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Register a new userA fast and accurate method for perturbative resummation of transverse momentum-dependent observables
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We propose a novel strategy for the perturbative resummation of transverse momentum-dependent (TMD) observables, using the $q_T$ spectra of gauge bosons ($gamma^*$, Higgs) in $pp$ collisions in the regime of low (but perturbative) transverse momentum $q_T$ 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 $q_T$ 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.
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We compute the quark and gluon transverse momentum dependent parton distribution functions at next-to-next-to-next-to-leading order (N$^3$LO) in perturbative QCD. Our calculation is based on an expansion of the differential Higgs boson and Drell-Yan production cross sections about their collinear limit. This method allows us to employ cutting edge techniques for the computation of cross sections to extract the universal building blocks in question. The corresponding perturbative matching kernels for all channels are expressed in terms of simple harmonic polylogarithms up to weight five. As a byproduct, we confirm a previous computation of the soft function for transverse momentum factorization at N$^3$LO. Our results are the last missing ingredient to extend the $q_T$ subtraction methods to N$^3$LO and to obtain resummed $q_T$ spectra at N$^3$LL$^prime$ accuracy both for gluon as well as for quark initiated processes.
Transverse momentum dependent (TMD) distributions at small x exhibit a rich infinite twist structure that encompasses the leading twist (partonic) distributions as well as the physics of gluon saturation. Progress to further the connection between the standard TMD framework at moderate x and small x has been recently made. In this context, we show that light cone Wilson line operators at small-x can be formulated in terms of transverse gauge links. This new formulation of small x operators allows a direct matching with the standard leading twist gluon TMD distributions and provides an efficient and general prescription for computing TMD distributions at small x beyond leading twist.
In this contribution, we will present a short overview of the transverse momentum dependent (TMD) approach as a tool for studying the 3-dimensional structure of hadrons in high-energy (un)polarized hadron collisions. We will then summarize the present status of a running research programme that aims at constraining the poorly known transverse momentum dependent gluon Sivers function, through the study of single spin asymmetries in quarkonium (mainly $J/psi$), pion, and $D$-meson production in polarized proton-proton collisions at RHIC. Finally, we will shortly discuss perspectives for this field of research, emphasizing in particular its role in the physics programme of LHC in the fixed-target setup and NICA.
The transverse momentum distributions of various hadrons produced in most central Pb+Pb collisions at LHC energy Root(s_NN) = 2.76 TeV have been studied using our earlier proposed unified statistical thermal freeze-out model. The calculated results are found to be in good agreement with the experimental data measured by the ALICE experiment. The model calculation fits provide the thermal freeze-out conditions in terms of the temperature and collective flow effect parameters for different particle species. Interestingly the model parameter fits reveal a strong collective flow in the system which appears to be a consequence of the increasing particle density at LHC. The model used incorporates a longitudinal as well as transverse hydrodynamic flow. The chemical potential has been assumed to be nearly equal to zero for the bulk of the matter owing to a high degree of nuclear transparency effect at such energies. The contributions from heavier decay resonances are also taken into account in our calculations.
Broadening of the transverse momentum of a parton propagating through a medium is treated using the color dipole formalism, which has the advantage of being a well developed phenomenology in deep-inelastic scattering and soft processes. Within this approach, nuclear broadening should be treated as color filtering, i.e. absorption of large-size dipoles leading to diminishing (enlarged) transverse separation (momentum). We also present a more intuitive derivation based on the classic scattering theory of Moli`ere. This derivation helps to understand the origin of the dipole cross section, part of which comes from attenuation of the quark, while another part is due to multiple interactions of the quark. It also demonstrates that the lowest-order rescattering term provides an A-dependence very different from the generally accepted A^{1/3} behavior. The effect of broadening increases with energy, and we evaluate it using different phenomenological models for the unintegrated gluon density. Although the process is dominated by soft interactions, the phenomenology we use is tested using hadronic cross section data.
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