2 TeV Higgs boson and diboson excess at the LHC

Diboson resonance with mass around 2 TeV in the dijet invariant mass spectrum is reported by ATLAS experiment in proton-proton collisions at $\sqrt{s}=8$ TeV. We propose that the candidate of resonance is a heavy neutral Higgs $H^0$ or charged Higgs $H^\pm$ and use the extended two-Higgs-doublet (THD) to demonstrate the potentiality. We find that the large Yukawa coupling to the first generation of quarks can be realized in THD and the required value for producing the right resonance production cross section is of ${\cal O}(0.06-0.2)$. Besides $WW/ZZ$ channels, we find that if the mass of pseudoscalar $A^0$ satisfies the jet mass tagging condition $|m_j - m_{Z/W}|<13$ GeV, the diboson excess could be also caused by $ZA^0$ or $WA^0$ channel.

A resonance of around 2 TeV in the dijet invariant mass spectrum is recently reported by ATLAS with the data collected at √ s = 8 TeV and 20.3 fb −1 [1], where each jet is recognized as resulting from a boson decay. A moderate excess at the same mass region is also found by CMS [2]. Since the tagged jet mass m j is determined by |m j − m V | < 13 GeV, the reconstructed boson could be W or Z in the standard model (SM). The resultant significances at ATLAS in the region around 2 TeV for W Z, W W and ZZ channels are 3.4σ, 2.6σ and 2.9σ, respectively. The associated cross sections σ(pp → R)BR(R → V V ′ ) are in the region of 16 − 30 fb, where R is the resonance and V (′) is the weak gauge boson W/Z. In order to interpret the diboson excess, the possible candidates are a spin-2 Kaluza-Klein mode of the bulk Randall-Sundrum graviton [1], composite spin-1 particle [3][4][5], spin-1 bosons e.g. W ′ /Z ′ [6][7][8][9][10][11][12][13][14][15][16][17], and composite spin-0 and/or spin-2 particles [18][19][20]. A possible interpretation by triboson mode is also discussed in Ref. [21].
We propose another alternative, where the resonance of TeV scale is the heavy scalar boson and it could be a neutral or charged particle. In conventional approach, due to the small couplings to the light quarks, the difficulty for a scalar to be the resonance candidate is the low production cross section. We will show how the large couplings of scalar to the first generation of quarks work in the framework of two-Higgs-doublet (THD light A 0 and Z then could match the ATLAS limit. We note that since the gluon sub-jets provide unbalanced sub-jet momenta and have a higher number of charged-particle tracks (n trk ), ATLAS also applies the sub-jet analysis and imposes a cut on the n trk to reduce QCD backgrounds. Hence, when the A 0 decays into quark jets, the cut efficiency of A 0 should be same as that of Z .
As known, the custodial symmetry is preserved in multi-Higgs-doublet models and ρ = m 2 W /m 2 Z cos 2 θ W = 1 is guaranteed at the tree level. Due to the custodial symmetry, the interaction H ± W ∓ Z is forbidden. However, the coupling H ± W ∓ A 0 in THD is allowed. If m A 0 ∼ m W/Z , the events from W A 0 channel will be similar to those from W Z. Similar to the case of decay H 0 → ZA 0 , the decay width of W A 0 channel in THD is over NRR of ATLAS. Therefore, we need to extend the Higgs sector to get a light pseudoscalar. Hence, in this work we are going to explore the potentiality of H 0 or H ± as the 2 TeV resonance and investigate the influence of a pseudoscalar with mass of O(100) GeV.
At first, we demonstrate how the couplings of a scalar to the first generation of quarks can be large in the THD model. We start writing the Yukawa sector of quarks as [22,23] withH k = iτ 2 H * k . By recombining H 1 and H 2 , the new doublets are expressed by where Eq. (8) can be rewritten by withȲ whereȲ U (D) 1 (2) are related to the mass matrices of quarks whileȲ provide the couplings of new neutral and charged Higgses to the SM particles. Since the couplings to leptons are irrelevant issue, we do not further discuss the leptonic couplings. In terms of Eqs. (2) and (3), the physical mass matrix for quarks is given by where α = 1(2) while F = U(D) and V F L,R are the unitary matrices for diagonalizing the quark mass matrix. Clearly, ifȲ F 1(2) andȲ F 2(1) cannot be diagonalized simultaneously, the flavor changing neutral currents (FCNCs) at tree level will occur and the associated effects are related to the doublet H.
