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Combined threshold and transverse momentum resummation for inclusive observables
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Journal Article
Combined threshold and transverse momentum resummation for inclusive observables
2017
Overview
A
bstract
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.
Publisher
Springer Berlin Heidelberg,Springer Nature B.V
