Gaining analytic control of parton showers

Parton showers are widely used to generate fully exclusive final states needed to compare theoretical models to experimental observations. While, in general, parton showers give a good description of the experimental data, the precise functional form of the probability distribution underlying the event generation is generally not known. The reason is that realistic parton showers are required to conserve four-momentum at each vertex. In this paper we investigate in detail how four-momentum conservation is enforced in a standard parton shower and why this destroys the analytic control of the probability distribution. We show how to modify a parton shower algorithm such that it conserves four-momentum at each vertex, but for which the full analytic form of the probability distribution is known. We then comment how this analytic control can be used to match matrix element calculations with parton showers, and to estimate effects of power corrections and other uncertainties in parton showers.Comment: 12 pages, 6 figures, v2: final journal versio

Full-Phase-Space Twist Expansion in Semileptonic and Radiative B-Meson Decays

We study the Lambda_QCD/M_B corrections from subleading shape functions in inclusive B-meson decays. We propose a natural and smooth interpolation from the endpoint region to the full phase space, and derive expressions for the triple differential decay rate in B -> X_u l nu and the photon energy spectrum in B -> X_s gamma. Our results are valid to order Lambda_QCD/M_B for hadronic invariant masses of order Lambda_QCD M_B and to order Lambda_QCD^2/M_B^2 for larger hadronic masses. They allow a systematic investigation of the transition between the separate regimes of the local and nonlocal expansions, and can be used to study decay distributions in any kinematic variables. We consider several examples of interest and point out that a combined measurement of hadronic energy and invariant mass provides an alternative to the extraction of |V_ub| which is largely independent of shape function effects and in principle allows a higher accuracy than the combined measurement of leptonic and hadronic invariant masses. We perform the expansion directly in QCD light-cone operators, and give a discussion of the general basis of light-cone operators. Reparametrization invariance under the change of the light-cone direction reduces the number of independent shape functions. We show that differing previous results for the lepton energy spectrum obtained from different choices of light-cone coordinates are in agreement.Comment: 41 pages, 20 figures, v2: few references added, slightly extended discussion (2 figures added to illustrate m_b dependence), v3: final journal versio

Precise predictions for B -> Xc tau nu decay distributions

We derive precise standard model predictions for the dilepton invariant mass and the tau energy distributions in inclusive B -> Xc tau nu decay. We include Lambda_QCD^2/m_b^2 and alpha_s corrections using the 1S short-distance mass scheme, and estimate shape function effects near maximal tau energy. These results can improve the sensitivity of b -> c tau nu related observables to beyond standard model physics.Comment: 7 pages, 4 figures; v2: journal versio

Theory Uncertainties for Higgs and Other Searches Using Jet Bins

Bounds on the Higgs mass from the Tevatron and LHC are determined using exclusive jet bins to maximize sensitivity. Scale variation in exclusive fixed-order predictions underestimates the perturbative uncertainty for these cross sections, due to cancellations between the perturbative corrections leading to large K factors and those that induce logarithmic sensitivity to the jet-bin boundary. To account for this, we propose that scale variation in the fixed-order calculations should be used to determine theory uncertainties for inclusive jet cross sections, whose differences yield exclusive jet cross sections. This yields a theory correlation matrix for the jet bins such that the additional uncertainty from large logarithms due to the jet boundary cancels when neighboring bins are added. This procedure is tested for H + 0, 1 jets, WW + 0 jets, and W + 0, 1, 2 jets, and found to be generally applicable. For a case where the higher-order resummation of the jet boundary corrections is known, we show that this procedure yields fixed-order uncertainties which are theoretically consistent with those obtained in the resummed calculation.Comment: 13 pages, 4 figures; v2: journal versio

The Gluon Beam Function at Two Loops

The virtuality-dependent beam function is a universal ingredient in the resummation for observables probing the virtuality of incoming partons, including N-jettiness and beam thrust. We compute the gluon beam function at two-loop order. Together with our previous results for the two-loop quark beam function, this completes the full set of virtuality-dependent beam functions at next-to-next-to-leading order (NNLO). Our results are required to account for all collinear ISR effects to the N-jettiness event shape through N^3LL order. We present numerical results for both the quark and gluon beam functions up to NNLO and N^3LL order. Numerically, the NNLO matching corrections are important. They reduce the residual matching scale dependence in the resummed beam function by about a factor of two.Comment: 21 pages, 6 figures; v2: journal versio

