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 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 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 Factorization of e+e− → H X cross section, differential in zh, PT and thrust, in the 2-jet limit

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
M. Boglione ◽  
A. Simonelli
Keyword(s):  
Transverse Momentum ◽  
Cross Section ◽  
Belle Collaboration ◽  
Hadron Production ◽  
Leading Order ◽  
Transverse Momentum Dependent ◽  
Factorization Scheme ◽  
Phenomenological Studies ◽  
Cross Section Differential ◽  
Perturbative Part

Abstract Factorizing the cross section for single hadron production in e+e− annihilations is a highly non trivial task when the transverse momentum of the outgoing hadron with respect to the thrust axis is taken into account. We work in a scheme that allows to factorize the e+e−→ H X cross section as a convolution of a calculable hard coefficient and a Transverse Momentum Dependent (TMD) fragmentation function. The result, differential in zh, PT and thrust, will be given to all orders in perturbation theory and explicitly computed to Next to Leading Order (NLO) and Next to Leading Log (NLL) accuracy. The predictions obtained from our computation, applying the simplest and most natural ansatz to model the non-perturbative part of the TMD, are in exceptional agreement with the experimental measurements of the BELLE Collaboration. The factorization scheme we propose relates the TMD parton densities defined in 1-hadron and 2-hadron processes, restoring the possi- bility to perform global phenomenological studies of TMD physics including experimental data from semi-inclusive deep inelastic scattering, Drell-Yan processes, e+e−→ H1H2X and e+e−→ H X annihilations.

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 JET QUENCHING PARAMETER VIA SOFT COLLINEAR EFFECTIVE THEORY (SCET)

2011 ◽  
Vol 20 (07) ◽  
pp. 1610-1615 ◽  
Author(s):  
FRANCESCO D'ERAMO ◽  
HONG LIU ◽  
KRISHNA RAJAGOPAL
Keyword(s):  
Transverse Momentum ◽  
Quark Gluon Plasma ◽  
Gluon Plasma ◽  
Jet Quenching ◽  
Effective Theory ◽  
Strongly Coupled ◽  
Expectation Value ◽  
Soft Collinear Effective Theory ◽  
Strongly Coupled Plasma ◽  
The Fourier Transform

We analyze the transverse momentum broadening in the absence of radiation of an energetic parton propagating through quark-gluon plasma via Soft Collinear Effective Theory (SCET). We show that the probability for picking up transverse momentum k⊥ is given by the Fourier transform of the expectation value of two transversely separated light-like path-ordered Wilson lines. The subtleties about the ordering of operators do not change the [Formula: see text] value for the strongly coupled plasma of [Formula: see text] SYM theory.

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.

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.

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