Searcharxiv⌕ Search

arXiv subjects

Ahmad Idilbi

Publications and source records attributed to Ahmad Idilbi.

27 records · Page 2Linked to original sources
arXiv2007

Demonstration of the Equivalence of Soft and Zero-Bin Subtractions

Calculations of collinear correlation functions in perturbative QCD and Soft-Collinear Effective Theory (SCET) require a prescription for subtracting soft or zero-bin contributions in order to avoid double counting the contributions from soft modes. At leading order in $λ$, where $λ$ is the SCET expansion parameter, the zero-bin subtractions have been argued to be equivalent to convolution with soft Wilson lines. We give a proof of the factorization of naive collinear Wilson lines that is crucial for the derivation of the equivalence. We then check the equivalence by computing the non-Abelian two-loop mixed collinear-soft contribution to the jet function in the quark form factor. These results provide strong support for the equivalence, which can be used to give a nonperturbative definition of the zero-bin subtraction at lowest order in $λ$.

hep-ph↗
arXiv2007

On The Equivalence of Soft and Zero-Bin Subtractions

Zero-bin subtractions are required to avoid double counting soft contributions in collinear loop integrals in Soft-Collinear Effective Theory (SCET). In traditional approaches to factorization, double counting is avoided by dividing jet functions by matrix elements of soft Wilson lines. In this paper, we compare the two approaches to double counting, studying the quark form factor and deep inelastic scattering (DIS) as x_B \to 1 as examples. We explain how the zero-bin subtractions in SCET are required to reproduce the well-established factorization theorem for DIS as x_B \to 1. We study one-loop virtual contributions to the quark form factor and real gluon emission diagrams in DIS. The two approaches to double counting are equivalent if dimensional regularization (DR) is used to regulate infrared (IR) divergences. We discuss in detail ambiguities in the calculation of one-loop scaleless integrals in DR in SCET and perturbative QCD. We also demonstrate a nontrivial check of the equivalence of the zero-bin subtraction and the soft Wilson line subtraction in the virtual two-loop Abelian contributions to the quark form factor.

hep-ph↗
arXiv2006

Resummation of Threshold Logarithms in Effective Field Theory For DIS, Drell-Yan and Higgs Production

We apply the effective field theoretic (EFT) approach to resum the large perturbative logarithms arising when partonic hard scattering cross-sections are taken to the threshold limit. We consider deep inelastic scattering, Drell-Yan lepton pair production and the standard model Higgs production through gluon-gluon fusion via heavy-top loop. We demonstrate the equivalence of the EFT approach with the more conventional, factorization-based methods to all logarithmic accuracies and to all orders in perturbation theory. Specific EFT results are shown for the resummation up to next-to-next-to-next leading logarithmic accuracy for the above mentioned processes. We emphasize the relative simplicity by which we derive most of the results and more importantly their clear physical origin. We find a new relation between the functions $f_{(q,g)}$ in the quark and gluon form factors and the matching coefficients in Drell-Yan and Higgs production, which may explain their universality believed to hold to all orders in perturbation theory.

hep-ph↗
arXiv2006

QCD Factorization for Deep-Inelastic Scattering At Large Bjorken $x_B \sim 1-{\cal O}(Λ_{\rm QCD}/Q$

We study deep-inelastic scattering factorization on a nucleon in the end-point regime $x_B \sim 1-{\cal O}(Λ_{\rm QCD}/Q)$ where the traditional operator product expansion is supposed to fail. We argue, nevertheless, that the standard result holds to leading order in $1-x_B$ due to the absence of the scale dependence on $(1-x_B)Q$. Refactorization of the scale $(1-x_B)Q^2$ in the coefficient function can be made in the soft-collinear effective theory and remains valid in the end-point regime. On the other hand, the traditional refactorization approach introduces the spurious scale $(1-x_B)Q$ in various factors, which drives them nonperturbative in the region of our interest. We show how to improve the situation by introducing a rapidity cut-off scheme, and how to recover the effective theory refactorization by choosing appropriately the cut-off parameter. Through a one-loop calculation, we demonstrate explicitly that the proper soft subtractions must be made in the collinear matrix elements to avoid double counting.

hep-ph↗
arXiv2006

Threshold Resummation for Higgs Production in Effective Field Theory

We present an effective field theory to resum the large double logarithms originated from soft-gluon radiations at small final-state hadron invariant masses in Higgs and vector boson (γ^*, $W$ and $Z$) production at hadron colliders. The approach is conceptually simple, indepaendent of details of an effective field theory formulation, and valid to all orders in sub-leading logarithms. As an example, we show the result of summing the next-to-next-to-next leading logarithms is identical to that of standard pQCD factorization method.

hep-ph↗
arXiv2005

Threshold Resummation for Drell-Yan Process in Soft-Collinear Effective Theory

We consider Drell-Yan process in the threshold region $z\to 1$ where large logarithms appear due to soft-gluon radiations. We present a soft-collinear effective theory approach to re-sum these Sudakov-type logarithms following an earlier treatment of deep inelastic scattering, and the result is consistent with that obtained earlier through perturbative QCD factorization

hep-ph↗
arXiv2005

Transverse Momentum Distribution Through Soft-Gluon Resummation in Effective Field Theory

We study resummation of transverse-momentum-related large logarithms generated from soft-gluon radiations in soft-collinear effective field theory. The anomalous dimensions of the effective quark and gluon currents, an important ingredient for the resummation, are calculated to two-loop order. the result at next-to-leading-log reproduces that obtained using the standard method for deep-inelastic scattering, Drell-Yan process, and Higgs production through gluon-gluon fusion. We comment on the extension of the calculation to next-to-next-to-leading logarithms.

hep-ph↗
arXiv2003

Delta-to-N-gamma Coulomb Quadrupole Amplitude in PQCD

We present a leading-order pQCD calculation of the helicity-flip $Δ\to Nγ^*$ matrix element $G_0$ (Coulomb quadrupole amplitude $C2$), taking into account the transverse momenta of the quarks and the contribution from the gluons. In the large $Q^2$ limit, its scaling behavior acquires a double-logarithmic correction $\log^2{(Q^2/Λ^2)}$ compared with the standard scaling analysis, due to the contribution from the orbital motion of the small-$x$ partons. Based on this and on the latest JLab experimental results of the $C2-M1$ ratio $R_{SM}$ at $Q^2$ = 3 $\sim$ 4 GeV$^2$, we make a phenomenological prediction for the latter at higher values of $Q^2$.

hep-ph↗