Abstract
We present virtual contributions up to two loop level in perturbative Quantum Chromodynamic (QCD) to the decay of pseudo-scalar Higgs boson (A) to three gluons (g) and also to quark (q), anti-quark (\( \overline{q} \)) and a gluon. With appropriate crossing, they are well suited for predicting the differential distribution of A in association with a jet in hadron colliders up to next-to-next-to-leading order (NNLO) in strong coupling constant and also for the subsequent decay of A to hadrons. We use effective field theory approach to integrate out the top quarks in the heavy top limit. The resulting theory involves two pseudo-scalar composite operators describing the interaction of A with gluons as well as with quark and anti-quark. We perform our computation in dimensional regularisation and use minimal subtraction (\( \overline{MS} \)) scheme to renormalise strong coupling constant as well as the composite operators. The ultraviolet (UV) finite amplitudes contain infrared (IR) divergences that are found to be in agreement with the predictions by Catani. For both the amplitudes namely A → ggg and \( A\to q\overline{q}g \), the leading transcendental terms at one and two loops are found to be identical to those in a three point form factor (FF) of the half-BPS operator in \( \mathcal{N}=4 \) Supersymmetric Yang Mills (SYM) theory when the QCD color factors are adjusted in a specific way. We present our results in terms of harmonic polylogs well suited for further numerical study.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
ATLAS collaboration, Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC, Phys. Lett. B 716 (2012) 1 [arXiv:1207.7214] [INSPIRE].
CMS collaboration, Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC, Phys. Lett. B 716 (2012) 30 [arXiv:1207.7235] [INSPIRE].
P. Fayet, Supergauge Invariant Extension of the Higgs Mechanism and a Model for the electron and Its Neutrino, Nucl. Phys. B 90 (1975) 104 [INSPIRE].
P. Fayet, Supersymmetry and Weak, Electromagnetic and Strong Interactions, Phys. Lett. B 64 (1976) 159 [INSPIRE].
P. Fayet, Spontaneously Broken Supersymmetric Theories of Weak, Electromagnetic and Strong Interactions, Phys. Lett. B 69 (1977) 489 [INSPIRE].
S. Dimopoulos and H. Georgi, Softly Broken Supersymmetry and SU(5), Nucl. Phys. B 193 (1981) 150 [INSPIRE].
N. Sakai, Naturalness in Supersymmetric Guts, Z. Phys. C 11 (1981) 153 [INSPIRE].
K. Inoue, A. Kakuto, H. Komatsu and S. Takeshita, Aspects of Grand Unified Models with Softly Broken Supersymmetry, Prog. Theor. Phys. 68 (1982) 927 [Erratum ibid. 70 (1983) 330] [INSPIRE].
K. Inoue, A. Kakuto, H. Komatsu and S. Takeshita, Low-Energy Parameters and Particle Masses in a Supersymmetric Grand Unified Model, Prog. Theor. Phys. 67 (1982) 1889 [INSPIRE].
K. Inoue, A. Kakuto, H. Komatsu and S. Takeshita, Renormalization of Supersymmetry Breaking Parameters Revisited, Prog. Theor. Phys. 71 (1984) 413 [INSPIRE].
R.P. Kauffman and W. Schaffer, QCD corrections to production of Higgs pseudoscalars, Phys. Rev. D 49 (1994) 551 [hep-ph/9305279] [INSPIRE].
A. Djouadi, M. Spira and P.M. Zerwas, Two photon decay widths of Higgs particles, Phys. Lett. B 311 (1993) 255 [hep-ph/9305335] [INSPIRE].
M. Spira, A. Djouadi, D. Graudenz and P.M. Zerwas, SUSY Higgs production at proton colliders, Phys. Lett. B 318 (1993) 347 [INSPIRE].
M. Spira, A. Djouadi, D. Graudenz and P.M. Zerwas, Higgs boson production at the LHC, Nucl. Phys. B 453 (1995) 17 [hep-ph/9504378] [INSPIRE].
