Ignazio Scimemi

Factorization theorem for Drell-Yan at low q T and transverse-momentum distributions on-the-light-cone

A bstractWe derive a factorization theorem for Drell-Yan process at low qT using effective field theory methods. In this theorem all the obtained quantities are gauge invariant and the special role of the soft function — and its subtraction thereof — is emphasized. We define transverse-momentum dependent parton distribution functions (TMDPDFs) which are free from light-cone singularities while all the Wilson lines are defined on-the-light-cone. We show explicitly to first order in αs that the partonic Feynman PDF can be obtained from the newly defined partonic TMDPDF by integrating over the transverse momentum of the parton inside the hadron. We obtain a resummed expression for the TMDPDF, and hence for the cross section, in impact parameter space. The universality of the newly defined matrix elements is established perturbatively to first order in αs. The factorization theorem is validated to first order in αs and also the gauge invariance between Feynman and light-cone gauges.

Soft and collinear factorization and transverse momentum dependent parton distribution functions

Abstract In this work we consider how a parton distribution function, with an explicit transverse momentum dependence can be properly defined in a regularization-scheme independent manner. We argue that by considering a factorized form of the transverse momentum dependent spectrum for the production of a heavy lepton pair in Drell–Yan reaction, one should first split the relevant soft function into two boost invariant contributions. When those soft contributions are added to the pure collinear contributions, well-defined hadronic matrix elements emerge, i.e., the transverse momentum dependent distributions. We also perform a comparison with Collinsʼ definition.

Unified treatment of the QCD evolution of all (un-)polarized transverse momentum dependent functions: Collins function as a study case

By considering semi-inclusive deep-inelastic scattering and the (complementary) qT-spectrum for Drell-Yan lepton pair production we derive the QCD evolution for all the leading-twist transverse momentum dependent distribution and fragmentation functions. We argue that all of those functions evolve with Q2 following a single evolution kernel. This kernel is independent of the underlying kinematics and it is also spin independent. Those features hold, in impact parameter space, to all values of bT. The evolution kernel presented has all of its large logarithms resummed up to next-to-next-to leading logarithmic accuracy, which is the highest possible accuracy given the existing perturbative calculations. As a study case we apply this kernel to investigate the evolution of the Collins function, one of the ingredients that have recently attracted much attention within the phenomenological studies of spin asymmetries. Our analysis can be readily implemented to revisit previously obtained fits that involve data at different scales for other spin-dependent functions. Such improved fits are important to get better predictions—with the correct evolution kernel—for certain upcoming experiments aiming to measure the Sivers function, Collins function, transversity, and other spin-dependent functions as well.

Infrared Renormalization-Group Flow for Heavy-Quark Masses

A short-distance heavy-quark mass depends on two parameters: the renormalization scale mu and a scale R controlling the absorption of infrared fluctuations. The radius for perturbative corrections that build up the mass beyond its pointlike definition in the pole scheme is approximately 1/R. Treating R as a variable gives a renormalization-group equation. R evolution improves the stability of conversion between short-distance mass schemes, allowing us to avoid large logs and the renormalon. R evolution can also be used to study IR renormalons without using bubble chains, yielding a convergent sum rule for the coefficient of the O(Lambda(QCD)) renormalon ambiguity of the pole mass.

Singular and regular gauges in soft–collinear effective theory: The introduction of the new Wilson line T

Abstract Gauge invariance in soft–collinear effective theory (SCET) is discussed in regular (covariant) and singular (light-cone) gauges. It is argued that SCET, as it stands, is not capable to define in a gauge invariant way certain non-perturbative matrix elements that are an integral part of many factorization theorems. Those matrix elements involve two quark or gluon fields separated not only in light-cone direction but also in the transverse one. This observation limits the range of applicability of SCET. To remedy this we argue that one needs to introduce a new Wilson line as part of SCET formalism, that we call T . This Wilson line depends only on the transverse component of the gluon field. As such it is a new feature to the SCET formalism and it guarantees gauge invariance of the non-perturbative matrix elements in both classes of gauges.

