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Energy-Energy Correlation in the back-to-back region at N$^3$LL+NNLO in QCD (2403.04077v2)

Published 6 Mar 2024 in hep-ph

Abstract: We consider the Energy-Energy Correlation (EEC) function in high-energy electron-positron annihilation to hadrons. In the back-to-back (two-jet) region, we perform the all-order resummation of the logarithmically-enhanced contributions in QCD perturbation theory up to next-to-next-to-next-to-leading logarithmic (N$3$LL) accuracy. Away from the back-to-back region, we consistently combine resummed predictions with the known fixed-order results up to next-to-next-to-leading order (NNLO) and we are able to obtain an accurate fit of the $\mathcal{O}(\alpha_S3)$ remainder function from the numerical QCD computation of the full spectrum. All perturbative terms up to order $\alpha_S3$ are included in our calculation and a non-trivial cross-check in the back-to-back region is obtained by comparing the SCET analytic calculation against the corresponding numerical QCD computation. In particular, the values of the $\mathcal{O}(\alpha_S3)$ resummation coefficients have been numerically verified. We regularize the Landau singularity of the QCD coupling within the so-called Minimal Prescription and we discuss the reduction of the perturbative scale dependence of distributions at higher orders, as a means to estimate the corresponding residual perturbative uncertainty. Finally, after introducing within a dispersive approach non-perturbative power corrections, we are able to obtain an accurate description of experimental data at LEP and SLC accelerators.

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References (44)
  1. S. Catani, L. Trentadue, G. Turnock and B. R. Webber, “Resummation of large logarithms in e+ e- event shape distributions,” Nucl. Phys. B 407 (1993), 3-42 doi:10.1016/0550-3213(93)90271-P
  2. C. L. Basham, L. S. Brown, S. D. Ellis and S. T. Love, “Energy Correlations in electron - Positron Annihilation: Testing QCD,” Phys. Rev. Lett. 41 (1978), 1585 doi:10.1103/PhysRevLett.41.1585
  3. J. C. Collins and D. E. Soper, “Back-To-Back Jets in QCD,” Nucl. Phys. B 193 (1981), 381 [erratum: Nucl. Phys. B 213 (1983), 545] doi:10.1016/0550-3213(81)90339-4
  4. J. C. Collins and D. E. Soper, “Back-To-Back Jets: Fourier Transform from B to K-Transverse,” Nucl. Phys. B 197 (1982), 446-476 doi:10.1016/0550-3213(82)90453-9
  5. J. C. Collins and D. E. Soper, “The Two Particle Inclusive Cross-section in e+⁢e−superscript𝑒superscript𝑒e^{+}e^{-}italic_e start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT italic_e start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT Annihilation at PETRA, PEP and LEP Energies,” Nucl. Phys. B 284 (1987), 253-270 doi:10.1016/0550-3213(87)90035-6
  6. J. Kodaira and L. Trentadue, “Summing Soft Emission in QCD,” Phys. Lett. B 112 (1982), 66 doi:10.1016/0370-2693(82)90907-8.
  7. J. Kodaira and L. Trentadue, “Single Logarithm Effects in electron-Positron Annihilation,” Phys. Lett. B 123 (1983), 335-338 doi:10.1016/0370-2693(83)91213-3
  8. D. de Florian and M. Grazzini, “The Back-to-back region in e+ e- energy-energy correlation,” Nucl. Phys. B 704 (2005), 387-403 doi:10.1016/j.nuclphysb.2004.10.051 [arXiv:hep-ph/0407241 [hep-ph]].
  9. Z. Tulipánt, A. Kardos and G. Somogyi, “Energy–energy correlation in electron–positron annihilation at NNLL + NNLO accuracy,” Eur. Phys. J. C 77 (2017) no.11, 749 doi:10.1140/epjc/s10052-017-5320-9 [arXiv:1708.04093 [hep-ph]].
