Abstract
The decay of a light Higgs boson to bottom quarks is dominant and can be exploited for the discovery of the Higgs particle and the measurement of its properties at the LHC and future collider experiments. We perform a first computation of the fully differential decay at next-next-to-leading order in perturbative QCD. We employ a novel method of non-linear mappings for the treatment of singularities in the radiative processes which contribute to the decay width. This constitutes the first physical application of the method.
Similar content being viewed by others
References
P. Baikov, K. Chetyrkin and J.H. Kuhn, Scalar correlator at \( O\left( {\alpha_s^4} \right) \) , Higgs decay into b-quarks and bounds on the light quark masses, Phys. Rev. Lett. 96 (2006) 012003 [hep-ph/0511063] [INSPIRE].
S. Gorishnii, A. Kataev and S. Larin, The width of Higgs boson decay into hadrons: three loop corrections of strong interactions, Sov. J. Nucl. Phys. 40 (1984) 329 [INSPIRE].
S. Gorishnii, A. Kataev, S. Larin and L. Surguladze, Corrected three loop QCD correction to the correlator of the quark scalar currents and Γ tot (H 0 → hadrons), Mod. Phys. Lett. A 5 (1990) 2703 [INSPIRE].
S. Gorishnii, A. Kataev, S. Larin and L. Surguladze, Scheme dependence of the next to next-to-leading QCD corrections to Γ tot (H 0 → hadrons) and the spurious QCD infrared fixed point, Phys. Rev. D 43 (1991) 1633 [INSPIRE].
C. Becchi, S. Narison, E. de Rafael and F. Yndurain, Light quark masses in quantum chromodynamics and chiral symmetry breaking, Z. Phys. C 8 (1981) 335 [INSPIRE].
N. Sakai, Perturbative QCD corrections to the hadronic decay width of the Higgs boson, Phys. Rev. D 22 (1980) 2220 [INSPIRE].
T. Inami and T. Kubota, Renormalization group estimate of the hadronic decay width of the Higgs boson, Nucl. Phys. B 179 (1981) 171 [INSPIRE].
K. Chetyrkin, Correlator of the quark scalar currents and Γ tot (H → hadrons) at \( O{ }\left( {\alpha_S^3} \right) \) in pQCD, Phys. Lett. B 390 (1997) 309 [hep-ph/9608318] [INSPIRE].
K. Chetyrkin and M. Steinhauser, Complete QCD corrections of order \( O{ }\left( {\alpha_S^3} \right) \) to the hadronic Higgs decay, Phys. Lett. B 408 (1997) 320 [hep-ph/9706462] [INSPIRE].
J.M. Butterworth, A.R. Davison, M. Rubin and G.P. Salam, Jet substructure as a new Higgs search channel at the LHC, Phys. Rev. Lett. 100 (2008) 242001 [arXiv:0802.2470] [INSPIRE].
T. Plehn, G.P. Salam and M. Spannowsky, Fat jets for a light Higgs, Phys. Rev. Lett. 104 (2010) 111801 [arXiv:0910.5472] [INSPIRE].
ATLAS collaboration, ATLAS sensitivity to the standard model Higgs in the HW and HZ channels at High transverse momenta, PHYS-PUB-2009-088 (2009).
D.E. Soper and M. Spannowsky, Combining subjet algorithms to enhance ZH detection at the LHC, JHEP 08 (2010) 029 [arXiv:1005.0417] [INSPIRE].
A. Bredenstein, A. Denner, S. Dittmaier and S. Pozzorini, NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. full hadronic results, JHEP 03 (2010) 021 [arXiv:1001.4006] [INSPIRE].
A. Denner, S. Dittmaier, S. Kallweit and S. Pozzorini, NLO QCD corrections to WWbb production at hadron colliders, Phys. Rev. Lett. 106 (2011) 052001 [arXiv:1012.3975] [INSPIRE].
T. Melia, K. Melnikov, R. Rontsch and G. Zanderighi, Next-to-leading order QCD predictions for W + W + jj production at the LHC, JHEP 12 (2010) 053 [arXiv:1007.5313] [INSPIRE].
R. Ellis, K. Melnikov and G. Zanderighi, W + 3 jet production at the Tevatron, Phys. Rev. D 80 (2009) 094002 [arXiv:0906.1445] [INSPIRE].
C. Berger et al., Precise predictions for W + 4 jet production at the large hadron collider, Phys. Rev. Lett. 106 (2011) 092001 [arXiv:1009.2338] [INSPIRE].
