Difficulties in the description of Drell-Yan processes at moderate invariant mass and high transverse momentum

Abstract

We study the Drell-Yan cross section differential with respect to the transverse momentum of the produced lepton pair. We consider data with moderate invariant mass Q of the lepton pair, between 4.5 GeV and 13.5 GeV, and similar (although slightly smaller) values of the transverse momentum qT . We approach the problem by deriving predictions based on standard collinear factorization, which are expected to be valid toward the high-qT end of the spectrum and to which any description of the spectrum at lower qT using transverse-momentum dependent parton distributions ultimately needs to be matched. We find that the collinear framework predicts cross sections that in most cases are significantly below available data at high qT . We discuss additional perturbative and possible non-perturbative effects that increase the predicted cross section, but not by a sufficient amount. PACS numbers: 12.38.Bx, 12.39.St, 13.85.Qk I. INTRODUCTIONThe Drell-Yan (DY) process [1] is one of the main sources of information about the internal structure of the nucleon (for a recent review, see [2]). Factorization theorems were first established for DY [3], and global extractions of parton distribution functions (PDFs) heavily rely on measurements of the DY cross section differential in the rapidity of the produced boson (see, e.g., [4,5] and references therein). DY processes also offer the possibility to access transverse momentum distributions (TMDs) [6][7][8][9][10][11][12][13][14][15], if the cross section is kept differential in the transverse momentum of the produced boson.Considering the invariant mass of the produced boson, Q, its transverse momentum, q T , and a typical QCD scale, Λ QCD , we can distinguish a region of "high transverse momentum" 1 where Λ QCD q T ∼ Q and a region of "low transverse momentum" where q T Q. In the first region, the cross section should be well described by a collinear factorization framework in terms of collinear PDFs convoluted with a partonic hard scattering calculated up to a fixed order in α s . This calculation is nowadays possible even up to order α 3 s (NNLO) [17], but most of the phenomenology is carried out at order α 2 s (NLO) [18][19][20][21][22][23][24][25] or even only order α s (LO). In the low transverse momentum region, the cross section should be described in the framework of TMD factorization, which also incorporates the effects of the resummation of large logarithms in q T /Q. The all-order corrections dominating the cross section in this region are embodied in the so-called "W term" of the Collins-Soper-Sterman formalism [26]. The matching of the collinear formalism at high-q T with the TMD resummation at low-q T is usually performed through the introduction of the so-called "Y term", i.e., the difference of the fixed-order perturbative result and the asymptotic expansion of the resummed result. In the low-q T region, the asymptotic piece and the fixed-order one ideally cancel each other, leaving only the W term. In the high-q T region, on the other hand, the cancellation takes pla...

Pion-induced Drell-Yan processes within TMD factorization

“…The authors have tested several ways to improve the theory predictions (threshold resummation, k T -smearing) but were not able to resolve the problem. In the TMD regime the same effect has been observed in [1] (for the same experiments that are considered in [21]), namely, about 40% deficit in the normalization that decreases with the increase of energy (see table 3 in [1]). Note, both analyses [21] and [1] have not a problem with the description of PHENIX data [47] that have a similar range of Q but measured in the collider regime.…”

“…The data analyzed in ref. [21] belong to the same kinematic domain as the data discussed here. The comparison has been done in the regime q T ∼ Q where the collinear factorization is well established.…”

“…Also in ref. [21] a more accurate analysis has been performed, and it has been shown that the threshold resummation does not solve the problem…”

DYTurbo: fast predictions for Drell–Yan processes

“…[30][31][32][33][34][35][36][37][38]. Analogous resummed calculations have been performed by applying Soft Collinear Effective Theory methods [39][40][41][42][43] and transverse-momentum dependent factorisation [44][45][46][47][48][49][50][51][52]. Electroweak (EW) [53][54][55][56][57][58][59][60][61] and mixed QCD-EW [62][63][64][65][66][67][68] radiative corrections have also been considered.…”

Drell-Yan plus jet production and BFKL evolution

“…This is justified since the CCFM-K evolution includes elements of the CSS resummation. In this sense our paper should be treated as a step towards unified description of the low mass DY data, where the CSS approach matched to the fixed order calculation experiences some troubles [9].…”