Abstract
We propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the qT spectra of gauge bosons (γ∗, Higgs) in pp collisions in the regime of low (but perturbative) transverse momentum qT as a specific example. First we introduce a scheme to choose the factorization scale for virtuality in momentum space instead of in impact parameter space, allowing us to avoid integrating over (or cutting off) a Landau pole in the inverse Fourier transform of the latter to the former. The factorization scale for rapidity is still chosen as a function of impact parameter b, but in such a way designed to obtain a Gaussian form (in ln b) for the exponentiated rapidity evolution kernel, guaranteeing convergence of the b integral. We then apply this scheme to obtain the qT spectra for Drell-Yan and Higgs production at NNLL accuracy. In addition, using this scheme we are able to obtain a fast semi-analytic formula for the perturbative resummed cross sections in momentum space: analytic in its dependence on all physical variables at each order of logarithmic accuracy, up to a numerical expansion for the pure mathematical Bessel function in the inverse Fourier transform that needs to be performed just once for all observables and kinematics, to any desired accuracy.
Highlights
The transverse momentum spectra of gauge bosons is well trodden territory
We propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the qT spectra of gauge bosons (γ∗, Higgs) in pp collisions in the regime of low transverse momentum qT as a specific example
We took a fresh look at resummation for transverse momentum spectra of gauge bosons in momentum space
Summary
The transverse momentum spectra of gauge bosons is well trodden territory. They are important for measurements of, e.g. Higgs production, as well as the dynamics of QCD in Drell-Yan (DY) processes. (For DY, γCt2 = 0.) RG evolution of each factor — hard, soft, and collinear — in both virtuality and rapidity space from scales where the logs are minimized, namely, μH ∼ Q, μT ∼ Mt and, naively, μS,f ∼ 1/b0 for the virtuality scales, while νS ∼ μS and νf ∼ Q for the rapidity scales, to the common scales μ, ν achieve resummation of the large logs, to an order of accuracy determined by the order to which the anomalous dimensions and boundary conditions for each function are known and included
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