arXiv subjects

Jonathan R. Walsh

Publications and source records attributed to Jonathan R. Walsh.

35 records · Page 2Linked to original sources

arXiv2014

Comparing and Counting Logs in Direct and Effective Methods of Resummation

We compare methods to resum logarithms in event shape distributions as they have been used in perturbative QCD directly and in effective field theory. We demonstrate that they are equivalent. In showing this equivalence, we are able to put standard soft-collinear effective theory (SCET) formulae for cross sections in momentum space into a novel form more directly comparable with standard QCD formulae, and endow the QCD formulae with dependence on separated hard, jet, and soft scales, providing potential ways to improve estimates of theoretical uncertainty. We show how to compute cross sections in momentum space to keep them as accurate as the corresponding expressions in Laplace space. In particular, we point out that that care is required in truncating differential distributions at N$^k$LL accuracy to ensure they match the accuracy of the corresponding cumulant or Laplace transform. We explain how to avoid such mismatches at N$^k$LL accuracy, and observe why they can also be avoided by working to N$^k$LL$'$ accuracy.

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arXiv2014

Resummation Properties of Jet Vetoes at the LHC

Jet vetoes play an important role at the LHC in the search for the Higgs and ultimately in precise measurements of its properties. Many Higgs analyses divide the cross section into exclusive jet bins to maximize the sensitivity in different production and decay channels. For a given jet category, the veto on additional jets introduces sensitivity to soft and collinear emissions, which causes logarithms in the perturbative expansion that need to be resummed to obtain precise predictions. We study the higher-order resummation properties of several conceptually distinct kinematic variables that can be used to veto jets in hadronic collisions. We consider two inclusive variables, the scalar sum over pT and beam thrust, and two corresponding exclusive variables based on jet algorithms, namely the largest pT and largest beam thrust of a jet. The inclusive variables can, in principle, be resummed to higher orders. We show that for the jet-based variables, there are dual effects due to clustering in the jet algorithm for both large and small jet radius R that make a complete resummation at or beyond next-to-leading logarithmic order (NLL) challenging. For R~1, the clustering of soft and collinear emissions gives O(1) contributions starting at next-to-next-to-leading logarithmic order that are not reproduced by an all-orders soft-collinear factorization formula and therefore are not automatically resummed by it. For R<<1, clustering induces logarithms of R that contribute at NLL in the exponent of the cross section, which cannot be resummed with currently available methods. We explicitly compute the leading jet clustering effects at two loops and comment on their numerical size.

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arXiv2013

Combining Resummed Higgs Predictions Across Jet Bins

Experimental analyses often use jet binning to distinguish between different kinematic regimes and separate contributions from background processes. To accurately model theoretical uncertainties in these measurements, a consistent description of the jet bins is required. We present a complete framework for the combination of resummed results for production processes in different exclusive jet bins, focusing on Higgs production in gluon fusion as an example. We extend the resummation of the Higgs + 1-jet cross section into the challenging low transverse momentum region, lowering the uncertainties considerably. We provide combined predictions with resummation for cross sections in the Higgs + 0-jet and Higgs + 1-jet bins, and give an improved theory covariance matrix for use in experimental studies. We estimate that the relevant theoretical uncertainties on the signal strength in the Higgs to WW analysis are reduced by nearly a factor of 2 compared to the current value.

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arXiv2013

Matching Fully Differential NNLO Calculations and Parton Showers

We present a general method to match fully differential next-to-next-to-leading (NNLO) calculations to parton shower programs. We discuss in detail the perturbative accuracy criteria a complete NNLO+PS matching has to satisfy. Our method is based on consistently improving a given NNLO calculation with the leading-logarithmic (LL) resummation in a chosen jet resolution variable. The resulting NNLO$+$LL calculation is cast in the form of an event generator for physical events that can be directly interfaced with a parton shower routine, and we give an explicit construction of the input "Monte Carlo cross sections" satisfying all required criteria. We also show how other proposed approaches naturally arise as special cases in our method.

