arXiv subjects

Iain W. Stewart

Publications and source records attributed to Iain W. Stewart.

At least 109 records · Page 6Linked to original sources

arXiv2011

Fragmentation inside an identified jet

Using Soft-Collinear Effective Theory we derive factorization formulae for semi-inclusive processes where a light hadron h fragments from a jet whose invariant mass is measured. Our analysis yields a novel "fragmenting jet function" G_i^h(s,z) that depends on the jet invariant mass \sqrt{s}, and on the fraction z of the large light-cone momentum components of the hadron and the parent parton i. We show that G_i^h(s,z) can be computed in terms of perturbatively calculable coefficients, J_{ij}(s,z/x), integrated against standard non-perturbative fragmentation functions, D_j^h(x). Our analysis yields a simple replacement rule that allows any factorization theorem depending on a jet function J_i to be converted to a semi-inclusive process with a fragmenting hadron h.

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arXiv2011

Quark Fragmentation within an Identified Jet

We derive a factorization theorem that describes an energetic hadron h fragmenting from a jet produced by a parton i, where the jet invariant mass is measured. The analysis yields a "fragmenting jet function" G_i^h(s,z) that depends on the jet invariant mass s, and on the energy fraction z of the fragmentation hadron. We show that G^h_i can be computed in terms of perturbatively calculable coefficients, J_{ij}(s,z/x), integrated against standard non-perturbative fragmentation functions, D_j^{h}(x). We also show that the sum over h of the integral over z of z G_i^h(s,z) is given by the standard inclusive jet function J_i(s) which is perturbatively calculable in QCD. We use Soft-Collinear Effective Theory and for simplicity carry out our derivation for a process with a single jet, B -> X h l nu, with invariant mass m_{X h}^2 >> Lambda_QCD^2. Our analysis yields a simple replacement rule that allows any factorization theorem depending on an inclusive jet function J_i to be converted to a semi-inclusive process with a fragmenting hadron h. We apply this rule to derive factorization theorems for B -> X K gamma which is the fragmentation to a Kaon in b -> s gamma, and for e^+e^- -> (dijets)+h with measured hemisphere dijet invariant masses.

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arXiv2011

Systematic Improvement of Parton Showers with Effective Theory

We carry out a systematic classification and computation of next-to-leading order kinematic power corrections to the fully differential cross section in the parton shower. To do this we devise a map between ingredients in a parton shower and operators in a traditional effective field theory framework using a chain of soft-collinear effective theories. Our approach overcomes several difficulties including avoiding double counting and distinguishing approximations that are coordinate choices from true power corrections. Branching corrections can be classified as hard-scattering, that occur near the top of the shower, and jet-structure, that can occur at any point inside it. Hard-scattering corrections include matrix elements with additional hard partons, as well as power suppressed contributions to the branching for the leading jet. Jet-structure corrections require simultaneous consideration of potential 1 -> 2 and 1 -> 3 branchings. The interference structure induced by collinear terms with subleading powers remains localized in the shower.

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arXiv2011

Status of SIMBA

The goal of the SIMBA collaboration is to provide a global fit to the available data in 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 input parameters, most importantly the b-quark mass and the b-quark distribution function in the B-meson, called the shape function. This strategy is analogous to the determination of |Vcb| from global fits to inclusive B -> X_c l nu decays. In this talk, we present preliminary results for the shape function and |C_7^incl Vtb Vts^*|, which parametrizes the total B -> X_s gamma rate, from a global fit to the available B -> X_s gamma measurements from BABAR and Belle.

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arXiv2011

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.

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arXiv2010

The Quark Beam Function at NNLL

In hard collisions at a hadron collider the most appropriate description of the initial state depends on what is measured in the final state. Parton distribution functions (PDFs) evolved to the hard collision scale Q are appropriate for inclusive observables, but not for measurements with a specific number of hard jets, leptons, and photons. Here the incoming protons are probed and lose their identity to an incoming jet at a scale μ_B << Q, and the initial state is described by universal beam functions. We discuss the field-theoretic treatment of beam functions, and show that the beam function has the same RG evolution as the jet function to all orders in perturbation theory. In contrast to PDF evolution, the beam function evolution does not mix quarks and gluons and changes the virtuality of the colliding parton at fixed momentum fraction. At μ_B, the incoming jet can be described perturbatively, and we give a detailed derivation of the one-loop matching of the quark beam function onto quark and gluon PDFs. We compute the associated NLO Wilson coefficients and explicitly verify the cancellation of IR singularities. As an application, we give an expression for the next-to-next-to-leading logarithmic order (NNLL) resummed Drell-Yan beam thrust cross section.

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arXiv2010

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.

