Parallel Universe, Dark Matter and Invisible Higgs Decays

The existence of the dark matter with amount about five times the ordinary matter is now well established experimentally. There are now many candidates for this dark matter. However, dark matter could be just like the ordinary matter in a parallel universe. If both universes are described by a non-abelian gauge symmetries, then there will be no kinetic mixing between the ordinary photon and the dark photon, and the dark proton, dark electron and the corresponding dark nuclei, belonging to the parallel universe, will be stable. If the strong coupling constant, $(\alpha_s)_{dark}$ in the parallel universe is five times that of $\alpha_s$, then the dark proton will be about five time heavier, explaining why the dark matter is five times the ordinary matter. However, the two sectors will still interact via the Higgs boson of the two sectors. This will lead to the existence of a second light Higss boson, just like the Standard Model Higgs boson. This gives rise to the invisible decay modes of the Higgs boson which can be tested at the LHC, and the proposed ILC.


Introduction
Symmetry seems to play an important role in the classification and interactions of the elementary particles. The Standard Model (SM) based on the gauge symmetry SU (3) C × SU (2) L × U Y (1) has been extremely successful in describing all experimental results so far to a precision less than one percent. The final ingredient of the SM, namely the Higgs boson, has finally been observed at the LHC [1]. However, SM is unable to explain why the charges of the elementary particle are quantized because of the presence of U (1) Y . This was remedied by enlarging the SU (3) C symmetry to SU (4) C with the lepton number as the fourth color,(or grand unifying all three interaction in SM in SU (5) [2] or SO(10) [3]). SM also has no candidate for the dark matter whose existence is now well established experimentally [4]. Many extensions of the SM models, such as models with weakly interacting massive particles (WIMP) can explain the dark matter [4]. The most poplar examples are the lightest stable particles in supersymmetry [4], or the lightest Kaluza-Klein partcle in extra dimensions [5]. Of course, axion [6] is also a good candidate for dark matter. Several experiments are ongoing to detect signals of dark matter in the laboratory. However, it is possible that the dark matter is just the analogue of ordinary matter belonging to a parallel universe. Such a parallel universe naturally appears in the superstring theory with the E 8 × E 8 gauge symmetry before compactification [7].
Parallel universe in which the gauge symmetry is just the replication of our ordinary universe, i,e the gauge symmetry in the parallel universe being SU (3) × SU (2) × U (1) has also been considered [8]. If the particles analogous to the proton and neutron in the parallel universe is about five times heavier than the proton and neutron of our universe, then that will naturally explain why the dark matter of the universe is about five times the ordinary matter. This can be easily arranged by assuming strong coupling constant square/4π, α s is about five times larger than the QCD α s . Thus, in this work, we assume that the two universe where the electroweak sector is exactly symmetric, whereas the corresponding couplings in the strong sector are different, explaining why the dark matter is larger than the ordinary matter. Also, we assume that both universes are described by non-abelian gauge symmetry so that the kinetic mixing between the photon (γ) and the parallel photon (γ ) is forbidden. We also assume that post-inflationary reheating in the two worlds are different, and the the parallel universe is colder than our universe [9]. This makes it possible to maintain the successful prediction of the big bang nucleosynthesis, though the number of degrees of freedom is increased from the usual SM of 10.75 at the time of nucleosynthesis due the extra light degrees of freedom (due to the γ , e and three ν s).
In this work, we explore the LHC implications of this scenario due to the mixing among the Higgs bosons in the two electroweak sectors. Such a mixing, which is allowed by the gauge symmetry, will mix the lightest Higgs bosons of our universe (h 1 ) and the lightest Higgs boson of the parallel universe (h 2 ), which we will call the dark Higgs. One of the corresponding mass eigenstates, h SM we identify with the observed Higgs boson with mass of 125 GeV. The other mass eigenstate, which we denote by h DS , the dark Higgs, will also have a mass in the electroweak scale. Due to the mixing effects, both Higgs will decay to the kinematically allowed modes in our universe and as well as to the modes of the dark universe. One particularly interesting scenario is when the two Higgs bosons are very close in mass, say within 4 GeV so that the LHC can not resolve it [10] .
However, this scenario will lead to the invisible decay modes [11] . The existence of such invisible decay modes can be established at the LHC when sufficient data accumulates.
(The current upper limit on the invisible decay branching ratio of the observed Higgs at the LHC is 0.65). At the proposed future International Linear Collider (ILC) [12], the existence of such invisible modes can be easily established, and the model can be tested in much more detail.

