In this work, we investigate the prospects for detecting the Inert Doublet Model via the trilepton channel at the LHC. We present a set of representative benchmark scenarios in which all applicable constraints are satisfied, and show that in some of these scenarios, it is possible to obtain a signal at the $5\sigma$ significance level or better with integrated luminosity of $300{\mathrm{fb}}^{-1}$.

In the SU(3) symmetry limit, semileptonic $D^{+}\to S{l}^{+}\nu$ and $B^{-}\to S{l}^{-}\overline{\nu }$ decays, with $S=a_0(980)$, $f_0(980)$, and $f_0(600)$, are found to obey different sum rules in the $\overline{q}q$ and the tetraquark descriptions for scalar mesons. Thus these sum rules can distinguish the two scenarios for light scalar mesons model independently. This method also applies to the ${\overline{B}}^0\to J/\psi ({\eta }_c)S$ decays. Two kinds of SU(3) symmetry breaking effects are found to be under control, which will not spoil our method. The branching fractions of the $D^{+}\to S{l}^{+}\nu$, $B^{-}\to S{l}^{-}\overline{\nu }$, and ${\overline{B}}^0\to J/\psi ({\eta }_c)S$ decays roughly have the order ${10}^{-4}$, ${10}^{-5}$, and ${10}^{-6}$, respectively. The ongoing BEPC II and the forthcoming Super B experiments are able to measure these channels and, accordingly, to provide detailed information of the scalar meson inner structure.

We investigate the chiral condensate and the dressed Polyakov loop or dual chiral condensate at finite temperature and density in the two-flavor Nambu–Jona-Lasinio model. The dressed Polyakov loop is regarded as an equivalent order parameter of deconfinement phase transition in a confining theory. We find the behavior of a dressed Polyakov loop in the absence of any confinement mechanism quite interesting. With only quark degrees of freedom present, it still shows an order parameter like behavior. It is found that in the chiral limit, the critical temperature for chiral phase transition coincides with that of the dressed Polyakov loop in the whole $(T,\mu )$ plane. In the case of explicit chiral symmetry breaking, it is found that the transition temperature for chiral restoration $T_c^{\chi }$ is smaller than that of the dressed Polyakov loop $T_c^{\mathcal{D}}$ in the low baryon density region where the transition is a crossover. With the increase of the current quark mass the difference between the two transition temperatures is found to be increasing. However, the two critical temperatures coincide in the high baryon density region where the phase transition is of first order. We give an explanation on the feature of $T_c^{\chi }=T_c^{\mathcal{D}}$ in the case of 1st and 2nd order phase transitions, and $T_c^{\chi }<T_c^{\mathcal{D}}$ in the case of crossover, and expect this feature is general and can be extended to full QCD theory. Our result might indicate that in the case of crossover, there exists a small region where chiral symmetry is restored, but the color degrees of freedom are still confined.

We extend our recent work and study implications of the standard model with four generations (SM4) for rare $B$ and $K$ decays. We again take seriously the several $2–3\sigma$ anomalies seen in $B$, $B_s$ decays and interpret them in the context of this simple extension of the SM. SM4 is also of course of considerable interest for its potential relevance to dynamical electroweak symmetry breaking and to baryogenesis. Using experimental information from processes such as $B\to X_s\gamma$, $B_d$ and $B_s$ mixings, indirect $CP$-violation from $K_L\to \pi \pi$ etc. along with oblique corrections, we constrain the relevant parameter space of the SM4, and find $m_{t^{\prime }}$ of about 400–600 GeV with a mixing angle $|V_{t^{\prime }b}^{*}{V}_{t^{\prime }s}|$ in the range of about $0.05–1.4\times {10}^{-2}$ and with an appreciable $CP$-odd associated phase, are favored by the current data. Given the unique role of the $CP$ asymmetry in $B_s\to \psi \varphi$ due to its gold-plated nature, correlation of that with many other interesting observables, including the semileptonic asymmetry ($A_{\mathrm{SL}}$) are studied in SM4. We also identify several processes, such as $B\to X_s\nu \overline{\nu }$, $K_L\to {\pi }^0\nu \overline{\nu }$ etc., that are significantly different in SM4 from the SM. Experimentally the very distinctive process $B_s\to {\mu }^{+}{\mu }^{-}$ is also discussed; the branching ratio can be larger or smaller than in SM, $(3.2\to 4.2)\times {10}^{-9}$, by a factor of $\mathcal{O}(3)$.

