scholarly journals The Energy-Energy Correlation in the back-to-back limit at N3LO and N3LL′

2021 ◽  
Vol 2021 (8) ◽  
Author(s):  
Markus A. Ebert ◽  
Bernhard Mistlberger ◽  
Gherardo Vita
Keyword(s):  
Analytic Formula ◽  
Effective Theory ◽  
Energy Correlation ◽  
Transverse Momentum Dependent ◽  
Yang Mills ◽  
Mellin Moment ◽  
Soft Collinear Effective Theory ◽  
Electron Positron Annihilation ◽  
Electron Positron ◽  
Inclusive Decay

Abstract We present the analytic formula for the Energy-Energy Correlation (EEC) in electron-positron annihilation computed in perturbative QCD to next-to-next-to-next-to-leading order (N3LO) in the back-to-back limit. In particular, we consider the EEC arising from the annihilation of an electron-positron pair into a virtual photon as well as a Higgs boson and their subsequent inclusive decay into hadrons. Our computation is based on a factorization theorem of the EEC formulated within Soft-Collinear Effective Theory (SCET) for the back-to-back limit. We obtain the last missing ingredient for our computation — the jet function — from a recent calculation of the transverse-momentum dependent fragmentation function (TMDFF) at N3LO. We combine the newly obtained N3LO jet function with the well known hard and soft function to predict the EEC in the back-to-back limit. The leading transcendental contribution of our analytic formula agrees with previously obtained results in $$ \mathcal{N} $$ N = 4 supersymmetric Yang-Mills theory. We obtain the N = 2 Mellin moment of the bulk region of the EEC using momentum sum rules. Finally, we obtain the first resummation of the EEC in the back-to-back limit at N3LL′ accuracy, resulting in a factor of ∼ 4 reduction of uncertainties in the peak region compared to N3LL predictions.

scholarly journals Joint thrust and TMD resummation in electron-positron and electron-proton collisions

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Yiannis Makris ◽  
Felix Ringer ◽  
Wouter J. Waalewijn
Keyword(s):  
Transverse Momentum ◽  
Belle Collaboration ◽  
Effective Theory ◽  
Recent Measurement ◽  
Event Shape ◽  
Transverse Momentum Dependent ◽  
Soft Collinear Effective Theory ◽  
Thrust Axis ◽  
Electron Positron ◽  
Crossing Symmetry

Abstract We present the framework for obtaining precise predictions for the transverse momentum of hadrons with respect to the thrust axis in e+e− collisions. This will enable a precise extraction of transverse momentum dependent (TMD) fragmentation functions from a recent measurement by the Belle Collaboration. Our analysis takes into account, for the first time, the nontrivial interplay between the hadron transverse momentum and the cut on the thrust event shape. To this end, we identify three different kinematic regions, derive the corresponding factorization theorems within Soft Collinear Effective Theory, and present all ingredients needed for the joint resummation of the transverse momentum and thrust spectrum at NNLL accuracy. One kinematic region can give rise to non-global logarithms (NGLs), and we describe how to include the leading NGLs. We also discuss alternative measurements in e+e− collisions that can be used to access the TMD fragmentation function. Finally, by using crossing symmetry, we obtain a new way to constrain TMD parton distributions, by measuring the displacement of the thrust axis in ep collisions.

scholarly journals QCD evolution of the gluon Sivers function in heavy flavor dijet production at the Electron-Ion Collider

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Zhong-Bo Kang ◽  
Jared Reiten ◽  
Ding Yu Shao ◽  
John Terry
Keyword(s):  
Evolution Equations ◽  
Effective Theory ◽  
Heavy Flavor ◽  
Dijet Production ◽  
Electron Collisions ◽  
Transverse Momentum Dependent ◽  
Quark Masses ◽  
Soft Collinear Effective Theory ◽  
Theoretical Predictions ◽  
Sivers Function

Abstract Using Soft-Collinear Effective Theory, we develop the transverse-momentum-dependent factorization formalism for heavy flavor dijet production in polarized-proton-electron collisions. We consider heavy flavor mass corrections in the collinear-soft and jet functions, as well as the associated evolution equations. Using this formalism, we generate a prediction for the gluon Sivers asymmetry for charm and bottom dijet production at the future Electron-Ion Collider. Furthermore, we compare theoretical predictions with and without the inclusion of finite quark masses. We find that the heavy flavor mass effects can give sizable corrections to the predicted asymmetry.

