scholarly journals Factorization ofe+e−event shape distributions with hadronic final states in soft collinear effective theory

2008 ◽  
Vol 78 (3) ◽  
Author(s):  
Christian W. Bauer ◽  
Sean Fleming ◽  
Christopher Lee ◽  
George Sterman
Keyword(s):  
Effective Theory ◽  
Event Shape ◽  
Final States ◽  
Soft Collinear Effective Theory ◽  
Hadronic Final States

Soft-Collinear Effective Theory

2020 ◽  
pp. 307-361 ◽  
Author(s):  
Thomas Becher
Keyword(s):  
Cross Sections ◽  
Vector Current ◽  
Jet Physics ◽  
Effective Theory ◽  
Event Shape ◽  
Sudakov Form Factor ◽  
Shape Variable ◽  
Soft Collinear Effective Theory ◽  
Jet Cross Sections ◽  
Event Shape Variable

The lectures that appear within this chapter provide an introduction to soft-collinear effective theory (SCET). It begins by discussing resummation for soft-photon effects in QED, including soft photons in electron–electron scattering and the expansion of loop integrals and the method of regions event-shape variables. It then covers SCET specifically, including the method of regions for the Sudakov form factor, effective Lagrangians, the vector current in SCET, and resummation by renormalization group (RG) evolution. It covers applications of SCET in jet physics, describes the characteristic feature in jet processes of Sudakov logarithms, and discusses factorization for the event-shape variable thrust and factorization and resummation for jet cross sections.

scholarly journals Massive event-shape distributions at N2LL

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Alejandro Bris ◽  
Vicent Mateu ◽  
Moritz Preisser
Keyword(s):  
Cross Sections ◽  
Numerical Study ◽  
Renormalization Group Equation ◽  
Effective Theory ◽  
Event Shape ◽  
Group Equation ◽  
Soft Collinear Effective Theory ◽  
Fixed Order ◽  
Collinear Limit ◽  
Event Shapes

Abstract In a recent paper we have shown how to optimally compute the differential and cumulative cross sections for massive event-shapes at $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s in full QCD. In the present article we complete our study by obtaining resummed expressions for non-recoil-sensitive observables to N2LL + $$ \mathcal{O}\left({\alpha}_s\right) $$ O α s precision. Our results can be used for thrust, heavy jet mass and C-parameter distributions in any massive scheme, and are easily generalized to angularities and other event shapes. We show that the so-called E- and P-schemes coincide in the collinear limit, and compute the missing pieces to achieve this level of accuracy: the P-scheme massive jet function in Soft-Collinear Effective Theory (SCET) and boosted Heavy Quark Effective Theory (bHQET). The resummed expression is subsequently matched into fixed-order QCD to extend its validity towards the tail and far- tail of the distribution. The computation of the jet function cannot be cast as the dis- continuity of a forward-scattering matrix element, and involves phase space integrals in d = 4 − 2ε dimensions. We show how to analytically solve the renormalization group equation for the P-scheme SCET jet function, which is significantly more complicated than its 2-jettiness counterpart, and derive rapidly-convergent expansions in various kinematic regimes. Finally, we perform a numerical study to pin down when mass effects become more relevant.

scholarly journals THE 1-JETTINESS EVENT-SHAPE FOR DIS WITH NNLL RESUMMATION

2014 ◽  
Vol 25 ◽  
pp. 1460041 ◽  
Author(s):  
ZHONG-BO KANG ◽  
XIAOHUI LIU ◽  
SONNY MANTRY ◽  
JIANWEI QIU
Keyword(s):  
Nuclear Physics ◽  
Quantitative Measure ◽  
Effective Theory ◽  
Event Shape ◽  
Final State ◽  
Global Event ◽  
Soft Collinear Effective Theory ◽  
Factorization Formula ◽  
Single Jet ◽  
Nuclear Targets

We propose the use of 1-jettiness, a global event shape, for exclusive single jet production in lepton-nucleus deep inelastic scattering (DIS). We derive a factorization formula, using the Soft-Collinear Effective Theory, differential in the transverse momentum and rapidity of the jet and the 1-jettiness event shape. It provides a quantitative measure of the shape of the final-state QCD radiation in the presence of the hard jet, providing a useful powerful probe of QCD and nuclear physics. For example, one expects differences in the observed pattern of QCD radiation between large and small nuclei and these can be quantified by the 1-jettiness event shape. Numerical results are given for this new DIS event shape at leading twist with resummation at the next-to-next-to-leading logarithmic (NNLL) level of accuracy, for a variety of nuclear targets. Such studies would be ideal at a future EIC or LHeC electron-ion collider, where a range of nuclear targets are planned.

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 UNIVERSAL NONPERTURBATIVE EFFECTS IN EVENT SHAPES FROM SOFT-COLLINEAR EFFECTIVE THEORY

2007 ◽  
Vol 22 (12) ◽  
pp. 835-851 ◽  
Author(s):  
CHRISTOPHER LEE
Keyword(s):  
Nonperturbative Effects ◽  
Perturbative Qcd ◽  
Energy Flow ◽  
Effective Theory ◽  
Higher Moments ◽  
Event Shape ◽  
Mean Values ◽  
Soft Collinear Effective Theory ◽  
The Mean ◽  
Soft Radiation

Two-jet event shape distributions, traditionally studied in the language of perturbative QCD, can be described naturally in soft-collinear effective theory. In this language, we demonstrate factorization of event shape distributions into perturbatively-calculable hard and jet functions and nonperturbative soft functions, and show how the latter contribute universal shifts to the mean values of various event shape distributions. Violations of universality in shifts of higher moments can give information on correlations of energy flow in soft radiation.

scholarly journals Angularity in DIS at next-to-next-to-leading log accuracy

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Jiawei Zhu ◽  
Daekyoung Kang ◽  
Tanmay Maji
Keyword(s):  
Inelastic Scattering ◽  
Deep Inelastic Scattering ◽  
Cross Section ◽  
Effective Theory ◽  
Event Shape ◽  
Soft Collinear Effective Theory ◽  
Continuous Parameter ◽  
Beam Function ◽  
Wide Range ◽  
Definition Of

Abstract Angularity is a class of event-shape observables that can be measured in deep-inelastic scattering. With its continuous parameter a one can interpolate angularity between thrust and broadening and further access beyond the region. Providing such systematic way to access various observables makes angularity attractive in analysis with event shapes. We give the definition of angularity for DIS and factorize the cross section by using soft-collinear effective theory. The factorization is valid in a wide range of a below and above thrust region but invalid in broadening limit. It contains an angularity beam function, which is new result and we give the expression at $$ \mathcal{O} $$ O (αs). We also perform large log resummation of angularity and make predictions at various values of a at next-to-next-to-leading log accuracy.

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.

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