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arXiv2010

N-Jettiness: An Inclusive Event Shape to Veto Jets

Jet vetoes are essential in many Higgs and new-physics analyses at the LHC and Tevatron. The signals are typically characterized by a specific number of hard jets, leptons, or photons, while the backgrounds often have additional jets. In such cases vetoing undesired additional jets is an effective way to discriminate signals and background. Given an inclusive event sample with N or more jets, the veto to have only N energetic jets defines an "exclusive" N-jet cross section. This strongly restricts the phase space of the underlying inclusive N-jet cross section and causes large double logarithms in perturbation theory that must be summed to obtain theory predictions. Jet vetoes are typically implemented using jet algorithms. This yields complicated phase-space restrictions and one often relies on parton-shower Monte Carlos, which are limited to leading-logarithmic accuracy. We introduce a global event shape "N-jettiness", tau_N, which is defined for events with N signal jets and vanishes in the limit of exactly N infinitely narrow jets. Requiring tau_N << 1 constrains radiation between the N signal jets and vetoes additional undesired jets. This provides an inclusive method to veto jets and to define an exclusive N-jet cross section that can be well-controlled theoretically. N-jettiness yields a factorization formula with inclusive jet and beam functions.

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arXiv2010

Thrust at N^3LL with Power Corrections and a Precision Global Fit for alphas(mZ)

We give a factorization formula for the e+e- thrust distribution dsigma/dtau with tau=1-T based on soft-collinear effective theory. The result is applicable for all tau, i.e. in the peak, tail, and far-tail regions. The formula includes O(alphas^3) fixed-order QCD results, resummation of singular partonic alphas^j ln^k(tau)/tau terms with N^3LL accuracy, hadronization effects from fitting a universal nonperturbative soft function defined in field theory, bottom quark mass effects, QED corrections, and the dominant top mass dependent terms from the axial anomaly. We do not rely on Monte Carlo generators to determine nonperturbative effects since they are not compatible with higher order perturbative analyses. Instead our treatment is based on fitting nonperturbative matrix elements in field theory, which are moments Omega_i of a nonperturbative soft function. We present a global analysis of all available thrust data measured at center-of-mass energies Q=35 to 207 GeV in the tail region, where a two parameter fit to $α_s(m_Z)$ and the first moment Omega_1 suffices. We use a short distance scheme to define Omega_1, called the R-gap scheme, thus ensuring that the perturbative dsigma/dtau does not suffer from an O(Lambda_QCD) renormalon ambiguity. We find alphas(mZ)=0.1135 \pm (0.0002)_{expt} \pm (0.0005)_{hadr} \pm (0.0009)_{pert}, with chi^2/dof=0.91, where the displayed 1-sigma errors are the total experimental error, the hadronization uncertainty, and the perturbative theory uncertainty, respectively. The hadronization uncertainty in alphas is significantly decreased compared to earlier analyses by our two parameter fit, which determines Omega_1=0.323 GeV with 16% uncertainty.

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arXiv2010

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 μ_B << Q and probes the proton prior to the hard collision. This corresponds to evaluating the PDFs at the scale μ_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 μ_B, the beam function factorizes into a convolution of calculable Wilson coefficients and PDFs. Below μ_B, the initial-state evolution is described by the usual PDF evolution which changes x, while above μ_B it is governed by a different renormalization group evolution which sums double logarithms of μ_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.

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arXiv2010

Global Fit of alpha_s(m_Z) to Thrust at NNNLL Order with Power Corrections

From soft-collinear effective theory one can derive a factorization formula for the e+e- thrust distribution dsigma/dtau with tau = 1-T that is applicable for all tau. The formula accommodates available O(alpha_s^3) fixed-order QCD results, resummation of logarithms at NNNLL order, a universal nonperturbative soft function for hadronization effects, factorization of nonperturbative effects in subleading power contributions, bottom mass effects and QED corrections. We emphasize that the use of Monte Carlos to estimate hadronization effects is not compatible with high-precision, high-order analyses. We present a global analysis of all available e+e- thrust data measured at Q = 35 to 207 GeV in the tail region, where a two-parameter fit can be carried out for alpha_s(m_Z) and Omega_1, the first moment of the soft function. To obtain small theoretical errors it is essential to define Omega_1 in a short-distance scheme, free of an O(Lambda_QCD) renormalon ambiguity. We find alpha_s(m_Z) = 0.1135 +- (0.0002)_expt +- (0.0005)_Omega_1 +- (0.0009)_pert with chi^2/dof = 0.9.

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arXiv2009

R-evolution: Improving perturbative QCD

Perturbative QCD results in the MSbar scheme can be dramatically improved by switching to a scheme that accounts for the dominant power law dependence on the factorization scale in the operator product expansion. We introduce the ``MSR scheme'' which achieves this in a Lorentz and gauge invariant way. The MSR scheme has a very simple relation to MSbar, and can be easily used to reanalyze MSbar results. Results in MSR depend on a cutoff parameter R, in addition to the mu of MSbar. R variations can be used to independently estimate i) the size of power corrections, and ii) higher order perturbative corrections (much like mu in MSbar). We give two examples at three-loop order, the ratio of mass splittings in the B*-B and D*-D systems, and the Ellis-Jaffe sum rule as a function of momentum transfer Q in deep inelastic scattering. Comparing to data, the perturbative MSR results work well even for Q ~ 1 GeV, and the size of power corrections is reduced compared to those in MSbar.

