for this disagreement were outlined in [2]. In addition, as we mentioned above, the equations from [1-3, 6-8, 12] were recently independently re-derived using the background field method [16] (see also [81]).…”

Section: Discussionmentioning

confidence: 78%

“…As was recently demonstrated in [17], these equations are capable of precisely accomplishing the low-x predictions and extrapolations listed in the above items (i) and (ii), respectively. The equations from [1-3, 6-8, 12] have recently been verified by an independent calculation in [16] using the background field method.…”

Section: Introductionmentioning

confidence: 92%

“…( 33) contains both the flavor-singlet and non-singlet terms (cf. [16]): the latter cancel in the evolution for the sum of the two traces (33), corresponding to the flavor-singlet amplitude (see [2,3]), and are not shown in Eq. (36).…”

Section: Evolution Equationsmentioning

confidence: 99%

“…The small-x asymptotics of helicity distributions for quarks and gluons have been the subject of intense studies in recent years [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. The goal of these ongoing efforts is to provide a reliable first-principles theoretical framework for predicting helicity parton distribution functions (helicity PDFs or hPDFs) at small values of Bjorken x.…”

Section: Introductionmentioning

confidence: 99%

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Helicity Evolution at Small $x$: the Single-Logarithmic Contribution

Kovchegov,

Tarasov,

Tawabutr

2021

Preprint

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We calculate single-logarithmic corrections to the small-x flavor-singlet helicity evolution equations derived recently [1][2][3] in the double-logarithmic approximation. The new single-logarithmic part of the evolution kernel sums up powers of αs ln(1/x), which are an important correction to the dominant powers of αs ln 2 (1/x) summed up by the double-logarithmic kernel from [1-3] at small values of Bjorken x and with αs the strong coupling constant. The single-logarithmic terms arise separately from either the longitudinal or transverse momentum integrals. Consequently, the evolution equations we derive simultaneously include the small-x evolution kernel and the leading-order polarized DGLAP splitting functions. We further enhance the equations by calculating the running coupling corrections to the kernel.

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Section: Discussionmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 92%

Section: Evolution Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Helicity Evolution at Small $x$: the Single-Logarithmic Contribution

Kovchegov,

Tarasov,

Tawabutr

2021

Preprint

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“…The approach to helicity evolution in the s-channel formalism developed in [1-3, 31-33, 36, 37] resulted in the small-x asymptotics of ∆Σ and ∆G different from that found by BER. 1 Despite several cross-checks [2,39] the origin of the difference remained unknown. In this work we identify the sub-eikonal operator which was not included in the approach of [1-3, 31-33, 36, 37]: after including it, we obtain a new set of small-x evolution equations for helicity, whose solution gives the asymptotics (4) consistent with BER.…”

mentioning

confidence: 99%

Quark and Gluon Helicity Evolution at Small $x$: Revised and Updated

Cougoulic,

Kovchegov,

Tarasov

et al. 2022

Preprint

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We revisit the problem of small Bjorken-x evolution of the gluon and flavor-singlet quark helicity distributions in the shock wave (s-channel) formalism. Earlier works on the subject in the same framework [1][2][3] resulted in an evolution equation for the gluon field-strength F 12 and quark "axial current" ψγ + γ 5 ψ operators (sandwiched between the appropriate light-cone Wilson lines) in the double-logarithmic approximation (summing powers of αs ln 2 (1/x) with αs the strong coupling constant). In this work, we observe that an important mixing of the above operators with another gluon operator, D i D i , also sandwiched between the light-cone Wilson lines (with the repeated transverse index i = 1, 2 summed over), was missing in the previous works [1][2][3]. This operator has the physical meaning of the sub-eikonal (covariant) phase: its contribution to helicity evolution is shown to be proportional to another sub-eikonal operator, D i − D i , which is related to the Jaffe-Manohar polarized gluon distribution [4]. In this work we include this new operator into small-x helicity evolution, and construct novel evolution equations mixing all three operators (D i − D i , F 12 , and ψγ + γ 5 ψ), generalizing the results of [1][2][3]. We also construct closed double-logarithmic evolution equations in the large-Nc and large-Nc&N f limits, with Nc and N f the numbers of quark colors and flavors, respectively. Solving the large-Nc equations numerically we obtain the following small-x asymptotics of the quark and gluon helicity distributions ∆Σ and ∆G, along with the g1 structure function,3.66 αs Nc 2π , in complete agreement with the earlier work by Bartels, Ermolaev and Ryskin [5].

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Orbital angular momentum at small x revisited

Kovchegov,

Manley

2024

J. High Energ. Phys.

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We revisit the problem of the small Bjorken-x asymptotics of the quark and gluon orbital angular momentum (OAM) distributions in the proton utilizing the revised small-x helicity evolution derived recently in [1]. We relate the quark and gluon OAM distributions at small x to the polarized dipole amplitudes and their (first) impact-parameter moments. To obtain the OAM distributions, we derive novel small-x evolution equations for the impact-parameter moments of the polarized dipole amplitudes in the double-logarithmic approximation (summing powers of αs ln2(1/x) with αs the strong coupling constant). We solve these evolution equations numerically and extract the leading large-Nc, small-x asymptotics of the quark and gluon OAM distributions, which we determine to be$$ {L}_{q+\overline{q}}\left(x,{Q}^2\right)\sim {L}_G\left(x,{Q}^2\right)\sim \Delta \Sigma \left(x,{Q}^2\right)\sim \Delta G\left(x,{Q}^2\right)\sim {\left(\frac{1}{2}\right)}^{3.66\sqrt{\frac{\alpha_s{N}_c}{2\uppi}}}, $$ L q + q ¯ x Q 2 ~ L G x Q 2 ~ ∆ Σ x Q 2 ~ ∆ G x Q 2 ~ 1 2 3.66 α s N c 2 π , in agreement with [2] within the precision of our numerical evaluation. (Here Nc is the number of quark colors.) We also investigate the ratios of the quark and gluon OAM distributions to their helicity distribution counterparts in the small-x region.

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High-energy operator product expansion at sub-eikonal level

Cited by 34 publications

References 55 publications

Helicity Evolution at Small $x$: the Single-Logarithmic Contribution

Helicity Evolution at Small $x$: the Single-Logarithmic Contribution

Quark and Gluon Helicity Evolution at Small $x$: Revised and Updated

Orbital angular momentum at small x revisited

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