Abstract
When computing radiative corrections in models with compactified extra dimensions, one has to sum over the entire tower of Kaluza-Klein excitations inside the loops. The loop corrections generate a difference between the coupling strength of a zero-mode gauge boson and the coupling strength of its Kaluza-Klein excitation, although both originate from the same higher-dimensional gauge interaction. Furthermore, this discrepancy will in general depend on the cutoff scale and assumptions about the UV completion of the extra-dimensional theory. In this article, these effects are studied in detail within the context of the minimal universal extra dimension model (MUED). The broad features of the cutoff scale dependence can be captured through the solution of the functional flow equation in five-dimensional space. However, an explicit diagrammatic calculation reveals some modifications due to the compactification of the extra dimension. Nevertheless, when imposing a physical renormalization condition, one finds that the UV sensitivity of the effective Kaluza-Klein gauge-boson vertex is relatively small and not very important for most phenomenological purposes. Similar conclusions should hold in a larger class of extra-dimensional models besides MUED.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Appelquist, H.-C. Cheng and B.A. Dobrescu, Bounds on universal extra dimensions, Phys. Rev. D 64 (2001) 035002 [hep-ph/0012100] [INSPIRE].
K.R. Dienes, E. Dudas and T. Gherghetta, Extra space-time dimensions and unification, Phys. Lett. B 436 (1998) 55 [hep-ph/9803466] [INSPIRE].
K.R. Dienes, E. Dudas and T. Gherghetta, Grand unification at intermediate mass scales through extra dimensions, Nucl. Phys. B 537 (1999) 47 [hep-ph/9806292] [INSPIRE].
R.S. Chivukula, A. Farzinnia, E.H. Simmons and R. Foadi, Production of massive color-octet vector bosons at next-to-leading order, Phys. Rev. D 85 (2012) 054005 [arXiv:1111.7261] [INSPIRE].
A. Freitas and D. Wiegand, QCD corrections to massive color-octet vector boson pair production, JHEP 09 (2017) 058 [arXiv:1706.09442] [INSPIRE].
T.R. Taylor and G. Veneziano, Strings and D = 4, Phys. Lett. B 212 (1988) 147 [INSPIRE].
I. Antoniadis, A possible new dimension at a few TeV, Phys. Lett. B 246 (1990) 377 [INSPIRE].
A. Perez-Lorenzana and R.N. Mohapatra, Effect of extra dimensions on gauge coupling unification, Nucl. Phys. B 559 (1999) 255 [hep-ph/9904504] [INSPIRE].
H.-C. Cheng, B.A. Dobrescu and C.T. Hill, Gauge coupling unification with extra dimensions and gravitational scale effects, Nucl. Phys. B 573 (2000) 597 [hep-ph/9906327] [INSPIRE].
G. Bhattacharyya, A. Datta, S.K. Majee and A. Raychaudhuri, Power law blitzkrieg in universal extra dimension scenarios, Nucl. Phys. B 760 (2007) 117 [hep-ph/0608208] [INSPIRE].
S. Raychaudhuri and K. Sridhar, Particle physics of brane worlds and extra dimensions, Cambridge University Press, Cambridge, U.K., (2016) [INSPIRE].
H. Gies, Renormalizability of gauge theories in extra dimensions, Phys. Rev. D 68 (2003) 085015 [hep-th/0305208] [INSPIRE].
I.Z. Rothstein, TASI lectures on effective field theories, hep-ph/0308266 [INSPIRE].
H.-C. Cheng, K.T. Matchev and M. Schmaltz, Radiative corrections to Kaluza-Klein masses, Phys. Rev. D 66 (2002) 036005 [hep-ph/0204342] [INSPIRE].
A. Freitas, K. Kong and D. Wiegand, Radiative corrections to masses and couplings in universal extra dimensions, JHEP 03 (2018) 093 [arXiv:1711.07526] [INSPIRE].
T.R. Morris, Renormalizable extra-dimensional models, JHEP 01 (2005) 002 [hep-ph/0410142] [INSPIRE].
C. Wetterich, Average action and the renormalization group equations, Nucl. Phys. B 352 (1991) 529 [INSPIRE].
C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301 (1993) 90 [arXiv:1710.05815] [INSPIRE].