  10. A. Kardos, S. Kluth, G. Somogyi, Z. Tulipánt and A. Verbytskyi, “Precise determination of αS⁢(MZ)subscript𝛼𝑆subscript𝑀𝑍\alpha_{S}(M_{Z})italic_α start_POSTSUBSCRIPT italic_S end_POSTSUBSCRIPT ( italic_M start_POSTSUBSCRIPT italic_Z end_POSTSUBSCRIPT ) from a global fit of energy–energy correlation to NNLO+NNLL predictions,” Eur. Phys. J. C 78 (2018) no.6, 498 doi:10.1140/epjc/s10052-018-5963-1 [arXiv:1804.09146 [hep-ph]].
  11. I. Moult and H. X. Zhu, “Simplicity from Recoil: The Three-Loop Soft Function and Factorization for the Energy-Energy Correlation,” JHEP 08 (2018), 160 doi:10.1007/JHEP08(2018)160 [arXiv:1801.02627 [hep-ph]].
  12. M. A. Ebert, B. Mistlberger and G. Vita, “The Energy-Energy Correlation in the back-to-back limit at N33{}^{3}start_FLOATSUPERSCRIPT 3 end_FLOATSUPERSCRIPTLO and N33{}^{3}start_FLOATSUPERSCRIPT 3 end_FLOATSUPERSCRIPTLL’,” JHEP 08 (2021), 022 doi:10.1007/JHEP08(2021)022 [arXiv:2012.07859 [hep-ph]].
  13. C. Duhr, B. Mistlberger and G. Vita, “Four-Loop Rapidity Anomalous Dimension and Event Shapes to Fourth Logarithmic Order,” Phys. Rev. Lett. 129 (2022) no.16, 162001 doi:10.1103/PhysRevLett.129.162001 [arXiv:2205.02242 [hep-ph]].
  14. L. J. Dixon, I. Moult and H. X. Zhu, “Collinear limit of the energy-energy correlator,” Phys. Rev. D 100 (2019) no.1, 014009 doi:10.1103/PhysRevD.100.014009 [arXiv:1905.01310 [hep-ph]].
  15. D. G. Richards, W. J. Stirling and S. D. Ellis, “Second Order Corrections to the Energy-energy Correlation Function in Quantum Chromodynamics,” Phys. Lett. B 119 (1982), 193-197 doi:10.1016/0370-2693(82)90275-1
  16. D. G. Richards, W. J. Stirling and S. D. Ellis, “Energy-energy Correlations to Second Order in Quantum Chromodynamics,” Nucl. Phys. B 229 (1983), 317-346 doi:10.1016/0550-3213(83)90335-8
  17. L. J. Dixon, M. X. Luo, V. Shtabovenko, T. Z. Yang and H. X. Zhu, “Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD,” Phys. Rev. Lett. 120 (2018) no.10, 102001 doi:10.1103/PhysRevLett.120.102001 [arXiv:1801.03219 [hep-ph]].
  18. V. Del Duca, C. Duhr, A. Kardos, G. Somogyi and Z. Trócsányi, “Three-Jet Production in Electron-Positron Collisions at Next-to-Next-to-Leading Order Accuracy,” Phys. Rev. Lett. 117 (2016) no.15, 152004 doi:10.1103/PhysRevLett.117.152004 [arXiv:1603.08927 [hep-ph]].
  19. V. Del Duca, C. Duhr, A. Kardos, G. Somogyi, Z. Szőr, Z. Trócsányi and Z. Tulipánt, “Jet production in the CoLoRFulNNLO method: event shapes in electron-positron collisions,” Phys. Rev. D 94 (2016) no.7, 074019 doi:10.1103/PhysRevD.94.074019 [arXiv:1606.03453 [hep-ph]].
  20. G. Bozzi, S. Catani, D. de Florian and M. Grazzini, “Transverse-momentum resummation and the spectrum of the Higgs boson at the LHC,” Nucl. Phys. B 737 (2006), 73-120 doi:10.1016/j.nuclphysb.2005.12.022 [arXiv:hep-ph/0508068 [hep-ph]].
