Momentum-space resummation for transverse observables and the Higgs p⊥ at N3LL+NNLO

Abstract

We present an approach to the momentum-space resummation of global, recursively infrared and collinear safe observables that can vanish away from the Sudakov region. We focus on the hadro-production of a generic colour singlet, and we consider the class of observables that depend only upon the total transverse momentum of the radiation, prime examples being the transverse momentum of the singlet, and φ * in Drell-Yan pair production. We derive a resummation formula valid up to next-to-next-to-next-to-leading-logarithmic accuracy for the considered class of observables. We use this result to compute state-of-the-art predictions for the Higgs-boson transverse-momentum spectrum at the LHC at next-to-next-to-next-to-leading-logarithmic accuracy matched to fixed next-to-next-to-leading order. Our resummation formula reduces exactly to the customary resummation performed in impact-parameter space in the known cases, and it also predicts the correct power-behaved scaling of the cross section in the limit of small value of the observable. We show how this formalism is efficiently implemented by means of Monte Carlo techniques in a fully exclusive generator that allows one to apply arbitrary cuts on the Born variables for any colour singlet, as well as to automatically match the resummed results to fixed-order calculations. arXiv:1705.09127v3 [hep-ph] 15 May 2018 2 Derivation of the master formulaWe consider the resummation of a continuously global, recursive infrared and collinear (rIRC) safe [41] observable V in the reaction pp → B, B being a generic colourless system with high invariant mass M . It is instructive to work out in detail the case of NLL resummation first. This will be done in Section 2.1, where we assume that the parton densities are independent of the scale. We then discuss the inclusion of higher-order corrections in Section 2.3, and the correct treatment of the parton luminosity will be dealt with in Section 2.3.2. Finally, in Section 2.4, we discuss the connection to the impact-parameter space formulation for transverse-momentum resummation.

Resummation of boson-jet correlation at hadron colliders

“…Alternatively, the logarithms can also be resummed using renormalization group (RG) techniques and soft-collinear effective theory (SCET) [2][3][4][5] (see [6] for a review) as discussed in [7][8][9][10][11][12][13][14][15]. More recently, the resummation has been performed at next-to-next-to-next-to-leading logarithmic accuracy [16][17][18][19].…”

Transverse parton distribution and fragmentation functions at NNLO: the gluon case

“…Analytical calculations, phenomenological applications, and experimental determinations of the TMD distributions play important role in understanding the structure of hadrons [1,2]. TMDPDFs and TMDFFs have important applications in collider processes, such as Drell-Yan [3][4][5][6][7][8][9][10][11] and Higgs production [12][13][14][15][16][17][18][19], top quark pair production [20][21][22][23], hadronic J/ψ production, semi-inclusive deep-inelastic scattering [24][25][26][27][28], hadron or jet production in electron-positron annihilation [29][30][31][32][33][34], and energy correlators in both e + e − and hadron colliders [29,35,36]. The TMDPDFs and TMDFFs are intrinsically non-perturbative objects.…”

Transverse parton distribution and fragmentation functions at NNLO: the quark case

“…However, in certain regions of phase space, the transverse momenta of the partons become relevant, and one needs the transverse momentum dependent PDFs (TMDPDFs) and FFs (TMDFFs) in the corresponding factorization formulas. This is case for the small transverse momentum (Q T ) region in the Drell-Yan process [3][4][5][6][7][8][9][10][11], and also for similar regions in, e.g., semi-inclusive deep-inelastic scattering (SIDIS) [12][13][14][15][16], electron-positron annihilation to hadrons and jets [17][18][19][20][21][22], Higgs boson production [23][24][25][26][27][28][29][30], top quark pair production [31][32][33][34], as well as Energy-Energy Correlator (EEC) in the back-to-back limit at both lepton and hadron colliders [35,36]. To improve the theoretical predictions for these observables, it is desirable to have precise knowledges about these basic objects.…”