We analyze the rare semileptonic $B_s\to (\eta ,{\eta }^{\prime })l^{+}{l}^{-}$, $(l=e,\mu ,\tau )$, and $B_s\to (\eta ,{\eta }^{\prime })\nu \overline{\nu }$ transitions probing the $\overline{s}s$ content of the $\eta$ and ${\eta }^{\prime }$ mesons via three-point QCD sum rules. We calculate responsible form factors for these transitions in full theory. Using the obtained form factors, we also estimate the related branching fractions and longitudinal lepton polarization asymmetries. Our results are in a good consistency with the predictions of the other existing nonperturbative approaches.

We study Higgs boson pair production processes at future hadron and lepton colliders including the photon collision option in several new physics models; i.e., the two-Higgs-doublet model, the scalar leptoquark model, the sequential fourth generation fermion model and the vectorlike quark model. Cross sections for these processes can deviate significantly from the standard model predictions due to the one-loop correction to the triple Higgs boson coupling constant. For the one-loop induced processes such as $gg\to hh$ and $\gamma \gamma \to hh$, where $h$ is the (lightest) Higgs boson and $g$ and $\gamma$ respectively represent a gluon and a photon, the cross sections can also be affected by new physics particles via additional one-loop diagrams. In the two-Higgs-doublet model and scalar leptoquark models, cross sections of $e^{+}{e}^{-}\to hhZ$ and $\gamma \gamma \to hh$ can be enhanced due to the nondecoupling effect in the one-loop corrections to the triple Higgs boson coupling constant. In the sequential fourth generation fermion model, the cross section for $gg\to hh$ becomes very large because of the loop effect of the fermions. In the vectorlike quark model, effects are small because the theory has decoupling property. Measurements of the Higgs boson pair production processes can be useful to explore new physics through the determination of the Higgs potential.

We carry out an analysis of the potential of the Large Hadron Collider (LHC) to discover supersymmetry in runs at $\sqrt{s}=7\mathrm{TeV}$ with an accumulated luminosity of $(0.1–2){\mathrm{fb}}^{-1}$ of data. The analysis is done with both minimal supergravity and supergravity models with nonuniversal soft breaking. Benchmarks for early discovery with $(0.1–2){\mathrm{fb}}^{-1}$ of data are given. We provide an update of $b$-tagging efficiencies in PGS 4 appropriate for LHC analyses. A large number of signature channels are analyzed, and it is shown that each of the models exhibited are discoverable at the $5\sigma$ level or more above the standard model background in several signature channels which would provide cross checks for a discovery of supersymmetry. It is shown that some of the benchmarks are discoverable with $0.1{\mathrm{fb}}^{-1}$ of data again with detectable signals in several channels.

The bottomonium spectrum is computed in dynamical $2+1$ flavor lattice QCD, using nonrelativistic QCD for the $b$ quarks. The main calculations in this work are based on gauge field ensembles generated by the RBC and UKQCD Collaborations with the Iwasaki action for the gluons and a domain-wall action for the sea quarks. Lattice spacing values of approximately 0.08 fm and 0.11 fm are used, and simultaneous chiral extrapolations to the physical pion mass are performed. As a test for gluon-discretization errors, the calculations are repeated on two ensembles generated by the MILC Collaboration with the Lüscher-Weisz gauge action. Gluon-discretization errors are also studied in a lattice potential model using perturbation theory for four different gauge actions. The nonperturbative lattice QCD results for the radial and orbital bottomonium energy splittings obtained from the RBC/UKQCD ensembles are found to be in excellent agreement with experiment. To get accurate results for spin splittings, the spin-dependent order-$v^6$ terms are included in the nonrelativistic QCD action, and suitable ratios are calculated such that most of the unknown radiative corrections cancel. The cancellation of radiative corrections is verified explicitly by repeating the calculations with different values of the couplings in the nonrelativistic QCD action. Using the lattice ratios of the $S$-wave hyperfine and the $1P$ tensor splitting, and the experimental result for the $1P$ tensor splitting, the $1S$ hyperfine splitting is found to be $60.3\pm {5.5}_{\mathrm{stat}}\pm {5.0}_{\mathrm{syst}}\pm {2.1}_{\exp }\mathrm{MeV}$, and the $2S$ hyperfine splitting is predicted to be $23.5\pm {4.1}_{\mathrm{stat}}\pm {2.1}_{\mathrm{syst}}\pm {0.8}_{\exp }\mathrm{MeV}$.