C. Berger et al., Next-to-leading order QCD predictions for Z, γ * + 3-jet distributions at the Tevatron, Phys. Rev. D 82 (2010) 074002 [arXiv:1004.1659] [INSPIRE].
C. Berger et al., Next-to-leading order QCD Predictions for W + 3-jet distributions at hadron colliders, Phys. Rev. D 80 (2009) 074036 [arXiv:0907.1984] [INSPIRE].
H. Ita et al., Precise predictions for Z + 4 jets at hadron colliders, Phys. Rev. D 85 (2012) 031501 [arXiv:1108.2229] [INSPIRE].
G. Bevilacqua, M. Czakon, C. Papadopoulos, R. Pittau and M. Worek, Assault on the NLO Wishlist: \( pp \to t\overline t b\overline b \), JHEP 09 (2009) 109 [arXiv:0907.4723] [INSPIRE].
G. Bevilacqua, M. Czakon, C. Papadopoulos and M. Worek, Dominant QCD backgrounds in Higgs boson analyses at the LHC: A study of \( pp \to t\overline t + {2} \) jets at next-to-leading order, Phys. Rev. Lett. 104 (2010) 162002 [arXiv:1002.4009] [INSPIRE].
G. Bevilacqua, M. Czakon, A. van Hameren, C.G. Papadopoulos and M. Worek, Complete off-shell effects in top quark pair hadroproduction with leptonic decay at next-to-leading order, JHEP 02 (2011) 083 [arXiv:1012.4230] [INSPIRE].
N. Greiner, A. Guffanti, J.-P. Guillet, T. Reiter and J. Reuter, NLO QCD corrections to 4 b-quark production, PoS(DIS 2010)156 [arXiv:1006.5339] [INSPIRE].
R. Frederix et al., W and Z/γ* boson production in association with a bottom-antibottom pair, JHEP 09 (2011) 061 [arXiv:1106.6019] [INSPIRE].
C. Berger et al., An automated implementation of on-shell methods for one-loop amplitudes, Phys. Rev. D 78 (2008) 036003 [arXiv:0803.4180] [INSPIRE].
R. Ellis, W.T. Giele, Z. Kunszt and K. Melnikov, Masses, fermions and generalized D-dimensional unitarity, Nucl. Phys. B 822 (2009) 270 [arXiv:0806.3467] [INSPIRE].
A. van Hameren, C. Papadopoulos and R. Pittau, Automated one-loop calculations: a proof of concept, JHEP 09 (2009) 106 [arXiv:0903.4665] [INSPIRE].
V. Hirschi et al., Automation of one-loop QCD corrections, JHEP 05 (2011) 044 [arXiv:1103.0621] [INSPIRE].
R. Frederix, S. Frixione, F. Maltoni and T. Stelzer, Automation of next-to-leading order computations in QCD: the FKS subtraction, JHEP 10 (2009) 003 [arXiv:0908.4272] [INSPIRE].
R. Frederix, T. Gehrmann and N. Greiner, Automation of the dipole subtraction method in MadGraph/MadEvent, JHEP 09 (2008) 122 [arXiv:0808.2128] [INSPIRE].
T. Gleisberg and F. Krauss, Automating dipole subtraction for QCD NLO calculations, Eur. Phys. J. C 53 (2008) 501 [arXiv:0709.2881] [INSPIRE].
T. Binoth, J.-P. Guillet, G. Heinrich, E. Pilon and T. Reiter, Golem95: a numerical program to calculate one-loop tensor integrals with up to six external legs, Comput. Phys. Commun. 180 (2009) 2317 [arXiv:0810.0992] [INSPIRE].
P. Mastrolia, G. Ossola, T. Reiter and F. Tramontano, Scattering AMplitudes from unitarity-based reduction algorithm at the integrand-level, JHEP 08 (2010) 080 [arXiv:1006.0710] [INSPIRE].
D.A. Kosower, Antenna factorization of gauge theory amplitudes, Phys. Rev. D 57 (1998) 5410 [hep-ph/9710213] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and G. Heinrich, Four particle phase space integrals in massless QCD, Nucl. Phys. B 682 (2004) 265 [hep-ph/0311276] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and E. Glover, Antenna subtraction at NNLO, JHEP 09 (2005) 056 [hep-ph/0505111] [INSPIRE].
A. Daleo, T. Gehrmann and D. Maître, Antenna subtraction with hadronic initial states, JHEP 04 (2007) 016 [hep-ph/0612257] [INSPIRE].
