Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD

Dixon, Lance J.; Luo, M. X.; Shtabovenko, Vladyslav; Yang, Tong Zhi; Zhu, Hua Xing

doi:10.1103/physrevlett.120.102001

Cited by 79 publications

(130 citation statements)

References 61 publications

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“…The two-loop plus distribution terms D n (z) are in full agreement with the analytical NLO calculation in Ref. [82], while the two-loop δ(1 − z) term is new. Eq.…”

Section: Jet Function For the Eec In The Back-to-back Limitsupporting

confidence: 79%

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Transverse parton distribution and fragmentation functions at NNLO: the quark case

Luo

Wang

et al. 2019

J. High Energ. Phys.

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We revisit the calculation of perturbative quark transverse momentum dependent parton distribution functions and fragmentation functions using the exponential regulator for rapidity divergences. We show that the exponential regulator provides a consistent framework for the calculation of various ingredients in transverse momentum dependent factorization. Compared to existing regulators in the literature, the exponential regulator has a couple of advantages which we explain in detail. As a result, the calculation is greatly simplified and we are able to obtain the next-to-next-to-leading order results up to O( 2 ) in dimensional regularization. These terms are necessary for a higher order calculation which is made possible with the simplification brought by the new regulator. As a by-product, we have obtained the two-loop quark jet function for the Energy-Energy Correlator in the back-to-back limit, which is the last missing ingredient for its N 3 LL resummation.

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“…The two-loop plus distribution terms D n (z) are in full agreement with the analytical NLO calculation in Ref. [82], while the two-loop δ(1 − z) term is new. Eq.…”

Section: Jet Function For the Eec In The Back-to-back Limitsupporting

confidence: 79%

“…tot is the total hadronic cross section for e + e − including higher order QCD corrections. Using the analytical NLO formula of EEC for 0 < z < 1 from[82], and the end point contribution in Eq. (4.17), we explicit verify the sum rule in Eq.…”

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confidence: 99%

Transverse parton distribution and fragmentation functions at NNLO: the quark case

Luo

Wang

et al. 2019

J. High Energ. Phys.

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“…This equation can be derived by requiring the cumulant Σ in Eq. (6) to be RG invariant, combined with the evolution equation (8) for the hard function. As indicated in Eq.…”

Section: Factorization Formulamentioning

confidence: 99%

Collinear limit of the energy-energy correlator

2019

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The energy-energy-correlator (EEC) observable in e + e − annihilation measures the energy deposited in two detectors as a function of the angle between the detectors. The collinear limit, where the angle between the two detectors approaches zero, is of particular interest for describing the substructure of jets produced at hadron colliders as well as in e + e − annihilation. We derive a factorization formula for the leading power asymptotic behavior in the collinear limit of a generic quantum field theory, which allows for the resummation of logarithmically enhanced terms to all orders by renormalization group evolution. The relevant anomalous dimensions are expressed in terms of the timelike data of the theory, in particular the moments of the timelike splitting functions, which are known to high perturbative orders. We relate the small angle and back-to-back limits to each other via the total cross section and an integral over intermediate angles. This relation, for the EEC in e + e − and in Higgs decay to gluons, provides us with the initial conditions for quark and gluon jet functions at order α 2 s . In QCD and in N = 1 super-Yang-Mills theory, we then perform the resummation to next-to-next-to-leading logarithm, improving previous calculations by two perturbative orders. We highlight the important role played by the non-vanishing β function in these theories, which while subdominant for Higgs decays to gluons, dominates the behavior of the EEC in the collinear limit for e + e − annihilation, and in N = 1 super-Yang-Mills theory. In conformally invariant N = 4 super-Yang-Mills theory, reciprocity between timelike and spacelike evolution can be used to express our factorization formula as a power law with exponent equal to the spacelike twist-two spin-three anomalous dimensions, thus providing a connection between timelike and spacelike approaches.

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“…The availability of reliable numerical NNLO predictions for event shape observables in e + e − annihilation is undoubtedly useful, but the corresponding analytic results (even at NLO) are still interesting and desirable. Currently, the standard EEC is the only QCD event shape observable known analytically at NLO [56]. There has also been remarkable progress in computing EEC analytically in N = 4 supersymmetric Yang-Mills theory [57,58].…”

Section: Introductionmentioning

confidence: 99%

Analytic next-to-leading order calculation of energy-energy correlation in gluon-initiated Higgs decays

Luo

Shtabovenko

Yang

et al. 2019

J. High Energ. Phys.

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The energy-energy correlation (EEC) function in e + e − annihilation is currently the only QCD event shape observable for which we know the full analytic result at the next-to-leading order (NLO). In this work we calculate the EEC observable for gluon initiated Higgs decay analytically at NLO in the Higgs Effective Field Theory (HEFT) framework and provide the full results expressed in terms of classical polylogarithms, including the asymptotic behavior in the collinear and back-to-back limits. This observable can be, in principle, measured at the future e + e − colliders such as CEPC, ILC, FCC-ee or CLIC. It provides an interesting opportunity to simultaneously probe our understanding of the strong and Higgs sectors and can be used for the determinations of the strong coupling.

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Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD

Cited by 79 publications

References 61 publications

Transverse parton distribution and fragmentation functions at NNLO: the quark case

Transverse parton distribution and fragmentation functions at NNLO: the quark case

Collinear limit of the energy-energy correlator

Analytic next-to-leading order calculation of energy-energy correlation in gluon-initiated Higgs decays

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