R.V. Harlander and W.B. Kilgore, Production of a pseudoscalar Higgs boson at hadron colliders at next-to-next-to leading order, JHEP 10 (2002) 017 [hep-ph/0208096] [INSPIRE].
C. Anastasiou and K. Melnikov, Pseudoscalar Higgs boson production at hadron colliders in NNLO QCD, Phys. Rev. D 67 (2003) 037501 [hep-ph/0208115] [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].
T. Ahmed, T. Gehrmann, P. Mathews, N. Rana and V. Ravindran, Pseudo-scalar Form Factors at Three Loops in QCD, JHEP 11 (2015) 169 [arXiv:1510.01715] [INSPIRE].
V. Ravindran, On Sudakov and soft resummations in QCD, Nucl. Phys. B 746 (2006) 58 [hep-ph/0512249] [INSPIRE].
V. Ravindran, Higher-order threshold effects to inclusive processes in QCD, Nucl. Phys. B 752 (2006) 173 [hep-ph/0603041] [INSPIRE].
T. Ahmed, M. Mahakhud, N. Rana and V. Ravindran, Drell-Yan Production at Threshold to Third Order in QCD, Phys. Rev. Lett. 113 (2014) 112002 [arXiv:1404.0366] [INSPIRE].
S.A. Larin, The renormalization of the axial anomaly in dimensional regularization, Phys. Lett. B 303 (1993) 113 [hep-ph/9302240] [INSPIRE].
M.F. Zoller, OPE of the pseudoscalar gluonium correlator in massless QCD to three-loop order, JHEP 07 (2013) 040 [arXiv:1304.2232] [INSPIRE].
A. Vogt, S. Moch and J.A.M. Vermaseren, The three-loop splitting functions in QCD: The Singlet case, Nucl. Phys. B 691 (2004) 129 [hep-ph/0404111] [INSPIRE].
S. Moch, J.A.M. Vermaseren and A. Vogt, The three loop splitting functions in QCD: The Nonsinglet case, Nucl. Phys. B 688 (2004) 101 [hep-ph/0403192] [INSPIRE].
T. Ahmed, M.C. Kumar, P. Mathews, N. Rana and V. Ravindran, Pseudo-scalar Higgs boson production at threshold N 3 LO and N 3 LL QCD, Eur. Phys. J. C 76 (2016) 355 [arXiv:1510.02235] [INSPIRE].
G.F. Sterman, Summation of Large Corrections to Short Distance Hadronic Cross-Sections, Nucl. Phys. B 281 (1987) 310 [INSPIRE].
S. Catani and L. Trentadue, Resummation of the QCD Perturbative Series for Hard Processes, Nucl. Phys. B 327 (1989) 323 [INSPIRE].
T. Ahmed et al., Pseudo-scalar Higgs boson production at N 3 LO A + N 3 LL′, Eur. Phys. J. C 76 (2016) 663 [arXiv:1606.00837] [INSPIRE].
C.W. Bauer, S. Fleming and M.E. Luke, Summing Sudakov logarithms in B → X(sγ) in effective field theory, Phys. Rev. D 63 (2000) 014006 [hep-ph/0005275] [INSPIRE].
C.W. Bauer, S. Fleming, D. Pirjol and I.W. Stewart, An effective field theory for collinear and soft gluons: Heavy to light decays, Phys. Rev. D 63 (2001) 114020 [hep-ph/0011336] [INSPIRE].
C.W. Bauer and I.W. Stewart, Invariant operators in collinear effective theory, Phys. Lett. B 516 (2001) 134 [hep-ph/0107001] [INSPIRE].
C.W. Bauer, D. Pirjol and I.W. Stewart, Soft collinear factorization in effective field theory, Phys. Rev. D 65 (2002) 054022 [hep-ph/0109045] [INSPIRE].
M. Beneke, A.P. Chapovsky, M. Diehl and T. Feldmann, Soft collinear effective theory and heavy to light currents beyond leading power, Nucl. Phys. B 643 (2002) 431 [hep-ph/0206152] [INSPIRE].