Model and the Formalism
The gauge symmetry we propose for our work is SU (4) C × SU (2) L × SU (2) R for our universe, and SU (4) C × SU (2) L × SU (2) R for the parallel universe. Note that we choose this non-abelian symmetry not only to explain charge quantization (as in Pati-Salam model [13]), but also to avoid the kinetic mixing of γ and γ as would be allowed in not assume that the coupling for SU (4) and SU (4) interactions are the same, but strong coupling in the parallel universe is larger in order to account for the p (proton of the parallel universe) mass to be about five times larger than the proton. For the electroweak sector, we assume the exact symmetry between our universe and the parallel universe.
The fermions belong to the fundamental representations (4, 2, 1) + (4, 1, 2). The 4 represent three color of quarks and the lepton number as the 4th color, (2,1) and (1,2) represent the left and right handed doublets. The forty eight Weyl fermions belonging to three generations may be represented by the matrix (1) We have similar fermion representations for the parallel universe, denoted by primes.
The model has 3 gauge coupling constants: g 4 for SU (4) color which we will identify with the strong coupling constant of our universe, g 4 for SU (4) color of the parallel universe, and g for SU (2) L and SU (2) R , and corresponding electroweak couplings for the parallel universe (g L = g R = g L = g R = g (we assume that the gauge couplings of the electroweak sectors of the two universe are the same).

Symmetry breaking
SU (4) color symmetry is spontaneously broken to SU (3) C × U (1) B−L in the usual Pati-Salam way using the Higgs fields (15, 1, 1) at a scale V c . The most stringent limit on the scale of this symmetry breaking comes from the upper limit of the rare decay mode study of the Higgs potential shows that there exist a parameter space where only one neutral Higgs in the bi-doublet remains light, and becomes very similar to the SM Higgs in our universe [16]. All other Higgs fields become very heavy compared to the EW scale.
Similar is true in the parallel universe. The symmetry of the Higgs fields in the EW sector between our universe and the parallel universe will make the two electroweak VEV's the same. Thus the mixing terms between the two bi-doublets (one in our universe and one in the parallel universe) then leads to mixing between the two remaining SM like Higgs fields. The resulting mass terms for the remaining two light Higgs fields can be written as m 2 and v DS are the electroweak symmetric breaking scale in the visible sector and dark sector respectively) from which the two mass eigenstates and the mixing can be calculated. The implications for this is when the two light Higgses are very close in mass (within about 4 GeV, which LHC can not resolve) leads to the invisible decay of the observed Higgs boson. Below we discuss the phenomenological implications for this scenario at the LHC, and briefly at the proposed ILC [12].

Phenomenological Implications
In the framework of this model, interaction between fermions and/or gauge bosons of dark sector and visible sector (the SM particles) are forbidden by the gauge symmetry. In this section, we will discuss the phenomenological implications of the lightest dark and visible neutral Higgs mixing (h 1 and h 2 ). As discussed in the previous section, the bi-linear terms involving the lightest visible sector (denoted by h 1 ) and dark sector (denoted by h 2 ) Higgses in the scalar potential are given by, 2 ) are determined by these parameters:

However, quartic Higgs interactions of the form λ(H
where the masses and the mixing angle of these physical states are given by, In the framework of this model, we have two light physical neutral Higgs (h

