The soft function for exclusive N-jet production at hadron colliders

Abstract

Abstract. The N-jettiness event shape divides phase space into N + 2 regions, each containing one jet or beam. These jet regions are insensitive to the distribution of soft radiation and, with a geometric measure for N-jettiness, have circular boundaries. We give a factorization theorem for the cross section which is fully differential in the mass of each jet, and compute the corresponding soft function at next-to-leading order (NLO). For N-jettiness, all ingredients are now available to extend NLO cross sections to resummed predictions at next-to-next-to-leading logarithmic order.Keywords: Hadron colliders, jet production, resummation. PACS: 13.87.Ce, 12.38.Cy, 13.85.Qk Talk given by T.T. Jouttenus at the PANIC 2011 conference. Preprint: The measurement of exclusive jet cross sections, where one identifies a certain number of signal jets but vetoes additional jets, is an important aspect of Higgs and new-physics searches at the LHC and Tevatron. Since the relative contributions of various signal and background channels often vary with the number of hard jets in the event, the sensitivity of the search is improved by optimizing the analysis for each separate jet bin. Thus, reliable theoretical calculations of exclusive jet cross sections are essential.The complication compared to the calculation of an inclusive N-jet cross section, where one sums over additional jets, comes from the fact that the veto on additional jets imposes a restriction on the energetic initial-and final-state radiation off the primary hard partons, as well as the overall soft radiation in the event. This restriction on additional emissions leads to the appearance of large Sudakov double logarithms in perturbation theory. For this reason, the calculation of exclusive jet cross sections is traditionally carried out with parton-shower Monte Carlo programs, where the parton shower allows one to resum the most singular leading double logarithms.An alternative analytic approach to calculate exclusive jet cross sections is possible using factorization and the methods of soft-collinear effective theory (SCET) [1]. SCET allows one to factorize the N-jet cross section into pieces depending on only one scale and resum the large logarithmic contributions. An advantage of this approach is that the resummation can be carried out to much higher orders than is possible with parton showers. Schematically, the cross section for pp → N jets (plus some nonhadronic final state like a W , Z, or Higgs if desired) can be factorized asThis formula directly applies to observables that implement a veto on additional jets. The hard function H N encodes hard virtual corrections to the underlying partonic 2 → N process, the beam functions B a,b contain the parton distributions and perturbative collinear initial-state radiation from the colliding hard partons, and the jet functions J i describe energetic collinear final-state radiation from the primary N hard partons produced in the collision. The soft function S N describes the soft radiation in the event that couples...

Combining higher-order resummation with multiple NLO calculations and parton showers in GENEVA

“…Therefore, it is important to choose a resolution variable with simple resummation properties. An example is N -jettiness, for which the complete NNLL resummation for arbitrary N is known [46,47]. For the purpose of our discussion below, we will assume that a resummed result for the spectrum and its cumulant in eq.…”

“…This flavor sum is an important consideration when implementing the master formula in Geneva, since the Monte Carlo generates events for each flavor combination, and the flavor sum is performed in the sum over events. For processes with final-state jets, the extension of the beam thrust factorization theorem to N -jettiness is known and has the schematic form [46,47] …”

Jet maximization, axis minimization, and stable cone finding

“…• 1-jettiness minimization [6][7][8][9]. This approach is based on finding a light-like jet axis n = (1,n) that minimizes 1-jettiness T 1 (n).…”

“…In this paper, we expose a surprising connection between three seemingly unrelated approaches to jet finding: jet function maximization [3][4][5], 1-jettiness minimization [6][7][8][9], and stable cone finding [10][11][12], all reviewed in Sec. II.…”

An on-shell approach to factorization

“…For example, the most accurate calculations of the Higgs-boson cross section includes contributions from logarithmically enhanced terms derived using a factorization formula [7,8]. Other examples are the inclusive photon [9][10][11][12] or W -boson [13,14] transverse momentum spectrum, the tt cross section [15,16], and jet shapes such as jet mass [17][18][19] or n-subjettiness [20,21].…”