Abstract
We present the \( \mathcal{O}\left( {\alpha_s^3} \right) \) virtual QCD corrections to the process h → g + g + g due to interference of born and two-loop amplitudes, where h is a massive spin-2 particle and g is the gluon. We assume that the SM fields couple to h through the SM energy momentum tensor. Our result constitutes one of the ingredients to full NNLO QCD contribution to production of a massive spin-2 particle along with a jet in the scattering process at the LHC. In particular, this massive spin-2 could be a KK mode of a ADD graviton in large extra dimensional model or a RS KK mode in warped extra dimensional model or a generic massive spin-2. In addition, it provides an opportunity to study the ultraviolet and infrared structures of QCD amplitudes involving tensorial coupling resulting from energy momentum operator. Using dimensional regularization, we find that infrared poles of this amplitude are in agreement with the proposal by Catani confirming the factorization property of QCD amplitudes with tensorial insertion.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
ATLAS collaboration, Search for Extra Dimensions using diphoton events in 7 TeV proton-proton collisions with the ATLAS detector, Phys. Lett. B 710 (2012) 538 [arXiv:1112.2194] [INSPIRE].
CMS collaboration, Search for signatures of extra dimensions in the diphoton mass spectrum at the Large Hadron Collider, Phys. Rev. Lett. 108 (2012) 111801 [arXiv:1112.0688] [INSPIRE].
J. Ellis, D.S. Hwang, V. Sanz and T. You, A Fast Track towards the ‘Higgs’ Spin and Parity, JHEP 11 (2012) 134 [arXiv:1208.6002] [INSPIRE].
J. Ellis, R. Fok, D.S. Hwang, V. Sanz and T. You, Distinguishing ’Higgs’ spin hypotheses using γγ and WW ∗ decays, Eur. Phys. J. C 73 (2013) 2488 [arXiv:1210.5229] [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].
I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, New dimensions at a millimeter to a Fermi and superstrings at a TeV, Phys. Lett. B 436 (1998) 257 [hep-ph/9804398] [INSPIRE].
N. Arkani-Hamed, S. Dimopoulos and G.R. Dvali, Phenomenology, astrophysics and cosmology of theories with submillimeter dimensions and TeV scale quantum gravity, Phys. Rev. D 59 (1999) 086004 [hep-ph/9807344] [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].
T. Han, J.D. Lykken and R.-J. Zhang, On Kaluza-Klein states from large extra dimensions, Phys. Rev. D 59 (1999) 105006 [hep-ph/9811350] [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].
J.L. Hewett, Indirect collider signals for extra dimensions, Phys. Rev. Lett. 82 (1999) 4765 [hep-ph/9811356] [INSPIRE].
P. Mathews, S. Raychaudhuri and K. Sridhar, Getting to the top with extra dimensions, Phys. Lett. B 450 (1999) 343 [hep-ph/9811501] [INSPIRE].
P. Mathews, S. Raychaudhuri and K. Sridhar, Testing TeV scale quantum gravity using dijet production at the Tevatron, JHEP 07 (2000) 008 [hep-ph/9904232] [INSPIRE].
M.C. Kumar, P. Mathews, V. Ravindran and S. Seth, Neutral triple electroweak gauge boson production in the large extra-dimension model at the LHC, Phys. Rev. D 85 (2012) 094507 [arXiv:1111.7063] [INSPIRE].
L. Xiao-Zhou, D. Peng-Fei, M. Wen-Gan, Z. Ren-You and G. Lei, WWZ/γ production in large extra dimensions model at LHC and ILC, Phys. Rev. D 86 (2012) 095008 [arXiv:1209.6401] [INSPIRE].
P. Mathews, V. Ravindran, K. Sridhar and W.L. van Neerven, Next-to-leading order QCD corrections to the Drell-Yan cross section in models of TeV-scale gravity, Nucl. Phys. B 713 (2005) 333 [hep-ph/0411018] [INSPIRE].
P. Mathews and V. Ravindran, Angular distribution of Drell-Yan process at hadron colliders to NLO-QCD in models of TeV scale gravity, Nucl. Phys. B 753 (2006) 1 [hep-ph/0507250] [INSPIRE].
M.C. Kumar, P. Mathews and V. Ravindran, PDF and scale uncertainties of various DY distributions in ADD and RS models at hadron colliders, Eur. Phys. J. C 49 (2007) 599 [hep-ph/0604135] [INSPIRE].