K→3π final state interactions at NLO in CHPT and Cabibbo’s proposal to measure a0-a2

We present the analytical results for the K→3π final state interaction phases at next-to-leading order (NLO) in CHPT. We also study the recent proposal of Cabibbo to measure the ππ scattering lengths combination a0-a2 from the cusp effect in the π0π0 energy spectrum at threshold for K+→π0π0π+ and KL→π0π0π0, and we give the relevant formulas to describe it at NLO. We estimate the theoretical uncertainty of the a0-a2 determination at NLO in our approach and obtain the result that it is not smaller than 5% if added quadratically and 7% if added linearly, for K+→π0π0π+. One gets similar theoretical uncertainties if the neutral KL→π0π0π0 decay data below threshold are used instead. For this decay, there are very large theoretical uncertainties above threshold due to cancellations, and data above threshold cannot be used to get the scattering lengths. We do not include isospin corrections apart from two-pion phase space factors which are physical. We compare our results for the cusp effect with those due to Cabibbo and Isidori.

Soft-collinear effective theory, light-cone gauge, and theT-Wilson lines

Soft-Collinear Effective Theory (SCET) has been formulated since a decade now in covariant gauges. In this work we derive a modified SCET Lagrangian applicable in both classes of gauges: regular and singular ones. This extends the range of applicability of SCET. The new Lagrangian must be used to obtain factorization theorems in cases where the transverse momenta of the particles in the final states are not integrated over, such as semi-inclusive deep inelastic scattering, DrellYan and the Higgs production cross-section at low transverse momentum. By doing so all nonperturbative matrix elements appearing in the factorized cross-sections are gauge invariant.

Non-perturbative QCD effects in qT spectra of Drell-Yan and Z-boson production

A bstractThe factorization theorems for transverse momentum distributions of dilepton/boson production, recently formulated by Collins and Echevarria-Idilbi-Scimemi in terms of well-defined transverse momentum dependent distributions (TMDs), allows for a systematic and quantitative analysis of non-perturbative QCD effects of the cross sections involving these quantities. In this paper we perform a global fit using all current available data for Drell-Yan and Z-boson production at hadron colliders within this framework. The perturbative calculable pieces of our estimates are included using a complete resummation at next-to-next-to-leading-logarithmic accuracy. Performing the matching of transverse momentum distributions onto the standard collinear parton distribution functions and recalling that the corresponding matching coefficient can be partially exponentiated, we find that this exponentiated part is spin-independent and resummable. We argue that the inclusion of higher order perturbative pieces is necessary when data from lower energy scales are analyzed. We consider non-perturbative corrections both to the intrinsic nucleon structure and to the evolution kernel and find that the non-perturbative part of the TMDs could be parametrized in terms of a minimal set of parameters (namely 2-3). When all corrections are included the global fit so performed gives a χ2/d.o.f. ≲ 1 and a very precise prediction for vector boson production at the Large Hadron Collider (LHC).

Universal transverse momentum dependent soft function at NNLO

All (un)polarized transverse momentum dependent functions (TMDs), both distribution and fragmentation functions, are defined with the same universal soft function, which cancels spurious rapidity divergences within an individual TMD and renders them well-defined hadronic quantities. Moreover, it is independent of the kinematics, whether it is Drell-Yan, deep inelastic scattering, or e^+e^−→2 hadrons. In this paper, we provide this soft function at next-to-next-to-leading order (NNLO), necessary for the calculation of all TMDs at the same order, and to perform the resummation of large logarithms at next-to-next-to-next-to-leading-logarithmic accuracy. From the results we obtain the D function at NNLO, which governs the evolution of all TMDs. This work represents the first independent and direct calculation of this quantity. Given the all-order relation through a Casimir scaling between the soft function relevant for gluon TMDs and the one for quark TMDs, we also obtain the first at NNLO. The used regularization method to deal with the rapidity divergences is discussed as well.

Two-loop jet function and jet mass for top quarks

We compute the two-loop heavy-quark jet function in the heavy-quark limit. This is one of the key ingredients in next-to-next-to-leading order and next-to-next-to-leading-log order computations of the invariant mass distribution of top-jets at a future e{sup +}e{sup -} collider. The shape of the top-invariant mass distribution is affected by large logs which we compute at next-to-next-to-leading-log order. Exploiting the non-Abelian exponentiation theorem, a definition of the top jet mass is given which is transitive and whose renormalization group evolution is determined by the cusp-anomalous dimension to all orders in perturbation theory. Relations of the jet mass to the pole, MS, and 1S masses are presented at two-loop order.