The Transverse Momentum Dependent Fragmentation Function at NNLO

Abstract

We calculate the unpolarized transverse momentum dependent fragmentation function (TMDFF) at next-to-next-to-leading order (NNLO), evaluating separately TMD soft factor and TMD collinear correlator. For the first time the cancellation of spurious rapidity divergences in a properly defined individual TMD beyond the first non-trivial order is shown. This represents a strong check of the given TMD definition. We extract the matching coefficient necessary to perform the transverse momentum resummation at next-to-next-to-next-to-leading-logarithmic accuracy. The universal character of the soft function, which enters the definition of all (un)polarized TMD distribution/fragmentation functions, facilitates the future calculation of all the other TMDs and their coefficients at NNLO, pushing forward the accuracy of theoretical predictions for the current and next generation of high energy colliders.

v2: published version. v3: small corrections as published in erratum. List of changes at the end of preprint

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Cited by in corpus (41)

• Large-Momentum Effective Theory
• Unpolarized Transverse Momentum Dependent Parton Distribution and Fragmentation Functions at next-to-next-to-leading order
• Parton Fragmentation Functions
• Analysis of vector boson production within TMD factorization
• Non-perturbative structure of semi-inclusive deep-inelastic and Drell-Yan scattering at small transverse momentum
• The Universal Transverse Momentum Dependent Soft Function at NNLO
• Extraction of unpolarized quark transverse momentum dependent parton distributions from Drell-Yan/Z-boson production
• Towards Quasi-Transverse Momentum Dependent PDFs Computable on the Lattice
• Rapidity renormalized TMD soft and beam functions at two loops
• Cancellation of Glauber gluon exchange in the double Drell-Yan process
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Quark Case
• Transverse momentum dependent distributions with jets
• Transverse momentum dependent distributions in $e^{+}{e}^{-}$ and semi-inclusive deep-inelastic scattering using jets
• Systematic analysis of double-scale evolution
• Linearly polarized gluons at next-to-next-to leading order and the Higgs transverse momentum distribution
• Proper TMD factorization for quarkonia production: $pp\to {\eta }_{c,b}$ as a study case
• Transverse Parton Distribution and Fragmentation Functions at NNLO: the Gluon Case
• Twist-2 matching of transverse momentum dependent distributions
• Computing Light-Front Wave Functions Without Light-Front Quantization: A Large-Momentum Effective Theory Approach
• Collinear matching for Sivers function at next-to-leading order
• Energy-energy correlators in Deep Inelastic Scattering
• TMD Fragmentation Functions at N${}^3$LO
• Transverse-momentum-dependent wave functions and Soft functions at one-loop in Large Momentum Effective Theory
• The Asymptotic Form of Non-Global Logarithms, Black Disc Saturation, and Gluonic Deserts
• Soft factors for double parton scattering at NNLO
• Connections between collinear and transverse-momentum-dependent polarized observables within the Collins-Soper-Sterman formalism
• Joint thrust and TMD resummation in electron-positron and electron-proton collisions
• Double parton distribution of valence quarks in the pion in chiral quark models
• Prospects for quarkonium studies at the high-luminosity LHC
• Structure of rapidity divergences in soft factors
• Quarkonium TMD fragmentation functions in NRQCD
• Transverse momentum moments
• Collinear functions for QCD resummations
• Quark-Jet model for transverse momentum dependent fragmentation functions
• QCD$\times$QED evolution of TMDs
• Rapidity evolution of TMDs with running coupling
• $q_T$-slicing with multiple jets
• W-boson production in TMD factorization
• Nucleon tomography. What can we do better today than Rutherford 100 years ago?
• Revisiting the time-ordering issue of TMD soft factors: causality, coordinate space analyticity and new equalities
• Linearly polarised Transverse Momentum Dependent Parton Distribution Function at NNLO in QCD