Abstract:
Analysis of contributions from vector-like leptonic supermultiplets to the Higgs diphoton decay rate and to the Higgs boson mass is given. Corrections arising from the exchange of the new leptons and their super-partners, as well as their mirrors are computed analytically and numerically. We also study the correlation between the enhanced Higgs diphoton rate and the Higgs mass corrections. Specifically, we find two branches in the numerical analysis: on the lower branch the diphoton rate enhancement is flat while on the upper branch it has a strong correlation with the Higgs mass enhancement. It is seen that a factor of 1.4-1.8 enhancement of the Higgs diphoton rate on the upper branch can be achieved, and a 4-10 GeV positive correction to the Higgs mass can also be obtained simultaneously. The effect of this extra contribution to the Higgs mass is to release the constraint on weak scale supersymmetry, allowing its scale to be lower than in the theory without extra contributions. The vector-like supermultiplets also have collider implications which can be tested at the LHC and at the ILC.

Abstract:
We consider a gauged $U(1)_x$ extension of the standard model and of the minimal supersymmetric standard model where the dark matter fields are charged under $U(1)_x$ and carry lepton number while the standard model fields and fields of the minimal supersymmetric standard model are neutral under $U(1)_x$. We consider leptogenesis in this class of models with all fundamental interactions having no violation of lepton number, and the total $B-L$ in the universe vanishes. Such leptogenesis leads to equal and opposite lepton numbers in the visible sector and in the dark sector, and thus also produces asymmetric dark matter. Part of the lepton numbers generated in the leptonic sector subsequently transfer to the baryonic sector via sphaleron interactions. The stability of the dark particles is protected by the $U(1)_x$ gauge symmetry. A kinetic mixing between the $U(1)_x$ and the $U(1)_Y$ gauge bosons allows for dissipation of the symmetric component of dark matter. The case when $U(1)_x$ is $U(1)_{B-L}$ is also discussed for the supersymmetric case. This case is particularly interesting in that we have a gauged $U(1)_{B-L}$ which ensures the conservation of $B-L$ with an initial condition of a vanishing $B-L$ in the universe. Phenomenological implications of the proposed extensions are discussed, which include implications for electroweak physics, neutrino masses and mixings, and lepton flavor changing processes such as $\ell_i \to \ell_j \gamma$. We also briefly discuss the direct detection of the dark matter in the model.

Abstract:
Analysis of contributions from vector-like leptonic supermultiplets to the Higgs diphoton decay rate and to the Higgs boson mass is given. Corrections arising from the exchange of the new leptons and their super-partners, as well as their mirrors are computed analytically and numerically. We also study the correlation between the enhanced Higgs diphoton rate and the Higgs mass corrections. Specifically, we find two branches in the numerical analysis: on the lower branch the diphoton rate enhancement is flat while on the upper branch it has a strong correlation with the Higgs mass enhancement. It is seen that a factor of 1.4-1.8 enhancement of the Higgs diphoton rate on the upper branch can be achieved, and a 4-10 GeV positive correction to the Higgs mass can also be obtained simultaneously. The effect of this extra contribution to the Higgs mass is to release the constraint on weak scale supersymmetry, allowing its scale to be lower than in the theory without extra contributions. The vector-like supermultiplets also have collider implications which can be tested at the LHC and at the ILC.

Abstract:
Let ${\mathbb F}_q$ be a finite field of characteristic two and ${\mathbb F}_q(X_1,...,X_n)$ a rational function field. We use matrix methods to obtain explicit transcendental bases of the invariant subfields of orthogonal groups and pseudo-symplectic groups on ${\mathbb F}_q(X_1,...,X_n)$ over ${\mathbb F}_q$.

Abstract:
A new family of strongly regular graphs, called the general symplectic graphs $Sp(2\nu, q)$, associated with nonsingular alternate matrices is introduced. Their parameters as strongly regular graphs, their chromatic numbers as well as their groups of graph automorphisms are determined.

Abstract:
We consider the possibility that in an inflationary universe, the inflaton field decays purely into the dark sector creating asymmetric dark matter at the end of inflation. This asymmetry is subsequently transmuted into leptons and baryons. We consider this possibility in the framework of a generic inflation model, and compute the amount of asymmetric dark matter created from the out of equilibrium decays of the inflaton with CP violating Yukawa couplings. The dark matter asymmetry is then transferred to the visible sector by the asymmetry transfer equation and generates an excess of $B-L$. Baryogenesis occurs via sphaleron processes which conserve $B-L$ but violate $B+L$. A mechanism for the annihilation of the symmetric component of dark matter is also discussed. The model leads to multi-component dark matter consisting of both bosonic and fermionic components.