A. Gehrmann-De Ridder and M. Ritzmann, NLO antenna subtraction with massive fermions, JHEP 07 (2009) 041 [arXiv:0904.3297] [INSPIRE].
A. Daleo, A. Gehrmann-De Ridder, T. Gehrmann and G. Luisoni, Antenna subtraction at NNLO with hadronic initial states: initial-final configurations, JHEP 01 (2010) 118 [arXiv:0912.0374] [INSPIRE].
E. Nigel Glover and J. Pires, Antenna subtraction for gluon scattering at NNLO, JHEP 06 (2010) 096 [arXiv:1003.2824] [INSPIRE].
R. Boughezal, A. Gehrmann-De Ridder and M. Ritzmann, Antenna subtraction at NNLO with hadronic initial states: double real radiation for initial-initial configurations with two quark flavours, JHEP 02 (2011) 098 [arXiv:1011.6631] [INSPIRE].
G. Abelof and A. Gehrmann-De Ridder, Antenna subtraction for the production of heavy particles at hadron colliders, JHEP 04 (2011) 063 [arXiv:1102.2443] [INSPIRE].
T. Gehrmann and P.F. Monni, Antenna subtraction at NNLO with hadronic initial states: real-virtual initial-initial configurations, JHEP 12 (2011) 049 [arXiv:1107.4037] [INSPIRE].
S. Weinzierl, Subtraction terms at NNLO, JHEP 03 (2003) 062 [hep-ph/0302180] [INSPIRE].
S. Frixione and M. Grazzini, Subtraction at NNLO, JHEP 06 (2005) 010 [hep-ph/0411399] [INSPIRE].
G. Somogyi, Z. Trócsányi and V. Del Duca, Matching of singly- and doubly-unresolved limits of tree-level QCD squared matrix elements, JHEP 06 (2005) 024 [hep-ph/0502226] [INSPIRE].
G. Somogyi, Z. Trócsányi and V. Del Duca, A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of doubly-real emissions, JHEP 01 (2007) 070 [hep-ph/0609042] [INSPIRE].
G. Somogyi and Z. Trócsányi, A subtraction scheme for computing QCD jet cross sections at NNLO: regularization of real-virtual emission, JHEP 01 (2007) 052 [hep-ph/0609043] [INSPIRE].
P. Bolzoni, S.-O. Moch, G. Somogyi and Z. Trócsányi, Analytic integration of real-virtual counterterms in NNLO jet cross sections. II., JHEP 08 (2009) 079 [arXiv:0905.4390] [INSPIRE].
P. Bolzoni, G. Somogyi and Z. Trócsányi, A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the iterated singly-unresolved subtraction terms, JHEP 01 (2011) 059 [arXiv:1011.1909] [INSPIRE].
G. Somogyi and Z. Trócsányi, A subtraction scheme for computing QCD jet cross sections at NNLO: integrating the subtraction terms. I., JHEP 08 (2008) 042 [arXiv:0807.0509] [INSPIRE].
U. Aglietti, V. Del Duca, C. Duhr, G. Somogyi and Z. Trócsányi, Analytic integration of real-virtual counterterms in NNLO jet cross sections. I., JHEP 09 (2008) 107 [arXiv:0807.0514] [INSPIRE].
M. Czakon, A novel subtraction scheme for double-real radiation at NNLO, Phys. Lett. B 693 (2010) 259 [arXiv:1005.0274] [INSPIRE].
M. Czakon, Double-real radiation in hadronic top quark pair production as a proof of a certain concept, Nucl. Phys. B 849 (2011) 250 [arXiv:1101.0642] [INSPIRE].
C. Anastasiou, K. Melnikov and F. Petriello, A new method for real radiation at NNLO, Phys. Rev. D 69 (2004) 076010 [hep-ph/0311311] [INSPIRE].
S. Catani and M. Grazzini, An NNLO subtraction formalism in hadron collisions and its application to Higgs boson production at the LHC, Phys. Rev. Lett. 98 (2007) 222002 [hep-ph/0703012] [INSPIRE].
T. Binoth and G. Heinrich, An automatized algorithm to compute infrared divergent multiloop integrals, Nucl. Phys. B 585 (2000) 741 [hep-ph/0004013] [INSPIRE].
T. Binoth and G. Heinrich, Numerical evaluation of phase space integrals by sector decomposition, Nucl. Phys. B 693 (2004) 134 [hep-ph/0402265] [INSPIRE].
