arXiv subjects

Wouter J. Waalewijn

Publications and source records attributed to Wouter J. Waalewijn.

81 records · Page 5Linked to original sources

arXiv2011

Parton Fragmentation within an Identified Jet at NNLL

The fragmentation of a light parton i to a jet containing a light energetic hadron h, where the momentum fraction of this hadron as well as the invariant mass of the jet is measured, is described by "fragmenting jet functions". We calculate the one-loop matching coefficients J_{ij} that relate the fragmenting jet functions G_i^h to the standard, unpolarized fragmentation functions D_j^h for quark and gluon jets. We perform this calculation using various IR regulators and show explicitly how the IR divergences cancel in the matching. We derive the relationship between the coefficients J_{ij} and the quark and gluon jet functions. This provides a cross-check of our results. As an application we study the process e+ e- to X pi+ on the Upsilon(4S) resonance where we measure the momentum fraction of the pi+ and restrict to the dijet limit by imposing a cut on thrust T. In our analysis we sum the logarithms of tau=1-T in the cross section to next-to-next-to-leading-logarithmic accuracy (NNLL). We find that including contributions up to NNLL (or NLO) can have a large impact on extracting fragmentation functions from e+ e- to dijet + h.

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arXiv2011

The Soft Function for Exclusive N-Jet Production at Hadron Colliders

The N-jettiness event shape divides phase space into N+2 regions, each containing one jet or beam. Using a geometric measure these regions correspond to jets with circular boundaries. We give a factorization theorem for the cross section fully differential in the (transverse) mass of each jet, and compute the corresponding soft function at next-to-leading order (NLO). The ultraviolet divergences are analytically extracted by exploiting hemispheres for interactions between each pair of hard partons, leaving only convergent integrals that are sensitive to the precise boundaries. This method can be applied in general to N-jet soft functions, including other observables. For N-jettiness, the final result for the soft function involves stable one-dimensional numerical integrals, and all ingredients are now available to extend NLO cross sections to resummed predictions at next-to-next-to-leading logarithmic order.

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arXiv2011

Factorization at the LHC: From PDFs to Initial State Jets (Ph.D. thesis)

New physics searches at the LHC or Tevatron typically look for a specific number of hard jets, leptons and photons. To obtain an exclusive N-jet sample, one can measure the event shape "N-jettiness" τ_N and veto additional undesired jets by requiring τ_N <<1. However, this leads to large logarithms of τ_N in the cross section, that need to be summed for reliable theory predictions. For N=0 in hadronic collisions, τ_N reduces to the "beam thrust" eventshape τ_B. We derive a factorization theorem for pp -> XL, where a central jet veto τ_B<<1 is imposed on the hadronic final state X and L is non-hadronic. This factorization theorem enables us to sum large logarithms of τ_B in the cross section. The initial state is described by "beam functions", which depend on the momentum fraction x and the (transverse) virtuality t of the colliding partons. The dependence on t can be calculated in perturbation theory by matching beam functions onto the parton distribution functions (PDFs) at the intermediate scale μ_B^2 ~ t, and we have calculated all one-loop matching coefficients. Unlike the PDFs, the evolution of the beam function is in t and does not affect x or the parton type. We show results for the beam thrust cross section for Drell-Yan and Higgs production through gluon fusion at next-to-next-to-leading-logarithmic order. For N>0, we obtain a factorization formula with inclusive jet and beam functions that allows us to sum the large logarithms of τ_N.

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arXiv2011

Higgs Production with a Central Jet Veto at NNLL+NNLO

A major ingredient in Higgs searches at the Tevatron and LHC is the elimination of backgrounds with jets. In current H -> WW -> lnulnu searches, jet algorithms are used to veto central jets to obtain a 0-jet sample, which is then analyzed to discover the Higgs signal. Imposing this tight jet veto induces large double logarithms which significantly modify the Higgs production cross section. These jet-veto logarithms are presently only accounted for at fixed order or with the leading-logarithmic summation from parton-shower Monte Carlos. Here we consider Higgs production with an inclusive event-shape variable for the jet veto, namely beam thrust Tau_cm, which has a close correspondence with a traditional p_T jet veto. Tau_cm allows us to systematically sum the large jet-veto logarithms to higher orders and to provide better estimates for theoretical uncertainties. We present results for the 0-jet Higgs production cross section from gluon fusion at next-to-next-to-leading-logarithmic order (NNLL), fully incorporating fixed-order results at next-to-next-to-leading order (NNLO). At this order the scale uncertainty is 15-20%, depending on the cut, implying that a larger scale uncertainty should be used in current Tevatron bounds on the Higgs.

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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

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

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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arXiv2008

The Chiral Anomaly in SCET

Anomalies are an infrared effect, but are often realized in effective theories in a non-trivial way. We study the chiral anomaly in Soft Collinear Effective Theory (SCET), where the anomaly equation has terms contributing at different orders in the power expansion. The chiral anomaly equations in SCET are computed up to NNLO in the power counting with external collinear and/or ultrasoft gluons. We do this by expanding the QCD anomaly equation, using the tree level (LO in α_s) relations between QCD and SCET fields. The validity of this correspondence between the anomaly equations is confirmed by direct computation of the one-loop diagrams in SCET.

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