We present a study of the dijet invariant mass distribution for the reaction $\overline{p}p\to \mathrm{two}\mathrm{jets}+\gamma +X$, at a center of mass energy of 1.8 TeV, using data collected by the CDF experiment. We compare the data to predictions for the production of a photon with two jets, together with the resonant processes $\overline{p}p\to W/Z+\gamma +X$, in which the $W$ and $Z$ bosons decay hadronically. A fit is made to the dijet invariant mass distribution combining the nonresonant background and resonant processes. We use the result to establish a limit for the inclusive production cross section of $W/Z+\gamma$ with hadronic decay of the $W$ and $Z$ bosons.

I analyze numerically a two-dimensional $\lambda {\varphi }^4$ theory showing that in the limit of a strong coupling $\lambda \to \infty$ just the homogeneous solutions for time evolution are relevant in agreement with the duality principle in perturbation theory as presented in [M. Frasca, Phys. Rev. A 58, 3439 (1998)], being negligible the contribution of the spatial varying parts of the dynamical equations. A consequence is that the Green function method works for this nonlinear problem in the large coupling limit as in a linear theory. A numerical proof is given for this. With these results at hand, I built a strongly coupled quantum field theory for a $\lambda {\varphi }^4$ interacting field computing the first order correction to the generating functional. Mass spectrum of the theory is obtained turning out to be that of a harmonic oscillator with no dependence on the dimensionality of space-time. The agreement with the Lehmann-Källen representation of the perturbation series is then shown at the first order.

It is necessary to calculate the $\mathcal{C}$ operator for the non-Hermitian $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian $H=\frac{1}{2}{p}^2+\frac{1}{2}{\mu }^2{x}^2-\lambda x^4$ in order to demonstrate that $H$ defines a consistent unitary theory of quantum mechanics. However, the $\mathcal{C}$ operator cannot be obtained by using perturbative methods. Including a small imaginary cubic term gives the Hamiltonian $H=\frac{1}{2}{p}^2+\frac{1}{2}{\mu }^2{x}^2+ig{x}^3-\lambda x^4$, whose $\mathcal{C}$ operator can be obtained perturbatively. In the semiclassical limit all terms in the perturbation series can be calculated in closed form and the perturbation series can be summed exactly. The result is a closed-form expression for $\mathcal{C}$ having a nontrivial dependence on the dynamical variables $x$ and $p$ and on the parameter $\lambda$.

We suggest that quantum transitions of black holes comply with selection rules, analogous to those of atomic spectroscopy. In order to identify such rules, we apply Bohr’s correspondence principle to the quasinormal ringing frequencies of black holes. In this context, classical ringing frequencies with an asymptotically vanishing real part ${\omega }_R$ correspond to virtual quanta, and may thus be interpreted as forbidden quantum transitions. With this motivation, we calculate the quasinormal spectrum of neutrino fields in spherically symmetric black-hole spacetimes. It is shown that ${\omega }_R\to 0$ for these resonances, suggesting that the corresponding fermionic transitions are quantum mechanically forbidden.

Beetle and Burko recently introduced a background-independent scalar curvature invariant for general relativity that carries information about the gravitational radiation in generic spacetimes, in cases where such radiation is incontrovertibly defined. In this paper we adopt a formalism that only uses spatial data as they are used in numerical relativity and compute the Beetle-Burko radiation scalar for a number of analytical examples, specifically linearized Einstein-Rosen cylindrical waves, linearized quadrupole waves, the Kerr spacetime, Bowen-York initial data, and the Kasner spacetime. These examples illustrate how the Beetle-Burko radiation scalar can be used to examine the gravitational wave content of numerically generated spacetimes, and how it may provide a useful diagnostic for initial data sets.

We analyze the dynamics of models of warm inflation with general dissipative effects. We consider phenomenological terms both for the inflaton decay rate and for viscous effects within matter. We provide a classification of the asymptotic behavior of these models and show that the existence of a late-time scaling regime depends not only on an asymptotic behavior of the scalar field potential, but also on an appropriate asymptotic behavior of the inflaton decay rate. There are scaling solutions whenever the latter evolves to become proportional to the Hubble rate of expansion regardless of the steepness of the scalar field exponential potential. We show from thermodynamic arguments that the scaling regime is associated with a power-law dependence of the matter-radiation temperature on the scale factor, which allows a mild variation of the temperature of the matter/radiation fluid. We also show that the late-time contribution of the dissipative terms alleviates the depletion of matter, and increases the duration of inflation.

We calculate the neutrino self-energy operator $\Sigma (p)$ in the presence of a magnetic field $B$. In particular, we consider the weak-field limit $eB\ll m_{\ell }^2$, where $m_{\ell }$ is the charged-lepton mass corresponding to the neutrino flavor ${\nu }_{\ell }$, and we consider a “moderate field” $m_{\ell }^2\ll eB\ll m_W^2$. Our results differ substantially from the previous literature. For a moderate field, we show that it is crucial to include the contributions from all Landau levels of the intermediate charged lepton, not just the ground state. For the conditions of the early universe where the background medium consists of a charge-symmetric plasma, the pure $B$-field contribution to the neutrino dispersion relation is proportional to $(eB{)}^2$ and thus comparable to the contribution of the magnetized plasma.

