Paper
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A Bayesian view of the Higgs sector with higher dimensional operators
Authors
Beranger Dumont,Sylvain Fichet
GERO VON GERSDORFF,Roberto Llorens,Robert Piehler,Artur Mariusz Trudzik,Ronald Navarro,Rafael Correa-Rocha,Jacqueline Daykin,David Valentiner,Ferdinando Gliozzi,Igor Nikitin,Aibin Zhan,Natalia Semenova,Kristjan Kannike,Jon Kerridge,Katsushi Ito,Jorge Guillermo Russo,Kunghung Lin,Carmelo P. Martin,Jose Vega,Celso Martinez Rivero,Ariana Gaytan Peñuñuri,Terry Griswold,Лариса Моргоева,Esben Moland Olsen,Ignas Grigelionis,Andrew Donnell,DIGAMBER PAWAR,Valentin Hirschi,Carlos Miguel Rios-González,Kunal Vyas,Kristen Smith,Nenad Đurđević,Christa Musial,Dejan Matić,Milivoje Lapčević,Veljko Vlašković,Bojan Urdarević,Zoran Vuković,Zoran Jovanović,Radoje Brković,Vladimir Mićić,Miodrag Mićović,Emilija Stanković,Milena Petrović,Vlastimir Leković,Verica Babić,Jelena Vučković,Tamara Đurđić Milošević,Srđan Vladetić,Sveto Puríć,Dragica Živojinović, Dj,Dragan Vujisić,Milan Palević,Božin Vlašković,Peter Wolfsteiner,Vanik Kakoyan,Nenad Janković,Nina Planojević,Bharat Char,Siniša Varga,Milena M. Jakšić,Nenad Tomić,Violeta Todorović,Vladan Ivanović,Srdjan Đorđević,Torben Gaedt,Vesna Janjić,Jasmina Labudović Stanković,Jelena Eric Nielsen,Jasmina Bogićević,Violeta Domanović,Aleksandra Bošković,Lela Ristić,Milan Dana,Wei Li,ana nikezic,Dragan Stojković,Carolyn Dzierba,Tijana Tubić Ćurčić,Mikołaj Baranowski,Benjamin Bellenie,Miroslav Zetek,Bartomeu Fiol,Andrew Degnan,Andy Van Brocklin,Stevan Luković,Srđan Furtula,Nemanja Lojanica,Luis Garcés-Erice,Joseph Fotsing,Vasilis Niarchos,Digamber Porob,David Van Wie,Nikolay Bobev,Andrej Micovic,Eleni Vryonidou,Robert Stala,Gianluca Calcagni,Christoph Luhn,Anne Kuhn,Keisuke Harigaya,Vishnu Ram OV,Jonathan Wall,Marie Connett,Urfat Nuriyev,Frank Saueressig,Felice Pantaleo,Thorsten Alexander Kern,David Clarke,Frank Krauss,Bo Feng,Pierre Vanhove,Josep M. Villar Mir,Mikko Heino,Nasuf SONMEZ,Fabio Maltoni,Ramon Gomez Jimenez,Elias Lopez Asamar,Antonio Ortiz,Paz Lloria Garcia,Francisco Palomares,Sebastian Linß,Bernard J. Costello,Bruno Dufour,Stefan Fredenhagen,Eran Palti,Claudia Garcia-Garcia,Nathaniel Butlin,Mark Mezei,Barbara Abbott,Rafael Delgado,Luiz Agostinho Ferreira,Nilanjan Brahma,Carlos Tamarit,Dzmitry Ivanou,Engel Roza,Grzegorz Stefanek,Vladimir Korobov,Gustavo Niz,Matthias Ihl,Shinji Hirano,edouard alphandéry,Pedro Gil Martins Vieira,Carlos Alberto Vaquera-Araujo,Sebastian Sapeta,Chaitali Sengupta,Nico Callewaert,Marcos Endo,Nick Evans,Carlos A. 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CPHT-RR025.0413
ICTP-SAIFR/2013-005
LPSC13097
A Bayesian view of the Higgs sector with higher dimensional
operators
B´eranger Dumont a, Sylvain Fichet b, Gero von Gersdorff c,d ∗
a Laboratoire de Physique Subatomique et de Cosmologie, UJF Grenoble 1, CNRS/IN2P3,
INPG, 53 Avenue des Martyrs, F-38026 Grenoble, France
b International Institute of Physics, UFRN, Av. Odilon Gomes de Lima, 1722 -
Capim Macio - 59078-400 - Natal-RN, Brazil
c Centre de Physique Th´eorique, ´Ecole Polytechnique and CNRS, F-91128 Palaiseau,
France
d ICTP South American Institute for Fundamental Research, Instituto de Fisica Teorica,
Sao Paulo State University, Brazil
Abstract
We investigate the possibilities of New Physics affecting the Standard Model (SM)
Higgs sector. An effective Lagrangian with dimension-six operators is used to capture the
effect of New Physics. We carry out a global Bayesian inference analysis, considering the
recent LHC data set including all available correlations, as well as results from Tevatron.