Data used in Collider Analysis
In this section, we discuss the collider phenomenology of invisible Higgs Decays. Before going into the details of the collider prediction, we first need to study the constraints on the parameter space coming from present Standard Model predictions and experimental data. The Higgs mass eigenstates of h SM and h DS will be produced in Colliders through the top loop as top quark has Standard Model couplings to the h SM mass eigen state.
The Higgs, which comprises of both h 1 and h 2 eigen states, will then decay in both the Standard Model decay modes along with Dark sector decay modes. We will perceive these dark sector decay modes as enhancement in the invisible Branching Fraction of the Higgs.
We first discuss the different constraints on the mixing angle θ between the two eigenstates coming from experimental data of H → W W → lνlν and H → γγ channels.
Along with these experimental data in Higgs decays in different modes, we have also taken into account constraints on the mixing angle parameter space coming from the ATLAS search for the invisible decays of a 125 GeV Higgs Boson produced in association with a Z boson [11].
The Standard Model production cross-sections in different channels (such as gluon-  Table 3: Experimental values of best fit signal strength µ = σ/σ SM at E CM = 8 TeV.
ratios in different channels in our analysis. The relevant cross-sections and branching ratios used for our analysis are presented in Table 1 and Table 2 respectively. We have taken the mass range between 123 − 127 GeV which is the interesting parameter space for our analysis.
In Table 3 we present the results of the different experimental searches in the H → W W → lνlν channel by ATLAS collaborations [19] and CMS collaboration [20] and in H → γγ channel by ATLAS collaborations [21] CMS collaborations [22] .

Bounds on Mixing Angle
In this section we use the data that we presented in the previous section to constrain the mixing angle parameter space. In Fig 2, we present the total invisible decay rate i.e σ ×BR in the invisible channel vs the mixing angle θ for m ATLAS collaboration has set an upper limit of 65% on the invisible decay branching of a SM higgs boson of mass 125 GeV [11]. Assuming σ total = 22.32 pb Higgs crosssection at 125 GeV (see Table 1), 65% upper limit on invisible decay branching ratio corresponds to 14.5 pb upper limit on the invisible Higgs decay rate. This limit is shown in the shaded green region in Fig 2. It can be seen from the plot that present model We would also like to comment that in a linear collider like the proposed International Linear Collider(ILC) this analysis can be done without any ambiguity about the resolution of the two Higgs in the close range of 4GeV . In a e + e− collider the Higgs will be produced in association with a Z boson and from the mass recoil of the Z boson the peak resolution of the Higgs boson can be measured in the limit of 40 MeV [12]. So from linear colliders we will be able to tell for sure if there are two Higgs bosons in the comparable mass range between (123 − 127GeV), which is not possible in this precision from Hadron Collider like LHC.

Summary and Conclusions
Motivated by the fact that the dark matter is about five times the ordinary matter, we have proposed that the dark matter can just be like the ordinary matter in a parallel universe with the corresponding strong coupling constant, α s about five times the strong coupling, α s of our universe. The parallel universe needs to be much colder than our universe to keep the successful prediction for the big bang nucleosynthesis. We have used the non-abelian Pati-Salam gauge symmetry for both universe to have the charge quantization, as well as, to avoid any kinetic mixing between the photon of our universe and the parallel universe. However, the two universes will be connected via the electroweak Higgs bosons of the two universes. If the electroweak sector of the two universes are symmetric, the lightest Higgs bosons of the two universes will mix. In particular, if these two Higgses mix significantly, and their masses are close (say within 4 GeV), LHC will not be able to resolve if it is observing one Higgs or two Higgses. However, each Higgs will decay to the particles of our universe as well as to the corresponding particles of the the parallel universe. This leads to the invisible decays of the observed Higgs boson (or bosons). We have used all the available experimental data at the LHC to set constraint on this mixing angle, and find that in can be as large as 16 o . If the mixing angle is not very small, LHC will be able to infer the existence of such invisible decays when sufficient data accumulates. (The current limit on the invisible branching ratio from the LHC data is < 65%). We also find that the cross section times the branching ratio for Higgs to γγ channel is fully consistent with our model as measured by the CMS collaboration, but not by the ATLAS collaboration. The results by the ATLAS collaboration for this channel has to come down if our model is realized by nature. Our proposal of two Higgses around 125 GeV , and significant invisible decay fraction can easily be tested in the proposed ILC where peak resolution of the Higgs boson can be measured to about 40 MeV.