Combined threshold and transverse momentum resummation for inclusive observables

  • Claudio Muselli
  • Stefano ForteEmail author
  • Giovanni Ridolfi
Open Access
Regular Article - Theoretical Physics


We present a combined resummation for the transverse momentum distribution of a colorless final state in perturbative QCD, expressed as a function of transverse momentum p T and the scaling variable x. Its expression satisfies three requirements: it reduces to standard transverse momentum resummation to any desired logarithmic order in the limit p T → 0 for fixed x, up to power suppressed corrections in p T; it reduces to threshold resummation to any desired logarithmic order in the limit x → 1 for fixed p T, up to power suppressed correction in 1 − x; upon integration over transverse momentum it reproduces the resummation of the total cross cross at any given logarithmic order in the threshold x → 1 limit, up to power suppressed correction in 1 − x. Its main ingredient, and our main new result, is a modified form of transverse momentum resummation, which leads to threshold resummation upon integration over p T , and for which we provide a simple closed-form analytic expression in Fourier-Mellin (b, N ) space. We give explicit coefficients up to NNLL order for the specific case of Higgs production in gluon fusion in the effective field theory limit. Our result allows for a systematic improvement of the transverse momentum distribution through threshold resummation which holds for all p T, and elucidates the relation between transverse momentum resummation and threshold resummation at the inclusive level, specifically by providing within perturbative QCD a simple derivation of the main consequence of the so-called collinear anomaly of SCET.


Perturbative QCD Resummation Higgs Physics Renormalization Group 


Open Access

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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Claudio Muselli
    • 1
  • Stefano Forte
    • 1
    Email author
  • Giovanni Ridolfi
    • 2
  1. 1.Tif Lab, Dipartimento di FisicaUniversità di Milano and INFN, Sezione di MilanoMilanoItaly
  2. 2.Dipartimento di FisicaUniversità di Genova and INFN, Sezione di GenovaGenovaItaly

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