zbMATH — the first resource for mathematics

From correlation functions to event shapes in QCD. (English) Zbl 1460.81109
Summary: We present a method for calculating event shapes in QCD based on correlation functions of conserved currents. The method has been previously applied to the maximally supersymmetric Yang-Mills theory, but we demonstrate that supersymmetry is not essential. As a proof of concept, we consider the simplest example of a charge-charge correlation at one loop (leading order). We compute the correlation function of four electromagnetic currents and explain in detail the steps needed to extract the event shape from it. The result is compared to the standard amplitude calculation. The explicit four-point correlation function may also be of interest for the CFT community.
81V05 Strong interaction, including quantum chromodynamics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
PDF BibTeX Cite
Full Text: DOI arXiv
[1] Fox, GC; Wolfram, S., Observables for the Analysis of Event Shapes in e^+e^−Annihilation and Other Processes, Phys. Rev. Lett., 41, 1581 (1978)
[2] Basham, CL; Brown, LS; Ellis, SD; Love, ST, Energy Correlations in Electron-Positron Annihilation: Testing QCD, Phys. Rev. Lett., 41, 1585 (1978)
[3] Basham, CL; Brown, LS; Ellis, SD; Love, ST, Energy Correlations in electron-Positron Annihilation in Quantum Chromodynamics: Asymptotically Free Perturbation Theory, Phys. Rev. D, 19, 2018 (1979)
[4] Ellis, RK; Ross, DA; Terrano, AE, The Perturbative Calculation of Jet Structure in e^+e^−Annihilation, Nucl. Phys. B, 178, 421 (1981)
[5] Z. Kunszt, P. Nason, G. Marchesini and B.R. Webber, QCD at LEP, ETH-PT-89-39, [INSPIRE].
[6] Kunszt, Z.; Soper, DE, Calculation of jet cross sections in hadron collisions at order α^3, Phys. Rev. D, 46, 192 (1992)
[7] Biebel, O., Experimental tests of the strong interaction and its energy dependence in electron positron annihilation, Phys. Rept., 340, 165 (2001)
[8] Belitsky, AV; Korchemsky, GP; Sterman, GF, Energy flow in QCD and event shape functions, Phys. Lett. B, 515, 297 (2001)
[9] Dixon, LJ; Luo, M-X; Shtabovenko, V.; Yang, T-Z; Zhu, HX, Analytical Computation of Energy-Energy Correlation at Next-to-Leading Order in QCD, Phys. Rev. Lett., 120, 102001 (2018)
[10] Glover, EWN; Sutton, MR, The energy-energy correlation function revisited, Phys. Lett. B, 342, 375 (1995)
[11] Belitsky, AV; Hohenegger, S.; Korchemsky, GP; Sokatchev, E.; Zhiboedov, A., Energy-Energy Correlations in N = 4 Supersymmetric Yang-Mills Theory, Phys. Rev. Lett., 112 (2014) · Zbl 1323.81056
[12] Del Duca, V., Jet production in the CoLoRFulNNLO method: event shapes in electron-positron collisions, Phys. Rev. D, 94 (2016)
[13] Henn, JM; Sokatchev, E.; Yan, K.; Zhiboedov, A., Energy-energy correlation in N =4 super Yang-Mills theory at next-to-next-to-leading order, Phys. Rev. D, 100 (2019)
[14] Hofman, DM; Maldacena, J., Conformal collider physics: Energy and charge correlations, JHEP, 05, 012 (2008)
[15] Belitsky, AV; Hohenegger, S.; Korchemsky, GP; Sokatchev, E.; Zhiboedov, A., From correlation functions to event shapes, Nucl. Phys. B, 884, 305 (2014) · Zbl 1323.81084
[16] Belitsky, AV; Hohenegger, S.; Korchemsky, GP; Sokatchev, E.; Zhiboedov, A., Event shapes in \(\mathcal{N} = 4\) super-Yang-Mills theory, Nucl. Phys. B, 884, 206 (2014) · Zbl 1323.81056
[17] Korchemsky, GP, Energy correlations in the end-point region, JHEP, 01, 008 (2020) · Zbl 1434.81105
[18] Dixon, LJ; Moult, I.; Zhu, HX, Collinear limit of the energy-energy correlator, Phys. Rev. D, 100 (2019)
[19] Kologlu, M.; Kravchuk, P.; Simmons-Duffin, D.; Zhiboedov, A., The light-ray OPE and conformal colliders, JHEP, 01, 128 (2021)
[20] Belitsky, AV; Hohenegger, S.; Korchemsky, GP; Sokatchev, E., N = 4 superconformal Ward identities for correlation functions, Nucl. Phys. B, 904, 176 (2016) · Zbl 1332.81201
[21] Korchemsky, GP; Sokatchev, E., Four-point correlation function of stress-energy tensors in \(\mathcal{N} = 4\) superconformal theories, JHEP, 12, 133 (2015) · Zbl 1388.81053
[22] Sotkov, GM; Zaikov, RP, On the Structure of the Conformal Covariant N Point Functions, Rept. Math. Phys., 19, 335 (1984) · Zbl 0555.22005
[23] Dymarsky, A., On the four-point function of the stress-energy tensors in a CFT, JHEP, 10, 075 (2015) · Zbl 1388.81408
[24] Kravchuk, P.; Simmons-Duffin, D., Counting Conformal Correlators, JHEP, 02, 096 (2018) · Zbl 1387.81325
[25] D. Karateev, Kinematics of 4D Conformal Field Theories, Ph.D. Thesis, unpublished.