We demonstrate that a Jackiw-Nohl-Rebbi solution, as the most general two-instanton, generates a circular loop of magnetic monopole in four-dimensional Euclidean $SU(2)$ Yang-Mills theory, in contrast to the one-instanton solution in the regular gauge for which no such magnetic monopole loops exist. These results together with our previous result indicate that a two-instanton solution and a two-meron solution with the same asymptotic behavior in the long distance are responsible for quark confinement based on the dual superconductivity picture.

It is shown that on curved backgrounds, the Coulomb gauge Faddeev-Popov operator can have zero modes even in the Abelian case. These zero modes cannot be eliminated by restricting the path integral over a certain region in the space of gauge potentials. The conditions for the existence of these zero modes are studied for static spherically symmetric spacetimes in arbitrary dimensions. For this class of metrics, the general analytic expression of the metric components in terms of the zero modes is constructed. Such expression allows one to find the asymptotic behavior of background metrics, which induce zero modes in the Coulomb gauge, an interesting example being the three-dimensional anti–de Sitter spacetime. Some of the implications for quantum field theory on curved spacetimes are discussed.

In a general time-dependent ($3+1$)-dimensional spherically symmetric spacetime, the so-called Kodama vector is a naturally defined geometric quantity that is timelike outside the evolving horizon and so defines a preferred class of fiducial observers. However the Kodama vector does not by itself define any preferred notion of time. We first extract as much information as possible by invoking the “warped product” structure of spherically symmetric spacetime to study the Kodama vector, and the associated Kodama energy flux, in a coordinate-independent manner. Using this formalism we construct a general class of conservation laws, generalizing Kodama’s energy flux. We then demonstrate that a preferred time coordinate—which we shall call Kodama time—can be introduced by taking the additional step of applying the Clebsch decomposition theorem to the Kodama vector. We thus construct a geometrically preferred coordinate system for any time-dependent spherically symmetric spacetime, and explore its properties. We study the geometrically preferred fiducial observers, and demonstrate that it is possible to define and calculate a generalized notion of surface gravity that is valid throughout the entire evolving spacetime. Furthermore, by building and suitably normalizing a set of radial null geodesics, we can show that this generalized surface gravity passes several consistency tests and has a physically appropriate static limit.

We study the phenomenological implications stemming from the dependence of the tidal charge on the brane thickness $L$ for the evaporation and decay of microscopic black holes. In general, the larger $L$, the longer are the black hole lifetimes and the greater their maximum mass for those cases in which the black hole can grow. In particular, we again find that tidal-charged black holes might live long enough to escape the detectors and even the gravitational field of the Earth, thus resulting in large amounts of missing energy. However, under no circumstances could TeV-scale black holes grow enough to enter the regime of Bondi accretion.

We investigate the application of the singular value decomposition to compact-binary, gravitational-wave data-analysis. We find that the truncated singular value decomposition reduces the number of filters required to analyze a given region of parameter space of compact-binary coalescence waveforms by an order of magnitude with high reconstruction accuracy. We also compute an analytic expression for the expected signal loss due to the singular value decomposition truncation.

We discuss the phenomenology of doubly and singly charged Higgs bosons [of $SU(2{)}_L$-triplet fields] in the simplest $A_4$-symmetric version of the Higgs triplet model. Mass eigenstates of these Higgs bosons are obtained explicitly from the Higgs potential. It is shown that their decays into a pair of leptons have unique flavor structures which can be tested at the LHC if some of their masses are below the TeV scale. Sizable decay rates for $\tau \to \overline{\mu }ee$ and $\tau \to \overline{e}\mu \mu$ can be obtained naturally, while other $\tau \to \overline{\ell }{\ell }^{\prime }{\ell }^{\prime \prime }$, $\mu \to \overline{e}ee$, and $\ell \to {\ell }^{\prime }\gamma$, are almost forbidden in this model. Contributions of these Higgs bosons to the nonstandard interactions of neutrinos are also considered.

We consider a model where right-handed neutrinos and sneutrinos are introduced to the minimal supersymmetric standard model. In the scalar potential of this model, there exist trilinear and quartic terms in scalar potential that are proportional to Yukawa couplings of neutrinos. Because of these trilinear and quartic terms, color and/or charge breaking (CCB) and unbounded-from-below (UFB) directions appear along which sneutrinos have a vacuum expectation value, making the vacuum of the electroweak symmetry breaking unstable. We analyze the scalar potential of this model and derive necessary conditions for color and/or charge breaking and unbounded-from-below directions to vanish.