Abstract:
We discuss the possibility of cogenesis generating the ratio of baryon asymmetry to dark matter in a Stueckelberg U(1) extension of the standard model and of the minimal supersymmetric standard model. For the U(1) we choose $L_{\mu}-L_{\tau}$ which is anomaly free and can be gauged. The dark matter candidate arising from this extension is a singlet of the standard model gauge group but is charged under $L_{\mu}-L_{\tau}$. Solutions to the Boltzmann equations for relics in the presence of asymmetric dark matter are discussed. It is shown that the ratio of the baryon asymmetry to dark matter consistent with the current WMAP data, i.e., the cosmic coincidence, can be successfully explained in this model with the depletion of the symmetric component of dark matter from resonant annihilation via the Stueckelberg gauge boson. For the extended MSSM model it is shown that one has a two component dark matter picture with asymmetric dark matter being the dominant component and the neutralino being the subdominant component (i.e., with relic density a small fraction of the WMAP cold dark matter value). Remarkably, the subdominant component can be detected in direct detection experiments such as SuperCDMS and XENON-100. Further, it is shown that the class of Stueckelberg models with a gauged $L_{\mu}-L_{\tau}$ will produce a dramatic signature at a muon collider with the $\sigma(\mu^+\mu^-\to \mu^+\mu^-,\tau^+\tau^-)$ showing a detectable $Z'$ resonance while $\sigma(\mu^+\mu^-\to e^+e^-)$ is devoid of this resonance. Asymmetric dark matter arising from a $U(1)_{B-L}$ Stueckelberg extension is also briefly discussed. Finally, in the models we propose the asymmetric dark matter does not oscillate and there is no danger of it being washed out from oscillations.

Abstract:
We propose a framework in which visible matter interacts with matter from a hidden sector through mass mixings of St\"uckelberg U(1) gauge fields. In contrast to other Z' mediation scenarios, our setup has the added appealing features that (i) the choice of Z's can be significantly broadened without necessarily introducing unwanted exotic matter and (ii) there can be sizable tree-level interactions between the visible and hidden sectors. String theory embeddings of this scenario and their phenomenological features are briefly discussed.

Abstract:
We consider the possibility that some primordial fields decay purely into the dark sector creating asymmetric dark matter. This asymmetry is subsequently transmuted into leptons and baryons. Within this paradigm we compute the amount of asymmetric dark matter created from the out of equilibrium decays of the primordial fields with CP violating Yukawa couplings. The dark matter asymmetry is then transferred to the visible sector by the asymmetry transfer equation and generates an excess of $B-L$. Baryogenesis occurs via sphaleron processes which conserve $B-L$ but violate $B+L$. A mechanism for the annihilation of the symmetric component of dark matter is also discussed. The model leads to multi-component dark matter consisting of both bosonic and fermionic components.

Abstract:
We discuss the diboson excess seen by the ATLAS detector around 2 TeV in the LHC run I at $\sqrt{s}=8$ TeV. We explore the possibility that such an excess can arise from a $Z'$ boson which acquires mass through a {$U(1)_X$} Stueckelberg extension. The corresponding $Z'$ gauge boson} is leptophobic with a mass of around 2 TeV and has interactions with $SU(2)_L$ Yang-Mills fields {and gauge fields of the hypercharge. The analysis predicts $Z'$ decays into $WW$ and $ZZ$ as well as into $Z\gamma$. Further three-body as well as four-body decays of the $Z'$ such as $WWZ, WW\gamma, WWZZ$ etc are predicted. In the analysis we use the helicity formalism which allows us to exhibit the helicity structure of the $Z'$ decay processes in an transparent manner. In particular, we are able to show the set of vanishing helicity amplitudes in the decay of the massive $Z'$ into two vector bosons due to angular momentum conservation with a special choice of the reference momenta. The residual set of non-vanishing helicity amplitudes are identified. The parameter space of the model compatible with the diboson excess seen by the ATLAS experiment at $\sqrt s=8$ TeV is exhibited. Estimate of the diboson excess expected at $\sqrt s= 13$ TeV with 20 fb$^{-1}$ of integrated luminosity at LHC run II is also given. It is shown that the $WW$, $ZZ$ and $Z\gamma$ modes are predicted to be in the approximate ratio $1:\cos^2\theta_W (1+ \alpha \tan^2\theta_W)^2/2: (1-\alpha)^2\sin^2\theta_W/2$} where $\alpha$ is the relative strength of the couplings of hypercharge gauge fields to the couplings of the Yang-Mills gauge fields. Thus observation of the $Z\gamma$ mode as well as three-body and four-body decay modes of the $Z'$ will provide a definite test of the model and of a possible new source of interaction beyond the standard model.