Analytic next-to-leading order calculation of energy-energy correlation in gluon-initiated Higgs decays

Abstract

The energy-energy correlation (EEC) function in e + e − annihilation is currently the only QCD event shape observable for which we know the full analytic result at the next-to-leading order (NLO). In this work we calculate the EEC observable for gluon initiated Higgs decay analytically at NLO in the Higgs Effective Field Theory (HEFT) framework and provide the full results expressed in terms of classical polylogarithms, including the asymptotic behavior in the collinear and back-to-back limits. This observable can be, in principle, measured at the future e + e − colliders such as CEPC, ILC, FCC-ee or CLIC. It provides an interesting opportunity to simultaneously probe our understanding of the strong and Higgs sectors and can be used for the determinations of the strong coupling.

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

“…[88] to extract the collinear contact terms for the Higgs EEC using energy-conservation sum rule. We note that the two-loop jet function has also been computed explicitly [89] from taking the asymptotic expansion of the differential equation satisfied by the master integrals for the Higgs EEC at finite angle [87]. Our results in this paper for the jet function agree perfectly with the brute force calculation in Ref.…”

“…The gluon TMDFFs can be used to calculate the gluon jet function for the back-to-back resummation of the EEC in the Higgs gluonic decay [87]. Such jet functions also appear in the back-to-back resummation for TEEC [36].…”

Transverse momentum dependent PDFs at N3LO

“…Their knowledge at N 3 LO is the only missing ingredient to achieve resummation of the EEC in the back-to-back limit at N 3 LL accuracy. Note that at fixed order the full angle EEC has been calculated analytically through O(α 2 s ) [148,149]. It will also be interesting to study the collinear expansions beyond leading power to shed light on the structure of TMD factorization at subleading power, in particular on the structure of rapidity divergences at subleading power [89,150,151].…”

Rethinking jets with energy correlators: Tracks, resummation, and analytic continuation

“…Weighted observables are therefore directly expressible as matrix elements of energy flow operators. As mentioned in the introduction, the simple field theoretic definition of these objects has allowed significant recent progress in their understanding [24,[28][29][30][32][33][34][35][36].…”

“…(2) are in a sense the simplest observables in a field theory that measure the flow of energy. In particular, they inherit a number of simple theoretical properties from their direct representation as a matrix element: They have manifest symmetry properties [22,23,28,29], enjoy simple factorization properties in limits [28][29][30][31][32][33], have simple nonperturbative behavior even away from singular regions of phase space [19], can be analytically calculated to high perturbative orders [24,[34][35][36], and can be directly studied using sophisticated techniques from conformal field theory (CFT) [28,33,37,38], including at strong coupling in N ¼ 4 super Yang-Mills (SYM) using the AdS/CFT correspondence [21]. Furthermore, all infrared and collinear safe energy flow observables can be expressed in terms of these basic objects [17,18] (for recent work, see [39,40]).…”