Supersymmetry (SUSY) with a long-lived stau is an attractive scenario in the LHC experiments because one can directly observe stau tracks in each SUSY event, and thus precise measurements of SUSY particle masses are possible. In this scenario, we discuss the possibility to observe/measure parity violation in interactions among SUSY particles. Such a measurement will be important in determining the spins and chiralities of SUSY particles. We use the last step of the cascade-decay chain: ${\chi }^0\to \tilde{\tau }\tau \to \tilde{\tau }(l\nu \overline{\nu })$, where the polarization of the tau lepton can be determined statistically by looking at the energy distribution of the final state lepton. Comparing with the theoretical formula of the neutralino differential decay width, one can extract the size of parity violation in the interaction vertices among the stau, the tau lepton, and the neutralino. We perform a Monte Carlo simulation to see if the effect is visible at the LHC experiments.

We present a detailed description of the extraction of the highly excited isovector meson spectrum on dynamical anisotropic lattices using a new quark-field construction algorithm and a large variational basis of operators. With careful operator construction, the combination of these techniques is used to identify the continuum spin of extracted states reliably, overcoming the reduced rotational symmetry of the cubic lattice. Excited states, states with exotic quantum numbers ($0^{+-}$, $1^{-+}$ and $2^{+-}$), and states of high spin are resolved, including, for the first time in a lattice QCD calculation, spin-four states. The determinations of the spectrum of isovector mesons and kaons are performed on dynamical lattices with two volumes and with pion masses down to $\sim 400\mathrm{MeV}$, with statistical precision typically at or below 1% even for highly excited states.

We study the charmless decays $B\to K_h\eta$ and $B\to K_h{\eta }^{\prime }$ within the framework of QCD factorization (QCDF) for $K_h=K$, $K^{*}$, $K_0^{*}(1430)$ and naive factorization for $K_h=K_2^{*}(1430)$. There are three distinct types of penguin contributions: (i) $b\to sq\overline{q}\to s{\eta }_q$, (ii) $b\to ss\overline{s}\to s{\eta }_s$, and (iii) $b\to sq\overline{q}\to q{\overline{K}}_h$, where ${\eta }_q=(u\overline{u}+d\overline{d})/\sqrt{2}$ and ${\eta }_s=s\overline{s}$. $B\to K^{(*)}{\eta }^{{(}^{\prime })}$ decays are dominated by type-II and type-III penguin contributions. The interference, constructive for $K{\eta }^{\prime }$ and $K^{*}\eta$ and destructive for $K\eta$ and $K^{*}{\eta }^{\prime }$, between type-II and type-III diagrams explains the pattern of $\Gamma (B\to K{\eta }^{\prime })\gg \Gamma (B\to K\eta )$ and $\Gamma (B\to K^{*}{\eta }^{\prime })\ll \Gamma (B\to K^{*}\eta )$. Within QCDF, the observed large rate of the $K{\eta }^{\prime }$ mode can be naturally explained without invoking flavor-singlet contributions or something exotic. The decay pattern for $B\to K_0^{*}(1430){\eta }^{{(}^{\prime })}$ decays depends on whether the scalar meson $K_0^{*}(1430)$ is an excited state of $\kappa$ or a lowest-lying $P$-wave $q\overline{q}$ state. Hence, the experimental measurements of $B\to K_0^{*}(1430){\eta }^{{(}^{\prime })}$ can be used to explore the quark structure of $K_0^{*}(1430)$. If $K_0^{*}(1430)$ is a low-lying $q\overline{q}$ bound state, we find that $K_0^{*}\eta$ has a rate slightly larger than $K_0^{*}{\eta }^{\prime }$ owing to the fact that the $\eta -{\eta }^{\prime }$ mixing angle in the ${\eta }_q$, ${\eta }_s$ flavor basis is less than 45°, in agreement with experiment. The type-III penguin diagram does not contribute to $B\to K_2^{*}{\eta }^{{(}^{\prime })}$ under the factorization hypothesis and the type-II diagram dominates. The ratio $\Gamma (B\to K_2^{*}{\eta }^{\prime })/\Gamma (B\to K_2^{*}\eta )$ is expected to be of order 2.5 as a consequence of (i) $|f_{{\eta }^{\prime }}^s|>|f_{\eta }^s|$ and (ii) a destructive (constructive) interference between type-I and type-II penguin diagrams for $K_2^{*}\eta$ ($K_2^{*}{\eta }^{\prime }$). However, the predicted rates of $B\to K_2^{*}{\eta }^{{(}^{\prime })}$ in naive factorization are too small by 1 order of magnitude and this issue remains to be resolved. There are two $K^{(*)}{\eta }^{{(}^{\prime })}$ modes in which direct $CP$ asymmetries have been measured with significance around $4\sigma$: $A_{CP}(K^{-}\eta )=-0.37\pm 0.09$ and $A_{CP}({\overline{K}}^{*0}\eta )=0.19\pm 0.05$. In QCDF, power corrections from penguin annihilation which are needed to resolve $CP$ puzzles in $K^{-}{\pi }^{+}$ and ${\pi }^{+}{\pi }^{-}$ modes will flip $A_{CP}(K^{-}\eta )$ into a wrong sign. We show that soft corrections to the color-suppressed tree amplitude $a_2$ in conjunction with the charm content of the $\eta$ will finally lead to $A_{CP}(K^{-}\eta )=-{0.15}_{-0.28}^{+0.19}$. Likewise, this power correction is needed to improve the prediction for $A_{CP}({\overline{K}}^{*0}\eta )$.

