Abstract
The splitting processes of bremsstrahlung and pair production in a medium are coherent over large distances in the very high energy limit, which leads to a suppression known as the Landau-Pomeranchuk-Migdal (LPM) effect. We continue study of the case when the coherence lengths of two consecutive splitting processes overlap (which is important for understanding corrections to standard treatments of the LPM effect in QCD), avoiding soft-emission approximations. Previous work has computed overlap effects for double splitting g → gg → ggg. To make use of those results, one also needs calculations of related virtual loop corrections to single splitting g → gg in order to cancel severe (power-law) infrared (IR) divergences. This paper provides calculations of nearly all such processes involving gluons and discusses how to organize the results to demonstrate the cancellation. In the soft emission limit, our results reproduce the known double-log behavior of earlier authors who worked in leading-log approximation. We also present a first (albeit numerical and not yet analytic) investigation of sub-leading, single IR logarithms. Ultraviolet divergences appearing in our calculations correctly renormalize the coupling αs in the usual LPM result for leading-order g → gg.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Change history
18 May 2022
An Erratum to this paper has been published: https://doi.org/10.1007/JHEP05(2022)114
References
L.D. Landau and I. Pomeranchuk, Limits of applicability of the theory of bremsstrahlung electrons and pair production at high-energies, Dokl. Akad. Nauk Ser. Fiz. 92 (1953) 535 [INSPIRE].
L.D. Landau and I. Pomeranchuk, ‘Electron cascade process at very high energies, Dokl. Akad. Nauk Ser. Fiz. 92 (1953) 735 [INSPIRE].
A.B. Migdal, Bremsstrahlung and pair production in condensed media at high-energies, Phys. Rev. 103 (1956) 1811 [INSPIRE].
L. Landau, The Collected Papers of L.D. Landau, Pergamon Press, New York U.S.A. (1965).
R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, The Landau-Pomeranchuk-Migdal effect in QED, Nucl. Phys. B 478 (1996) 577 [hep-ph/9604327] [INSPIRE].
R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Radiative energy loss of high-energy quarks and gluons in a finite volume quark-gluon plasma, Nucl. Phys. B 483 (1997) 291 [hep-ph/9607355] [INSPIRE].
R. Baier, Y.L. Dokshitzer, A.H. Mueller, S. Peigne and D. Schiff, Radiative energy loss and p⊥ broadening of high-energy partons in nuclei, Nucl. Phys. B 484 (1997) 265 [hep-ph/9608322] [INSPIRE].
B.G. Zakharov, Fully quantum treatment of the Landau-Pomeranchuk-Migdal effect in QED and QCD, JETP Lett. 63 (1996) 952 [hep-ph/9607440] [INSPIRE].
B.G. Zakharov, Radiative energy loss of high-energy quarks in finite size nuclear matter and quark-gluon plasma, JETP Lett. 65 (1997) 615 [hep-ph/9704255] [INSPIRE].
J.-P. Blaizot and Y. Mehtar-Tani, Renormalization of the jet-quenching parameter, Nucl. Phys. A 929 (2014) 202 [arXiv:1403.2323] [INSPIRE].
E. Iancu, The non-linear evolution of jet quenching, JHEP 10 (2014) 095 [arXiv:1403.1996] [INSPIRE].
B. Wu, Radiative energy loss and radiative p⊥-broadening of high-energy partons in QCD matter, JHEP 12 (2014) 081 [arXiv:1408.5459] [INSPIRE].
P. Arnold, S. Iqbal and T. Rase, Strong- vs. weak-coupling pictures of jet quenching: a dry run using QED, JHEP 05 (2019) 004 [arXiv:1810.06578] [INSPIRE].
S.S. Gubser, D.R. Gulotta, S.S. Pufu and F.D. Rocha, Gluon energy loss in the gauge-string duality, JHEP 10 (2008) 052 [arXiv:0803.1470] [INSPIRE].
Y. Hatta, E. Iancu and A.H. Mueller, Jet evolution in the \( \mathcal{N} \) = 4 SYM plasma at strong coupling, JHEP 05 (2008) 037 [arXiv:0803.2481] [INSPIRE].
P.M. Chesler, K. Jensen, A. Karch and L.G. Yaffe, Light quark energy loss in strongly-coupled \( \mathcal{N} \) = 4 supersymmetric Yang-Mills plasma, Phys. Rev. D 79 (2009) 125015 [arXiv:0810.1985] [INSPIRE].
P. Arnold and D. Vaman, Jet quenching in hot strongly coupled gauge theories revisited: 3-point correlators with gauge-gravity duality, JHEP 10 (2010) 099 [arXiv:1008.4023] [INSPIRE].
P. Arnold and D. Vaman, Jet quenching in hot strongly coupled gauge theories simplified, JHEP 04 (2011) 027 [arXiv:1101.2689] [INSPIRE].
P. Arnold and S. Iqbal, In-medium loop corrections and longitudinally polarized gauge bosons in high-energy showers, JHEP 12 (2018) 120 [arXiv:1806.08796] [INSPIRE].
G. Lepage and S.J. Brodsky, Exclusive Processes in Perturbative Quantum Chromodynamics, Phys. Rev. D 22 (1980) 2157 [INSPIRE].