It is found that ifȲ F 1(2) andȲ F 2(1) exist some nontrivial relation, not only could FCNCs be avoided but also new scalars have unusual couplings to quarks [22,23]. To see how this happens, we set where a, b and c are arbitrary complex numbers. Multiplying the mass matrix of Eq. (5) by Besides the diagonal forms are preserved, the diagonal matrices of Eq. (7) may not have the same mass hierarchy as shown in Eq. (5). Since there are many possible I ij , here we just show two examples. The detailed discussions could be referred to [22,23]. As a result, the Yukawa couplings of new Higgs bosons to the first generation of quarks could be of order one in principle.
Hence, the couplings of H 0 and H ± to quarks in THD could be formulated by where V is Cabibbo-Kobayashi-Maskawa (CKM) matrix and diaη U = (y u , y c , y t ) and As mentioned earlier, we need to modify the THD model to get a light pseudoscalar. Although it is not our purpose to establish a complete model in this paper, however, the simplest extension is to introduce a light complex scalar SU(2) L singlet. By the mixture with Higgs doublets, the light pseudoscalar could couple to gauge bosons. Hence, by referring to the structure of gauge interactions in THD, we parametrize the relevant couplings of scalars as [26] L where A 0 denotes the light pseudoscalar, g is the gauge coupling of SU(2) L , θ W is Weinberg angle, s X = sin(β − α), c X = cos(β − α), angle α is the mixing angle of two CP-even scalars in THD, and ξ stands for the mixing effect of A 0 and light pseudoscalar. If we take m H 0 /H ± ≈ 2 TeV as an input, the involving new free parameters are y u,d , c X , ξ and m A 0 .
We note that although the interactions H 0 (h 0 h 0 , A 0 A 0 ) are allowed, however the decay rates , hereafter we ignore their effects. In addition, the coupling H ± W ∓ h 0 may cause a large width for H ± . We find that with c X O(0.1) and m H ± = 2 TeV, we get Γ(H ± → W ± h 0 ) 20 GeV. Since h → bb dominates and ATLAS does not find the excess from the b-jet, we do not further discuss its effect.
In terms of the introduced couplings in Eq. (8) and the adoption of y u,d , the hadronic decay rates of H 0 and H ± are formulated by with N c = 3 being the number of color. When the scalar mass is fixed to be 2 TeV, the free parameters are only the new Yukawa couplings y u,d . By Eq. (9), the two-body bosonic decay rates are given by with λ(a , b) The main free parameters are c X , ξ and m A 0 .
Since m H 0 /H ± ≫ m Z,W,A 0 in our approach, Eq. (11) could be simplified to be The dependence of m A 0 is suppressed in all decay rates. By Eq. (12), we find that Γ(H 0 → W W/ZZ) could constrain the c X while Γ(H 0 → ZA 0 ) could bound ξ. It is worth mentioning that with the limit m A 0 ≪ m H ± = 2 TeV, the process H ± → W ± A 0 only depends on ξ.
It is known that in THD model, when c X → 0 and s X → 1, the SM-like Higgs couplings will return to the SM. In this circumstance, if m A 0 satisfies the jet tagging condition |m j − m W/Z | < 13 GeV, the dijet only can be generated through ZA 0 or W A 0 channel. Using Eqs. (8) and (12), we present the correlation between total width Γ H 0 and free parameters in Fig. 1(a), where we have adopted m H 0 = 2 TeV and y q = y u = y d = 0.1. By taking m H ± and y q = 0.1, the total width Γ H ± as a function of ξ is given in Fig. 1(b).
