Factorization and N^3LL_p+NNLO Predictions for the Higgs Cross Section with a Jet Veto

We have recently derived a factorization formula for the Higgs-boson production cross section in the presence of a jet veto, which allows for a systematic resummation of large Sudakov logarithms of the form alpha_s^n ln^m(p_T^veto/m_H), along with the large virtual corrections known to affect also the total cross section. Here we determine the ingredients entering this formula at two-loop accuracy. Specifically, we compute the dependence on the jet-radius parameter R, which is encoded in the two-loop coefficient of the collinear anomaly, by means of a direct, fully analytic calculation in the framework of soft-collinear effective theory. We confirm the result obtained by Banfi et al. from a related calculation in QCD, and demonstrate that factorization-breaking, soft-collinear mixing effects do not arise at leading power in p_T^veto/m_H, even for R=O(1). In addition, we extract the two-loop collinear beam functions numerically. We present detailed numerical predictions for the jet-veto cross section with partial next-to-next-to-next-to-leading logarithmic accuracy, matched to the next-to-next-to-leading order cross section in fixed-order perturbation theory. The only missing ingredients at this level of accuracy are the three-loop anomaly coefficient and the four-loop cusp anomalous dimension, whose numerical effects we estimate to be small.Comment: 43 pages, 12 figures; minor changes, references updated; version published in JHE

An Effective Field Theory for Jet Processes

Processes involving narrow jets receive perturbative corrections enhanced by logarithms of the jet opening angle and the ratio of the energies inside and outside the jets. Analyzing cone-jet processes in effective field theory, we find that in addition to soft and collinear fields their description requires degrees of freedom which are simultaneously soft and collinear to the jets. These collinear-soft particles can resolve individual collinear partons, leading to a complicated multi-Wilson-line structure of the associated operators at higher orders. Our effective field theory provides, for the first time, a factorization formula for a cone-jet process, which fully separates the physics at different energy scales. Its renormalization-group equations control all logarithmically enhanced higher-order terms, in particular also the non-global logarithms.Comment: 9 pages, 1 figure. v2: PRL versio

N-Jettiness Subtractions for gg→Hgg\to H at Subleading Power

$N$-jettiness subtractions provide a general approach for performing fully-differential next-to-next-to-leading order (NNLO) calculations. Since they are based on the physical resolution variable $N$-jettiness, $\mathcal{T}_N$, subleading power corrections in $\tau=\mathcal{T}_N/Q$, with $Q$ a hard interaction scale, can also be systematically computed. We study the structure of power corrections for $0$-jettiness, $\mathcal{T}_0$, for the $gg\to H$ process. Using the soft-collinear effective theory we analytically compute the leading power corrections $\alpha_s \tau \ln\tau$ and $\alpha_s^2 \tau \ln^3\tau$ (finding partial agreement with a previous result in the literature), and perform a detailed numerical study of the power corrections in the $gg$, $gq$, and $q\bar q$ channels. This includes a numerical extraction of the $\alpha_s\tau$ and $\alpha_s^2 \tau \ln^2\tau$ corrections, and a study of the dependence on the $\mathcal{T}_0$ definition. Including such power suppressed logarithms significantly reduces the size of missing power corrections, and hence improves the numerical efficiency of the subtraction method. Having a more detailed understanding of the power corrections for both $q\bar q$ and $gg$ initiated processes also provides insight into their universality, and hence their behavior in more complicated processes where they have not yet been analytically calculated.Comment: 16 pages, 12 figure

