Unitarity Constraints On Color-Octet-Electro Weak-Doublet Scalars Model

There exist evidences in both theories and experiments that LHC may find a scalar Higgs particle,search and find the Higgs particle is the main purpose of recent experiments, but it still remainsundiscovered. So, people tried to study it in models beyond the Standard Model (SM). The simplestextension of SM is the Two Higgs Doublet Model (THDM), after that people tried to introduce colorindices such as Color-Octet-Electroweak-Doublet Scalars Model (COEDSM). It’s relatively easy to dounitarity constraints on SM and THDM, but not so simple on COEDSM, because that if two color octetscalar multiply together, then we will get a representation of64dimensions, difficult to do unitarityconstraints. We have found a way to deal with this difficulty.First we used knowledge of group theory to decompose the dimension64representation intorepresentations, then we chose different basis according to them, at the sametime we considered the conversation of charge and CP properties. In this paper, we introduced theory ofunitarity constraints and COEDSM. Just like THDM, COEDSM has two Higgs doublets. The difference isthat in COEDSM, only one Higgs doublet is responsible for the broken of electroweak symmetry, andanother one has color indices. The neutral doublet component contains two parts: real scalar part andpseudo-scalar part. They couple with SM fermions, get the Lagrangian. According to the most generalrenormalizable scalar potential, we considered all possible interactions. With the property of the model,considering the conversation of charge and conversation of CP, the basis vectors we chose belong todifferent representations of group, thus we have scalar scattering matrix S(51×51), which consist of tensubmatrices.There is no interaction between particles that belong to different submatrices. We tried to diagonalizethese submatrices, but doing it analytically is almost impossible while the parameters of this model are toomany, so we used computer to reach our goal numerically. After that we made the largest eigenvalue ofthese matrices less than8, which is the requirement of unitarity. Through computation we found that, theunitarity required to be not larger than19.3.We tried to explain3.2excess observed by the CDF collaboration in COEDSM whichunder unitarity constraints. At the same time we also considered limitations from diphoton and STU variables, and found that the limitations on parameters of the model are strong. We chose a parameter spacein which we scanned108random samplings and studied the properties of the surviving parameters whichsatisfied both limitations of diphoton and STU variables.As required by unitarity constraints, we made equal to19, and according to results ofparameters scanning, we chose some parameters range to compute the cross section of scattering process ofwhich the result is12.4302, it’s large enough to be helpful on explaining the CDF3.2excess. And our research results imply that in COEDSM, the mass range of S and H is very small, almostcan be seen as definite, this means two results: first, it can afford a strong prediction, and has definiteinstructive significance on Higgs hunting in COEDSM. Second, a parameter space like this one is so smallthat it may soon be excluded by new experiments, thereby exclude the COEDSM. No matter which result itwill be, our work still has its significance.