M.C. Kumar, P. Mathews, V. Ravindran and A. Tripathi, Diphoton signals in theories with large extra dimensions to NLO QCD at hadron colliders, Phys. Lett. B 672 (2009) 45 [arXiv:0811.1670] [INSPIRE].
M.C. Kumar, P. Mathews, V. Ravindran and A. Tripathi, Direct photon pair production at the LHC to order α s in TeV scale gravity models, Nucl. Phys. B 818 (2009) 28 [arXiv:0902.4894] [INSPIRE].
N. Agarwal, V. Ravindran, V.K. Tiwari and A. Tripathi, Z boson pair production at the LHC to O(α s ) in TeV scale gravity models, Nucl. Phys. B 830 (2010) 248 [arXiv:0909.2651] [INSPIRE].
N. Agarwal, V. Ravindran, V.K. Tiwari and A. Tripathi, Next-to-leading order QCD corrections to the Z boson pair production at the LHC in Randall Sundrum model, Phys. Lett. B 686 (2010) 244 [arXiv:0910.1551] [INSPIRE].
N. Agarwal, V. Ravindran, V.K. Tiwari and A. Tripathi, W + W − production in Large extra dimension model at next-to-leading order in QCD at the LHC, Phys. Rev. D 82 (2010) 036001 [arXiv:1003.5450] [INSPIRE].
N. Agarwal, V. Ravindran, V.K. Tiwari and A. Tripathi, Next-to-leading order QCD corrections to W + W − production at the LHC in Randall Sundrum model, Phys. Lett. B 690 (2010)390 [arXiv:1003.5445] [INSPIRE].
R. Frederix et al., Diphoton production in the ADD model to NLO + parton shower accuracy at the LHC, JHEP 12 (2012) 102 [arXiv:1209.6527] [INSPIRE].
R. Frederix, M.K. Mandal, P. Mathews, V. Ravindran and S. Seth, Drell-Yan, ZZ, W + W − production in SM \( \& \) ADD model to NLO + PS accuracy at the LHC, Eur. Phys. J. C 74 (2014) 2745 [arXiv:1307.7013] [INSPIRE].
S. Karg, M. Krämer, Q. Li and D. Zeppenfeld, NLO QCD corrections to graviton production at hadron colliders, Phys. Rev. D 81 (2010) 094036 [arXiv:0911.5095] [INSPIRE].
X. Gao, C.S. Li, J. Gao, J. Wang and R.J. Oakes, Next-to-leading order QCD predictions for graviton and photon associated production in the Large Extra Dimensions model at the LHC, Phys. Rev. D 81 (2010) 036008 [arXiv:0912.0199] [INSPIRE].
M.C. Kumar, P. Mathews, V. Ravindran and S. Seth, Graviton plus vector boson production to NLO in QCD at the LHC, Nucl. Phys. B 847 (2011) 54 [arXiv:1011.6199] [INSPIRE].
M.C. Kumar, P. Mathews, V. Ravindran and S. Seth, Vector boson production in association with KK modes of the ADD model to NLO in QCD at LHC, J. Phys. G 38 (2011) 055001 [arXiv:1004.5519] [INSPIRE].
D. de Florian, M. Mahakhud, P. Mathews, J. Mazzitelli and V. Ravindran, Next-to-Next-to-Leading Order QCD Corrections in Models of TeV-Scale Gravity, JHEP 04 (2014) 028 [arXiv:1312.7173] [INSPIRE].
D. de Florian, M. Mahakhud, P. Mathews, J. Mazzitelli and V. Ravindran, Quark and gluon spin-2 form factors to two-loops in QCD, JHEP 02 (2014) 035 [arXiv:1312.6528] [INSPIRE].
T. Gehrmann and E. Remiddi, Analytic continuation of massless two loop four point functions, Nucl. Phys. B 640 (2002) 379 [hep-ph/0207020] [INSPIRE].
T. Gehrmann, M. Jaquier, E.W.N. Glover and A. Koukoutsakis, Two-Loop QCD Corrections to the Helicity Amplitudes for H → 3 partons, JHEP 02 (2012) 056 [arXiv:1112.3554] [INSPIRE].
T. Gehrmann, L. Tancredi and E. Weihs, Two-loop QCD helicity amplitudes for g g → Z g and g g → Z γ, JHEP 04 (2013) 101 [arXiv:1302.2630] [INSPIRE].
S. Catani, The Singular behavior of QCD amplitudes at two loop order, Phys. Lett. B 427 (1998) 161 [hep-ph/9802439] [INSPIRE].