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arXiv2013

Combining Higher-Order Resummation with Multiple NLO Calculations and Parton Showers in GENEVA

We extend the lowest-order matching of tree-level matrix elements with parton showers to give a complete description at the next higher perturbative accuracy in alpha_s at both small and large jet resolutions, which has not been achieved so far. This requires the combination of the higher-order resummation of large Sudakov logarithms at small values of the jet resolution variable with the full next-to-leading order (NLO) matrix-element corrections at large values. As a by-product this combination naturally leads to a smooth connection of the NLO calculations for different jet multiplicities. In this paper, we focus on the general construction of our method and discuss its application to e+e and pp collisions. We present first results of the implementation in the GENEVA Monte Carlo framework, where we employ N-jettiness as the jet resolution variable, combining its next-to-next-to-leading logarithmic resummation with fully exclusive NLO matrix elements, and PYTHIA8 as the backend for further parton showering and hadronization. For hadronic collisions, we take Drell-Yan production as an example to apply our construction. For e+e- -> jets, taking alpha_s(mZ) = 0.1135 from fits to LEP thrust data, together with the PYTHIA8 hadronization model, we obtain good agreement with LEP data for a variety of 2-jet observables.

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arXiv2013

Jet p_T Resummation in Higgs Production at NNLL'+NNLO

We present predictions for Higgs production via gluon fusion with a p_T veto on jets and with the resummation of jet-veto logarithms at NNLL'+$NNLO order. These results incorporate explicit O(alphas^2) calculations of soft and beam functions, which include the dominant dependence on the jet radius R. In particular the NNLL' order accounts for the correct boundary conditions for the N3LL resummation, for which the only unknown ingredients are higher-order anomalous dimensions. We use scale variations in a factorization theorem in both rapidity and virtuality space to estimate the perturbative uncertainties, accounting for both higher fixed-order corrections as well as higher-order towers of jet-p_T logarithms. This formalism also predicts the correlations in the theory uncertainty between the exclusive 0-jet and inclusive 1-jet bins. At the values of R used experimentally, there are important corrections due to jet algorithm clustering that include logarithms of R. Although we do not sum logarithms of R, we do include an explicit contribution in our uncertainty estimate to account for higher-order jet clustering logarithms. Precision predictions for this H+0-jet cross section and its theoretical uncertainty are an integral part of Higgs analyses that employ jet binning.

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arXiv2013

Combining Higher-Order Resummation with Multiple NLO Calculations and Parton Showers in the GENEVA Monte Carlo Framework

We discuss the GENEVA Monte Carlo framework, which combines higher-order resummation (NNLL) of large Sudakov logarithms with multiple next-to-leading-order (NLO) matrix-element corrections and parton showering (using PYTHIA8) to give a complete description at the next higher perturbative accuracy in alpha_s at both small and large jet resolution scales. Results for e+e- -> jets compared to LEP data and for Drell-Yan production are presented.

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arXiv2012

Factorization and Resummation for Dijet Invariant Mass Spectra

Multijet cross sections at the LHC and Tevatron are sensitive to several distinct kinematic energy scales. When measuring the dijet invariant mass m_jj between two signal jets produced in association with other jets or weak bosons, m_jj will typically be much smaller than the total partonic center-of-mass energy Q, but larger than the individual jet masses m, such that there can be a hierarchy of scales m << m_jj << Q. This situation arises in many new-physics analyses at the LHC, where the invariant mass between jets is used to gain access to the masses of new-physics particles in a decay chain. At present, the logarithms arising from such a hierarchy of kinematic scales can only be summed at the leading-logarithmic level provided by parton-shower programs. We construct an effective field theory, SCET+, which is an extension of soft-collinear effective theory that applies to this situation of hierarchical jets. It allows for a rigorous separation of different scales in a multiscale soft function and for a systematic resummation of logarithms of both m_jj/Q and m/Q. As an explicit example, we consider the invariant mass spectrum of the two closest jets in e+e- -> 3 jets. We also give the generalization to pp -> N jets plus leptons relevant for the LHC.