M. Beneke and T. Feldmann, Multipole expanded soft collinear effective theory with nonAbelian gauge symmetry, Phys. Lett. B 553 (2003) 267 [hep-ph/0211358] [INSPIRE].
C.W. Bauer, S. Fleming, D. Pirjol, I.Z. Rothstein and I.W. Stewart, Hard scattering factorization from effective field theory, Phys. Rev. D 66 (2002) 014017 [hep-ph/0202088] [INSPIRE].
C. Anastasiou, K. Melnikov and F. Petriello, Fully differential Higgs boson production and the di-photon signal through next-to-next-to-leading order, Nucl. Phys. B 724 (2005) 197 [hep-ph/0501130] [INSPIRE].
C. Anastasiou, G. Dissertori and F. Stöckli, NNLO QCD predictions for the H → WW → ℓνℓν signal at the LHC, JHEP 09 (2007) 018 [arXiv:0707.2373] [INSPIRE].
M. Grazzini, NNLO predictions for the Higgs boson signal in the H → WW → lνlν and H → ZZ → 4l decay channels, JHEP 02 (2008) 043 [arXiv:0801.3232] [INSPIRE].
S. Catani, D. de Florian and M. Grazzini, Direct Higgs production and jet veto at the Tevatron and the LHC in NNLO QCD, JHEP 01 (2002) 015 [hep-ph/0111164] [INSPIRE].
C.F. Berger, C. Marcantonini, I.W. Stewart, F.J. Tackmann and W.J. Waalewijn, Higgs Production with a Central Jet Veto at NNLL+NNLO, JHEP 04 (2011) 092 [arXiv:1012.4480] [INSPIRE].
X. Chen, J. Cruz-Martinez, T. Gehrmann, E.W.N. Glover and M. Jaquier, NNLO QCD corrections to Higgs boson production at large transverse momentum, JHEP 10 (2016) 066 [arXiv:1607.08817] [INSPIRE].
R. Boughezal, F. Caola, K. Melnikov, F. Petriello and M. Schulze, Higgs boson production in association with a jet at next-to-next-to-leading order in perturbative QCD, JHEP 06 (2013) 072 [arXiv:1302.6216] [INSPIRE].
X. Chen, T. Gehrmann, E.W.N. Glover and M. Jaquier, Precise QCD predictions for the production of Higgs + jet final states, Phys. Lett. B 740 (2015) 147 [arXiv:1408.5325] [INSPIRE].
R. Boughezal, F. Caola, K. Melnikov, F. Petriello and M. Schulze, Higgs boson production in association with a jet at next-to-next-to-leading order, Phys. Rev. Lett. 115 (2015) 082003 [arXiv:1504.07922] [INSPIRE].
R. Boughezal, C. Focke, W. Giele, X. Liu and F. Petriello, Higgs boson production in association with a jet at NNLO using jettiness subtraction, Phys. Lett. B 748 (2015) 5 [arXiv:1505.03893] [INSPIRE].
F. Caola, K. Melnikov and M. Schulze, Fiducial cross sections for Higgs boson production in association with a jet at next-to-next-to-leading order in QCD, Phys. Rev. D 92 (2015) 074032 [arXiv:1508.02684] [INSPIRE].
L.J. Dixon, E.W.N. Glover and V.V. Khoze, MHV rules for Higgs plus multi-gluon amplitudes, JHEP 12 (2004) 015 [hep-th/0411092] [INSPIRE].
S.D. Badger, E.W.N. Glover and V.V. Khoze, MHV rules for Higgs plus multi-parton amplitudes, JHEP 03 (2005) 023 [hep-th/0412275] [INSPIRE].
S.D. Badger and E.W.N. Glover, One-loop helicity amplitudes for H → gluons: The All-minus configuration, Nucl. Phys. Proc. Suppl. 160 (2006) 71 [hep-ph/0607139] [INSPIRE].
L.J. Dixon and Y. Sofianatos, Analytic one-loop amplitudes for a Higgs boson plus four partons, JHEP 08 (2009) 058 [arXiv:0906.0008] [INSPIRE].