The overlap fermion propagator is calculated on $2+1$ flavor domain-wall fermion gauge configurations on ${16}^3\times 32$, ${24}^3\times 64$ and ${32}^3\times 64$ lattices. With hyper-cubic (HYP) smearing and low eigenmode deflation, it is shown that the inversion of the overlap operator can be expedited by $\sim 20$ times for the ${16}^3\times 32$ lattice and $\sim 80$ times for the ${32}^3\times 64$ lattice. The overhead cost for calculating eigenmodes ranges from 4.5 to 7.9 propagators for the above lattices. Through the study of hyperfine splitting, we found that the $O(m^2{a}^2)$ error is small and these dynamical fermion lattices can adequately accommodate quark mass up to the charm quark. A preliminary calculation of the low-energy constant ${\Delta }_{\mathrm{mix}}$ which characterizes the discretization error of the pion made up of a pair of sea and valence quarks in this mixed-action approach is carried out via the scalar correlator with periodic and antiperiodic boundary conditions. It is found to be small which shifts a 300 MeV pion mass by $\sim 10$ to 19 MeV on these sets of lattices. We have studied the signal-to-noise issue of the noise source for the meson and baryon. We introduce a new algorithm with $Z_3$ grid source and low eigenmode substitution to study the many-to-all meson and baryon correlators. It is found to be efficient in reducing errors for the correlators of both mesons and baryons. With 64-point $Z_3$ grid source and low-mode substitution, it can reduce the statistical errors of the light quark ($m_{\pi }\sim 200–300\mathrm{MeV}$) meson and nucleon correlators by a factor of $\sim 3–4$ as compared to the point source. The $Z_3$ grid source itself can reduce the errors of the charmonium correlators by a factor of $\sim 3$.

We study the pion mass dependence of the $\rho (770)$ and $f_0(600)$ masses and widths from one and two-loop unitarized chiral perturbation theory (ChPT). We show the consistency of one-loop calculations with lattice results for the $M_{\rho }$, $f_{\pi }$, and the isospin-2 scattering length $a_{20}$. Then, we develop and apply the modified inverse amplitude method formalism for two-loop ChPT. In contrast to the $f_0(600)$, the $\rho (770)$ is rather sensitive to the two-loop ChPT parameters—our main source of systematic uncertainty. We thus provide two-loop unitarized fits constrained by lattice information on $M_{\rho }$, $f_{\pi }$, by the $q\overline{q}$ leading $1/N_c$ behavior of the $\rho$ and by existing estimates of low-energy constants. These fits yield relatively stable predictions up to $m_{\pi }\simeq 300–350\mathrm{MeV}$ for the $\rho$ coupling and width as well as for all the $f_0(600)$ parameters. We confirm, to two loops, the weak $m_{\pi }$ dependence of the $\rho$ coupling and the Kawarabayashi-Suzuki-Riazuddin-Fayyazuddin relation, and the existence of two virtual $f_0(600)$ poles for sufficiently high $m_{\pi }$. At two loops one of these poles becomes a bound state when $m_{\pi }$ is somewhat larger than 300 MeV.

We compute the conversion factors needed to obtain the $\overline{\mathrm{MS}}$ and renormalization-group-invariant (RGI) up, down, and strange quark masses at next-to-next-to-leading order from the corresponding parameters renormalized in the recently proposed RI/SMOM and $\mathrm{RI}/{\mathrm{SMOM}}_{{\gamma }_{\mu }}$ renormalization schemes. This is important for obtaining the $\overline{\mathrm{MS}}$ masses with the best possible precision from numerical lattice QCD simulations, because the customary ${\mathrm{RI}}^{(\prime )}/\mathrm{MOM}$ scheme is afflicted with large irreducible uncertainties both on the lattice and in perturbation theory. We find that the smallness of the known one-loop matching coefficients is accompanied by even smaller two-loop contributions. From a study of residual scale dependences, we estimate the resulting perturbative uncertainty on the light-quark masses to be about 2% in the RI/SMOM scheme and about 3% in the $\mathrm{RI}/{\mathrm{SMOM}}_{{\gamma }_{\mu }}$ scheme. Our conversion factors are given in fully analytic form, for general covariant gauge and renormalization point. We provide expressions for the associated anomalous dimensions.

A mechanism has been suggested recently to generate the neutrino mass out of a dimension-seven operator. This is expected to relieve the tension between the occurrence of a tiny neutrino mass and the observability of other physics effects beyond it. Such a mechanism would inevitably entail lepton flavor violating effects. We study in this work the radiative and purely leptonic transitions of the light charged leptons. In so doing we make a systematic analysis of the flavor structure by providing a convenient parametrization of the mass matrices in terms of independent physical parameters and diagonalizing them explicitly. We illustrate our numerical results by sampling over two $CP$ phases and one Yukawa coupling which are the essential parameters in addition to the heavy lepton mass. We find that with the stringent constraints coming from the muon decays and the muon-electron conversion in nuclei taken into account the decays of the tau lepton are severely suppressed in the majority of parameter space. There exist, however, small regions in which some tau decays can reach a level that is about 2 orders of magnitude below their current bounds.