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arXiv2012

Double Non-Global Logarithms In-N-Out of Jets

We derive the leading non-global logarithms (NGLs) of ratios of jet masses m_{1,2} and a jet energy veto Λdue to soft gluons splitting into regions in and out of jets. Such NGLs appear in any exclusive jet cross section with multiple jet measurements or with a veto imposed on additional jets. Here, we consider back-to-back jets of radius R produced in e^+e^- collisions, found with a cone or recombination algorithm. The leading NGLs are of the form α_s^2 \ln^2(Λ/m_{1,2}) or α_s^2\ln^2(m_1/m_2). Their coefficients depend both on the algorithm and on R. We consider cone, \kt, anti-\kt, and Cambridge-Aachen algorithms. In addition to determining the full algorithmic and R dependence of the leading NGLs, we derive new relations among their coefficients. We also derive to all orders in α_s a factorized form for the soft function S(k_L,k_R,Λ) in the cross section σ(m_1,m_2,Λ) in which dependence on each of the global logs of μ/k_L, μ/k_R and μ/Λdetermined by the renormalization group are separated from one another and from the non-global logs. The same kind of soft function, its associated non-global structure, and the algorithmic dependence we derive here will also arise in exclusive jet cross sections at hadron colliders, and must be understood and brought under control to achieve precise theoretical predictions.

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arXiv2012

Disentangling Clustering Effects in Jet Algorithms

Clustering algorithms build jets though the iterative application of single particle and pairwise metrics. This leads to phase space constraints that are extremely complicated beyond the lowest orders in perturbation theory, and in practice they must be implemented numerically. This complication presents a significant barrier to gaining an analytic understanding of the perturbative structure of jet cross sections. We present a novel framework to express the jet algorithm's phase space constraints as a function of clustered groups of particles, which are the possible outcomes of the algorithm. This approach highlights the analytic properties of jet observables, rather than the explicit constraints on individual final state momenta, which can be unwieldy at higher orders. We derive the form of the n-particle phase space constraints for a jet algorithm with any measurement. We provide an expression for the measurement that makes clustering effects manifest and relates them to constraints from clustering at lower orders. The utility of this framework is demonstrated by using it to understand clustering effects for a large class of jet shape observables in the soft/collinear limit. We apply this framework to isolate divergences and analyze the logarithmic structure of the Abelian terms in the soft function, providing the all-orders form of these terms and showing that corrections from clustering start at next-to-leading logarithmic order in the exponent of the cross section.

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arXiv2012

Abelian Non-Global Logarithms from Soft Gluon Clustering

Most recombination-style jet algorithms cluster soft gluons in a complex way. This leads to correlations in the soft gluon phase space and introduces logarithmic corrections to jet cross sections. The leading Abelian clustering logarithms occur at least at next-to leading logarithm (NLL) in the exponent of the distribution, and we show that new clustering effects contributing at NLL likely arise at each order. Therefore we find that it is unlikely that clustering logs can be resummed to NLL. Clustering logarithms make the anti-kT algorithm theoretically preferred, for which they are power suppressed. They can arise in Abelian and non-Abelian terms, and we calculate the Abelian clustering logarithms at two loops for the jet mass distribution using the Cambridge/Aachen and kT algorithms, including jet radius dependence, which extends previous results. We find that previously identified logarithms from clustering effects can be naturally thought of as a class of non-global logarithms (NGLs), which have traditionally been tied to non-Abelian correlations in soft gluon emission.

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arXiv2011

Factorization Constraints on Jet Substructure

Factorization underpins our ability to make predictions at the LHC, both in Monte Carlo simulations and direct calculations. An improved theoretical understanding of jet substructure can lead to calculations that can confront data and validate the Monte Carlo description of jets. We derive constraints on jet substructure algorithms from factorization, focusing on the broad class of jet observables where the soft and collinear dynamics of QCD dominate. A necessary condition for factorization is that the phase space constraints on soft and collinear dynamics for a given observable are independent of each other. This condition allows us to use a simple power counting analysis to place strong constraints on the form of jet substructure methods that can factorize. We illustrate this approach by considering four substructure algorithms, the mass-drop filter Higgs tagger, pruning, trimming, and N-subjettiness. We find that factorization constrains the scaling of parameters in all of the substructure algorithms, and that the generic declustering and filtering techniques do not factorize. However, we determine simple modifications that can be made to allow for factorization.

