TAMING THE OFF-SHELL HIGGS BOSON
A. Azatov"*, C. Grojeanb**, A. Paul€***, E. Salvionid****
a Theory Division, Physics Department. CERN CH-1211, Geneva 23, Switzerland
bICREA at IFAE, Universität Autönoma de Barcelona E-0S193, Bellaterra, Spain
€ IN FN, Sezione di Roma 1-00185, Rome, Italy
d Physics Department, University of California Davis, CA 95616, USA
Received July 22, 2014
We study the off-shell Higgs data in the process pp -¥ hS*) -¥ Z<-*)Z<-*) -¥ 4(, to constrain deviations of the Higgs couplings. We point out that this channel can be used to resolve the long- and short-distance contributions to Higgs production by gluon fusion and can thus be complementary to pp hit in measuring the top Yukawa coupling. Our analysis, performed in the context of effective field theory, shows that current data do not allow drawing any model-independent conclusions. We study the prospects at future hadron colliders, including the high-luminosity LHC and accelerators with higher energy, up to 100 TeV. The available QCD calculations and the theoretical uncertainties affecting our analysis are also briefly discussed.
Cwitribvtiwi for the JETP special issue in honor of V. A. Rubakov's 60th birthday
DOI: 10.7868/S0044451015030039
1. INTRODUCTION
With the discovery of the Higgs boson by the ATLAS and CMS experiments fl, 2], high-energy physics experiences a transition: after a long period of search and exploration, an era of consolidation and precise measurements has just started and it will complement the direct search for the new physics beyond the Standard Model (SM). With a mass around 125GeV, the Higgs boson offers various production modes and decay channels directly accessible to observation, supplying a wealth of data that can be used to learn about the Higgs couplings. In the absence of any indication of new light degrees of freedom below the TeV scale, effects of the BSM physics can be conveniently parame-
* E-mail: Aleksandr.Azatov'&cern.ch
**E-mail: Christophe.Grojean'öcern.ch
E-mail: Ayan.Paul'&Tomal.infn.it
E-mail: esalvioni'&ucdavis.edu
terized in terms of higher-dimensional operators for the SM fields. This effective field theory (EFT) approach relates Higgs data to measurements of other sectors of the SM, like electroweak (EW) precision data, and gives a systematic way for controling the deviations from the SM, organized as an expansion in powers of the ratio of the momentum over the new physics scale. To date, a large amount of information has been extracted from inclusive rates, which are dominated by resonant production of the Higgs boson near the IIlclSS peak, i.e., at scales close to the Higgs IIlclSS itself.
As for any other quantum particle, the influence of the Higgs boson is not limited to its mass shell. Recently, the CMS and ATLAS collaborations reported the differential cross-section measurement of pp Z^Z^ 1/.2/2/.' (i = ..//) at high invariant mass of the ZZ system [3 5]. This process receives a sizable contribution from a Higgs boson produced offshell by gluon fusion [6, 7]. As such, this process potentially carries information relevant for probing the EFT at large momenta and could therefore reveal the en-
orgy dependence of the Higgs couplings controlled by higher-dimensional operators with extra derivatives. It was proposed in [8] to use the off-shell Higgs data to bound the Higgs width in a model-independent way. However, as was emphasized in Rof. [9], this bound actually holds under the assumption that the Higgs couplings remain the same over a large range of energy scales. The EFT Lagrangian captures and organizes precisely this energy dependence of the Higgs couplings and therefore offers a coherent framework for analyzing the off-shell Higgs data. The situation seems a priori similar to the precision measurements of the EW obsorvablos, where the off-shell Z data at LEP2 complemented the Z-poak data and bounded 0(p4) dimonsion-6 operators, like the W and 1" oblique parameters [10], in addition to the 0(p2) dimonsion-6 operators, the S and T oblique parameters [11], already-probed at LEP1. However, a careful exploration of the complete list of all dimonsion-6 operators deforming the SM Lagrangian1) reveals [13, 14] that the operators modifying the Lorentz structure of the SM Higgs couplings are already severely constrained by the EW precision data or by the bounds on anomalous gauge couplings. Thus, qualitatively, the off-shell data do not open a new window, i.e., they do not probe new dimension-6 operators.