In this note, we calculate the branching ratio and $CP$ asymmetry parameters of $B_s\to \pi \rho$ in the framework of perturbative QCD approach based on $k_T$ factorization. This decay can occur only via annihilation diagrams in the standard model. We find that (a) the charge averaged $\mathrm{Br}(B_s\to {\pi }^{+}{\rho }^{-}+{\pi }^{-}{\rho }^{+})$ is about $(9-12)\times {10}^{-7}$; $\mathrm{Br}(B_s\to {\pi }^0{\rho }^0)\simeq 4\times {10}^{-7}$; and (b) there are sizable $CP$ asymmetries in the processes, which can be tested in the near future Large Hadron Collider beauty experiments (LHC-b) at CERN.

Recent experiments suggest that certain data of $B\to \pi \pi ,\pi K$ decays are inconsistent with the standard model expectations. We try to explain the discrepancies with R-parity violating supersymmetry. By employing the QCD factorization approach, we study these decays in the minimal supersymmetric standard model with R-parity violation. We show that R-parity violation can resolve the discrepancies in both $B\to \pi \pi$ and $B\to \pi K$ decays, and find that in some regions of parameter space all these requirements, including the $CP$ averaged branching ratios and the direct $CP$ asymmetries, can be satisfied. Furthermore, we have derived stringent bounds on relevant R-parity violating couplings from the latest experimental data, and some of these constraints are stronger than the existing bounds.

Relying upon the usefulness of the $\mu \mathrm{\text{−}}\tau$ symmetry, we find a new type of neutrino mass texture with a single phase parameter $\delta$ that describes maximal atmospheric neutrino mixing and Dirac $CP$ violation due to the presence of $\delta$. The Majorana phase associated with the third massive neutrino turns out to be identical to the Dirac phase while other Majorana phases vanish. The nonvanishing reactor neutrino mixing angle ${\theta }_{13}$ is induced by a $\mu \mathrm{\text{−}}\tau$ symmetry breaking effect. Flavor neutrino masses that supply the $\mu \mathrm{\text{−}}\tau$ symmetry breaking terms become pure imaginary for $\delta =\pm \pi /2$, leading to maximal $CP$ violation. There is a parameter denoted by $\eta$, which is either $\mathcal{O}(\sqrt{\Delta m_{\odot }^2/\Delta m_{\mathrm{atm}}^2})$ in the normal mass hierarchy, or $\mathcal{O}(\Delta m_{\odot }^2/\Delta m_{\mathrm{atm}}^2)$ in the inverted mass hierarchy. In the inverted mass hierarchy, the contribution of $\mathcal{O}({sin}^2{\theta }_{13})$ is found to be significant and cannot be neglected. Our texture also leads to quasidegenerate neutrinos with masses of $\mathcal{O}(\sqrt{\Delta m_{\mathrm{atm}}^2})$, which serves as the scale for the effective neutrino mass in $(\beta \beta {)}_{0\nu }$ decay. This texture does not include $\eta$, and $\Delta m_{\odot }^2$ naturally arises from contributions of $\mathcal{O}({sin}^2{\theta }_{13})$ to give $\Delta m_{\odot }^2/\Delta m_{\mathrm{atm}}^2\sim {sin}^2{\theta }_{13}$, yielding the prediction of ${sin}^2{\theta }_{13}=\mathcal{O}({10}^{-2})$.

Strong model independent upper bounds on $\mathrm{Br}(K_S\to {\pi }^{0}e\mu )$ may be inferred from recent experimental limits on $\mathrm{Br}(K_L\to {\pi }^{0}e\mu )$ and $\mathrm{Br}(K^{+}\to {\pi }^{+}{e}^{+}{\mu }^{-})$. From this result, upper bounds for $\mathrm{Br}(K_S\to e\mu )$ may be obtained for a broad class of models. Models outside of this class seem unlikely.

We propose a simple but suggestive seesaw model with two phenomenological conjectures: three heavy (right-handed) Majorana neutrinos are degenerate in mass in the symmetry limit and three light Majorana neutrinos have the tri-bimaximal mixing pattern $V_0$. We show that a small mass splitting between the first generation and the other two generations of heavy Majorana neutrinos is responsible for the deviation of the solar neutrino mixing angle ${\theta }_{12}$ from its initial value $35.3°$ given by $V_0$, and the slight breaking of the mass degeneracy between the second and third generations of heavy Majorana neutrinos results in a small mixing angle ${\theta }_{13}$ and a tiny departure of the atmospheric neutrino mixing angle ${\theta }_{23}$ from $45°$. It turns out that a normal hierarchy of the light neutrino mass spectrum is favored in this seesaw scenario.