G. Ferrera, M. Grazzini and F. Tramontano, Associated WH production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 107 (2011) 152003 [arXiv:1107.1164] [INSPIRE].
S. Catani, L. Cieri, G. Ferrera, D. de Florian and M. Grazzini, Vector boson production at hadron colliders: a fully exclusive QCD calculation at NNLO, Phys. Rev. Lett. 103 (2009) 082001 [arXiv:0903.2120] [INSPIRE].
K. Melnikov and F. Petriello, Electroweak gauge boson production at hadron colliders through \( {\text{O}}\left( {\alpha_s^2} \right) \), Phys. Rev. D 74 (2006) 114017 [hep-ph/0609070] [INSPIRE].
C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, Dilepton rapidity distribution in the Drell-Yan process at NNLO in QCD, Phys. Rev. Lett. 91 (2003) 182002 [hep-ph/0306192] [INSPIRE].
C. Anastasiou, L.J. Dixon, K. Melnikov and F. Petriello, High precision QCD at hadron colliders: electroweak gauge boson rapidity distributions at NNLO, Phys. Rev. D 69 (2004) 094008 [hep-ph/0312266] [INSPIRE].
C. Anastasiou, L.J. Dixon and K. Melnikov, NLO Higgs boson rapidity distributions at hadron colliders, Nucl. Phys. Proc. Suppl. 116 (2003) 193 [hep-ph/0211141] [INSPIRE].
C. Anastasiou, K. Melnikov and F. Petriello, Higgs boson production at hadron colliders: Differential cross sections through next-to-next-to-leading order, Phys. Rev. Lett. 93 (2004) 262002 [hep-ph/0409088] [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].
M. Grazzini, NNLO predictions for the Higgs boson signal in the H → W W → lνlν and H →ZZ →4l decay channels, JHEP 02 (2008) 043 [arXiv:0801.3232] [INSPIRE].
C. Anastasiou, K. Melnikov and F. Petriello, Real radiation at NNLO: e + e − → 2 jets through \( O\left( {\alpha_s^2} \right) \), Phys. Rev. Lett. 93 (2004) 032002 [hep-ph/0402280] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann and E. Glover, Infrared structure of e + e − → 2 jets at NNLO, Nucl. Phys. B 691 (2004) 195 [hep-ph/0403057] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, NNLO corrections to event shapes in e + e − annihilation, JHEP 12 (2007) 094 [arXiv:0711.4711] [INSPIRE].
A. Gehrmann-De Ridder, T. Gehrmann, E. Glover and G. Heinrich, Infrared structure of e + e − → 3 jets at NNLO, JHEP 11 (2007) 058 [arXiv:0710.0346] [INSPIRE].
C. Anastasiou, F. Herzog and A. Lazopoulos, On the factorization of overlapping singularities at NNLO, JHEP 03 (2011) 038 [arXiv:1011.4867] [INSPIRE].
R.V. Harlander and W.B. Kilgore, Higgs boson production in bottom quark fusion at next-to-next-to leading order, Phys. Rev. D 68 (2003) 013001 [hep-ph/0304035] [INSPIRE].
P. Nogueira, Automatic Feynman graph generation, J. Comput. Phys. 105 (1993) 279 [INSPIRE].
J. Vermaseren, New features of FORM, math-ph/0010025 [INSPIRE].
MAPLE, http://www.maplesoft.com.
K. Chetyrkin and F. Tkachov, Integration by parts: the algorithm to calculate β-functions in 4 loops, Nucl. Phys. B 192 (1981) 159 [INSPIRE].
F. Tkachov, a theorem on analytical calculability of four loop renormalization group functions, Phys. Lett. B 100 (1981) 65 [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].
S. Biswas and K. Melnikov, Second order QCD corrections to inclusive semileptonic \( b \to {X_c}l{\overline \nu_l} \) decays with massless and massive lepton, JHEP 02 (2010) 089 [arXiv:0911.4142] [INSPIRE].
JADE collaboration, W. Bartel et al., Experimental studies on multi-jet production in e + e − annihilation at PETRA energies, Z. Phys. C 33 (1986) 23 [INSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1110.2368
Rights and permissions
About this article
Cite this article
Anastasiou, C., Herzog, F. & Lazopoulos, A. The fully differential decay rate of a Higgs boson to bottom-quarks at NNLO in QCD. J. High Energ. Phys. 2012, 35 (2012). https://doi.org/10.1007/JHEP03(2012)035
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP03(2012)035