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 Factorization at subleading power and endpoint divergences in h → γγ decay. Part II. Renormalization and scale evolution

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ze Long Liu ◽  
Bianka Mecaj ◽  
Matthias Neubert ◽  
Xing Wang
Keyword(s):  
Decay Amplitude ◽  
Factorization Theorem ◽  
Effective Theory ◽  
Operator Matrix ◽  
Quark Loop ◽  
Perfect Agreement ◽  
Soft Collinear Effective Theory ◽  
Convolution Integrals ◽  
Factorization Formula ◽  
Massless Quark

Abstract Building on the recent derivation of a bare factorization theorem for the b-quark induced contribution to the h → γγ decay amplitude based on soft-collinear effective theory, we derive the first renormalized factorization theorem for a process described at subleading power in scale ratios, where λ = mb/Mh « 1 in our case. We prove two refactorization conditions for a matching coefficient and an operator matrix element in the endpoint region, where they exhibit singularities giving rise to divergent convolution integrals. The refactorization conditions ensure that the dependence of the decay amplitude on the rapidity regulator, which regularizes the endpoint singularities, cancels out to all orders of perturbation theory. We establish the renormalized form of the factorization formula, proving that extra contributions arising from the fact that “endpoint regularization” does not commute with renormalization can be absorbed, to all orders, by a redefinition of one of the matching coefficients. We derive the renormalization-group evolution equation satisfied by all quantities in the factorization formula and use them to predict the large logarithms of order $$ {\alpha \alpha}_s^2{L}^k $$ αα s 2 L k in the three-loop decay amplitude, where $$ L=\ln \left(-{M}_h^2/{m}_b^2\right) $$ L = ln − M h 2 / m b 2 and k = 6, 5, 4, 3. We find perfect agreement with existing numerical results for the amplitude and analytical results for the three-loop contributions involving a massless quark loop. On the other hand, we disagree with the results of previous attempts to predict the series of subleading logarithms $$ \sim {\alpha \alpha}_s^n{L}^{2n+1} $$ ∼ αα s n L 2 n + 1 .

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 TRANSVERSE MOMENTUM DISTRIBUTIONS FROM EFFECTIVE FIELD THEORY

2011 ◽  
Vol 04 ◽  
pp. 106-114
Author(s):  
SONNY MANTRY ◽  
FRANK PETRIELLO
Keyword(s):  
Transverse Momentum ◽  
Z Boson ◽  
Effective Field ◽  
Factorization Theorem ◽  
Effective Theory ◽  
Gauge Bosons ◽  
Soft Collinear Effective Theory ◽  
Factorization Formula ◽  
Momentum Distributions ◽  
Momentum Function

We present a factorization theorem for the low transverse momentum (pT) and rapidity (Y) distribution of the Higgs and electroweak gauge bosons using the Soft-Collinear Effective Theory. In the region M ≫ pT ≫ ΛQCD, where M denotes the mass of the electroweak object, the factorization formula is given in terms of perturbatively calculable functions and the standard PDFs. For pT ~ ΛQCD, the factorization theorem is given in terms of non-perturbative Impact-parameter Beam Functions (iBFs) and an Inverse Soft Function (iSF). The iBFs correspond to completely unintegrated PDFs and can be interesting probes of momentum distributions in the nucleon. The iBFs and the iSF are grouped together and written as a product of a gauge invariant and non-perturbative Transverse Momentum Function (TMF) with the standard PDFs. We present results of NLL resummation for the Higgs and Z-boson distributions and give a comparison with Tevatron data.

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.

THE HEART OF FACTORIZATION

2014 ◽  
Vol 25 ◽  
pp. 1460014
Author(s):  
MATTHEW D. SCHWARTZ
Keyword(s):  
Effective Field Theory ◽  
Recent Progress ◽  
Gauge Theories ◽  
Effective Field ◽  
Effective Theory ◽  
Tree Level ◽  
Soft Collinear Effective Theory ◽  
Factorization Formula ◽  
The Many ◽  
Traditional Approaches

Factorization is at the heart of nearly any calculation in pertubative QCD. It follows from the universal behavior of gauge theories in soft and collinear limits. This talk gives a summary of recent progress on producing a more transparent understanding of factorization and connecting traditional approaches to those of Soft-Collinear Effective Theory. The main result is the formulation and proof, at tree-level, of a factorization formula in QCD. The proof exploits the many advantages of spinor helicity methods, but does not use any effective field theory tricks. Once the factorization formula is proven, the transition to an effective theory description is effortless.

scholarly journals The Evolution of Soft Collinear Effective Theory

2015 ◽  
Vol 37 ◽  
pp. 1560045 ◽  
Author(s):  
Christopher Lee
Keyword(s):  
Cross Sections ◽  
Nuclear Physics ◽  
Degrees Of Freedom ◽  
Heavy Ion ◽  
High Energy ◽  
Effective Field ◽  
Effective Theory ◽  
Ion Collisions ◽  
Soft Collinear Effective Theory ◽  
Single Scale

Soft Collinear Effective Theory (SCET) is an effective field theory of Quantum Chromodynamics (QCD) for processes where there are energetic, nearly lightlike degrees of freedom interacting with one another via soft radiation. SCET has found many applications in high-energy and nuclear physics, especially in recent years the physics of hadronic jets in e+e-, lepton-hadron, hadron-hadron, and heavy-ion collisions. SCET can be used to factorize multi-scale cross sections in these processes into single-scale hard, collinear, and soft functions, and to evolve these through the renormalization group to resum large logarithms of ratios of the scales that appear in the QCD perturbative expansion, as well as to study properties of nonperturbative effects. We overview the elementary concepts of SCET and describe how they can be applied in high-energy and nuclear physics.

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.

Sign in / Sign up

Export Citation Format

Share Document