A formalism for the resummation of non-factorizable observables in SCET
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Springer
Received: September 30, Revised: February 29, Accepted: March 3, Published: May 4,
2019 2020 2020 2020
Christian W. Bauera and Pier Francesco Monnib a
Ernest Orlando Lawrence Berkeley National Laboratory, University of California, Berkeley, 1 Cyclotron Road, Berkeley, CA 94720, U.S.A. b CERN, Theoretical Physics Department, 1 Esplanade des Particules, Geneva 23 CH-1211, Switzerland
E-mail: [email protected], [email protected] Abstract: In the framework of soft-collinear effective theory (SCET), we show how to formulate the resummation for a broad family of final-state, global observables in high-energy collisions in a general way that is suitable for a numerical calculation. Contrary to the standard SCET approach, this results in a method that does not require an observable-specific factorization theorem. We present a complete formulation at next-to-next-to-leading logarithmic order for e+ e− observables, and show how to systematically extend the framework to higher orders. This work paves the way to automated resummation in SCET for several physical observables within a single framework. Keywords: QCD Phenomenology ArXiv ePrint: 1906.11258
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)005
JHEP05(2020)005
A formalism for the resummation of non-factorizable observables in SCET
Contents 1 Introduction
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2 Remarks on the counting of logarithms
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3 Kinematics and notation
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5 General expressions for the fully differential transfer function 5.1 Numerical treatment of the UV and rapidity divergences 5.2 Numerical treatment of the IRC divergences 5.3 General expression for the transfer function at NLL 5.4 General expression for the transfer function at NNLL 5.4.1 The soft transfer function 5.4.2 The collinear transfer function
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6 Explicit results for transfer function 6.1 Explicit expressions at NLL 6.2 Explicit expressions at NNLL NLL 6.2.1 Expression for Ps,` 0 NNLL 6.2.2 δFs (v): the soft contribution 0 NNLL 6.2.3 δFn,¯ (v): the collinear contribution n
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7 Dealing with the observable 7.1 The soft sector 7.2 The collinear sector and the zero-bin subtraction
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8 Conclusions
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A Kinematics and phase space parametrization
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B SCET amplitudes
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C Numerical algorithms C.1 Results at NLL C.2 Results at NNLL NLL , V ](Φ ; v): higher order terms in the NLL transfer function C.2.1 F NLL [Ps,` B C.2.2 δFsNNLL (ΦB ; v): higher order corrections to the soft correlated clusters NNLL (Φ ; v): the collinear correction to the transfer function C.2.3 δFn,¯ B n LL , P NLL , V ](Φ ; v): expansion of P NLL in F NLL [P NLL , V ](Φ ; v) C.3 δF NLL [Ps,` B B ` s,` s,`
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JHEP05(2020)005
4 Basic idea of numerical resummation for rIRC safe observables 4.1 Factorization of the fully differential energy distribution 4.2 Definition of the simple observable 4.3 The SCET Lagrangian and resummation of the simple observable 4.4 Definition of the transfer function
D An D.1 D.2 D.3 D.4
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