Trilinear gauge boson couplings and electroweak precision observables are also taken into
account. The case of weak bosons tensorial couplings is closely examined and NLO QCD
corrections are taken into account in the deviations we predict. We consider two scenarios,
one where the coefficients of all the dimension-six operators are essentially unconstrained,
and one where a certain subset is loop suppressed. In both scenarios, we find that large
deviations from some of the SM Higgs couplings can still be present, assuming New Physics
arising at 3 TeV. In particular, we find that a significantly reduced coupling of the Higgs to
the top quark is possible and slightly favored by searches on Higgs production in association
with top quark pairs. The total width of the Higgs boson is only weakly constrained and
can vary between 0.7 and 2.7 times the Standard Model value within 95% Bayesian credible
interval (BCI). We also observe sizeable effects induced by New Physics contributions to
tensorial couplings. In particular, the Higgs boson decay width into Zγ can be enhanced
by up to a factor 12 within 95% BCI.
∗sylvain.fichet@lpsc.in2p3.fr, dumont@lpsc.in2p3.fr, gersdorff@gmail.com
arXiv:1304.3369v2 [hep-ph] 22 Jul 2013
ICTP-SAIFR/2013-005
LPSC13097
A Bayesian view of the Higgs sector with higher dimensional
operators
B´eranger Dumont a, Sylvain Fichet b, Gero von Gersdorff c,d ∗
a Laboratoire de Physique Subatomique et de Cosmologie, UJF Grenoble 1, CNRS/IN2P3,
INPG, 53 Avenue des Martyrs, F-38026 Grenoble, France
b International Institute of Physics, UFRN, Av. Odilon Gomes de Lima, 1722 -
Capim Macio - 59078-400 - Natal-RN, Brazil
c Centre de Physique Th´eorique, ´Ecole Polytechnique and CNRS, F-91128 Palaiseau,
France
d ICTP South American Institute for Fundamental Research, Instituto de Fisica Teorica,
Sao Paulo State University, Brazil
Abstract
We investigate the possibilities of New Physics affecting the Standard Model (SM)
Higgs sector. An effective Lagrangian with dimension-six operators is used to capture the
effect of New Physics. We carry out a global Bayesian inference analysis, considering the
recent LHC data set including all available correlations, as well as results from Tevatron.
Trilinear gauge boson couplings and electroweak precision observables are also taken into
account. The case of weak bosons tensorial couplings is closely examined and NLO QCD
corrections are taken into account in the deviations we predict. We consider two scenarios,
one where the coefficients of all the dimension-six operators are essentially unconstrained,
and one where a certain subset is loop suppressed. In both scenarios, we find that large
deviations from some of the SM Higgs couplings can still be present, assuming New Physics
arising at 3 TeV. In particular, we find that a significantly reduced coupling of the Higgs to
the top quark is possible and slightly favored by searches on Higgs production in association
with top quark pairs. The total width of the Higgs boson is only weakly constrained and
can vary between 0.7 and 2.7 times the Standard Model value within 95% Bayesian credible
interval (BCI). We also observe sizeable effects induced by New Physics contributions to
tensorial couplings. In particular, the Higgs boson decay width into Zγ can be enhanced
by up to a factor 12 within 95% BCI.
∗sylvain.fichet@lpsc.in2p3.fr, dumont@lpsc.in2p3.fr, gersdorff@gmail.com
arXiv:1304.3369v2 [hep-ph] 22 Jul 2013
1 Introduction
The existence of a scalar resonance compatible with the SM Higgs boson has now been
firmly established at the LHC by the ATLAS and CMS experiments [1, 2]. Based on the
latest results presented at the Rencontres de Moriond 2013, the combined significance of
the excess around 125 GeV reaches more than 7 σ in both experiments. The analyses are
based on up to 5 fb−1 at 7 TeV and 21 fb−1 at 8 TeV, collected in 2011 and 2012.