A case study of quark-gluon discrimination at NNLL' in comparison to parton showers

Predictions for our ability to distinguish quark and gluon jets vary by more than a factor of two between different parton showers. We study this problem using analytic resummed predictions for the thrust event shape up to NNLL' using $e^+e^- \to Z \to q \bar q$ and $e^+e^- \to H \to gg$ as proxies for quark and gluon jets. We account for hadronization effects through a nonperturbative shape function, and include an estimate of both perturbative and hadronization uncertainties. In contrast to previous studies, we find reasonable agreement between our results and predictions from both Pythia and Herwig parton showers. We find that this is due to a noticeable improvement in the description of gluon jets in the newest Herwig 7.1 compared to previous versions.Comment: 10 pages, 5 figure

Rapidity-Dependent Jet Vetoes

Jet vetoes are a prominent part of the signal selection in various analyses at the LHC. We discuss jet vetoes for which the transverse momentum of a jet is weighted by a smooth function of the jet rapidity. With a suitable choice of the rapidity-weighting function, such jet-veto variables can be factorized and resummed allowing for precise theory predictions. They thus provide a complementary way to divide phase space into exclusive jet bins. In particular, they provide a natural and theoretically clean way to implement a tight veto on central jets with the veto constraint getting looser for jets at increasingly forward rapidities. We mainly focus our discussion on the 0-jet case in color-singlet processes, using Higgs production through gluon fusion as a concrete example. For one of our jet-veto variables we compare the resummed theory prediction at NLL'+NLO with the recent differential cross section measurement by the ATLAS experiment in the $H\to\gamma\gamma$ channel, finding good agreement. We also propose that these jet-veto variables can be measured and tested against theory predictions in other SM processes, such as Drell-Yan, diphoton, and weak diboson production.Comment: 17 pages, 8 figure

Nonperturbative m_X cut effects in B -> Xs l+ l- observables

Recently, it was shown that in inclusive B -> Xs l+ l- decay, an angular decomposition provides three independent (q^2 dependent) observables. A strategy was formulated to extract all measurable Wilson coefficients in B -> Xs l+ l- from a few simple integrals of these observables in the low q^2 region. The experimental measurements in the low q^2 region require a cut on the hadronic invariant mass, which introduces a dependence on nonperturbative b quark distribution functions. The associated hadronic uncertainties could potentially limit the sensitivity of these decays to new physics. We compute the nonperturbative corrections to all three observables at leading and subleading order in the power expansion in \Lambda_QCD/m_b. We find that the subleading power corrections give sizeable corrections, of order -5% to -10% depending on the observable and the precise value of the hadronic mass cut. They cause a shift of order -0.05 GeV^2 to -0.1 GeV^2 in the zero of the forward-backward asymmetry.Comment: 11 pages, 4 figures, v2: corrected typos and Eq. (25), v3: journal versio

The Beam Thrust Cross Section for Drell-Yan at NNLL Order

At the LHC and Tevatron strong initial-state radiation (ISR) plays an important role. It can significantly affect the partonic luminosity available to the hard interaction or contaminate a signal with additional jets and soft radiation. An ideal process to study ISR is isolated Drell-Yan production, pp -> X l+l- without central jets, where the jet veto is provided by the hadronic event shape beam thrust tau_B. Most hadron collider event shapes are designed to study central jets. In contrast, requiring tau_B << 1 provides an inclusive veto of central jets and measures the spectrum of ISR. For tau_B << 1 we carry out a resummation of alpha_s^n ln^m tau_B corrections at next-to-next-to-leading-logarithmic order. This is the first resummation at this order for a hadron-hadron collider event shape. Measurements of tau_B at the Tevatron and LHC can provide crucial tests of our understanding of ISR and of tau_B's utility as a central jet veto.Comment: 4 pages, 5 figures, v2: journal versio