Advances in High Energy Physics

Volume 2016 (2016), Article ID 3279568, 8 pages

http://dx.doi.org/10.1155/2016/3279568

## On the Compatibility of the Diboson Excess with a -Initiated Composite Sector

Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK

Received 22 November 2015; Accepted 18 February 2016

Academic Editor: George Siopsis

Copyright © 2016 Verónica Sanz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

We propose that recent results by ATLAS and CMS searching for heavy resonances decaying into bosons could be a first hint of a new sector of pure gauge confining physics, possibly linked to the origin of the Higgs as a Composite Higgs. The lightest resonances (glueballs) of this new sector would be neutral, spin-zero, and spin-two, and their behaviour would resemble that of a radion and a massive graviton of extra dimensions. We outline how 13 TeV LHC data could be used to improve sensitivity on this scenario, as well as future characterization during the 13 TeV LHC run.

#### 1. Introduction

Search for heavy resonances decaying into a pair of bosons performed by CMS and ATLAS [1–5] shows tantalizing hints towards the existence of a new resonance at a mass of around 2 TeV, a possibility which has created quite some excitement [6–21].

In this paper we provide an alternative interpretation in terms of a new strong sector, possibly linked to the origin of the Higgs particle as a composite state. We will consider new states, singlet under the SM interactions, which can be produced and decay through their coupling to the stress-energy tensor. An example of such a theory is a new pure gauge sector which undergoes confinement at energies around the TeV scale. The spectrum of this theory contains glueballs, with spin-zero and spin-two resonances at the bottom of the spectrum [22–26]. Focusing on the low-lying, conceivably narrow states, we concentrate in the scenario where the new states couple to gluons through anomalies and decay predominantly to massive vector bosons or Higgses.

#### 2. Glueballs: Theoretical Aspects

Consider a new nonabelian gauge sector, for example, gauge group, which undergoes confinement leading to a low energy spectrum of glueballs. Glueballs are bound states of gauge fields and their behaviour has been studied both in the case of QCD and in the case of more general gauge theories. The ordering of states can be understood by examining the interpolating operators of minimal canonical dimension [27, 28], a prescription which lattice simulations seem to confirm [22].

With this prescription, the lightest states would then correspond to those generated by the lowest dimensional singlet operator, namely, a four-dimension operator , which generates glueballs with quantum numbers , , , and (note that these quantum numbers could also be achieved within* oddballs* [29]).

The next level of resonances would be associated with the five-dimension operator, , leading to resonances with quantum numbers and . One could continue this procedure to classify resonances by examining six-dimension and higher operators generated by gauge fields.

In the following we are going to focus on the lowest resonances: spin-zero and spin-two. Lattice studies on gauge theories find that the lowest resonances correspond to ; hence we will denote them by Determining the separation between the scalar () and tensor states () is a difficult task in lattice gauge theories. Lattice resulting in a pure glueball calculation indicates that the tensor mode is about 60% heavier than the scalar, even in the large- limit. Nevertheless, this result will likely change once the pure gauge theory is coupled to the Standard Model. In the following, I will consider these two lightest states as two distinct possibilities for the lightest state in a glueball spectrum.

The resonances and propagate as Klein-Gordon and Fierz-Pauli [30] fields. The Fierz-Pauli Lagrangian describes a massive spin-two field, a rank-two symmetric, and traceless tensor. Additionally, a positive-energy condition must be satisfied (see [31] and references therein).

##### 2.1. Generic Couplings of the Spin-Zero and Spin-Two States

Contrary to the case of QCD, a pure gauge theory has no global (chiral) symmetries which would be broken by the confinement dynamics. On the other hand, space-time symmetries can be broken by confinement. For example, glueballs break spontaneously scale invariance of the gauge theory. Hence, the lightest spin-zero resonance could play the role of a dilaton, the Goldstone boson of the spontaneous breaking of scale invariance. In this case, the couplings of the dilaton resonance are of the form , where is the global current whose spontaneous breaking at the scale leads to the emergence of the Goldstone boson . The global current is given by , where is the generator of dilatation symmetry , which then implies that the dilaton couples to trace of the stress tensor ; consider where is the symmetry breaking scale and the index refers to species; that is, . In our set-up the dimensionless parameter encodes the degree of compositeness of species , with an order one value indicating a large mixture with the composite sector. Note that this coupling vanishes for massless gauge bosons (gluon and photon) as , but a coupling would be induced nevertheless at one loop through the anomaly [32–34] where here denotes the gluon or photon field strength.

We encounter a similar situation for the spin-two state whose properties are derived from diffeomorphism invariance, broken spontaneously by the gauge dynamics. Indeed, a massless spin-two object is conserved, , in the absence of breaking. As in case, couples to a conserved current . The breaking of this diffeomorphism invariance can be parametrized by , where corresponds to a massive vector field, which is* eaten* by the massless spin-two field [35–37]. When joining together, the spin-two massless field and the massive vector will lead to the massive spin-two state . As long as the composite sector preserves Lorentz, gauge, and CP invariance, the coupling of the massive spin-two resonance to* two* SM particles will be given by [31] where corresponds to the stress tensor of species . Studies of couplings to the tensor state to SM particles have been done in the context of glueballs in QCD [38]. Note that these analyses differ from ours in which the tensor two-point function is treated as containing a massless state, and the constraints from diffeomorphism invariance are not included.

##### 2.2. A Set-Up for Glueballs and a Composite Higgs

In a scenario where EWSB is due to strong dynamics, such as Composite Higgs scenarios [39–41], the glueball sector could be involved in causing the spontaneous breaking of the global symmetry responsible for the pseudo-Goldstone Higgs. In this section we explore this possibility.

Let us imagine a sector with a large global symmetry and a gauge symmetry with no fundamental fermions. Assume then that the dynamics of become strong at some scale , which then triggers the spontaneous breaking of down to a smaller subgroup . An example would be sector and gauge strong dynamics leading to the breaking of to ; see Figure 1. One could then proceed as usual in the minimal Composite Higgs scenarios, by partly gauging interactions. To achieve EWSB, one would likely need to use a mechanism as explored in [42], where the Higgs potential is generated via a sequential breaking which one could link to the strong sector producing both the spin-zero and spin-two resonances and breaking the global symmetry. The spectrum at low energies would then contain the Goldstone bosons (a doublet under ) and the glueballs.