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arXiv2010

Jet Shapes and Jet Algorithms in SCET

Jet shapes are weighted sums over the four-momenta of the constituents of a jet and reveal details of its internal structure, potentially allowing discrimination of its partonic origin. In this work we make predictions for quark and gluon jet shape distributions in N-jet final states in e+e- collisions, defined with a cone or recombination algorithm, where we measure some jet shape observable on a subset of these jets. Using the framework of Soft-Collinear Effective Theory, we prove a factorization theorem for jet shape distributions and demonstrate the consistent renormalization-group running of the functions in the factorization theorem for any number of measured and unmeasured jets, any number of quark and gluon jets, and any angular size R of the jets, as long as R is much smaller than the angular separation between jets. We calculate the jet and soft functions for angularity jet shapes τ_a to one-loop order (O(alpha_s)) and resum a subset of the large logarithms of τ_a needed for next-to-leading logarithmic (NLL) accuracy for both cone and kT-type jets. We compare our predictions for the resummed τ_a distribution of a quark or a gluon jet produced in a 3-jet final state in e+e- annihilation to the output of a Monte Carlo event generator and find that the dependence on a and R is very similar.

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arXiv2010

Apparent CPT Violation in Neutrino Oscillation Experiments

We consider searching for light sterile fermions and new forces by using long baseline oscillations of neutrinos and antineutrinos. A new light sterile state and/or a new force can lead to apparent CPT violation in muon neutrino and antineutrino oscillations. As an example, we present an economical model of neutrino masses containing a sterile neutrino. The potential from the Standard Model neutral current gives rise to a difference between the disappearance probabilities of neutrinos and antineutrinos, when mixing with a light sterile neutrino is considered. The addition of a B-L interaction adds coherently to the neutrino current potential and increases the difference between neutrino and antineutrino disappearance. We find that this model can improve the fit to the results of MINOS for both neutrinos and antineutrinos, without any CPT violation, and that the regions of parameter space which improve the fit are within experimental constraints.

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arXiv2010

Consistent Factorization of Jet Observables in Exclusive Multijet Cross-Sections

We demonstrate the consistency at the next-to-leading-logarithmic (NLL) level of a factorization theorem based on Soft-Collinear Effective Theory (SCET) for jet shapes in e+e- collisions. We consider measuring jet observables in exclusive multijet final states defined with cone and k_T-type jet algorithms. Consistency of the factorization theorem requires that the renormalization group evolution of hard, jet, and soft functions is such that the physical cross-section is independent of the factorization scale mu. The anomalous dimensions of the various factorized pieces, however, depend on the color representation of jets, choice of jet observable, the number of jets whose shapes are measured, and the jet algorithm, making it highly nontrivial to satisfy the consistency condition. We demonstrate the intricate cancellations between anomalous dimensions that occur at the NLL level, so that, up to power corrections that we identify, our factorization of the jet shape distributions is consistent for any number of quark and gluon jets, for any number of jets whose shapes are measured or unmeasured, for any angular size R of the jets, and for any of the algorithms we consider. Corrections to these results are suppressed by the SCET expansion parameter lambda (the ratio of soft to collinear or collinear to hard scales) and in the jet separation measure 1/t^2 = tan^2(R/2)/tan^2(psi/2), where psi is the angular separation between jets. Our results can be used to calculate a wide variety of jet observables in multijet final states to NLL accuracy.

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arXiv2009

Recombination Algorithms and Jet Substructure: Pruning as a Tool for Heavy Particle Searches

We discuss jet substructure in recombination algorithms for QCD jets and single jets from heavy particle decays. We demonstrate that the jet algorithm can introduce significant systematic effects into the substructure. By characterizing these systematic effects and the substructure from QCD, splash-in, and heavy particle decays, we identify a technique, pruning, to better identify heavy particle decays into single jets and distinguish them from QCD jets. Pruning removes protojets typical of soft, wide angle radiation, improves the mass resolution of jets reconstructing a heavy particle decay, and decreases the QCD background. We show that pruning provides significant improvements over unpruned jets in identifying top quarks and W bosons and separating them from a QCD background, and may be useful in a search for heavy particles.

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arXiv2009

Techniques for improved heavy particle searches with jet substructure

We present a generic method for improving the effectiveness of heavy particle searches in hadronic channels at the Large Hadron Collider. By selectively removing, or pruning, protojets from the substructure provided by a k_T-style jet algorithm, we improve the mass resolution for heavy decays and decrease the QCD background. We show that the protojets removed are typical of soft radiation and underlying event contributions, and atypical of accurately reconstructed heavy particles.

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