Jet substructure using semi-inclusive jet functions in SCET

Abstract

We propose a new method to evaluate jet substructure observables in inclusive jet measurements, based upon semi-inclusive jet functions in the framework of Soft Collinear Effective Theory (SCET). As a first example, we consider the jet fragmentation function, where a hadron h is identified inside a fully reconstructed jet. We introduce a new semi-inclusive fragmenting jet function, which depends on the jet radius R and the large light-cone momenta of the parton 'i' initiating the jet (ω), the jet (ω J ), and the hadron h (ω h ). The jet fragmentation function can then be expressed as a semi-inclusive observable, in the spirit of actual experimental measurements, rather than as an exclusive one. We demonstrate the consistency of the effective field theory treatment and standard perturbative QCD calculations of this observable at nextto-leading order (NLO). The renormalization group (RG) equation for the semi-inclusive fragmenting jet function G h i (z, z h , ω J , R, µ) are also derived and shown to follow exactly the usual timelike DGLAP evolution equations for fragmentation functions. The newly obtained RG equations can be used to perform the resummation of single logarithms of the jet radius parameter R up to next-to-leading logarithmic (NLL R ) accuracy. In combination with the fixed NLO calculation, we obtain NLO+NLL R results for the hadron distribution inside the jet. We present numerical results for pp → (jet h)X in the new framework, and find excellent agreement with existing LHC experimental data.

J/ψ Production and Polarization within a Jet

“…The plus momentum is defined for any four vector v µ as v + = v 0 + v z in a frame where the "z"-axis is along the jet direction. The factorized form of the differential cross section for J/ψ production within a jet is given by [24,26] dσ J/ψ dp T dηdz h = a,b,c…”

Using hadron-in-jet data in a global analysis of D* fragmentation functions

“…Currently, the only available data set for D ÃAE -mesons within jets is provided by the ATLAS Collaboration [26] for which the anti-k T algorithm was used with a jet-size parameter of R ¼ 0.6. However, the results for cone [46] and J E T [47] jets are also available in the literature [23,24,48].…”

“…[22][23][24]. In [22], the NLO cross section was obtained using a Monte-Carlo (MC) phase space integrator.…”

“…[23,24] analytical results were obtained using the approximation that the jet is sufficiently collimated. The NLO result of [23] was derived within the standard pQCD framework, whereas [24] employed methods within SCET for inclusive jet production [42,43], which allows for the additional resummation of single logarithms of the jet-size parameter R. At NLO accuracy, the analytical result of the cross section can be schematically written as Aþ B log R þ OðR 2 Þ. If the jet is sufficiently narrow, i.e., R ≪ 1, power corrections of the order OðR 2 Þ can be neglected.…”

“…In Ref. [24] the result was rederived within SCET. Thanks to the effective field theory treatment, the additional all-order resummation of single logarithms in the jet-size parameter α n s ln n R was achieved, yielding consistent results at NLO þ NLL R accuracy.…”