The MINOS experiment at Fermilab has recently reported a tension between the oscillation results for neutrinos and antineutrinos. We show that this tension, if it persists, can be understood in the framework of nonstandard neutrino interactions (NSI). While neutral current NSI (nonstandard matter effects) are disfavored by atmospheric neutrinos, a new charged current coupling between tau neutrinos and nucleons can fit the MINOS data without violating other constraints. In particular, we show that loop-level contributions to flavor-violating $\tau$ decays are sufficiently suppressed. However, conflicts with existing bounds could arise once the effective theory considered here is embedded into a complete renormalizable model. We predict the future sensitivity of the T2K and NOνA experiments to the NSI parameter region favored by the MINOS fit, and show that both experiments are excellent tools to test the NSI interpretation of the MINOS data.

We investigate some QCD corrections that contribute to the Gross–Llewellyn Smith sum rule but have not been included in previous analyses of it. We first review the techniques by which the $x{F}_3$ structure function is extracted from combinations of neutrino and antineutrino cross sections. Next we investigate corrections to the Gross–Llewellyn Smith sum rule, with particular attention to contributions arising from strange quark distributions and from charge symmetry violating parton distributions. We find that additional corrections from strange quarks and parton charge symmetry violation are likely to have a small but potentially significant role in decreasing the current discrepancy between the experimental and theoretical estimates of the Gross–Llewellyn Smith sum rule.

We present a measurement of the $WW+WZ$ production cross section observed in a final state consisting of an identified electron or muon, two jets, and missing transverse energy. The measurement is carried out in a data sample corresponding to up to $4.6{\mathrm{fb}}^{-1}$ of integrated luminosity at $\sqrt{s}=1.96\mathrm{TeV}$ collected by the CDF II detector. Matrix element calculations are used to separate the diboson signal from the large backgrounds. The $WW+WZ$ cross section is measured to be $17.4\pm 3.3\mathrm{pb}$ in agreement with standard model predictions. A fit to the dijet invariant mass spectrum yields a compatible cross section measurement.

The form factor provides a convenient way to describe properties of topological solitons in the full quantum theory, when semiclassical concepts are not applicable. It is demonstrated that the form factor can be calculated numerically using lattice Monte Carlo simulations. The approach is very general and can be applied to essentially any type of soliton. The technique is illustrated by calculating the kink form factor near the critical point in $1+1$-dimensional scalar field theory. As expected from universality arguments, the result agrees with the exactly calculable scaling form factor of the two-dimensional Ising model.

We study three charmed resonances, $D(2550)$, $D(2610)$, and $D(2760)$, newly observed by the BABAR Collaboration, utilizing the mass spectra and investigating the strong decays. Our calculation indicates that $D(2610)$ is an admixture of $2{}^{3}S_1$ and $1{}^{3}D_1$ with $J^P=1^{-}$. $D(2760)$ can be explained as either the orthogonal partner of $D(2610)$ or $1{}^{3}D_3$. Our estimate of the decay width for $D(2550)$, assuming it as $2{}^{1}S_0$, is far below the experimental value. The decay behavior of the remaining two $1D$ charmed mesons, i.e., ${}^{3}D_2$ and ${}^{1}D_2$ ($J^P=2^{-}$) states, is predicted, which will help future experimental search for these missing $D$-wave charmed mesons.

We present a study of the $D^{+}{\pi }^{-}$, $D^0{\pi }^{+}$, and $D^{*+}{\pi }^{-}$ systems in inclusive $e^{+}{e}^{-}\to c\overline{c}$ interactions in a search for new excited $D$ meson states. We use a data set, consisting of $\sim 454{\mathrm{fb}}^{-1}$, collected at center-of-mass energies near 10.58 GeV by the BABAR detector at the SLAC PEP-II asymmetric-energy collider. We observe, for the first time, candidates for the radial excitations of the $D^0$, $D^{*0}$, and $D^{*+}$, as well as the $L=2$ excited states of the $D^0$ and $D^{+}$, where $L$ is the orbital angular momentum of the quarks.

Several classes of gravitational backgrounds in $3+1$ dimensions have been proposed as holographic duals to Lifshitz-like theories describing critical phenomena in $2+1$ dimensions with critical exponent $z\ge 1$. We numerically explore one such model, characterized by a temperature $T$ and chemical potential $\mu$, and find how to embed these solutions into anti–de Sitter (AdS) for a range of values of $z$. We find no phase transition going from the $T\ll \mu$ to the $T\gg \mu$ regimes, and find that the solutions smoothly interpolate between the Lifshitz-like behavior and the relativistic AdS-like behavior. Finally, we exploit some conserved quantities to find a relationship between the energy density $\mathcal{E}$, entropy density $s$, and number density $n$, $\mathcal{E}=\frac{2}{3}(Ts+\mu n)$. We show that this result is expected from general scaling arguments, and generalizes to $\mathcal{E}=\frac{d}{d+1}(Ts+\mu n)$ for a theory dual to ${\mathrm{AdS}}_{d+2}$ (Poincaré patch) asymptotics with a local $U(1)$ gauge invariance.

