Abstract
The Kaluza-Klein (KK) decomposition of higher-dimensional gravity gives rise to a tower of KK-gravitons in the effective four-dimensional (4D) theory. Such massive spin-2 fields are known to be connected with unitarity issues and easily lead to a breakdown of the effective theory well below the naive scale of the interaction. However, the breakdown of the effective 4D theory is expected to be controlled by the parameters of the 5D theory. Working in a simplified Randall-Sundrum model we study the matrix elements for matter annihilations into massive gravitons. We find that truncating the KK-tower leads to an early breakdown of perturbative unitarity. However, by considering the full tower we obtain a set of sum rules for the couplings between the different KK-fields that restore unitarity up to the scale of the 5D theory. We prove analytically that these are fulfilled in the model under consideration and present numerical tests of their convergence. This work complements earlier studies that focused on graviton self-interactions and yields additional sum rules that are required if matter fields are incorporated into warped extra-dimensions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
T. Kaluza, Zum Unitätsproblem der Physik, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1921 (1921) 966 [arXiv:1803.08616] [INSPIRE].
O. Klein, Quantum Theory and Five-Dimensional Theory of Relativity (in German and English), Z. Phys. 37 (1926) 895 [INSPIRE].
I. Antoniadis, A Possible new dimension at a few TeV, Phys. Lett. B 246 (1990) 377 [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos and G. R. Dvali, The Hierarchy problem and new dimensions at a millimeter, Phys. Lett. B 429 (1998) 263 [hep-ph/9803315] [INSPIRE].
T. Appelquist, H.-C. Cheng and B. A. Dobrescu, Bounds on universal extra dimensions, Phys. Rev. D 64 (2001) 035002 [hep-ph/0012100] [INSPIRE].
L. Randall and R. Sundrum, A Large mass hierarchy from a small extra dimension, Phys. Rev. Lett. 83 (1999) 3370 [hep-ph/9905221] [INSPIRE].
L. Randall and R. Sundrum, An Alternative to compactification, Phys. Rev. Lett. 83 (1999) 4690 [hep-th/9906064] [INSPIRE].
K. Hinterbichler, Theoretical Aspects of Massive Gravity, Rev. Mod. Phys. 84 (2012) 671 [arXiv:1105.3735] [INSPIRE].
G. F. Giudice, R. Rattazzi and J. D. Wells, Quantum gravity and extra dimensions at high-energy colliders, Nucl. Phys. B 544 (1999) 3 [hep-ph/9811291] [INSPIRE].
D. Hooper and S. Profumo, Dark Matter and Collider Phenomenology of Universal Extra Dimensions, Phys. Rept. 453 (2007) 29 [hep-ph/0701197] [INSPIRE].
K. Agashe, A. Belyaev, T. Krupovnickas, G. Perez and J. Virzi, LHC Signals from Warped Extra Dimensions, Phys. Rev. D 77 (2008) 015003 [hep-ph/0612015] [INSPIRE].
J. Bonifacio, K. Hinterbichler and R. A. Rosen, Constraints on a gravitational Higgs mechanism, Phys. Rev. D 100 (2019) 084017 [arXiv:1903.09643] [INSPIRE].
R. Sekhar Chivukula, D. Foren, K. A. Mohan, D. Sengupta and E. H. Simmons, Sum Rules for Massive Spin-2 Kaluza-Klein Elastic Scattering Amplitudes, Phys. Rev. D 100 (2019) 115033 [arXiv:1910.06159] [INSPIRE].
R. Sekhar Chivukula, D. Foren, K. A. Mohan, D. Sengupta and E. H. Simmons, Scattering amplitudes of massive spin-2 Kaluza-Klein states grow only as \( \mathcal{O}(s) \), Phys. Rev. D 101 (2020) 055013 [arXiv:1906.11098] [INSPIRE].
R. S. Chivukula, D. Foren, K. A. Mohan, D. Sengupta and E. H. Simmons, Massive Spin-2 Scattering Amplitudes in Extra-Dimensional Theories, Phys. Rev. D 101 (2020) 075013 [arXiv:2002.12458] [INSPIRE].
H. M. Lee, M. Park and V. Sanz, Gravity-mediated (or Composite) Dark Matter, Eur. Phys. J. C 74 (2014) 2715 [arXiv:1306.4107] [INSPIRE].
T. D. Rueter, T. G. Rizzo and J. L. Hewett, Gravity-Mediated Dark Matter Annihilation in the Randall-Sundrum Model, JHEP 10 (2017) 094 [arXiv:1706.07540] [INSPIRE].
M. G. Folgado, A. Donini and N. Rius, Gravity-mediated Scalar Dark Matter in Warped Extra-Dimensions, JHEP 01 (2020) 161 [arXiv:1907.04340] [INSPIRE].
A. Carmona, J. Castellano Ruiz and M. Neubert, A warped scalar portal to fermionic dark matter, Eur. Phys. J. C 81 (2021) 58 [arXiv:2011.09492] [INSPIRE].