S.J. Brodsky and G. Lepage, Exclusive Processes in Quantum Chromodynamics, Adv. Ser. Direct. High Energy Phys. 5 (1989) 93 [INSPIRE].
S.J. Brodsky, H.-C. Pauli and S.S. Pinsky, Quantum chromodynamics and other field theories on the light cone, Phys. Rept. 301 (1998) 299 [hep-ph/9705477] [INSPIRE].
Y.V. Kovchegov and E. Levin, Quantum chromodynamics at high energy, Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol. 33 (2012) 1, errata available, as of this writing, at https://www.asc.ohio-state.edu/kovchegov.1/typos.pdf, or on the publisher’s web site under the book’s resources.
P. Arnold, H.-C. Chang and S. Iqbal, The LPM effect in sequential bremsstrahlung: 4-gluon vertices, JHEP 10 (2016) 124 [arXiv:1608.05718] [INSPIRE].
P. Arnold and S. Iqbal, The LPM effect in sequential bremsstrahlung, JHEP 04 (2015) 070 [Erratum ibid. 09 (2016) 072] [arXiv:1501.04964] [INSPIRE].
P. Arnold, H.-C. Chang and S. Iqbal, The LPM effect in sequential bremsstrahlung 2: factorization, JHEP 09 (2016) 078 [arXiv:1605.07624] [INSPIRE].
P. Arnold, H.-C. Chang and S. Iqbal, The LPM effect in sequential bremsstrahlung: dimensional regularization, JHEP 10 (2016) 100 [arXiv:1606.08853] [INSPIRE].
P. Arnold, Landau-Pomeranchuk-Migdal effect in sequential bremsstrahlung: From large-N QCD to N = 3 via the SU(N) analog of Wigner 6-j symbols, Phys. Rev. D 100 (2019) 034030 [arXiv:1904.04264] [INSPIRE].
P. Arnold, Multi-particle potentials from light-like Wilson lines in quark-gluon plasmas: a generalized relation of in-medium splitting rates to jet-quenching parameters \( \hat{q} \), Phys. Rev. D 99 (2019) 054017 [arXiv:1901.05475] [INSPIRE].
G. Beuf, Dipole factorization for DIS at NLO: Loop correction to the \( {\gamma}_{T,L}^{\ast}\to q\overline{q} \) light-front wave functions, Phys. Rev. D 94 (2016) 054016 [arXiv:1606.00777] [INSPIRE].
G. Beuf, Dipole factorization for DIS at NLO: Combining the \( q\overline{q} \) and \( q\overline{q}g \) contributions, Phys. Rev. D 96 (2017) 074033 [arXiv:1708.06557] [INSPIRE].
T. Lappi and R. Paatelainen, The one loop gluon emission light cone wave function, Annals Phys. 379 (2017) 34 [arXiv:1611.00497] [INSPIRE].
H. Hänninen, T. Lappi and R. Paatelainen, One-loop corrections to light cone wave functions: the dipole picture DIS cross section, Annals Phys. 393 (2018) 358 [arXiv:1711.08207] [INSPIRE].
A. Harindranath and W.-M. Zhang, Light front QCD. 3: Coupling constant renormalization, Phys. Rev. D 48 (1993) 4903 [INSPIRE].
J.-P. Blaizot, E. Iancu and Y. Mehtar-Tani, Medium-induced QCD cascade: democratic branching and wave turbulence, Phys. Rev. Lett. 111 (2013) 052001 [arXiv:1301.6102] [INSPIRE].
J.-P. Blaizot and Y. Mehtar-Tani, Energy flow along the medium-induced parton cascade, Annals Phys. 368 (2016) 148 [arXiv:1501.03443] [INSPIRE].
S. Jeon and G.D. Moore, Energy loss of leading partons in a thermal QCD medium, Phys. Rev. C 71 (2005) 034901 [hep-ph/0309332] [INSPIRE].
P.B. Arnold, S. Cantrell and W. Xiao, Stopping distance for high energy jets in weakly-coupled quark-gluon plasmas, Phys. Rev. D 81 (2010) 045017 [arXiv:0912.3862] [INSPIRE].
J. Ghiglieri, G.D. Moore and D. Teaney, Jet-Medium Interactions at NLO in a Weakly-Coupled Quark-Gluon Plasma, JHEP 03 (2016) 095 [arXiv:1509.07773] [INSPIRE].
T. Liou, A.H. Mueller and B. Wu, Radiative p⊥-broadening of high-energy quarks and gluons in QCD matter, Nucl. Phys. A 916 (2013) 102 [arXiv:1304.7677] [INSPIRE].
I.S. Gradshteyn and I.M. Ryzhik, Table of Integrals, Series, and Products, fourth corrected and enlarged edition, Academic Press, New York U.S.A. (1980).
S. Catani and M. Grazzini, Collinear factorization and splitting functions for next-to-next-to-leading order QCD calculations, Phys. Lett. B 446 (1999) 143 [hep-ph/9810389] [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2007.15018
This work was completed while Shahin Iqbal was on leave from the National Centre for Physics, Quaid-i-Azam University Campus, Islamabad, Pakistan.
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Arnold, P., Gorda, T. & Iqbal, S. The LPM effect in sequential bremsstrahlung: nearly complete results for QCD. J. High Energ. Phys. 2020, 53 (2020). https://doi.org/10.1007/JHEP11(2020)053
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2020)053