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arXiv2009

The R-evolution of QCD matrix elements

Perturbation series in QCD are generally asymptotic and suffer from so-called infrared renormalon ambiguities. In the context of the standard operator product expansion in MS-bar these ambiguities are compensated by matrix elements of higher dimension operators, but the procedure can be difficult to control due to large numerical cancellations. Explicit subtractions for matrix elements and coefficients, depending on a subtraction scale R, can avoid this problem. The appropriate choice for R in the Wilson coefficients can widely vary for different processes. In this talk we discuss renormalization group evolution with the scale R, and show that it sums large logarithms in the difference of processes with widely different R's. We also show that the solution of the R-evolution equations can be used to recover the all order asymptotic form of the singularities in the Borel transform of the perturbative series. For the normalization of these singularities we obtain a quickly converging sum rule that only needs the known perturbative coefficients as an input. This sum rule can be used as a novel test for renormalon ambiguities without replying on the large-beta_0 approximation.

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arXiv2009

Reparameterization Invariant Collinear Operators

In constructing collinear operators, which describe the production of energetic jets or energetic hadrons, important constraints are provided by reparameterization invariance (RPI). RPI encodes Lorentz invariance in a power expansion about a collinear direction, and connects the Wilson coefficients of operators at different orders in this expansion to all orders in alphas. We construct reparameterization invariant collinear objects. The expansion of operators built from these objects provides an efficient way of deriving RPI relations and finding a minimal basis of operators, particularly when one has an observable with multiple collinear directions and/or soft particles. Complete basis of operators are constructed for pure glue currents at twist-4, and for operators involving multiple collinear directions, including those appearing in e+e- -> 3 jets, and for pp-> 2 jets initiated via gluon-fusion.

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arXiv2008

Treating the b quark distribution function with reliable uncertainties

The parton distribution function for a b quark in the B meson (called the shape function) plays an important role in the analysis of the B -> X_s gamma and B -> X_u l nu data, and gives one of the dominant uncertainties in the determination of |Vub|. We introduce a new framework to treat the shape function, which consistently incorporates its renormalization group evolution and all constraints on its shape and moments in any short distance mass scheme. At the same time it allows a reliable treatment of the uncertainties. We develop an expansion in a suitable complete set of orthonormal basis functions, which provides a procedure for systematically controlling the uncertainties due to the unknown functional form of the shape function. This is a significant improvement over fits to model functions. Given any model for the shape function, our construction gives an orthonormal basis in which the model occurs as the first term, and corrections to it can be studied. We introduce a new short distance scheme, the "invisible scheme", for the kinetic energy matrix element, lambda_1. We obtain closed form results for the differential rates that incorporate perturbative corrections and a summations of logarithms at any order in perturbation theory, and present results using known next-to-next-to-leading order expressions. The experimental implementation of our framework is straightforward.

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arXiv2008

Top Mass Measurements from Jets and the Tevatron Top-Quark Mass

Theoretical issues are discussed for the measurement of the top-mass using jets, including perturbative and non-perturbative effects that relate experimental observables to the Lagrangian mass, and appropriate choices for mass schemes. Full account for these issues is given for e+e--> t-tbar using a factorization theorem for event shapes for massive quarks. Implications for the Tevatron top-mass measurement are discussed. A mass-scheme, the "MSR-mass", is introduced which allows for a precise description of observables sensitive to scales R << m, but at the same time does not introduce perturbative matching uncertainties in conversion to the MSbar mass.

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arXiv2008

Infrared Renormalization Group Flow for Heavy Quark Masses

A short-distance heavy quark mass depends on two parameters, the renormalization scale mu controlling the absorption of ultraviolet fluctuations into the mass, and a scale R controlling the absorption of infrared fluctuations. 1/R can be thought of as the radius for perturbative corrections that build up the mass beyond its point-like definition in the pole scheme. Treating R as a variable gives a renormalization group equation. We argue that the sign of this anomalous dimension is universal: increasing R to add IR modes decreases m(R). The flow improves the stability of conversions between mass schemes, allowing us to avoid large logs and the renormalon. The flow in R can be used to study IR renormalons without using bubble chains, and we use it to determine the coefficient of the LambdaQCD renormalon ambiguity of the pole mass with a convergent sum-rule.

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arXiv2008

Two-loop Jet-Function and Jet-Mass for Top Quarks

We compute the two-loop heavy quark jet-function in the heavy quark limit. This is one of the key ingredients in next-to-next-to-leading order (NNLO) and next-to-next-to-leading-log order (NNLL) computations of the invariant mass distribution of top-jets at a future e+e- collider. The shape of the top invariant mass distribution is affected by large logs which we compute at NNLL order. Exploiting the non-abelian exponentiation theorem, a definition of the top jet-mass is given which is transitive and whose renormalization group evolution is determined by the cusp-anomalous dimension to all orders in perturbation theory. Relations of the jet-mass to the pole, MSbar, and 1S masses are presented at two-loop order.

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