scholarly journals QCD resummation on single hadron transverse momentum distribution with the thrust axis

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Zhong-Bo Kang ◽  
Ding Yu Shao ◽  
Fanyi Zhao
Keyword(s):  
Transverse Momentum ◽  
Momentum Distribution ◽  
Cross Sections ◽  
Belle Collaboration ◽  
Transverse Momentum Distribution ◽  
Effective Theory ◽  
Hard Scattering ◽  
Transverse Momentum Dependent ◽  
Thrust Axis ◽  
Electron Positron

Abstract We derive the transverse momentum dependent (TMD) factorization and resummation formula of the unpolarized transverse momentum distribution (jT) for the single hadron production with the thrust axis in an electron-positron collision. Two different kinematic regions are considered, including small transverse momentum limit jT « Q, and joint transverse momentum and threshold limit jT « Q(1 − zh) « Q, where Q and zh are the hard scattering energy and the observed hadron momentum fraction. Using effective theory methods, we resum logarithms ln(Q/jT) and ln(1 − zh) to all orders. In the end, we present the differential cross sections and Gaussian widths calculated for the inclusive charged pion production and find that our results are consistent with the measurements reported by the Belle collaboration.

scholarly journals Predictions for Transverse-Momentum Dependence in Electron-Positron Annihilation

2015 ◽  
Vol 37 ◽  
pp. 1560023
Author(s):  
Alessandro Bacchetta ◽  
Miguel García-Echevarría ◽  
Marco Radici ◽  
Andrea Signori
Keyword(s):  
Transverse Momentum ◽  
Positron Annihilation ◽  
Experimental Measurements ◽  
Momentum Dependence ◽  
Transverse Momentum Dependent ◽  
Transverse Momentum Dependence ◽  
Hermes Data ◽  
Electron Positron Annihilation ◽  
Electron Positron ◽  
Fragmentation Functions

We calculate the transverse momentum dependence of back-to-back production of one hadron and one jet in electron-positron annihilation, i.e., e+e- → h jet X, at Q2 = 100 GeV2. We use the parameters of the transverse-momentum-dependent (TMD) fragmentation functions we recently extracted from HERMES data at 2.4 GeV2. We apply TMD evolution according to two different approaches and using different parameters for the so-called nonperturbative part of TMD evolution. We discuss the differences in our predictions and how experimental measurements could discriminate between different implementations of TMD evolution and different choices of nonperturbative parameters.

Effective Field Theory in Particle Physics and Cosmology

2020 ◽  
Keyword(s):  
Field Theory ◽  
Effective Field Theory ◽  
Particle Physics ◽  
Large Scale ◽  
Effective Field ◽  
Effective Theory ◽  
Soft Collinear Effective Theory ◽  
Multiple Length Scales ◽  
Cosmological Observations ◽  
Standard Models

Effective field theory (EFT) is a general method for describing quantum systems with multiple-length scales in a tractable fashion. It allows us to perform precise calculations in established models (such as the standard models of particle physics and cosmology), as well as to concisely parametrize possible effects from physics beyond the standard models. EFTs have become key tools in the theoretical analysis of particle physics experiments and cosmological observations, despite being absent from many textbooks. This volume aims to provide a comprehensive introduction to many of the EFTs in use today, and covers topics that include large-scale structure, WIMPs, dark matter, heavy quark effective theory, flavour physics, soft-collinear effective theory, and more.

scholarly journals Consistent treatment of rapidity divergence in soft-collinear effective theory

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Junegone Chay ◽  
Chul Kim
Keyword(s):  
Heavy Quark ◽  
Soft Mode ◽  
Form Factors ◽  
Effective Theory ◽  
Large Rapidity ◽  
Soft Modes ◽  
Heavy Quark Mass ◽  
Soft Collinear Effective Theory ◽  
Matching Procedure ◽  
Consistent Treatment

