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<p>We use Soft Collinear Effective Theory (SCET) to factorize the polarized Deep Inelastic Scattering (DIS) structure functions <i>g</i><sub>1</sub>(<i>x</i>) and <i>g</i><sub>2</sub>(<i>x</i>), and to sum Sudakov double logarithms of 1 − <i>x</i>. The analysis is done both in terms of lightcone parton distributions and their moments. Computing <i>g</i><sub>2</sub> requires subleading SCET operators which contain gluons. We calculate the one-loop matching coefficients from QCD onto these subleading SCET operators, and the one-loop matching from SCET onto the parton distribution function (PDF). The PDF in SCET is given by a bilocal operator, rather than the trilocal operator used in the QCD analysis of <i>g</i><sub>2</sub> for generic <i>x</i>. We compute the one-loop anomalous dimension of the PDF operator for any <i>x</i>, and show that as <i>x</i> → 1, it factors into a single-variable evolution.</p><p>We comment on the QCD anomalous dimensions of twist-three operators, their equation-of-motion relation, and connection to the SCET analysis. We briefly discuss the definition of axial operators in the BMHV scheme. As a side result, we derive the 1/<i>N</i> dependence of the QCD coefficient functions for <i>F</i><sub>1</sub>, <i>F</i><sub><i>L</i></sub> and <i>g</i><sub>1</sub> in the <i>N</i> → ∞ limit, where <i>N</i> is the moment, which is expected to hold to all orders in <i>α</i><sub><i>s</i></sub>.</p>

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Polarized deep inelastic scattering as x → 1 using soft collinear effective theory

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  • 发表日期：

    2026年3月26日

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  • Jaipratap Singh Grewal,
  • Aneesh V. Manohar,
  • Jyotirmoy Roy

摘要

We use Soft Collinear Effective Theory (SCET) to factorize the polarized Deep Inelastic Scattering (DIS) structure functions g1(x) and g2(x), and to sum Sudakov double logarithms of 1 − x. The analysis is done both in terms of lightcone parton distributions and their moments. Computing g2 requires subleading SCET operators which contain gluons. We calculate the one-loop matching coefficients from QCD onto these subleading SCET operators, and the one-loop matching from SCET onto the parton distribution function (PDF). The PDF in SCET is given by a bilocal operator, rather than the trilocal operator used in the QCD analysis of g2 for generic x. We compute the one-loop anomalous dimension of the PDF operator for any x, and show that as x → 1, it factors into a single-variable evolution.

We comment on the QCD anomalous dimensions of twist-three operators, their equation-of-motion relation, and connection to the SCET analysis. We briefly discuss the definition of axial operators in the BMHV scheme. As a side result, we derive the 1/N dependence of the QCD coefficient functions for F1, FL and g1 in the N → ∞ limit, where N is the moment, which is expected to hold to all orders in αs.