M. Reuter and C. Wetterich, Effective average action for gauge theories and exact evolution equations, Nucl. Phys. B 417 (1994) 181 [INSPIRE].
H. Gies, Running coupling in Yang-Mills theory: a flow equation study, Phys. Rev. D 66 (2002) 025006 [hep-th/0202207] [INSPIRE].
A. Mück, A. Pilaftsis and R. Rückl, Minimal higher dimensional extensions of the Standard Model and electroweak observables, Phys. Rev. D 65 (2002) 085037 [hep-ph/0110391] [INSPIRE].
B.W. Harris and J.F. Owens, The two cutoff phase space slicing method, Phys. Rev. D 65 (2002) 094032 [hep-ph/0102128] [INSPIRE].
W. Beenakker, H. Kuijf, W.L. van Neerven and J. Smith, QCD corrections to heavy quark production in \( p\overline{p} \) collisions, Phys. Rev. D 40 (1989) 54 [INSPIRE].
W. Beenakker, M. Krämer, T. Plehn, M. Spira and P.M. Zerwas, Stop production at hadron colliders, Nucl. Phys. B 515 (1998) 3 [hep-ph/9710451] [INSPIRE].
T. Hahn, Generating Feynman diagrams and amplitudes with FeynArts 3, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260] [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, New developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
G. Passarino and M.J.G. Veltman, One loop corrections for e + e − annihilation into μ + μ − in the Weinberg model, Nucl. Phys. B 160 (1979) 151 [INSPIRE].
R. Höpker, Hadroproduction and decay of squarks and gluinos (in German), Ph.D. thesis, FB Physik, Univ. Hamburg, Hamburg, Germany, (1996) [DESY-T-96-02] [INT.REP.T-96-02] [INSPIRE].
D.F. Litim, Optimization of the exact renormalization group, Phys. Lett. B 486 (2000) 92 [hep-th/0005245] [INSPIRE].
D.F. Litim, Optimized renormalization group flows, Phys. Rev. D 64 (2001) 105007 [hep-th/0103195] [INSPIRE].
D.F. Litim, Mind the gap, Int. J. Mod. Phys. A 16 (2001) 2081 [hep-th/0104221] [INSPIRE].
A. Codello, R. Percacci, L. Rachwal and A. Tonero, Computing the effective action with the functional renormalization group, Eur. Phys. J. C 76 (2016) 226 [arXiv:1505.03119] [INSPIRE].
A.O. Barvinsky and G.A. Vilkovisky, Beyond the Schwinger-Dewitt technique: converting loops into trees and in-in currents, Nucl. Phys. B 282 (1987) 163 [INSPIRE].
A.O. Barvinsky and G.A. Vilkovisky, Covariant perturbation theory. 2: second order in the curvature. General algorithms, Nucl. Phys. B 333 (1990) 471 [INSPIRE].
I.G. Avramidi, The nonlocal structure of the one loop effective action via partial summation of the asymptotic expansion, Phys. Lett. B 236 (1990) 443 [INSPIRE].
I.G. Avramidi, The heat kernel approach for calculating the effective action in quantum field theory and quantum gravity, hep-th/9509077 [INSPIRE].
A. Codello and O. Zanusso, On the non-local heat kernel expansion, J. Math. Phys. 54 (2013) 013513 [arXiv:1203.2034] [INSPIRE].
A. Codello and A. Tonero, Renormalization group improved computation of correlation functions in theories with nontrivial phase diagram, Phys. Rev. D 94 (2016) 025015 [arXiv:1504.00225] [INSPIRE].
A. Codello, Renormalization group flow equations for the proper vertices of the background effective average action, Phys. Rev. D 91 (2015) 065032 [arXiv:1304.2059] [INSPIRE].
J. Kubo, H. Terao and G. Zoupanos, Kaluza-Klein thresholds and regularization (in)dependence, Nucl. Phys. B 574 (2000) 495 [hep-ph/9910277] [INSPIRE].
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.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1805.12142
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made.
The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
To view a copy of this licence, visit https://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Freitas, A., Wiegand, D. Renormalization and ultraviolet sensitivity of gauge vertices in universal extra dimensions. J. High Energ. Phys. 2018, 94 (2018). https://doi.org/10.1007/JHEP08(2018)094
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2018)094