Abstract In soft-collinear effective theory, we analyze the structure of rapidity divergence due to the collinear and soft modes residing in disparate phase spaces. The idea of an effective theory is applied to a system of collinear modes with large rapidity and soft modes with small rapidity. The large-rapidity (collinear) modes are integrated out to obtain the effective theory for the small-rapidity (soft) modes. The full SCET with the collinear and soft modes should be matched onto the soft theory at the rapidity boundary, and the matching procedure becomes exactly the zero-bin subtraction. The large-rapidity region is out of reach for the soft mode, which results in the rapidity divergence. The rapidity divergence in the collinear sector comes from the zero-bin subtraction, which ensures the cancellation of the rapidity divergences from the soft and collinear sectors. In order to treat the rapidity divergence, we construct the rapidity regulators consistently for all the modes. They are generalized by assigning independent rapidity scales for different collinear directions. The soft regulator incorporates the correct directional dependence when the innate collinear directions are not back-to-back, which is discussed in the N-jet operator. As an application, we consider the Sudakov form factor for the back-to-back collinear current and the soft-collinear current, where the soft rapidity regulator for a soft quark is developed. We extend the analysis to the boosted heavy quark sector and exploit the delicacy with the presence of the heavy quark mass. We present the resummed results of large logarithms in the form factors for various currents with the light and the heavy quarks, employing the renormalization group evolution on the renormalization and the rapidity scales.

scholarly journals Massive gravity from double copy

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Arshia Momeni ◽  
Justinas Rumbutis ◽  
Andrew J. Tolley
Keyword(s):  
Sigma Model ◽  
Massive Gravity ◽  
Effective Field ◽  
Effective Theory ◽  
Nonlinear Sigma Model ◽  
Limit Theory ◽  
Four Dimensions ◽  
Yang Mills ◽  
Massive Spin ◽  
Double Copy

Abstract We consider the double copy of massive Yang-Mills theory in four dimensions, whose decoupling limit is a nonlinear sigma model. The latter may be regarded as the leading terms in the low energy effective theory of a heavy Higgs model, in which the Higgs has been integrated out. The obtained double copy effective field theory contains a massive spin-2, massive spin-1 and a massive spin-0 field, and we construct explicitly its interacting Lagrangian up to fourth order in fields. We find that up to this order, the spin-2 self interactions match those of the dRGT massive gravity theory, and that all the interactions are consistent with a Λ3 = (m2MPl)1/3 cutoff. We construct explicitly the Λ3 decoupling limit of this theory and show that it is equivalent to a bi-Galileon extension of the standard Λ3 massive gravity decoupling limit theory. Although it is known that the double copy of a nonlinear sigma model is a special Galileon, the decoupling limit of massive Yang-Mills theory is a more general Galileon theory. This demonstrates that the decoupling limit and double copy procedures do not commute and we clarify why this is the case in terms of the scaling of their kinematic factors.

THE NLO QCD CALCULATION OF SEA QUARK DISTRIBUTIONS IN THE CORGI APPROACH, BASED ON THE CONSTITUENT QUARK MODEL

2007 ◽  
Vol 22 (24) ◽  
pp. 4519-4535 ◽  
Author(s):  
A. MIRJALILI ◽  
K. KESHAVARZIAN
Keyword(s):  
Quark Model ◽  
Mellin Transform ◽  
Constituent Quark ◽  
Constituent Quark Model ◽  
Standard Approach ◽  
Unknown Parameters ◽  
Electron Positron Annihilation ◽  
Electron Positron ◽  
Physical Scale ◽  
Good Agreement

Sea quark distributions in the NLO approximation, based on the phenomenological valon model or constituent quark model are analyzed. We use the parametrized inverse Mellin transform technique to perform a direct fit with available experimental data and obtain the unknown parameters of the distributions. We try to extend the calculation to the NLO approximation for the singlet and nonsinglet cases in DIS phenomena. We do also the same calculation for electron–positron annihilation. The resulting sea distributions are effectively independent of the process used. The approach of complete RG improvement (CORGI) is employed and the results are compared with the standard approach of perturbative QCD in the [Formula: see text] scheme with a physical scale. The comparisons with data are in good agreement. As is expected, the results in the CORGI approach indicate a better agreement to the data than the NLO calculation in the standard approach.

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