The branching ratio and other observables for the rare flavor-changing neutral current decay ${\overline{B}}_d^0\to {\overline{K}}^{*0}(\to K^{-}{\pi }^{+})e^{+}{e}^{-}$ are studied below the $\overline{c}c$ threshold. The total amplitude for this decay includes the term coming from the standard model effective Hamiltonian and the term generated by the processes ${\overline{B}}_d^0\to {\overline{K}}^{*0}(\to K^{-}{\pi }^{+})V$ with intermediate low-lying vector resonances $V=\rho (770)$, $\omega (782)$, $\varphi (1020)$ decaying into the $e^{+}{e}^{-}$ pair. The resonance contribution to the branching ratio, polarization fractions of the $K^{*}$ meson, and coefficients in the angular distribution is calculated. The influence of the resonances on the integrated observables in the region of electron-positron invariant mass up to 1 GeV is studied in view of the planned measurements of the photon polarization at the LHCb.

We evaluate the mass of the $B_{s0}$ scalar meson and the coupling constant in the $B_{s0}BK$ vertex in the framework of QCD sum rules. We consider the $B_{s0}$ as a tetraquark state to evaluate its mass. We get $m_{B_{s0}}=(5.85\pm 0.13)\mathrm{GeV}$, which is in agreement, considering the uncertainties, with predictions supposing it as a $b\overline{s}$ state or a $B\overline{K}$ bound state with $J^P=0^{+}$. To evaluate the $g_{B_{s0}BK}$ coupling, we use the three-point correlation functions of the vertex, considering $B_{s0}$ as a normal $b\overline{s}$ state. The obtained coupling constant is: $g_{B_{s0}BK}=(16.3\pm 3.2)\mathrm{GeV}$. This number is in agreement with light-cone QCD sum rules calculation. We have also compared the decay width of the $B_{s0}\to BK$ process considering the $B_{s0}$ to be a $b\overline{s}$ state and a $BK$ molecular state. The width obtained for the $BK$ molecular state is twice as big as the width obtained for the $b\overline{s}$ state. Therefore, we conclude that with the knowledge of the mass and the decay width of the $B_{s0}$ meson, one can discriminate between the different theoretical proposals for its structure.

We study the $SU(3)$ linear sigma model for the pseudoscalar mesons in the Gaussian functional approximation (GFA). We use the $SU(3)$ linear sigma model Lagrangian with nonet scalar and pseudoscalar mesons, including symmetry breaking terms. In the GFA, we take the Gaussian Ansatz for the ground state wave function and apply the variational method to minimize the ground state energy. We derive the gap equations for the dressed meson masses, which are actually just variational parameters in the GFA method. We use the Bethe-Salpeter equation for meson-meson scattering, which provides the masses of the physical nonet mesons. We construct the projection operators for the flavor $SU(3)$ in order to work out the scattering $T$ matrix in an efficient way. In this paper, we discuss the properties of the Nambu-Goldstone bosons in various limits of the chiral $U_L(3)\times U_R(3)$ symmetry.

We point out that same-sign multilepton events, not given due attention yet for new physics search, can be extremely useful at the Large Hadron Collider. After showing the easy reducibility of the standard model backgrounds, we demonstrate the viability of same-sign trilepton signals for R-parity breaking supersymmetry, at both 7 and 14 TeV. We find that same-sign four-leptons, too, can have appreciable rates. Same-sign trileptons are also expected, for example, in Little Higgs theories with T-parity broken by anomaly terms.

We investigate the interaction between a flat membrane and pointlike graviton in the plane-wave matrix model. The one-loop effective potential in the large-distance limit is computed and is shown to be of $r^{-3}$ type where $r$ is the distance between two objects. This type of interaction has been interpreted as the one incorporating the smearing effect due to the configuration of a flat membrane in a plane-wave background. Our results support this interpretation and provide more evidence about it.