S. Badger, E.W. Nigel Glover, P. Mastrolia and C. Williams, One-loop Higgs plus four gluon amplitudes: Full analytic results, JHEP 01 (2010) 036 [arXiv:0909.4475] [INSPIRE].
S. Badger, J.M. Campbell, R.K. Ellis and C. Williams, Analytic results for the one-loop NMHV Hqqgg amplitude, JHEP 12 (2009) 035 [arXiv:0910.4481] [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].
B. Field, J. Smith, M.E. Tejeda-Yeomans and W.L. van Neerven, NLO corrections to differential cross-sections for pseudoscalar Higgs boson production, Phys. Lett. B 551 (2003) 137 [hep-ph/0210369] [INSPIRE].
W. Bernreuther, P. Gonzalez and M. Wiebusch, Pseudoscalar Higgs Bosons at the LHC: Production and Decays into Electroweak Gauge Bosons Revisited, Eur. Phys. J. C 69 (2010) 31 [arXiv:1003.5585] [INSPIRE].
K.G. Chetyrkin, B.A. Kniehl, M. Steinhauser and W.A. Bardeen, Effective QCD interactions of CP odd Higgs bosons at three loops, Nucl. Phys. B 535 (1998) 3 [hep-ph/9807241] [INSPIRE].
S.L. Adler, Axial vector vertex in spinor electrodynamics, Phys. Rev. 177 (1969) 2426 [INSPIRE].
O.V. Tarasov, A.A. Vladimirov and A.Yu. Zharkov, The Gell-Mann-Low Function of QCD in the Three Loop Approximation, Phys. Lett. B 93 (1980) 429 [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].
G. ’t Hooft and M.J.G. Veltman, Regularization and Renormalization of Gauge Fields, Nucl. Phys. B 44 (1972) 189 [INSPIRE].
D.A. Akyeampong and R. Delbourgo, Dimensional regularization, abnormal amplitudes and anomalies, Nuovo Cim. A 17 (1973) 578 [INSPIRE].
J. Kodaira, QCD Higher Order Effects in Polarized Electroproduction: Flavor Singlet Coefficient Functions, Nucl. Phys. B 165 (1980) 129 [INSPIRE].
S.L. Adler and W.A. Bardeen, Absence of higher order corrections in the anomalous axial vector divergence equation, Phys. Rev. 182 (1969) 1517 [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].
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].
T. Gehrmann and D. Kara, The \( Hb\overline{b} \) form factor to three loops in QCD, JHEP 09 (2014) 174 [arXiv:1407.8114] [INSPIRE].
T. Ahmed, M. Mahakhud, P. Mathews, N. Rana and V. Ravindran, Two-Loop QCD Correction to massive spin-2 resonance → 3 gluons, JHEP 05 (2014) 107 [arXiv:1404.0028] [INSPIRE].
T. Ahmed, M. Mahakhud, P. Mathews, N. Rana and V. Ravindran, Two-loop QCD corrections to Higgs → b + \( \overline{b} \) + g amplitude, JHEP 08 (2014) 075 [arXiv:1405.2324] [INSPIRE].
T. Ahmed, G. Das, P. Mathews, N. Rana and V. Ravindran, Spin-2 Form Factors at Three Loop in QCD, JHEP 12 (2015) 084 [arXiv:1508.05043] [INSPIRE].
T. Ahmed et al., NNLO QCD corrections to the Drell-Yan cross section in models of TeV-scale gravity, Eur. Phys. J. C 77 (2017) 22 [arXiv:1606.08454] [INSPIRE].
T. Ahmed, G. Das, P. Mathews, N. Rana and V. Ravindran, The two-loop QCD correction to massive spin-2 resonance → \( q\overline{q}g \), Eur. Phys. J. C 76 (2016) 667 [arXiv:1608.05906] [INSPIRE].
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279.