Quantitatively, it is still worth exploring the actual bounds set by the off-shell data. Out of the eight CP-even dimension-6 operators uniquely probed by Higgs physics, five are already bounded by the decay channels of an on-shell Higgs boson. While double Higgs production, which could apprise us of the Higgs self-interaction, will mostly remain out-of-reach at the LHC, two additional channels, h —¥ Z7 and pp —¥ tth, will soon be accessible at run 2 of the LHC operation [15] and should bound two extra dimension-6 operators that remain unconstrained as yet. The latter channel will be particularly important to unambiguously pin down the top Yukawa coupling, which is currently accessed only radiatively via its one-loop contributions to the gg —¥ h and h —¥ 77 processes. It is well known that these two processes alone cannot resolve the top loop and distinguish it from effective contact interactions of the Higgs boson to gluons or photons, which parameterize the effect of a possible new physics at short distances. Therein lies the importance of the
11 Throughout this paper, we work under the assumption that the Higgs boson is a part of an EW doublet. This assumption was not made in Ref. [12], where the off-shell Higgs data was used to bound deviations of the Higgs couplings that in the doublet realization are either subdominant or correlated with other data from better measurements.
tth channel2). However, an accurate measurement of this process is known to be challenging, due to its suppressed cross section and to the high multiplicity of its final states. The latter implies that obtaining accurate predictions for some of the relevant backgrounds, such as, for example, pp —¥ tibb for the h —¥ bb channel, is a difficult task. Alternative and complementary ways to separate the long- and short-distance contributions to the ggh vertex are therefore welcome. Recently, it was proposed in [18 21] to study the hard recoil of the Higgs boson against an extra jet [22 24], which provides a second scale above the Higgs mass to probe the EFT structure (see also Ref. [25] for a study of h + 2jets). The double Higgs production by fusion of gluons also effectively introduces a second IIlclSS scale and can be used to separate the top Yukawa coupling from the contact interaction to gluons or photons [26, 27]. We note that these two channels will require some large integrated luminosity, beyond the run 2 of the LHC. In this paper, we want to advocate that off-shell Higgs production is another obvious place to break this degeneracy of the couplings and to learn about the top Yukawa coupling.
One advantage of the analysis of Higgs data in terms of an EFT, over a simple fit in terms of anomalous couplings, is that it conies with some simple consistency checks that guarantee the reliability of its results against our ignorance of the details of the new physics sector. For instance, it is possible to say when it is safe to neglect dimension-8 operators over the dimension-6 ones. As we illustrate in what follows, this is of prime importance when the data is not strong enough to derive stringent bounds. In particular, we see in this paper that no model-independent reliable bounds can be extracted from the 8ToV data. The situation improves at 14 ToV, and upon accumulating a luminosity of about 3ab_1, it will bo possible to derive meaningful constraints, at least for the rather strongly coupled new physics. Only at future, higher-energy accelerators, however, do the bounds become truly model-independent .
This paper is organized as follows. In Sec. 2, we present our analysis of the Higgs couplings using the 8TeV off-shell data and discuss the reliability of the results in an EFT framework. In Sec. 3, we study the prospects of the off-shell study at future facilities like
2! It has recently been pointed out that the measurement of the ratio a(tth)/a(ttZ) at very high energy could provide a very clean access to the top Yukawa coupling [16]. We also recall that the top Yukawa coupling can be constrained indirectly by the study of top pair production near the threshold at future e+e-colliders (see, e.g., Ref. [17]).
'0ÖÖÜÖÖÜÖC y
\QQQQQQQQQJ
Cl
^ööüüüüöüö" y
vwv^
Fig. 1. Sample diagrams contributing to yy ZZ
the high-luminosity LHC and very high-energy hadron hadron colliders. We conclude in Sec. 4, whereas some technical details are collected in three Appendices.
2. CONSTRAINING THE ANOMALOUS COUPLINGS OF THE HIGGS BOSON
Recently, a new method was suggested in Ref. [8] to indirectly constrain the Higgs width, by looking at the very high invariant mass region of the four-lopton final state in the pp 1/ channel, which
receives contributions from the exchange of a highly offshell Higgs boson, and comparing the event yields with the SM predictions. More precisely, information on the Higgs width can be extracted by comparing the event yields off and on the Broit Wignor peak. It follows that this method relies on the following assumptions:
• there is an invisible Higgs decay width, and hence the total width of the Higgs boson and its couplings can be varied independently;
• variations of all the Higgs couplings are universal;
• there are no higher-dimensional operators affecting either Higgs decay or production.
In this paper, we use the same process pp —¥ 4i to put constraints on the new physics, but we reverse the first and third assumptions: we assume the absence of an invisible decay
Для дальнейшего прочтения статьи необходимо приобрести полный текст. Статьи высылаются в формате PDF на указанную при оплате почту. Время доставки составляет менее 10 минут. Стоимость одной статьи — 150 рублей.