We derived analytical results for the gapless edge states of two-dimensional topological insulators in the presence of electron-surface optical (SO) phonon interaction due to substrates. We followed an analytical algorithm, called Lee-Low-Pines variational approximation in the conventional polaron theory, to examine the substrate induced effects on both bulk and edge states of a two dimensional topological insulator within the frame work of Bernevig-Hughes-Zhang (BHZ) model. By implementing this algorithm, we propose a novel phonon-dressed BHZ Hamiltonian which allows one to investigate the effects of various substrates not only on bulk states but also on the associated gapless helical edge states (HESs). We found that both the bulk and HESs are significantly renormalized in the momentum space due to the substrate-related polaronic effects. The model we developed here clarifies which subtrates favor the HESs of quantum spin Hall system and which are not. Correspondingly, our work demonstrates that the substrate related polaronic effects have significant role on the emergence of HESs. In other words, we show that SO phonons due to substrates modify the electronic band topology of topological insulators together with the associated HESs and therefore they can be used to tune quantum phase transitions between topological insulators and non-topological ones.

Pair production of tau leptons in two photon collision γγ → τ + τ − is studied at CLIC to test CP violating QED couplings of tau leptons. CP violating effects are investigated using tau pair spin correlations which are observed through the hadronic decay of each τ into πν. Competitive bounds with previous works on the electric dipole moment from CP odd terms have been obtained.

Pair production of tau leptons in two photon collision ${\\gamma\\gamma \\to \\tau^{+}\\tau}^{-}$ is studied at CLIC to test CP violating QED couplings of tau leptons. CP violating effects are investigated using tau pair spin correlations which are observed through the hadronic decay of each $\\tau$ into $\\pi\\nu$. Competitive bounds with previous works on the electric dipole moment from CP odd terms have been obtained.

Potential of the LHC to explore the phenomenology of the Kaluza-Klein (KK) tower of gravitons in the scenarios of the Arkani-Hamed, Dimopoulos and Dvali(ADD) model and Randall-Sundrum (RS) model is discussed via the process γγ → γγ including the Standard Model one loop diagram. The improved constraints on model parameters have been obtained compared to the LEP and Tevatron sensitivity.

Potential of the LHC to determine the electromagnetic couplings of the τ lepton is discussed via the process γγ → τ+ τ−. Highly improved constraints of the anomalous magnetic and electric dipole moments have been obtained compared to the LEP sensitivity.

Potential of the LHC to determine the electromagnetic couplings of the $\\tau$ lepton is discussed via the process ${\\gamma\\gamma \\to \\tau^{+}\\tau}^{-}$. Highly improved constraints of the anomalous magnetic and electric dipole moments have been obtained compared to the LEP sensitivity.

We study the possibility for directly measuring the polarized gluon distribution in the process γp→t¯t. It is shown that polarization asymmetry of the final top quarks is proportional to the gluon polarization. With available energy and luminosity, the collision of a polarized proton beam and a Compton backscattered photon beam can create polarized top quarks which carry the spin information of the process. Energy dependence and angular distributions of the polarization asymmetry of the top pairs has been discussed including statistical uncertainty.

We discuss the potential of the photon-induced two lepton final states at the LHC to explore the phenomenology of the Kaluza-Klein tower of gravitons in the scenarios of the Arkani-Hamed, Dimopoulos, and Dvali model and the Randall-Sundrum model. The sensitivity to model parameters can be improved compared to the present LEP or Tevatron sensitivity.

The constraints on the anomalous quartic $WW\ensuremath{\gamma}\ensuremath{\gamma}$ and $ZZ\ensuremath{\gamma}\ensuremath{\gamma}$ gauge boson couplings are investigated through the processes $e\ensuremath{\gamma}\ensuremath{\rightarrow}{W}^{\ensuremath{-}}\ensuremath{\gamma}{\ensuremath{\nu}}_{e}$ and $e\ensuremath{\gamma}\ensuremath{\rightarrow}Z\ensuremath{\gamma}e$. Considering the longitudinal and transverse polarization states of the final $W$ or $Z$ boson and incoming beam polarizations we find 95% confidence level limits on the anomalous coupling parameters ${a}_{0}$ and ${a}_{c}$ with an integrated luminosity of $500\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ and $\sqrt{s}=0.5$, 1 TeV energies. Assuming the ${W}^{+}{W}^{\ensuremath{-}}\ensuremath{\gamma}\ensuremath{\gamma}$ couplings are independent of the $ZZ\ensuremath{\gamma}\ensuremath{\gamma}$ couplings we show that the longitudinal polarization state of the final gauge boson improves the sensitivity to anomalous couplings by a factor of 2-3 depending on energy and coupling. An extra enhancement in sensitivity by a factor of 1.3 comes from a set of initial beam polarizations.