  21. G. Parisi and R. Petronzio, “Small Transverse Momentum Distributions in Hard Processes,” Nucl. Phys. B 154 (1979), 427-440 doi:10.1016/0550-3213(79)90040-3
  22. J. C. Collins, D. E. Soper and G. F. Sterman, “Transverse Momentum Distribution in Drell-Yan Pair and W and Z Boson Production,” Nucl. Phys. B 250 (1985), 199-224 doi:10.1016/0550-3213(85)90479-1
  23. S. Catani, D. de Florian and M. Grazzini, “Universality of nonleading logarithmic contributions in transverse momentum distributions,” Nucl. Phys. B 596 (2001), 299-312 doi:10.1016/S0550-3213(00)00617-9 [arXiv:hep-ph/0008184 [hep-ph]].
  24. S. G. Gorishnii, A. L. Kataev and S. A. Larin, “The O⁢(αs3)𝑂subscriptsuperscript𝛼3𝑠O(\alpha^{3}_{s})italic_O ( italic_α start_POSTSUPERSCRIPT 3 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_s end_POSTSUBSCRIPT )-corrections to σt⁢o⁢t⁢(e+⁢e−→h⁢a⁢d⁢r⁢o⁢n⁢s)subscript𝜎𝑡𝑜𝑡→superscript𝑒superscript𝑒ℎ𝑎𝑑𝑟𝑜𝑛𝑠\sigma_{tot}(e^{+}e^{-}\rightarrow hadrons)italic_σ start_POSTSUBSCRIPT italic_t italic_o italic_t end_POSTSUBSCRIPT ( italic_e start_POSTSUPERSCRIPT + end_POSTSUPERSCRIPT italic_e start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT → italic_h italic_a italic_d italic_r italic_o italic_n italic_s ) and Γ⁢(τ−→ντ+h⁢a⁢d⁢r⁢o⁢n⁢s)Γ→superscript𝜏subscript𝜈𝜏ℎ𝑎𝑑𝑟𝑜𝑛𝑠\Gamma(\tau^{-}\rightarrow\nu_{\tau}+hadrons)roman_Γ ( italic_τ start_POSTSUPERSCRIPT - end_POSTSUPERSCRIPT → italic_ν start_POSTSUBSCRIPT italic_τ end_POSTSUBSCRIPT + italic_h italic_a italic_d italic_r italic_o italic_n italic_s ) in QCD,” Phys. Lett. B 259 (1991), 144-150 doi:10.1016/0370-2693(91)90149-K.
  25. L. R. Surguladze and M. A. Samuel, “Total hadronic cross-section in e+ e- annihilation at the four loop level of perturbative QCD,” Phys. Rev. Lett. 66 (1991), 560-563 [erratum: Phys. Rev. Lett. 66 (1991), 2416] doi:10.1103/PhysRevLett.66.560
  26. S. Catani, M. L. Mangano, P. Nason and L. Trentadue, “The Resummation of soft gluons in hadronic collisions,” Nucl. Phys. B 478 (1996), 273-310 doi:10.1016/0550-3213(96)00399-9 [arXiv:hep-ph/9604351 [hep-ph]].
  27. E. Laenen, G. F. Sterman and W. Vogelsang, “Higher order QCD corrections in prompt photon production,” Phys. Rev. Lett. 84 (2000), 4296-4299 doi:10.1103/PhysRevLett.84.4296 [arXiv:hep-ph/0002078 [hep-ph]].
  28. A. Kulesza, G. F. Sterman and W. Vogelsang, “Joint resummation in electroweak boson production,” Phys. Rev. D 66 (2002), 014011 doi:10.1103/PhysRevD.66.014011 [arXiv:hep-ph/0202251 [hep-ph]].
  29. U. G. Aglietti, “Winter model in the quasi-continuum limit,” Int. J. Mod. Phys. A 35 (2020) no.06, 2050026 doi:10.1142/S0217751X20500268 [arXiv:1903.05051 [quant-ph]].
  30. U. G. Aglietti and A. Cubeddu, “Winter (or δ𝛿\deltaitalic_δ-shell) model at small and intermediate volumes,” Annals Phys. 444 (2022), 169047 doi:10.1016/j.aop.2022.169047 [arXiv:2202.07616 [quant-ph]].
