Factorization of the dijet cross section in electron-positron annihilation with jet algorithms

Abstract

We analyze the effects of jet algorithms on each factorized part of the dijet cross sections in e + e − annihilation using the soft-collinear effective theory. The jet function and the soft function with a cone-type jet algorithm and the Sterman-Weinberg jet algorithm are computed to nextto-leading order in α s , and are shown to be infrared finite using pure dimensional regularization. The integrated and unintegrated jet functions are presented, and compared with other types of jet functions. *

Jet angularity measurements for single inclusive jet production

“…In particular, the ln R dependence of the different functions is of interest and the obtained relation between the two cases may facilitate future higher order calculations for the inclusive jet spectrum. For exclusive jet production, a similar relation was obtained in [17,58] between the "measured" and "unmeasured" jet functions. The notion (un)measured jet function corresponds to jets where an additional measurement like the jet angularity is or is not performed.…”

“…Here we follow the procedure used in [17] for exclusive jet production and we include the known one-loop power corrections when performing the integration. Alternatively, in [58] the authors used a different power counting, τ 0 ∼ R 2 , when deriving the angularity measured cross section which can then be integrated up to the maximally allowed τ 0 . Note that only the collinear and soft functions discussed in sections 2.4 and 2.5 above depend on τ 0 , whereas the hard matching coefficients H ij of section 2.3 are τ 0 independent.…”

Heavy quark jet fragmentation

“…The result is IR finite. Moreover it does not involve the term ln(µ 2 /m 2 ), which represents the low energy dynamics with fluctuations of order p 2 ∼ m 2 if we consider the limit E J R m. We also checked that, as m goes to zero, J Q (µ; E J R , m) becomes the same as the integrated jet function initiated by a light quark, of which the NLO results are [40][41][42]…”

One-loop jet functions by geometric subtraction

“…Resummation at NLL includes the two-loop cusp anomalous dimension and one-loop (non-cusp) anomalous dimensions. Jet functions have been calculated for a wide range of observables, including the invariant mass [18][19][20][21][22][23], the family of e + e − event shapes called angularities with respect to the thrust axis [24][25][26] or Winner-Take-All axis [27,28], Sterman-Weinberg jets [29,30], the cone and the k T family of jet algorithms for exclusive [30,31] and inclusive [32,33] jet production. Jet functions have also been considered for a range of jet substructure observables, such as the jet shape [34][35][36].…”