J.A.M. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
A. von Manteuffel and C. Studerus, Reduze 2 — Distributed Feynman Integral Reduction, arXiv:1201.4330 [INSPIRE].
C. Studerus, Reduze-Feynman Integral Reduction in C++, Comput. Phys. Commun. 181 (2010) 1293 [arXiv:0912.2546] [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].
R.N. Lee, Group structure of the integration-by-part identities and its application to the reduction of multiloop integrals, JHEP 07 (2008) 031 [arXiv:0804.3008] [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].
R.N. Lee, LiteRed 1.4: a powerful tool for reduction of multiloop integrals, J. Phys. Conf. Ser. 523 (2014) 012059 [arXiv:1310.1145] [INSPIRE].
R.N. Lee, Presenting LiteRed: a tool for the Loop InTEgrals REDuction, arXiv:1212.2685 [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 [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].
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].
A.V. Kotikov and L.N. Lipatov, NLO corrections to the BFKL equation in QCD and in supersymmetric gauge theories, Nucl. Phys. B 582 (2000) 19 [hep-ph/0004008] [INSPIRE].
A.V. Kotikov and L.N. Lipatov, DGLAP and BFKL equations in the N = 4 supersymmetric gauge theory, Nucl. Phys. B 661 (2003) 19 [Erratum ibid. B 685 (2004) 405] [hep-ph/0208220] [INSPIRE].
A.V. Kotikov, L.N. Lipatov, A.I. Onishchenko and V.N. Velizhanin, Three loop universal anomalous dimension of the Wilson operators in N = 4 SUSY Yang-Mills model, Phys. Lett. B 595 (2004) 521 [Erratum ibid. B 632 (2006) 754] [hep-th/0404092] [INSPIRE].
A.V. Kotikov and L.N. Lipatov, DGLAP and BFKL evolution equations in the N = 4 supersymmetric gauge theory, hep-ph/0112346 [INSPIRE].
A.V. Kotikov and L.N. Lipatov, On the highest transcendentality in N = 4 SUSY, Nucl. Phys. B 769 (2007) 217 [hep-th/0611204] [INSPIRE].
A. Koukoutsakis, Higgs bosons and QCD jets at two loops, Ph.D. Thesis, Durham University (2003).
A. Brandhuber, G. Travaglini and G. Yang, Analytic two-loop form factors in N = 4 SYM, JHEP 05 (2012) 082 [arXiv:1201.4170] [INSPIRE].
T. Ahmed, P. Banerjee, P.K. Dhani, N. Rana, V. Ravindran and S. Seth, Konishi form factor at three loops in \( \mathcal{N}=4 \) supersymmetric Yang-Mills theory, Phys. Rev. D 95 (2017) 085019 [arXiv:1610.05317] [INSPIRE].
T. Ahmed, P. Banerjee, P.K. Dhani, P. Mathews, N. Rana and V. Ravindran, Three loop form factors of a massive spin-2 particle with nonuniversal coupling, Phys. Rev. D 95 (2017) 034035 [arXiv:1612.00024] [INSPIRE].
T. Gehrmann, E.W.N. Glover, T. Huber, N. Ikizlerli and C. Studerus, Calculation of the quark and gluon form factors to three loops in QCD, JHEP 06 (2010) 094 [arXiv:1004.3653] [INSPIRE].
P. Banerjee, P.K. Dhani, M. Mahakhud, V. Ravindran and S. Seth, Finite remainders of the Konishi at two loops in \( \mathcal{N}=4 \) SYM, JHEP 05 (2017) 085 [arXiv:1612.00885] [INSPIRE].
D. Nandan, C. Sieg, M. Wilhelm and G. Yang, Cutting through form factors and cross sections of non-protected operators in \( \mathcal{N}=4 \) SYM, JHEP 06 (2015) 156 [arXiv:1410.8485] [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: 1708.02387
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
Banerjee, P., Dhani, P.K. & Ravindran, V. Two loop QCD corrections for the process pseudo-scalar Higgs → 3 partons. J. High Energ. Phys. 2017, 67 (2017). https://doi.org/10.1007/JHEP10(2017)067
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP10(2017)067