We study quantum electrodynamics on the noncommutative Minkowski space (NCQED) in the Yang-Feldman formalism. Local observables are defined by using covariant coordinates. We compute the two-point function of the interacting field strength to second order and find the infrared divergent terms already known from computations using the so-called modified Feynman rules. It is shown that these lead to nonlocal renormalization ambiguities. Also new nonlocal divergences stemming from the covariant coordinates are found. Furthermore, we study the supersymmetric extension of the model. For this, the supersymmetric generalization of the covariant coordinates is introduced. We find that the nonlocal divergences cancel. At the one-loop level, the only effect of noncommutativity is then a momentum-dependent field strength normalization. We interpret it as an acausal effect and show that its range is independent of the noncommutativity scale.

We compute 1-loop corrections to Lorentz-signature de Sitter-invariant 2-point functions defined by the interacting Euclidean vacuum for massive scalar quantum fields with cubic and quartic interactions. Our results apply to all masses for which the free Euclidean de Sitter vacuum is well-defined, including values in both the complimentary and the principal series of $SO(D,1)$. In dimensions where the interactions are renormalizeable we provide absolutely convergent integral representations of the corrections. These representations suffice to analytically extract the leading behavior of the 2-point functions at large separations and may also be used for numerical computations. The interacting propagators decay at long distances at least as fast as one would naively expect, suggesting that such interacting de Sitter invariant vacuua are well-defined and are well-behaved in the IR. In fact, in some cases the interacting propagators decay faster than any free propagator with any value of $M^2>0$.

We show that the symplectic structure of the Snyder model on a de Sitter background can be derived from two-time physics in seven dimensions and propose a Hamiltonian for a free particle consistent with the symmetries of the model.

We describe in detail full numerical and perturbative techniques to compute the gravitational radiation from intermediate-mass-ratio black-hole-binary inspirals and mergers. We perform a series of full numerical simulations of nonspinning black holes with mass ratios $q=1/10$ and $q=1/15$ from different initial separations and for different finite-difference resolutions. In order to perform those full numerical runs, we adapt the gauge of the moving punctures approach with a variable damping term for the shift. We also derive an extrapolation (to infinite radius) formula for the waveform extracted at finite radius. For the perturbative evolutions we use the full numerical tracks, transformed into the Schwarzschild gauge, in the source terms of the Regge-Wheller-Zerilli Schwarzschild perturbations formalism. We then extend this perturbative formalism to take into account small intrinsic spins of the large black hole, and validate it by computing the quasinormal mode frequencies, where we find good agreement for spins $|a/M|<0.3$. Including the final spins improves the overlap functions when comparing full numerical and perturbative waveforms, reaching 99.5% for the leading $(\ell ,m)=(2,2)$ and (3, 3) modes, and 98.3% for the nonleading (2, 1) mode in the $q=1/10$ case, which includes 8 orbits before merger. For the $q=1/15$ case, we obtain overlaps near 99.7% for all three modes. We discuss the modeling of the full inspiral and merger based on a combined matching of post-Newtonian, full numerical, and geodesic trajectories.

The authors prove that the dynamics of spin $1/2$ particles in stationary gravitational fields can be described using an approach, which builds upon the formalism of pseudo-Hermitian Hamiltonians. The proof consists in the analysis of three expressions for Hamiltonians, which are derived from the Dirac equation and describe the dynamics of spin $1/2$ particles in the gravitational field of the Kerr solution. The Hamiltonians correspond to different choices of tetrad vectors and differ from each other. The differences between the Hamiltonians confirm the conclusion known from many studies that the Hamiltonians derived from the Dirac equation are nonunique. Application of standard pseudo-Hermitian quantum mechanics rules to each of these Hamiltonians produces the same Hermitian Hamiltonian. The eigenvalue spectrum of the resulting Hamiltonian is the same as that of the Hamiltonians derived from the Dirac equation with any chosen system of tetrad vectors. For description of the dynamics of spin $1/2$ particles in stationary gravitational fields can be used not only the formalism of pseudo-Hermitian Hamiltonians but also an alternative approach, which employs the Parker scalar product. The authors show that the alternative approach is equivalent to the formalism of pseudo-Hermitian Hamiltonians.