N. Arkani-Hamed, H. Georgi and M. D. Schwartz, Effective field theory for massive gravitons and gravity in theory space, Annals Phys. 305 (2003) 96 [hep-th/0210184] [INSPIRE].
M. D. Schwartz, Constructing gravitational dimensions, Phys. Rev. D 68 (2003) 024029 [hep-th/0303114] [INSPIRE].
C. de Rham and G. Gabadadze, Generalization of the Fierz-Pauli Action, Phys. Rev. D 82 (2010) 044020 [arXiv:1007.0443] [INSPIRE].
C. de Rham, G. Gabadadze and A. J. Tolley, Resummation of Massive Gravity, Phys. Rev. Lett. 106 (2011) 231101 [arXiv:1011.1232] [INSPIRE].
G. Gabadadze, D. Older and D. Pirtskhalava, Resolving the van Dam-Veltman-Zakharov and strong coupling problems in massive gravity and bigravity, Phys. Rev. D 100 (2019) 124017 [arXiv:1907.13491] [INSPIRE].
B. W. Lee, C. Quigg and H. B. Thacker, Weak Interactions at Very High-Energies: The Role of the Higgs Boson Mass, Phys. Rev. D 16 (1977) 1519 [INSPIRE].
J. Bonifacio and K. Hinterbichler, Unitarization from Geometry, JHEP 12 (2019) 165 [arXiv:1910.04767] [INSPIRE].
R. Rattazzi, Cargese lectures on extra-dimensions, in Cargese School of Particle Physics and Cosmology: the Interface, (2003) [hep-ph/0607055] [INSPIRE].
G. D. Kribs, TASI 2004 lectures on the phenomenology of extra dimensions, in Theoretical Advanced Study Institute in Elementary Particle Physics: Physics in D ≧ 4, (2006) [hep-ph/0605325] [INSPIRE].
S. Raychaudhuri and K. Sridhar, Particle Physics of Brane Worlds and Extra Dimensions, Cambridge Monographs on Mathematical Physics, Cambridge University Press, U.K. (2016) DOI.
P. Callin and F. Ravndal, Lagrangian formalism of gravity in the Randall-Sundrum model, Phys. Rev. D 72 (2005) 064026 [hep-ph/0412109] [INSPIRE].
C. Csáki, M. L. Graesser and G. D. Kribs, Radion dynamics and electroweak physics, Phys. Rev. D 63 (2001) 065002 [hep-th/0008151] [INSPIRE].
M. Fierz and W. Pauli, On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. Roy. Soc. Lond. A 173 (1939) 211 [INSPIRE].
H. Davoudiasl, J. L. Hewett and T. G. Rizzo, Phenomenology of the Randall-Sundrum Gauge Hierarchy Model, Phys. Rev. Lett. 84 (2000) 2080 [hep-ph/9909255] [INSPIRE].
T. Gleisberg, F. Krauss, K. T. Matchev, A. Schalicke, S. Schumann and G. Soff, Helicity formalism for spin-2 particles, JHEP 09 (2003) 001 [hep-ph/0306182] [INSPIRE].
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, ninth Dover printing, tenth gpo printing ed., Dover, New York, U.S.A. (1964).
Bessel Functions and Two-Dimensional Problems, https://math.libretexts.org/Bookshelves/Differential_Equations/Book%3A_Partial_Differential_Equations_(Walet)/10%3A_Bessel_Functions_and_Two-Dimensional_Problems.
I. N. Sneddon, On some infinite series involving the zeros of bessel functions of the first kind, Proceedings of the Glasgow Mathematical Association, 4 (1960) 144.
W. D. Goldberger and M. B. Wise, Modulus stabilization with bulk fields, Phys. Rev. Lett. 83 (1999) 4922 [hep-ph/9907447] [INSPIRE].
xAct: Efficient tensor computer algebra for the Wolfram Language, http://www.xact.es/.
D. Brizuela, J. M. Martín-García and G. A. Mena Marugán, xPert: Computer algebra for metric perturbation theory, Gen. Rel. Grav. 41 (2009) 2415 [arXiv:0807.0824] [INSPIRE].
N. D. Christensen and C. Duhr, FeynRules — Feynman rules made easy, Comput. Phys. Commun. 180 (2009) 1614 [arXiv:0806.4194] [INSPIRE].
R. Mertig, M. Böhm and A. Denner, FEYN CALC: Computer algebraic calculation of Feynman amplitudes, Comput. Phys. Commun. 64 (1991) 345 [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, New Developments in FeynCalc 9.0, Comput. Phys. Commun. 207 (2016) 432 [arXiv:1601.01167] [INSPIRE].
V. Shtabovenko, R. Mertig and F. Orellana, FeynCalc 9.3: New features and improvements, Comput. Phys. Commun. 256 (2020) 107478 [arXiv:2001.04407] [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: 2012.09672
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
de Giorgi, A., Vogl, S. Unitarity in KK-graviton production, a case study in warped extra-dimensions. J. High Energ. Phys. 2021, 143 (2021). https://doi.org/10.1007/JHEP04(2021)143
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP04(2021)143