We present results of a search for the $X(3872)$ in $B^0\to X(3872)K_S^0,X(3872)\to J/\psi {\pi }^{+}{\pi }^{-}$, improved measurements of $B^{-}\to X(3872)K^{-}$, and a study of the $J/\psi {\pi }^{+}{\pi }^{-}$ mass region above the $X(3872)$. We use $232\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ asymmetric-energy storage rings. The results include the 90% confidence interval $1.34\times {10}^{-6}<\mathcal{B}(B^0\to X(3872)K^0,X\to J/\psi {\pi }^{+}{\pi }^{-})<10.3\times {10}^{-6}$ and the branching fraction $\mathcal{B}(B^{-}\to X(3872)K^{-},X\to J/\psi {\pi }^{+}{\pi }^{-})=(10.1\pm 2.5\pm 1.0)\times {10}^{-6}$. We observe a $(2.7\pm 1.3\pm 0.2)\mathrm{MeV}/c^2$ mass difference of the $X(3872)$ produced in the two decay modes. Furthermore, we search for the $Y(4260)$ in $B$ decays and set the $95\%$ C.L. upper limit $\mathcal{B}(B^{-}\to Y(4260)K^{-},Y(4260)\to J/\psi {\pi }^{+}{\pi }^{-})<2.9\times {10}^{-5}$.

The isometries of $Ad{S}_5$ space and supersymmetric $Ad{S}_5\otimes S_1$ space are nonlinearly realized on four-dimensional Minkowski space. The resultant effective actions in terms of the Nambu-Goldstone modes are constructed. The dilatonic mode governing the motion of the Minkowski space probe brane into the covolume of supersymmetric $Ad{S}_5$ space is found to be unstable and the bulk of the $Ad{S}_5$ space is unable to sustain the brane. No such instability appears in the nonsupersymmetric case.

Numerical algorithms based on variational and symplectic integrators exhibit special features that make them promising candidates for application to general relativity and other constrained Hamiltonian systems. This paper lays part of the foundation for such applications. The midpoint rule for Hamilton’s equations is examined from the perspectives of variational and symplectic integrators. It is shown that the midpoint rule preserves the symplectic form, conserves Noether charges, and exhibits excellent long-term energy behavior. The energy behavior is explained by the result, shown here, that the midpoint rule exactly conserves a phase space function that is close to the Hamiltonian. The presentation includes several examples.

In universal extra dimension models, the lightest Kaluza-Klein (KK) particle is generically the first KK excitation of the photon and can be stable, serving as particle dark matter. We calculate the thermal relic abundance of the KK photon for a general mass spectrum of KK excitations including full coannihilation effects with all (level-one) KK excitations. We find that including coannihilation can significantly change the relic abundance when the coannihilating particles are within about 20% of the mass of the KK photon. Matching the relic abundance with cosmological data, we find the mass range of the KK photon is much wider than previously found, up to about 2 TeV if the masses of the strongly interacting level-one KK particles are within 5% of the mass of the KK photon. We also find cases where several coannihilation channels compete (constructively and destructively) with one another. The lower bound on the KK photon mass, about 540 GeV when just right-handed KK leptons coannihilate with the KK photon, relaxes upward by several hundred GeV when coannihilation with electroweak KK gauge bosons of the same mass is included.

The ghost condensate $⟨{\epsilon }^{abc}{\overline{c}}^b{c}^c⟩$ is considered together with the gluon condensate $⟨A_{\mu }^2⟩$ in $SU(2)$ Euclidean Yang-Mills theories quantized in the Landau gauge. The vacuum polarization ceases to be transverse due to the nonvanishing condensate $⟨{\epsilon }^{abc}{\overline{c}}^b{c}^c⟩$. The gluon propagator itself remains transverse. By polarization effects, this ghost condensate induces then a splitting in the gluon mass parameter, which is dynamically generated through $⟨A_{\mu }^2⟩$. The obtained effective masses are real when $⟨A_{\mu }^2⟩$ is included in the analysis. In the absence of $⟨A_{\mu }^2⟩$, the already known result that the ghost condensate induces effective tachyonic masses is recovered. At the one-loop level, we find that the effective diagonal mass becomes smaller than the off-diagonal one. This might serve as an indication for some kind of Abelian dominance in the Landau gauge, similar to what happens in the maximal Abelian gauge.

We study the out-of-equilibrium nonlinear dynamics of fields after post-inflationary preheating. During preheating, the energy in the homogeneous inflaton is exponentially rapidly transfered into highly occupied out-of-equilibrium inhomogeneous modes, which subsequently evolve towards equilibrium. The infrared modes excited during preheating evolve towards a saturated distribution long before thermalization completes. We compute the equation of state during and immediately after preheating. It rapidly evolves towards radiation domination long before the actual thermal equilibrium is established. The exact time of this transition is a nonmonotonic function of the coupling between the inflaton and the decay products, and it varies only very weakly (around ${10}^{-35}$ s) as this coupling changes over several orders of magnitude. This result is applied to refine the relation between the number of e-foldings $N$ and the physical wavelength of perturbations generated during inflation. We also discuss the implications for the theory of modulated perturbations from preheating. We finally argue that many questions of the thermal history of the universe should be addressed in terms of prethermalization, illustrating this point with a calculation of perturbative production of gravitinos immediately after chaotic inflation. We also highlight the effects of three-legs inflaton interactions on the dynamics of preheating and thermalization in an expanding universe.