G.F. Sterman and M.E. Tejeda-Yeomans, Multiloop amplitudes and resummation, Phys. Lett. B 552 (2003) 48 [hep-ph/0210130] [INSPIRE].
P. Mathews, V. Ravindran and K. Sridhar, NLO - QCD corrections to e + e − → hadrons in models of TeV-scale gravity, JHEP 08 (2004) 048 [hep-ph/0405292] [INSPIRE].
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms, Int. J. Mod. Phys. A 15 (2000) 725 [hep-ph/9905237] [INSPIRE].
T. Gehrmann and E. Remiddi, Two loop master integrals for γ∗ → 3 jets: The Planar topologies, Nucl. Phys. B 601 (2001) 248 [hep-ph/0008287] [INSPIRE].
T. Gehrmann and E. Remiddi, Two loop master integrals for γ∗ → 3 jets: The Nonplanar topologies, Nucl. Phys. B 601 (2001) 287 [hep-ph/0101124] [INSPIRE].
T. Kinoshita, Mass singularities of Feynman amplitudes, J. Math. Phys. 3 (1962) 650 [INSPIRE].
T.D. Lee and M. Nauenberg, Degenerate Systems and Mass Singularities, Phys. Rev. 133 (1964) B1549.
S.M. Aybat, L.J. Dixon and G.F. Sterman, The Two-loop anomalous dimension matrix for soft gluon exchange, Phys. Rev. Lett. 97 (2006) 072001 [hep-ph/0606254] [INSPIRE].
S.M. Aybat, L.J. Dixon and G.F. Sterman, The Two-loop soft anomalous dimension matrix and resummation at next-to-next-to leading pole, Phys. Rev. D 74 (2006) 074004 [hep-ph/0607309] [INSPIRE].
V. Ravindran, J. Smith and W.L. van Neerven, NNLO corrections to the total cross-section for Higgs boson production in hadron hadron collisions, Nucl. Phys. B 665 (2003) 325 [hep-ph/0302135] [INSPIRE].
V. Ravindran, J. Smith and W.L. van Neerven, Two-loop corrections to Higgs boson production, Nucl. Phys. B 704 (2005) 332 [hep-ph/0408315] [INSPIRE].
T. Becher and M. Neubert, Infrared singularities of scattering amplitudes in perturbative QCD, Phys. Rev. Lett. 102 (2009) 162001 [arXiv:0901.0722] [INSPIRE].
E. Gardi and L. Magnea, Factorization constraints for soft anomalous dimensions in QCD scattering amplitudes, JHEP 03 (2009) 079 [arXiv:0901.1091] [INSPIRE].
J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].
F.V. Tkachov, A Theorem on Analytical Calculability of Four Loop Renormalization Group Functions, Phys. Lett. B 100 (1981) 65 [INSPIRE].
K.G. Chetyrkin and F.V. Tkachov, Integration by Parts: The Algorithm to Calculate β-functions in 4 Loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions, Nucl. Phys. B 580 (2000) 485 [hep-ph/9912329] [INSPIRE].
S. Laporta, High precision calculation of multiloop Feynman integrals by difference equations, Int. J. Mod. Phys. A 15 (2000) 5087 [hep-ph/0102033] [INSPIRE].
C. Anastasiou and A. Lazopoulos, Automatic integral reduction for higher order perturbative calculations, JHEP 07 (2004) 046 [hep-ph/0404258] [INSPIRE].
A.V. Smirnov, Algorithm FIRE - Feynman Integral Reduction, JHEP 10 (2008) 107 [arXiv:0807.3243] [INSPIRE].
C. Studerus, Reduze-Feynman Integral Reduction in C++, Comput. Phys. Commun. 181 (2010) 1293 [arXiv:0912.2546] [INSPIRE].
A. von Manteuffel and C. Studerus, Reduze 2 - Distributed Feynman Integral Reduction, arXiv:1201.4330 [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [INSPIRE].
R.N. Lee, LiteRed 1.4: a powerful tool for the reduction of the multiloop integrals, arXiv:1310.1145 [INSPIRE].
P. Nason, MINT: A Computer program for adaptive Monte Carlo integration and generation of unweighted distributions, arXiv:0709.2085 [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: 1404.0028
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, 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 license, and indicate if changes were made.
About this article
Cite this article
Ahmed, T., Mahakhud, M., Mathews, P. et al. Two-Loop QCD correction to massive spin-2 resonance → 3 gluons. J. High Energ. Phys. 2014, 107 (2014). https://doi.org/10.1007/JHEP05(2014)107
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP05(2014)107