Hard Matching for Boosted Tops at Two Loops

Abstract

Cross sections for top quarks provide very interesting physics opportunities, being both sensitive to new physics and also perturbatively tractable due to the large top quark mass. Rigorous factorization theorems for top cross sections can be derived in several kinematic scenarios, including the boosted regime in the peak region that we consider here. In the context of the corresponding factorization theorem for $e^{+}{e}^{-}$ collisions we extract the last missing ingredient that is needed to evaluate the cross section differential in the jet-mass at two-loop order, namely the matching coefficient at the scale $\mu \simeq m_t$. Our extraction also yields the final ingredients needed to carry out logarithmic resummation at next-to-next-to-leading logarithmic order (or N${}^3$LL if we ignore the missing 4-loop cusp anomalous dimension). This coefficient exhibits an amplitude level rapidity logarithm starting at $\mathcal{O}({\alpha }_s^2)$ due to virtual top quark loops, which we treat using rapidity renormalization group (RG) evolution. Interestingly, this rapidity RG evolution appears in the matching coefficient between two effective theories around the heavy quark mass scale $\mu \simeq m_t$.

35 pages, 3 figures, v2: added extraction of 3-loop anon. dimension, journal version

References in corpus (12)

• Investigating the near-criticality of the Higgs boson
• The Zero-Bin and Mode Factorization in Quantum Field Theory
• A precise determination of alpha_s from LEP thrust data using effective field theory
• Stability, Higgs Boson Mass and New Physics
• Toward a NNLO calculation of the B-->X_s+gamma decay rate with a cut on photon energy: II. Two-loop result for the jet function
• Consistent Use of the Standard Model Effective Potential
• Top Mass Measurements from Jets and the Tevatron Top-Quark Mass
• The 3-Loop Non-Singlet Heavy Flavor Contributions and Anomalous Dimensions for the Structure Function $F_2(x,Q^2)$ and Transversity
• The three-loop cusp anomalous dimension in QCD
• Top mass determination, Higgs inflation, and vacuum stability
• Electroweak Sudakov Corrections using Effective Field Theory
• The QCD form factor of heavy quarks at NNLO

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• Measurement of the jet mass distribution and top quark mass in hadronic decays of boosted top quarks in pp collisions at $\sqrt{s}=$ 13 TeV
• Measurement of the jet mass in highly boosted t t-bar events from pp collisions at sqrt(s) = 8 TeV
• Boosted Top Quarks in the Peak Region with N${}^3$LL Resummation
• Three-loop soft function for heavy-to-light quark decays
• Massive Event-Shape Distributions at N${}^2$LL
• NLO Massive Event-Shape Differential and Cumulative Distributions