Introduction to GPDs and TMDs

Diehl, Markus

doi:10.48550/arxiv.1512.01328

Cited by 6 publications

(10 citation statements)

References 45 publications

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“…Γ (1,0) β (2,0) [β (1,0) ] 2 + 2D (1,0) The result for D (3,0) (0) has been recently computed in [18]. The rest can be found also in [15].…”

Section: Appendix a Anomalous Dimensionsmentioning

confidence: 93%

“…Transverse-momentum-dependent parton distribution and fragmentation functions (TMDs in general) encode the 3dimensional dynamics of partons in momentum space (see, e.g., Refs. [1][2][3] for recent reviews).…”

Section: Motivationmentioning

confidence: 99%

“…(A10) in [11] by replacing the color factor (T F ) by the proper charge factor (N c Q 2 i ). Notice that we have included a factor N c , which accounts for the color multiplicity of the quark 3 .…”

Section: Qed Corrections For F 1 At Large Transverse Momentummentioning

confidence: 99%

“…The cusp anomalous dimension Γ is: The coefficients of the D term are D (1,0) (L ⊥ ) = Γ (1,0) 2β (1,0) β (1,0) L ⊥ + D (1,0) (0) , D (2,0) (L ⊥ ) = Γ (1,0) 4β (1,0) β (1,0) L ⊥ 2 + Γ (2,0) 2β (1,0) + D (1,0) (0) β (1,0) L ⊥ + D (2,0) (0) , D (3,0) (L ⊥ ) = Γ (1,0) 6β (1,0) β (1,0)…”

Section: Appendix a Anomalous Dimensionsmentioning

confidence: 99%

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QCD×QED evolution of TMDs

Bacchetta

Echevarría

2019

Physics Letters B

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We consider for the first time the QED corrections to the evolution of (un)polarized quark and gluon transverse-momentum-dependent distribution and fragmentation functions (TMDs in general). By extending their operator definition to QCD×QED, we provide the mixed new anomalous dimensions up to O(α s α) and the pure QED ones up to O(α 2 ). These new corrections are universal for all TMDs up to the flavor of the considered parton, i.e., the full flavor universality of TMD evolution found in pure QCD is broken in QCD×QED by the presence of the electric charge. In addition, we provide the leading-order QED corrections to the matching coefficients of the unpolarized quark TMD parton distribution function onto its integrated counterparts at O(α 0 s α).

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“…Γ (1,0) β (2,0) [β (1,0) ] 2 + 2D (1,0) The result for D (3,0) (0) has been recently computed in [18]. The rest can be found also in [15].…”

Section: Appendix a Anomalous Dimensionsmentioning

confidence: 93%

Section: Motivationmentioning

confidence: 99%

Section: Qed Corrections For F 1 At Large Transverse Momentummentioning

confidence: 99%

Section: Appendix a Anomalous Dimensionsmentioning

confidence: 99%

See 2 more Smart Citations

QCD×QED evolution of TMDs

Bacchetta

Echevarría

2019

Physics Letters B

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“…Given some kinematics imposed by an underlying scattering process, one can consider a restricted class of matrix elements for which either z + = 0 or z − = 0. In this case the matrix elements reduce to what is known as generalized transverse momentum dependent parton distribution functions (GTMDPDFs or simply GTMDs) [7][8][9] (see also [10,11], and a recent review in [12]). These hadronic quantities are off-forward matrix elements with explicit dependence on the longitudinal and the transverse momentum components of partons inside hadrons.…”

Section: Motivationmentioning

confidence: 99%

Proper definition and evolution of generalized transverse momentum dependent distributions

et al. 2016

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We consider one of the most fundamental sets of hadronic matrix elements, namely the generalized transverse momentum dependent distributions (GTMDs), and argue that their existing definitions lack proper evolution properties. By exploiting the similarity of GTMDs with the much better understood transverse momentum distributions, we argue that the existing definitions of GTMDs have to include an additional dependence on soft gluon radiation in order to render them properly defined. With this, we manage to obtain the evolution kernel of all (un)polarized quark and gluon GTMDs, which turns out to be spin independent. As a byproduct, all large logarithms can be resummed up to next-to-next-to-leading-logarithmic accuracy with the currently known perturbative ingredients. I. MOTIVATIONIt has been known for quite some time that hadronic matrix elements such as generalized parton distributions [1-3] (GPDs) and transverse momentum dependent parton distribution/fragmentation functions [4-6] (TMDs in general) are indispensable objects for studying fundamental properties of hadrons. With them one can probe nucleon tomography by investigating their spin and three-dimensional momentum distributions.More recently a new class of hadronic matrix elements was introduced, which generalizes both GPDs and TMDs. In [7], correlation functions which describe off-forward scattering amplitudes were introduced, where the bi-local partonic fields are separated in all three light-front coordinates: (z + , z − and z ⊥ ). Given some kinematics imposed by an underlying scattering process, one can consider a restricted class of matrix elements for which either z + = 0 or z − = 0. In this case the matrix elements reduce to what is known as generalized transverse momentum dependent parton distribution functions (GTMDPDFs or simply GTMDs) [7-9] (see also [10,11], and a recent review in [12]). These hadronic quantities are off-forward matrix elements with explicit dependence on the longitudinal and the transverse momentum components of partons inside hadrons. As such, they are hybrid constructs of both classes of functions: GPDs and TMD bi-local correlators. Notice that here we make a distinction between TMDs and TMD correlators, where the latter, also called unsubtracted TMDs, are ill-defined due to uncanceled spurious rapidity divergences (see discussions in, e.g., [4][5][6]).In this work we argue that the hadronic matrix elements called in the literature GTMDs, as currently formulated and analyzed, are improperly defined. The last assertion results from the observation that these matrix elements lack proper evolution properties with respect to the renormalization scale µ and the rapidity scale Q. Also their operator product expansion into generalized parton distributions breaks down even for large enough transverse momentum, contrary to what the case should be. Definitely these facts severely limit the predictive power of the underlying theory: QCD. The upshot is that such matrix elements, although formulated from the basic QCD fields and being g...

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The effective cross section for double parton scattering within a holographic AdS/QCD approach

et al. 2017

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International audienceA first attempt to apply the AdS/QCD framework for a bottom–up approach to the evaluation of the effective cross section for double parton scattering in proton–proton collisions is presented. The main goal is the analytic evaluation of the dependence of the effective cross section on the longitudinal momenta of the involved partons, obtained within the holographic Soft-Wall model. If measured in high-energy processes at hadron colliders, this momentum dependence could open a new window on 2-parton correlations in a proton

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Introduction to GPDs and TMDs

Cited by 6 publications

References 45 publications

QCD×QED evolution of TMDs

QCD×QED evolution of TMDs

Proper definition and evolution of generalized transverse momentum dependent distributions

The effective cross section for double parton scattering within a holographic AdS/QCD approach

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