Automated NNLL+NLO Resummation for Jet-Veto Cross Sections

In electroweak-boson production processes with a jet veto, higher-order corrections are enhanced by logarithms of the veto scale over the invariant mass of the boson system. In this paper, we resum these Sudakov logarithms at next-to-next-to-leading logarithmic (NNLL) accuracy and match our predictions to next-to-leading order (NLO) fixed-order results. We perform the calculation in an automated way, for arbitrary electroweak final states and in the presence of kinematic cuts on the leptons produced in the decays of the electroweak bosons. The resummation is based on a factorization theorem for the cross sections into hard functions, which encode the virtual corrections to the boson production process, and beam functions, which describe the low-p_T emissions collinear to the beams. The one-loop hard functions for arbitrary processes are calculated using the MadGraph5_aMC@NLO framework, while the beam functions are process independent. We perform the resummation for a variety of processes, in particular for W+W- pair production followed by leptonic decays of the W bosons.Comment: 26 pages, 9 figures. v2: journal versio

Subleading power corrections for N-jettiness subtractions

The N-jettiness observable T[subscript N] provides a way of describing the leading singular behavior of the N-jet cross section in the τ=T[subscript N]/Q→0 limit, where Q is a hard interaction scale. We consider subleading-power corrections in the τ≪1 expansion, and employ soft-collinear effective theory to obtain analytic results for the dominant α[subscript s]τlnτ and α[superscript 2][subscript s]τln[superscript 3]τ subleading terms for thrust in e[superscript +]e[superscript -] collisions and 0-jettiness for q[bar over q]-initiated Drell-Yan–like processes at hadron colliders. These results can be used to significantly improve the numerical accuracy and stability of the N-jettiness subtraction technique for performing fixed-order calculations at next-to-leading order and next-to-next-to-leading order. They reduce the size of missing power corrections in the subtractions by an order of magnitude. We also point out that the precise definition of N-jettiness has an important impact on the size of the power corrections and thus the numerical accuracy of the subtractions. The sometimes employed definition of N-jettiness in the hadronic center-of-mass frame suffers from power corrections that grow exponentially with rapidity, causing the power expansion to deteriorate away from central rapidity. This degradation does not occur for the original N-jettiness definition, which explicitly accounts for the boost of the Born process relative to the frame of the hadronic collision, and has a well-behaved power expansion throughout the entire phase space. Integrated over rapidity, using this N-jettiness definition in the subtractions yields another order of magnitude improvement compared to employing the hadronic-frame definition.United States. Dept. of Energy. Office of Nuclear Physics (Contract DESC0011090)United States. Dept. of Energy. Office of High Energy Physics (Contract DE-AC02-05CH11231)Lawrence Berkeley National LaboratorySimons Foundation (Investigator Grant 327942

N-jettiness Subtractions

Recently significant advances have been achieved in precision calculations for the LHC. I will focus on the use of N-jettiness subtractions for generic NNLO calculations and discuss the relevant factorization theorem and perturbative ingredients, based on an effective field theory approach. Furthermore, I will discuss the recent progress in calculating subleading power corrections, which allow to improve the numerical accuracy and stability of the subtraction method significantly. Also I will examine how the choice of the N-jettiness observable affects the size of power corrections

Erratum to: Factorization and resummation for jet processes

From a detailed analysis of cone-jet cross sections in effective field theory, we obtain novel factorization theorems which separate the physics associated with different energy scales present in such processes. The relevant low-energy physics is encoded in Wilson lines along the directions of the energetic particles inside the jets. This multi-Wilson-line structure is present even for narrow-cone jets due to the relevance of small-angle soft radiation. We discuss the renormalization-group equations satisfied by these operators. Their solution resums all logarithmically enhanced contributions to such processes, including non-global logarithms. Such logarithms arise in many observables, in particular whenever hard phase-space constraints are imposed, and are not captured with standard resummation techniques. Our formalism provides the basis for higher-order logarithmic resummations of jet and other non-global observables. As a nontrivial consistency check, we use it to obtain explicit two-loop results for all logarithmically enhanced terms in cone-jet cross sections and verify those against numerical fixed-order computations

Erratum to: Factorization and resummation for jet processes

Equations (5.6) and (5.7) in the original paper were missing a sign from the sum over gluon polarizations. As a consequence, the sign of the anomalous dimension (5.11) must be changed