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

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

Towards a global fit to extract the B->Xs gamma decay rate and Vub

The total B->Xs gamma decay rate and the CKM-matrix element Vub play an important role in finding indirect evidence for new physics affecting the flavor sector of the Standard Model, complementary to direct searches at the LHC and Tevatron. Their determination from inclusive B-meson decays requires the precise knowledge of the parton distribution function of the b quark in the B meson, called the shape function. We implement a new model-independent framework for the shape function with reliable uncertainties based on an expansion in a suitable set of basis functions. We present the current status of a global fit to BaBar and Belle data to extract the shape function and the B->Xs gamma decay rate.Comment: 5 pages, 9 figure

A model independent determination of the B -> Xs gamma decay rate

The goal of the SIMBA collaboration is to provide a global fit to the available measurements of inclusive B -> X_s gamma and B -> X_u l nu decays. By performing a global fit one is able to simultaneously determine the relevant normalizations, i.e. the total B -> X_s gamma rate and the CKM-matrix element |Vub|, together with the required hadronic parameters, most importantly the b-quark mass and the b-quark distribution function in the B-meson, called the shape function. In this talk, the current status on the model-independent determination of the shape function and |C7^\incl Vtb Vts*|, which parametrizes the total B -> Xs gamma rate, from a global fit to the available B -> X_s gamma measurements from Babar and Belle is presented. In particular, the theoretical uncertainties originating from variations of the different factorization scales are evaluated.Comment: Proceedings of CKM 2012, the 7th International Workshop on the CKM Unitarity Triangle, University of Cincinnati, USA, 28 September - 2 October 201

GenEvA (II): A phase space generator from a reweighted parton shower

We introduce a new efficient algorithm for phase space generation. A parton shower is used to distribute events across all of multiplicity, flavor, and phase space, and these events can then be reweighted to any desired analytic distribution. To verify this method, we reproduce the e+e- -> n jets tree-level result of traditional matrix element tools. We also show how to improve tree-level matrix elements automatically with leading-logarithmic resummation. This algorithm is particularly useful in the context of a new framework for event generation called GenEvA. In a companion paper [arXiv:0801.4026], we show how the GenEvA framework can address contemporary issues in event generation.Comment: 54 pages, 20 figures, v2: corrected typos, added reference

Shape Function Effects in B -> X_c l \nu_l

Owing to the fact that m_c^2 ~ m_b \Lambda_QCD, the endpoint region of the charged lepton energy spectrum in the inclusive decay B -> X_c l \nu_l is affected by the Fermi motion of the initial-state b quark bound in the B meson. This effect is described in QCD by shape functions. Including the mass of the final-state quark, we find that a different set of operators as employed in Ref. hep-ph/0205150 is needed for a consistent matching, when incorporating the subleading contributions in B -> X_q l \nu_l for both q = u and q = c. In addition, we modify the usual twist expansion in such a way that it yields a description of the lepton energy spectrum which is not just valid in the endpoint region, but over the entire phase space.Comment: 8 Pages, LaTeX, 2 figures; a few typos corrected and some clarifications added, final journal versio

GenEvA (I): A new framework for event generation

We show how many contemporary issues in event generation can be recast in terms of partonic calculations with a matching scale. This framework is called GenEvA, and a key ingredient is a new notion of phase space which avoids the problem of phase space double-counting by construction and includes a built-in definition of a matching scale. This matching scale can be used to smoothly merge any partonic calculation with a parton shower. The best partonic calculation for a given region of phase space can be determined through physics considerations alone, independent of the algorithmic details of the merging. As an explicit example, we construct a positive-weight partonic calculation for e+e- -> n jets at next-to-leading order (NLO) with leading-logarithmic (LL) resummation. We improve on the NLO/LL result by adding additional higher-multiplicity tree-level (LO) calculations to obtain a merged NLO/LO/LL result. These results are implemented using a new phase space generator introduced in a companion paper [arXiv:0801.4028].Comment: 60 pages, 22 figures, v2: corrected typos, added reference

Exploiting jet binning to identify the initial state of high-mass resonances

If a new high-mass resonance is discovered at the Large Hadron Collider, model-independent techniques to identify the production mechanism will be crucial to understand its nature and effective couplings to Standard Model particles. We present a powerful and model-independent method to infer the initial state in the production of any high-mass color-singlet system by using a tight veto on accompanying hadronic jets to divide the data into two mutually exclusive event samples (jet bins). For a resonance of several hundred GeV, the jet binning cut needed to discriminate quark and gluon initial states is in the experimentally accessible range of several tens of GeV. It also yields comparable cross sections for both bins, making this method viable already with the small event samples available shortly after a discovery. Theoretically, the method is made feasible by utilizing an effective field theory setup to compute the jet cut dependence precisely and model independently and to systematically control all sources of theoretical uncertainties in the jet binning, as well as their correlations. We use a 750 GeV scalar resonance as an example to demonstrate the viability of our method.Comment: 6 pages, 2 figures, v2: journal versio

Factorization at the LHC: From PDFs to Initial State Jets

We study proton-(anti)proton collisions at the LHC or Tevatron in the presence of experimental restrictions on the hadronic final state and for generic parton momentum fractions. At the scale Q of the hard interaction, factorization does not yield standard parton distribution functions (PDFs) for the initial state. The measurement restricting the hadronic final state introduces a new scale \mu_B << Q and probes the proton prior to the hard collision. This corresponds to evaluating the PDFs at the scale \mu_B. After the proton is probed, the incoming hard parton is contained in an initial-state jet, and the hard collision occurs between partons inside these jets rather than inside protons. The proper description of such initial-state jets requires "beam functions". At the scale \mu_B, the beam function factorizes into a convolution of calculable Wilson coefficients and PDFs. Below \mu_B, the initial-state evolution is described by the usual PDF evolution which changes x, while above \mu_B it is governed by a different renormalization group evolution which sums double logarithms of \mu_B/Q and leaves x fixed. As an example, we prove a factorization theorem for "isolated Drell-Yan", pp -> Xl+l- where X is restricted to have no central jets. We comment on the extension to cases where the hadronic final state contains a certain number of isolated central jets.Comment: 41 pages (19 for everyone + 22 for experts), 16 figures; v2: Notational typos fixed. Added sentences to emphasize that measuring isolated Drell-Yan directly tests the initial state parton shower; v3: typos fixed, 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