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 PHENOMENOLOGY OF THE SIVERS EFFECT WITH TMD EVOLUTION

2012 ◽  
Vol 20 ◽  
pp. 145-152
Author(s):  
M. ANSELMINO ◽  
M. BOGLIONE ◽  
S. MELIS
Keyword(s):  
Transverse Momentum ◽  
Evolution Equations ◽  
Distribution Functions ◽  
Dependent Data ◽  
Clear Indication ◽  
Transverse Momentum Dependent ◽  
Sidis Data ◽  
Sivers Function ◽  
Theoretical Developments

Recently, theoretical developments have led to the QCD evolution equations for the unpolarized Transverse Momentum Dependent (TMD) distribution functions and for the Sivers function (TMD-evolution). We tested whether the proposed TMD-evolution can already be observed in the SIDIS data on the Sivers asymmetry. Although very preliminary, our analysis shows that data are compatible with such an evolution with a clear indication of evolution in the x-dependent data subsets.

scholarly journals Quark sivers function at small x: spin-dependent odderon and the sub-eikonal evolution

2021 ◽  
Vol 2021 (11) ◽  
Author(s):  
Yuri V. Kovchegov ◽  
M. Gabriel Santiago
Keyword(s):  
Evolution Equations ◽  
Wilson Line ◽  
Distribution Functions ◽  
Coupling Constant ◽  
Parton Distribution Functions ◽  
Transverse Momentum Dependent ◽  
Sivers Function ◽  
Small X ◽  
Dipole Scattering ◽  
Line Operator

Abstract We apply the formalism developed earlier [1, 2] for studying transverse momentum dependent parton distribution functions (TMDs) at small Bjorken x to construct the small-x asymptotics of the quark Sivers function. First, we explicitly construct the complete fundamental “polarized Wilson line” operator to sub-sub-eikonal order: this object can be used to study a variety of quark TMDs at small x. We then express the quark Sivers function in terms of dipole scattering amplitudes containing various components of the “polarized Wilson line” and show that the dominant (eikonal) term which contributes to the quark Sivers function at small x is the spin-dependent odderon, confirming the re- cent results of Dong, Zheng and Zhou [3]. Our conclusion is also similar to the case of the gluon Sivers function derived by Boer, Echevarria, Mulders and Zhou [4] (see also [5]). We also analyze the sub-eikonal corrections to the quark Sivers function using the constructed “polarized Wilson line” operator. We derive new small-x evolution equations re-summing double-logarithmic powers of αs ln2(1/x) with αs the strong coupling constant. We solve the corresponding novel evolution equations in the large-Nc limit, obtaining a sub-eikonal correction to the spin-dependent odderon contribution. We conclude that the quark Sivers function at small x receives contributions from two terms and is given by$$ {f}_{1T}^{\perp q}\left(x,{k}_T^2\right)={C}_O\left(x,{k}_T^2\right)\frac{1}{x}+{C}_1\left({k}_T^2\right){\left(\frac{1}{x}\right)}^0+\cdots $$ f 1 T ⊥ q x k T 2 = C O x k T 2 1 x + C 1 k T 2 1 x 0 + ⋯ with the function CO(x,$$ {k}_T^2 $$ k T 2 ) varying slowly with x and the ellipsis denoting the subasymptotic and sub-sub-eikonal (order-x) corrections.

scholarly journals Single Spin Asymmetry in Electroproduction of J/ψ and QCD-evolved TMD's

2015 ◽  
Vol 37 ◽  
pp. 1560069 ◽  
Author(s):  
Rohini M. Godbole ◽  
Abhiram Kaushik ◽  
Anuradha Misra ◽  
Vaibhav S. Rawoot
Keyword(s):  
Evolution Equations ◽  
Spin Asymmetry ◽  
Previous Analysis ◽  
Substantial Reduction ◽  
Dglap Evolution ◽  
Transverse Momentum Dependent ◽  
Single Spin ◽  
Sivers Function ◽  
Evolution Kernel ◽  
Perturbative Part

We estimate Sivers asymmetry in low virtuality photoproduction of J/ψ using color evaporation model and taking into account Q2- evolution of transverse momentum dependent PDF's and Sivers function. There is a substantial reduction in asymmetry as compared to our previous analysis wherein the Q2-dependence came only from DGLAP evolution of collinear part of TMDs. The estimates of asymmetry are comparable to our earlier estimates in which we had used analytical solution of only an approximated form of the evolution equations. We have also estimated asymmetry using the latest parametrization by Echevarria et al. which are based on an evolution kernel in which the perturbative part is resummed to NLL accuracy.

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 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.

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 Forward dijets in proton-nucleus collisions at next-to-leading order: the real corrections

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Edmond Iancu ◽  
Yair Mulian
Keyword(s):  
Cross Section ◽  
Soft Gluon ◽  
Effective Theory ◽  
Dglap Evolution ◽  
Leading Order ◽  
Final State ◽  
Dijet Production ◽  
The Real ◽  
First Case ◽  
Subsequent Publication

Abstract Using the CGC effective theory together with the hybrid factorisation, we study forward dijet production in proton-nucleus collisions beyond leading order. In this paper, we compute the “real” next-to-leading order (NLO) corrections, i.e. the radiative corrections associated with a three-parton final state, out of which only two are being measured. To that aim, we start by revisiting our previous results for the three-parton cross-section presented in [1]. After some reshuffling of terms, we deduce new expressions for these results, which not only look considerably simpler, but are also physically more transparent. We also correct several errors in this process. The real NLO corrections to inclusive dijet production are then obtained by integrating out the kinematics of any of the three final partons. We explicitly work out the interesting limits where the unmeasured parton is either a soft gluon, or the product of a collinear splitting. We find the expected results in both limits: the B-JIMWLK evolution of the leading-order dijet cross-section in the first case (soft gluon) and, respectively, the DGLAP evolution of the initial and final states in the second case (collinear splitting). The “virtual” NLO corrections to dijet production will be presented in a subsequent publication.

BESSEL-WEIGHTED ASYMMETRIES AND TRANSVERSE SPIN EFFECTS

2012 ◽  
Vol 20 ◽  
pp. 168-176
Author(s):  
LEONARD GAMBERG
Keyword(s):  
Transverse Momentum ◽  
Cross Section ◽  
Parton Distribution ◽  
Evolution Equations ◽  
Distribution Functions ◽  
Transverse Spin ◽  
High Transverse Momentum ◽  
Transverse Momentum Dependent ◽  
Fragmentation Functions ◽  
The Cross

We consider the cross section for semi-inclusive deep inelastic scattering in Fourier space, conjugate to the outgoing hadron's transverse momentum, where convolutions of transverse momentum dependent parton distribution functions and fragmentation functions become simple products. Individual asymmetric terms in the cross section can be projected out by means of a generalized set of weights involving Bessel functions. Advantages of employing these Bessel weights are that they suppress (divergent) contributions from high transverse momentum and that soft factors cancel in (Bessel-) weighted asymmetries. Also, the resulting compact expressions immediately connect to previous work on evolution equations for transverse momentum dependent parton distribution and fragmentation functions and to quantities accessible in lattice QCD. Bessel-weighted asymmetries are thus model independent observables that augment the description and our understanding of correlations of spin and momentum in nucleon structure.

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