  31. S. Camarda, L. Cieri and G. Ferrera, “Drell–Yan lepton-pair production: qT resummation at N4LL accuracy,” Phys. Lett. B 845 (2023), 138125 doi:10.1016/j.physletb.2023.138125 [arXiv:2303.12781 [hep-ph]].
  32. J. Kodaira and L. Trentadue, “SOFT GLUON EFFECTS IN PERTURBATIVE QUANTUM CHROMODYNAMICS,” SLAC-PUB-2934.
  33. O. V. Tarasov, A. A. Vladimirov and A. Y. Zharkov, “The Gell-Mann-Low Function of QCD in the Three Loop Approximation,” Phys. Lett. B 93 (1980), 429-432 doi:10.1016/0370-2693(80)90358-5
  34. S. A. Larin and J. A. M. Vermaseren, “The Three loop QCD Beta function and anomalous dimensions,” Phys. Lett. B 303 (1993), 334-336 doi:10.1016/0370-2693(93)91441-O [arXiv:hep-ph/9302208 [hep-ph]].
  35. T. van Ritbergen, J. A. M. Vermaseren and S. A. Larin, “The Four loop beta function in quantum chromodynamics,” Phys. Lett. B 400 (1997), 379-384 doi:10.1016/S0370-2693(97)00370-5 [arXiv:hep-ph/9701390 [hep-ph]].
  36. M. Czakon, “The Four-loop QCD beta-function and anomalous dimensions,” Nucl. Phys. B 710 (2005), 485-498 doi:10.1016/j.nuclphysb.2005.01.012 [arXiv:hep-ph/0411261 [hep-ph]].
  37. S. Moch, J. A. M. Vermaseren and A. Vogt, “The Three loop splitting functions in QCD: The Nonsinglet case,” Nucl. Phys. B 688 (2004), 101-134 doi:10.1016/j.nuclphysb.2004.03.030 [arXiv:hep-ph/0403192 [hep-ph]].
  38. T. Becher and M. Neubert,“Drell-Yan Production at Small qTsubscript𝑞𝑇q_{T}italic_q start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT, Transverse Parton Distributions and the Collinear Anomaly,” Eur. Phys. J. C 71 (2011), 1665 doi:10.1140/epjc/s10052-011-1665-7 [arXiv:1007.4005 [hep-ph]].
  39. S. Moch, B. Ruijl, T. Ueda, J. A. M. Vermaseren and A. Vogt, “On quartic colour factors in splitting functions and the gluon cusp anomalous dimension,” Phys. Lett. B 782 (2018), 627-632 doi:10.1016/j.physletb.2018.06.017 [arXiv:1805.09638 [hep-ph]].
  40. A. von Manteuffel, E. Panzer and R. M. Schabinger, “Cusp and collinear anomalous dimensions in four-loop QCD from form factors,” Phys. Rev. Lett. 124 (2020) no.16, 162001 doi:10.1103/PhysRevLett.124.162001 [arXiv:2002.04617 [hep-ph]].
  41. Y. Li and H. X. Zhu, “Bootstrapping Rapidity Anomalous Dimensions for Transverse-Momentum Resummation,” Phys. Rev. Lett. 118 (2017) no.2, 022004 doi:10.1103/PhysRevLett.118.022004 [arXiv:1604.01404 [hep-ph]].
  42. J. Kodaira and L. Trentadue, “CAN SOFT GLUON EFFECTS BE MEASURED IN ELECTRON - POSITRON ANNIHILATION?,” Prog. Theor. Phys. 69 (1983), 693 doi:10.1143/PTP.69.693
  43. R. Fiore, A. Quartarolo and L. Trentadue, “Energy-energy correlation for Theta —>>> 180-degrees at LEP,” Phys. Lett. B 294 (1992), 431-435 doi:10.1016/0370-2693(92)91545-K
  44. Y. L. Dokshitzer, G. Marchesini and B. R. Webber, “Nonperturbative effects in the energy energy correlation,” JHEP 07 (1999), 012 doi:10.1088/1126-6708/1999/07/012 [arXiv:hep-ph/9905339 [hep-ph]].
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