One-loop splitting amplitudes in gauge theory

Many experimental analyses separate events into exclusive jet bins, using a jet algorithm to cluster the final state and then veto on jets. Jet clustering induces logarithmic dependence on the jet radius R in the cross section for exclusive jet bins, a dependence that is poorly controlled due to the non-global nature of the clustering. At jet radii of experimental interest, the leading order (LO) clustering effects are numerically significant, but the higher order effects are currently unknown. We rectify this situation by calculating the most important part of the next-to-leading order (NLO) clustering logarithms of R for any 0-jet process, which enter as O(α 3 s ) corrections to the cross section. The calculation blends subtraction methods for NLO calculations with factorization properties of QCD and soft-collinear effective theory (SCET). We compare the size of the known LO and new NLO clustering logarithms and find that the impact of the NLO terms on the 0-jet cross section in Higgs production is small. This brings clustering effects under better control and may be used to improve uncertainty estimates on cross sections with a jet veto.

Section: Jhep03(2014)119mentioning

confidence: 99%

Jet veto clustering logarithms beyond leading order

Alioli

Walsh

2014

“…Explicit results for the splitting amplitudes Split (1) in d = 4−2ǫ dimensions (or, equivalently, the results to all orders in the ǫ expansion) were obtained in Refs. [12,25].…”

Section: Introductionmentioning

confidence: 99%

Space-like (vs. time-like) collinear limits in QCD: is factorization violated?

Catani

Florian

Rodrigo

2012

123

121

We consider the singular behaviour of QCD scattering amplitudes in kinematical configurations where two or more momenta of the external partons become collinear. At the tree level, this behaviour is known to be controlled by factorization formulae in which the singular collinear factor is universal (process independent). We show that this strict (process-independent) factorization is not valid at one-loop and higher-loop orders in the case of the collinear limit in space-like regions (e.g., collinear radiation from initial-state partons). We introduce a generalized version of all-order collinear factorization, in which the space-like singular factors retain some dependence on the momentum and colour charge of the non-collinear partons. We present explicit results on one-loop and two-loop amplitudes for both the two-parton and multiparton collinear limits. At the level of squared amplitudes and, more generally, cross sections in hadron-hadron collisions, the violation of strict collinear factorization has implications on the non-abelian structure of logarithmically-enhanced terms in perturbative calculations (starting from the next-to-next-to-leading order) and on various factorization issues of mass singularities (starting from the next-tonext-to-next-to-leading order).

“…On the other hand, the requirement of building m-jets from (m + 1)-partons allows one of the final state partons to become unresolved, leading to implicit local infrared singularities which become explicit only after integration over the unresolved patch of the final state (m + 1)-parton phase space. The single unresolved infrared singularity structure of one-and two-loop amplitudes has been studied in [78][79][80][81][82][83][84][85][86][87][88][89][90].…”

Section: Real-virtual Antenna Subtraction At Nnlomentioning

confidence: 99%

“…In single unresolved limits, the behaviour of (m+3)-parton one-loop amplitudes is described by the sum of two different contributions [78][79][80][81][82]: a single unresolved tree-level factor times a (m + 2)-parton one-loop amplitude and a single unresolved one-loop factor times a (m+2)-parton tree-level amplitude, as illustrated in Figure 1. Accordingly, we construct the one-loop single unresolved subtraction term from products of tree-and one-loop antenna functions with one-loop and tree-amplitudes respectively.…”

Section: One-loop Single-unresolved Contributions: Dσ V Sa N N Lomentioning

confidence: 99%

Real-virtual corrections for gluon scattering at NNLO

Ridder

Glover

Pires

2012

We use the antenna subtraction method to isolate the mixed real-virtual infrared singularities present in gluonic scattering amplitudes at next-to-next-to-leading order. In a previous paper, we derived the subtraction term that rendered the double real radiation tree-level process finite in the single and double unresolved regions of phase space. Here, we show how to construct the real-virtual subtraction term using antenna functions with both initial-and final-state partons which removes the explicit infrared poles present in the one-loop amplitude, as well as the implicit singularities that occur in the soft and collinear limits. As an explicit example, we write down the subtraction term that describes the single unresolved contributions from the five-gluon one-loop process. The infrared poles are explicitly and locally cancelled in all regions of phase space prior to integration, leaving a finite remainder that can be safely evaluated numerically in four-dimensions. We show numerically that the subtraction term correctly approximates the matrix elements in the various single unresolved configurations.