Ahmad Idilbi

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.

Model independent evolution of transverse momentum dependent distribution functions (TMDs) at NNLL

We discuss the evolution of the eight leading-twist transverse momentum dependent parton distribution functions, which turns out to be universal and spin independent. By using the highest order perturbatively calculable ingredients at our disposal, we perform the resummation of the large logarithms that appear in the evolution kernel of transverse momentum distributions up to next-to-next-to-leading logarithms (NNLL), thus obtaining an expression for the kernel with highly reduced model dependence. Our results can also be obtained using the standard CSS approach when a particular choice of the b∗ prescription is used. In this sense, and while restricted to the perturbative domain of applicability, we consider our results as a “prediction” of the correct value of bmax which is very close to 1.5xa0GeV−1. We explore under which kinematical conditions the effects of the non-perturbative region are negligible, and hence the evolution of transverse momentum distributions can be applied in a model independent way. The application of the kernel is illustrated by considering the unpolarized transverse momentum dependent parton distribution function and the Sivers function.

Extending soft collinear effective theory to describe hard jets in dense QCD media

An extension to the soft collinear effective theory description of hard jets is motivated to include the leading contributions between the propagating partons within the jet with partons radiated from a dense extended medium. The resulting effective Lagrangian, containing both a leading and a power suppressed (in the hard scale Q{sup 2}) contribution, arises primarily from interactions between the hard collinear modes in the jet with Glauber modes from the medium. In this first attempt, the interactions between the hard jet and soft and collinear partonic modes have been ignored, in an effort to focus solely on the interactions with the Glauber modes. While the effect of such modes on vacuum cross sections are suppressed by powers of the hard scale compared to the terms from the Lagrangian, such subleading contributions are enhanced by the extent of the medium and result in measurable corrections. The veracity of the derived Lagrangian is checked by direct comparison with known results from full QCD calculations of two physical observables: the transverse momentum broadening of hard jets in dense media and a reanalysis of the transverse momentum dependent parton distribution function.

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.

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.

Factorization and resummation for single color-octet scalar production at the LHC

Heavy colored scalar particles appear in a variety of new physics (NP) models and could be produced at the Large Hadron Collider. Knowing the total production cross section is important for searching for these states and establishing bounds on their masses and couplings. Using soft-collinear effective theory, we derive a factorization theorem for the process

On The Equivalence of Soft and Zero-Bin Subtractions

ppensuremath{rightarrow}SX

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

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Demonstration of the Equivalence of Soft and Zero-Bin Subtractions

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