Jets in Effective Theory: Summing Phase Space Logs

Abstract

We demonstrate how to resum phase space logarithms in the Sterman-Weinberg (SW) dijet decay rate within the context of Soft Collinear Effective theory (SCET). An operator basis corresponding to two and three jet events is defined in SCET and renormalized. We obtain the RGE of the two and three jet operators and run the operators from the scale ${\mu }^2=Q^2$ to the phase space scale ${\mu }_{\delta }^2={\delta }^2{Q}^2$. This phase space scale, where $\delta$ is the cone half angle of the jet, defines the angular region of the jet. At ${\mu }_{\delta }^2$ we determine the mixing of the three and two jet operators. We combine these results with the running of the two jet shape function, which we run down to an energy cut scale ${\mu }_{\beta }^2$. This defines the resumed SW dijet decay rate in the context of SCET. The approach outlined here demonstrates how to establish a jet definition in the context of SCET. This allows a program of systematically improving the theoretical precision of jet phenomenology to be carried out.

25 pages, 4 figures, V2: Typos fixed, writing clarified, detail on PSRG added. Matching onto jet definition changed to taking place at collinear scale

References in corpus (21)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• QCD Matrix Elements + Parton Showers
• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Invariant Operators in Collinear Effective Theory
• The Resummation of Soft Gluon in Hadronic Collisions
• Nonperturbative Corrections in Resummed Cross Sections
• Renormalization group scaling in nonrelativistic QCD
• Deep inelastic scattering as x -> 1 using soft-collinear effective theory
• Threshold Resummation for Dijet Cross Sections
• Enhanced Nonperturbative Effects in Z Decays to Hadrons
• Resumming the color-octet contribution to e+ e- -> J/psi + X
• Measuring Multijet Structure of Hadronic Energy Flow Or What IS A Jet?
• Enhanced nonperturbative effects in jet distributions
• Next-to-leading-log renormalization-group running in heavy-quarkonium creation and annihilation
• Logarithms of alpha in QED bound states from the renormalization group
• Improving Extractions of |Vcb| and mb from the Hadronic Invariant Mass Moments of Semileptonic Inclusive B decay
• Improving jet distributions with effective field theory
• The renormalization group for correlated scales: one-stage versus two-stage running
• Resumming Phase Space Logarithms in Inclusive Semileptonic $B$ Decays
• Towards the Anomalous Dimension to Order Lambda_QCD/m_b for Phase Space Restricted B --> X(u) ell anti-nu and B --> X(s) gamma

Cited by in corpus (20)

• Jet Shapes and Jet Algorithms in SCET
• Factorization at the LHC: From PDFs to Initial State Jets
• Top Jets in the Peak Region: Factorization Analysis with NLL Resummation
• Factorization of e+e- Event Shape Distributions with Hadronic Final States in Soft Collinear Effective Theory
• Resummation and NLO Matching of Event Shapes with Effective Field Theory
• The gluon jet function at two-loop order
• Electroweak Corrections in High Energy Processes using Effective Field Theory
• Electroweak Sudakov Corrections using Effective Field Theory
• Factorization and Resummation of Higgs Boson Differential Distributions in Soft-Collinear Effective Theory
• Electroweak Corrections using Effective Field Theory: Applications to the LHC
• Reparameterization Invariant Collinear Operators
• A Soft-Collinear Mode for Jet Cross Sections in Soft Collinear Effective Theory
• Angular correlations in multi-jet final states from kt-dependent parton showers
• Factorization for generic jet production
• Consistent Factorization of Jet Observables in Exclusive Multijet Cross-Sections
• Phase Space and Jet Definitions in SCET
• Jet Function with a Jet Algorithm in SCET
• Factorization of the dijet cross section in electron-positron annihilation with jet algorithms
• Factorization of Boosted Multijet Processes for Threshold Resummation
• Universal Nonperturbative Effects in Event Shapes from Soft-Collinear Effective Theory