Following this fundamental breakthrough, new questions need to be addressed. Some
of them may find an answer during the LHC era, through the analysis of the properties
of the new boson. A first question is whether or not this resonance is a Higgs boson, i.e.
the manifestation of a field involved in the electroweak symmetry breaking (EWSB) and
unitarization of W W scattering. Second, if it is indeed a Higgs, one may wonder to what
extent it is compatible with the Standard Model Higgs. Indeed, the properties of the Higgs
boson could be dramatically modified with the theoretical prejudice that New Physics has
to emerge near the electroweak scale. On the other hand, direct searches for new states
beyond the SM have so far turned out to be unsuccessful, and indirect constraints from
electroweak precision measurements at LEP push the limits on masses of new particles
somewhat further above the electroweak scale. If New Physics is indeed present and is
somehow separated from the electroweak scale, the couplings of the Higgs boson will be
close to those of the SM and will only be modified by the effect of a few higher dimensional
operators. In this paper, we will explore an effective field theory (EFT) with only relatively
few new parameters.
Many aspects of these fundamental questions have already been investigated in several
works (see e.g. [3–14] for studies based on the 8 TeV results). For example, the chiral
EW Lagrangian with a non-linear realization of the SU (2)L × U (1)Y symmetry is a quite
general framework in order to study the properties of electroweak symmetry breaking.
Many scenarios producing possibly large deviations with respect to the SM Higgs properties
are successfully captured in such EFT approach.
We are going to consider that new states appear at a typical scale Λ substantially larger
than the electroweak scale. For physical processes involving an energy scale smaller than
Λ, New Physics can be integrated out. As a consequence of this hypothesis, the resulting
low-energy effective theory consists in the Standard Model, supplemented by infinite series
of local operators with higher dimension, which involves negative powers of Λ,
Leff = LSM + ∑
i
αi
Λni Oi . (1.1)
The effects of such higher dimensional operators (HDOs) have been investigated in many
contexts such as flavor physics, or the study of the properties of the electroweak gauge
bosons through LEP precision measurements. The purpose of this paper is to study the
electroweak sector again, which now includes new Higgs observables. For our analysis,
we only have to consider the leading HDOs. The only operator with ni = 1 is the one
giving a Majorana mass to the neutrino, and is not relevant for our study. We will thus be
exclusively interested in the n = 2 terms, i.e. dimension-6 operators.
2
The existence of a scalar resonance compatible with the SM Higgs boson has now been
firmly established at the LHC by the ATLAS and CMS experiments [1, 2]. Based on the
latest results presented at the Rencontres de Moriond 2013, the combined significance of
the excess around 125 GeV reaches more than 7 σ in both experiments. The analyses are
based on up to 5 fb−1 at 7 TeV and 21 fb−1 at 8 TeV, collected in 2011 and 2012.
Following this fundamental breakthrough, new questions need to be addressed. Some
of them may find an answer during the LHC era, through the analysis of the properties
of the new boson. A first question is whether or not this resonance is a Higgs boson, i.e.
the manifestation of a field involved in the electroweak symmetry breaking (EWSB) and
unitarization of W W scattering. Second, if it is indeed a Higgs, one may wonder to what
extent it is compatible with the Standard Model Higgs. Indeed, the properties of the Higgs
boson could be dramatically modified with the theoretical prejudice that New Physics has
to emerge near the electroweak scale. On the other hand, direct searches for new states
beyond the SM have so far turned out to be unsuccessful, and indirect constraints from
electroweak precision measurements at LEP push the limits on masses of new particles
somewhat further above the electroweak scale. If New Physics is indeed present and is
somehow separated from the electroweak scale, the couplings of the Higgs boson will be
close to those of the SM and will only be modified by the effect of a few higher dimensional
operators. In this paper, we will explore an effective field theory (EFT) with only relatively
few new parameters.
Many aspects of these fundamental questions have already been investigated in several
works (see e.g. [3–14] for studies based on the 8 TeV results). For example, the chiral
EW Lagrangian with a non-linear realization of the SU (2)L × U (1)Y symmetry is a quite
general framework in order to study the properties of electroweak symmetry breaking.
Many scenarios producing possibly large deviations with respect to the SM Higgs properties
are successfully captured in such EFT approach.
We are going to consider that new states appear at a typical scale Λ substantially larger
than the electroweak scale. For physical processes involving an energy scale smaller than
Λ, New Physics can be integrated out. As a consequence of this hypothesis, the resulting
low-energy effective theory consists in the Standard Model, supplemented by infinite series
of local operators with higher dimension, which involves negative powers of Λ,
Leff = LSM + ∑
i
αi
Λni Oi . (1.1)
The effects of such higher dimensional operators (HDOs) have been investigated in many
contexts such as flavor physics, or the study of the properties of the electroweak gauge
bosons through LEP precision measurements. The purpose of this paper is to study the
electroweak sector again, which now includes new Higgs observables. For our analysis,
we only have to consider the leading HDOs. The only operator with ni = 1 is the one
giving a Majorana mass to the neutrino, and is not relevant for our study. We will thus be
exclusively interested in the n = 2 terms, i.e. dimension-6 operators.
2
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