It is not clear yet if the resonance is a neutral or charged particle, we separately study the decay branching ratio (BR) and production cross section. According to the decay rates shown in Eqs. (10) and (12), we see that H 0 can decay into qq with q = u, d, W + W − , ZZ and ZA 0 channels and the free parameters are y q , ξ and c X . We present the BRs for H 0 decays as a function of c X in Fig. 2(a), where we have used m H 0 = 2 TeV, y q = 0.1 and ξ = 0.1. From the results in Fig. 1(a), we see that with ξ = 0.1, if Γ H 0 < 100 GeV is required, the value of c X should be less than 0.14. In the region c X < 0.14, we find that diboson channel dominates the BR. Accordingly, the results could be consistent with the unseen dijet which is produced from H 0 directly. Additionally, we also find that ZA 0 mode plays an essential role at c X < 0.1.
For charged Higgs decays, we only have two channels W ± A 0 and qq ′ , therefore, the BRs of charged Higgs decays only depend on y q and ξ. With m H ± = 2 TeV and ξ = 0.1, the BRs of H ± decays as a function of y q are displayed in Fig. 2(b). In order to avoid the unseen dijet from H ± decays, we should limit y q < 0.5, where W ± A 0 channel dominates. If we further use y q < 0.2 in which the contribution of qq ′ mode is small, the BR of W A 0 is insensitive to ξ.
According to the number of events observed by ATLAS using 20.3 fb −1 , the cross section for pp → R → V V ′ is of order of 16 − 30 fb. Based on the results, we investigate if the introduced new interactions can lead to the same cross section in order of magnitude for σ(pp → R)BR(R → diboson). For estimating the production cross section σ(pp → H 0 /H ± ), we implement the relevant couplings to CalcHEP [24] and use it with CTEQ6L PDF [25] to calculate the numerical values. By using the cross symmetry, we see that the production of H 0 /H ± is through quark annihilations and σ(pp → H 0 /H ± ) only depends on y q . Combining the results in Fig. 2(a), we plot the contours for σ(pp → R)BR(R → diboson) as a function of y q and c X in Fig. 3, where figure (a)  stand for ZZ and ZA 0 channels, respectively.
If the resonance is a charged Higgs, similar to the situation of H 0 , the production cross section σ(pp → H ± ) only depends on y q . Although H ± can decay into W ± A 0 and qq ′ , if we focus on y q < 0.1, the BR of former will approach one while the latter is small and negligible.
We show σ(pp → H ± )BR(H ± → (W ± A 0 , qq ′ )) as a function of y q in Fig. 4. By the plot, it is clear that y q ∼ O(0.06) is good enough to interpret the ATLAS excess. Finally, we briefly discuss the constraint from leptonic H 0 /H ± decays. According to the measurements of ATLAS [27] and CMS [28], the current upper bound on the production cross section of dilepton resonance is known to be O(0. In summary, a diboson excess in dijet invariant mass spectrum is reported by ATLAS; as a result, the existence of a resonance with mass around 2 TeV is indicated. We propose the resonance could be the neutral or charged Higgs and employ the extended two Higgs doublets to demonstrate the possibility. We find that the coupling of scalar Higgs to the first generation quarks is not suppressed and the required value to produce a right production cross section for the resonance is of O(0.06 − 0.2). The involving free parameters are only y q , ξ and c X when m A 0 ≪ m H 0 /H ± and y q = y u = y d are adopted. Besides the W W and ZZ channels, we find that the channels ZA 0 and W A 0 in the frame of extended two Higgs doublets are also important. Since the tagged jet mass is only determined by |m j − m W/Z | < 13 GeV, therefore, any new particle with mass of O(100) GeV, e.g. A 0 in this approach, could also contribute to the excess. The current limit for light A 0 mass in supersymmetric model is m A 0 > 93.4 GeV [31,32], where the LEP data are applied and the related process is e + e − → A 0 h. In our model, the constraint is weaker by following reasons: (1) A 0 production cross section is suppressed by the mixing effect ξ; (2) unlike the case in Ref. [32] where A 0 decays into bb or ττ , the A 0 in the model predominantly decays into light quarks and the corresponding background events are larger. Therefore, the constraint of m A 0 in our model should be much weaker and m A 0 ≃ m Z is allowed. It will be interesting if a detailed analysis for light A 0 of O(100) GeV can be searched at the LHC.