The constraints on the anomalous quartic WW gamma gamma and ZZ gamma gamma gauge boson couplings are investigated through the processes e gamma -> W-gamma nu(e) and e gamma -> Z gamma e. Considering the longitudinal and transverse polarization states of the final W or Z boson and incoming beam polarizations we find 95% confidence level limits on the anomalous coupling parameters a(0) and a(c) with an integrated luminosity of 500 fb(-1) and root s = 0.5, 1 TeV energies. Assuming the W+W-gamma gamma couplings are independent of the ZZ gamma gamma couplings we show that the longitudinal polarization state of the final gauge boson improves the sensitivity to anomalous couplings by a factor of 2-3 depending on energy and coupling. An extra enhancement in sensitivity by a factor of 1.3 comes from a set of initial beam polarizations.

In our previous work [Phys. Rev. D 70, 037503 (2004)] for the e(+)p -> t (nu) over bar +X process, we have shown that the top quark possesses a high degree of spin polarization when its spin decomposition axis is along the incoming lepton beam. In this work, the potential of ep collisions to probe an anomalous Wtb vertex is investigated via the polarized single top quark production process for TESLA+HERAp energy. The effects of the top quark polarization to Wtb couplings F-2L and F-2R are discussed. It is possible to define a polarization axis for the top quark that is more sensitive to new physics than the unpolarized case.

We revised the discussion on the degree of spin polarization of single top quarks produced via Wg fusion process in ep collision at TESLA+HERAp and CLIC+LHC energies in connection with our article in [Phys. Rev. D 69, 034016 (2004)]. For eb-->t (nu) over bar subprocess we show that the top quark spin is completely polarized when the spin basis is chosen in the direction of the incoming positron beam in the rest frame of top quark. After combining properly the cross sections of e(+)b-->t (nu) over bar and e(+)g-->t (b) over bar(nu) over bar processes we find that 96% of the top quarks have their spins up in e(+)-beam direction with the asymmetry of 0.92. Some of the spin fractions and asymmetries have been corrected 2-5 % when compared to the previous paper. Consequently, this Brief Report improves the results of the previous paper about the ideal basis for studying the top quark spin in ep collision.

We search for lepton flavor violating couplings via doubly charged bilepton (or doubly charged Higgs) exchange in electron-positron annihilation process e(+)e(-)-->mu(+)mu(-),tau(+)tau(-) using CERN LEP data at the center of mass energies between 189-207 GeV. Standard model program ZFITTER has been used to calculate radiative corrections. We find that g(L)(2)/M-L(2)<O(10(-6)) GeV-2 at 95% C.L. for flavor violating scalar and vector bilepton couplings.

The constraints on the neutral gauge boson couplings, ZZgamma and Zgammagamma, are investigated at linear e(+)e(-) collider energies through the Zgamma production with longitudinal and transverse polarization states of the final Z boson. Because of high energy of linear electron-positron beams, initial state radiation (ISR) considerably changes the production cross section. We obtain an increase in the cross section by a factor of 2-3 due to ISR for transverse polarization and by a factor of 10-100 for longitudinal polarization states depending on the energy. We find the 95% C.L. limits on the CP conserving form factors h(3)(Z), h(4)(Z), h(3)(gamma), and h(4)(gamma) with integrated luminosity 500 fb(-1) and roots=0.5,1,1.5 TeV energies. It is shown that the longitudinal polarization of the Z boson, together with ISR, can improve sensitivities by factors 2-3.

Upper limits on doubly charged bilepton couplings and masses are extracted from CERN LEP data for Bhabha scattering in the energy range roots=183-202 GeV using the standard model program ZFITTER, which calculates radiative corrections. We find that g(L)(2)/M-L(2)<O(10(-5)) GeV-2 at 95% C.L. for scalar and vector bileptons.

The potential of $\gamma$e mode of linear $e^{+}e^{-}$ collider to probe $ZZ\gamma$ and $Z\gamma\gamma$ vertices is investigated through the Z boson production from the procees $\gamma e\to Z e$. Considering the longitudinal and transverse polarization states of the Z boson and incoming polarized beams we find the 95% C.L. limits on the form factors $h_{3}^{Z}$, $h_{4}^{Z}$, $h_{3}^{\gamma}$ and $h_{4}^{\gamma}$ with integrated luminosity 500$fb^{-1}$ and $\sqrt{s}=$0.5, 1, 1.5 TeV energies. It is shown that the polarization can improve sensitivities by factors 2-3 depending on the energy.