The two-loop hemisphere soft function

Abstract

The hemisphere soft function is calculated to order α 2 s . This is the first multi-scale soft function calculated to two loops. The renormalization scale dependence of the result agrees exactly with the prediction from effective field theory. This fixes the unknown coefficients of the singular parts of the two-loop thrust and heavy-jet mass distributions. There are four such coefficients, for 2 event shapes and 2 color structures, which are shown to be in excellent agreement with previous numerical extraction. The asymptotic behavior of the soft function has double logs in the C F C A color structure, which agree with non-global log calculations, but also has sub-leading single logs for both the C F C A and C F T F n f color structures. The general form of the soft function is complicated, does not factorize in a simple way, and disagrees with the Hoang-Kluth ansatz. The exact hemisphere soft function will remove one source of uncertainty on the α s fits from e + e − event shapes.

Studies of jet mass in dijet and W/Z + jet events

“…To understand these techniques in the context of searches for new phenomena, the jet mass must be well-modeled through leading-order (LO) or next-toleading-order (NLO) Monte Carlo (MC) simulations. Much recent theoretical work in QCD has focused on the computation of jet mass, including predictions using advances in an effective field theory of jets (soft collinear effective theory, SCET) [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. Studies of the kind reported in the present analysis can provide an understanding of the extent to which MC simulations that match matrix-element partons with parton showers can model the observed internal jet structure.…”

NNLL Resummation for Jet Broadening

“…Among the mixed virtual-real and double real emissions, only the diagrams in Figure 3 give nonvanishing contributions. The same matrix elements also arise in other two-loop computations of soft functions [24][25][26][27][28][29][30][31][32], what makes our case different are the phase-space constraints and the necessity of working with an additional analytic regulator. In the following, we denote the individual contributions of these diagrams to the soft function by…”

Color-singlet production at NNLO in MCFM

“…[69,70]. The corresponding two-loop soft functions are also known for zero-jettiness [71,72] and for general Njettiness [73]. The first process calculated at NNLO using this method was pp → W +jet [16], followed by calculations of the pp → Higgs+jet [8] and pp → Z +jet [18] processes, and by detailed phenomenological studies of these processes at this order [74][75][76].…”