[26] Ore, FR Jr; Sterman, GF, An Operator Approach To Weighted Cross-sections, Nucl. Phys. B, 165, 93 (1980)
[27] Sveshnikov, NA; Tkachov, FV, Jets and quantum field theory, Phys. Lett. B, 382, 403 (1996)
[28] Korchemsky, GP; Oderda, G.; Sterman, GF, Power corrections and nonlocal operators, AIP Conf. Proc., 407, 988 (1997)
[29] Korchemsky, GP; Sterman, GF, Power corrections to event shapes and factorization, Nucl. Phys. B, 555, 335 (1999)
[30] Belitsky, AV; Korchemsky, GP; Sterman, GF, Energy flow in QCD and event shape functions, Phys. Lett. B, 515, 297 (2001)
[31] R.K. Ellis, W.J. Stirling and B.R. Webber, QCD and collider physics, vol. 8, Cambridge University Press (2011) [INSPIRE].
[32] G. Mack, D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes, arXiv:0907.2407 [INSPIRE].
[33] Caron-Huot, S., Analyticity in Spin in Conformal Theories, JHEP, 09, 078 (2017) · Zbl 1382.81173
[34] Alday, LF; Caron-Huot, S., Gravitational S-matrix from CFT dispersion relations, JHEP, 12, 017 (2018) · Zbl 1405.81114
[35] Eden, B.; Schubert, C.; Sokatchev, E., Three loop four point correlator in N = 4 SYM, Phys. Lett. B, 482, 309 (2000) · Zbl 0990.81121
[36] Eden, B.; Korchemsky, GP; Sokatchev, E., From correlation functions to scattering amplitudes, JHEP, 12, 002 (2011) · Zbl 1306.81096
[37] Bern, Z.; Morgan, AG, Massive loop amplitudes from unitarity, Nucl. Phys. B, 467, 479 (1996)
[38] Usyukina, NI; Davydychev, AI, Exact results for three and four point ladder diagrams with an arbitrary number of rungs, Phys. Lett. B, 305, 136 (1993)
[39] N.I. Usyukina and A.I. Davydychev, Some exact results for two loop diagrams with three and four external lines, Phys. Atom. Nucl.56 (1993) 1553 [Yad. Fiz.56N11 (1993) 172] [hep-ph/9307327] [INSPIRE].
[40] Banfi, A.; Salam, GP; Zanderighi, G., Phenomenology of event shapes at hadron colliders, JHEP, 06, 038 (2010) · Zbl 1290.81159
[41] Drummond, J.; Duhr, C.; Eden, B.; Heslop, P.; Pennington, J.; Smirnov, VA, Leading singularities and off-shell conformal integrals, JHEP, 08, 133 (2013) · Zbl 1342.81574
[42] Eden, B.; Smirnov, VA, Evaluating four-loop conformal Feynman integrals by D-dimensional differential equations, JHEP, 10, 115 (2016) · Zbl 1390.81280
[43] Velizhanin, VN, Non-planar anomalous dimension of twist-2 operators: higher moments at four loops, Nucl. Phys. B, 885, 772 (2014) · Zbl 1323.81065
[44] Herzog, F.; Moch, S.; Ruijl, B.; Ueda, T.; Vermaseren, JAM; Vogt, A., Five-loop contributions to low-N non-singlet anomalous dimensions in QCD, Phys. Lett. B, 790, 436 (2019)
[45] Drummond, JM; Henn, J.; Smirnov, VA; Sokatchev, E., Magic identities for conformal four-point integrals, JHEP, 01, 064 (2007)
[46] Schnetz, O., Graphical functions and single-valued multiple polylogarithms, Commun. Num. Theor. Phys., 08, 589 (2014) · Zbl 1320.81075
[47] Braun, VM; Korchemsky, GP; Müller, D., The uses of conformal symmetry in QCD, Prog. Part. Nucl. Phys., 51, 311 (2003)
[48] Grozin, A.; Henn, JM; Korchemsky, GP; Marquard, P., The three-loop cusp anomalous dimension in QCD and its supersymmetric extensions, JHEP, 01, 140 (2016) · Zbl 1388.81323
[49] Braun, VM; Manashov, AN; Moch, SO; Strohmaier, M., Conformal symmetry of QCD in d-dimensions, Phys. Lett. B, 793, 78 (2019) · Zbl 1421.81156
[50] Chen, H.; Luo, M-X; Moult, I.; Yang, T-Z; Zhang, X.; Zhu, HX, Three point energy correlators in the collinear limit: symmetries, dualities and analytic results, JHEP, 08, 028 (2020)
[51] A. Galperin, E. Ivanov, S. Kalitsyn, V. Ogievetsky and E. Sokatchev, Unconstrained N = 2 Matter, Yang-Mills and Supergravity Theories in Harmonic Superspace, Class. Quant. Grav.1 (1984) 469 [Erratum ibid.2 (1985) 127] [INSPIRE].
[52] A.S. Galperin, E.A. Ivanov, V.I. Ogievetsky and E.S. Sokatchev, Harmonic superspace, Cambridge University Press, Cambridge, U.K. (2001), [DOI]. · Zbl 1029.81003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.