Abstract
We resum the leading logarithms αsn ln2n − 1(1 − z), n = 1, 2, . . . near the kine-matic threshold z = Q2/ŝ → 1 of the Drell-Yan process at next-to-leading power in the expansion in (1 − z). The derivation of this result employs soft-collinear effective theory in position space and the anomalous dimensions of subleading-power soft functions, which are computed. Expansion of the resummed result leads to the leading logarithms at fixed loop order, in agreement with exact results at NLO and NNLO and predictions from the physical evolution kernel at N3LO and N4LO, and to new results at the five-loop order and beyond.
Highlights
Fractions of the partons in the corresponding hadrons
Soft gluon resummation was first studied for the threshold of the DY process [1, 2] and extended to increasingly higher logarithmic accuracy at leading power in the expansion in the threshold variable (1 − z), based on the factorization into a hard and soft function
We considered the next-to-leading power (NLP) in (1 − z) and provided an all-order resummation of the leading NLP logarithms of the form αsn ln2n−1(1− z), n = 1, 2, . . . near the kinematic threshold z = Q2(1 − z)H (Q2)/s → 1
Summary
The following treatment makes use of SCET [13, 14] in the position-space representation [15, 16]. The LP factorization formula is recovered from the general formula as the special case when there are no collinear functions In this case the index set i is empty, the convolutions over the various ωi variables in (2.2) are absent and D(−s; ωi, ωi) → CA0(−s) ≡ CA0(xan+pA, xbn−pB), where the latter denotes the matching coefficient of the LP SCET current, ψγμψ(0) = dt dtCA0(t, t) JμA0(t, t). A novel feature of the NLP factorization formula for the DY process is the appearance of collinear functions at the amplitude level [12] They are defined as the matching coefficients of a product of generic collinear fields to collinear-PDF fields in the presence of soft field operators. These considerations generalize to all collinear matrix elements that appear upon working out the time-ordered products with the subleading SCET Lagrangian. Further simplifications can be made when one is interested only in the leading logarithms, as described
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