The short-distance coefficients for the color-octet ${}^{3}S_1$ term in the fragmentation function for a gluon to split into polarized heavy quarkonium states are recalculated to order ${\alpha }_s^2$. The light-cone gauge remarkably simplifies the calculation by eliminating many Feynman diagrams at the expense of introducing spurious poles in loop integrals. We do not use any conventional prescriptions for spurious pole. Instead, we only use gauge invariance with the aid of Collins-Soper definition of the fragmentation function. Our result agrees with a previous calculation of Braaten and Lee in the Feynman gauge, but disagrees with another previous calculation.

We use the framework of a relativistic constituent quark model to study the semileptonic transitions of the $B_c$ meson into $(\overline{c}c)$ charmonium states where $(\overline{c}c)={\eta }_c({}^{1}S_0)$, $J/\psi ({}^{3}S_1)$, ${\chi }_{c0}({}^{3}P_0)$, ${\chi }_{c1}({}^{3}P_1)$, $h_c({}^{1}P_1)$, ${\chi }_{c2}({}^{3}P_2)$, $\psi ({}^{3}D_2)$. We compute the $q^2$ dependence of all relevant form factors and give predictions for their semileptonic $B_c$ decay modes including also their $\tau$ modes. We derive a formula for the polar angle distribution of the charged lepton in the $(l{\nu }_l)$-c.m. frame and compute the partial helicity rates that multiply the angular factors in the decay distribution. For the discovery channel $B_c\to J/\psi (\to {\mu }^{+}{\mu }^{-})l\nu$ we compute the transverse/longitudinal composition of the $J/\psi$ which can be determined by an angular analysis of the decay $J/\psi \to {\mu }^{+}{\mu }^{-}$. We compare our results with the results of other calculations.

The possibility of an axial-vector isoscalar tetraquark with $ud\overline{s}\overline{s}$ is discussed. If the pentaquark ${\Theta }^{+}(1540)$ has the $(qq{)}_{\overline{3}}(qq{)}_{\overline{3}}\overline{q}$ configuration, the isoscalar $ud\overline{s}\overline{s}$ (${\vartheta }^{+}$-meson) state with $J^P=1^{+}$ is expected to exist in the mass region lower than, or close to, the mass of ${\Theta }^{+}(1540)$. Within a flux-tube quark model, a possible resonant state of $ud\overline{s}\overline{s}(J^P=1^{+})$ is suggested to appear around 1.4 GeV with the width $\mathcal{O}(20\sim 80)\mathrm{MeV}$. We propose that the ${\vartheta }^{+}$-meson is a good candidate for the tetraquark search, which would be observed in the $K^{+}{K}^{+}{\pi }^{-}$ decay channel.

The magnetic moments of negative-parity low-lying nucleon resonances are studied in different quark models. The effect of Goldstone Boson degrees of freedom is discussed. The obtained results of chiral quark model are compared with the calculations of conventional constituent quark model. Moreover, mixing angles of the resonance wave functions induced by different hyperfine interactions between constituent quarks are also analyzed.

We further study the “complementary” ansatz, $\mathrm{Tr}(M_{\nu })=0$, for a prediagonal light Majorana type neutrino mass matrix. Previously, this was studied for the $CP$ conserving case and the case where the two Majorana type $CP$ violating phases were present but the Dirac type $CP$ violating phase was neglected. Here we employ a simple geometric algorithm which enables us to “solve” the ansatz including all three $CP$ violating phases. Specifically, given the known neutrino oscillation data and an assumed two parameter (the third neutrino mass $m_3$ and the Dirac $CP$ phase $\delta$) family of inputs we predict the neutrino masses and Majorana $CP$ phases. Despite the two parameter ambiguity, interesting statements emerge. There is a characteristic pattern of interconnected masses and $CP$ phases. For large $m_3$ the three neutrinos are approximately degenerate. The only possibility for a mass hierarchy is to have $m_3$ smaller than the other two. A hierarchy with $m_3$ largest is not allowed. Small $CP$ violation is possible only near two special values of $m_3$. Also, the neutrinoless double beta decay parameter is approximately bounded as $0.020\mathrm{eV}<|m_{ee}|<0.185\mathrm{eV}$. As a by-product of looking at physical amplitudes we discuss an alternative parametrization of the lepton mixing matrix which results in simpler formulas. The physical meaning of this parametrization is explained.

In the standard approaches to neutrino transport in the simulation of core-collapse supernovas, one will often start from the classical Boltzmann equation for the neutrino’s spatial, temporal, and spectral evolution. For each neutrino species, and its antiparticle, the classical density in phase space, or the associated specific intensity, will be calculated as a function of time. The neutrino radiation is coupled to matter by source and sink terms on the “right-hand side” of the transport equation and together with the equations of hydrodynamics this set of coupled partial differential equations for classical densities describes, in principle, the evolution of core collapse and explosion. However, with the possibility of neutrino oscillations between species, a purely quantum-physical effect, how to generalize this set of Boltzmann equations for classical quantities to reflect oscillation physics has not been clear. To date, the formalisms developed have retained the character of quantum operator physics involving complex quantities and have not been suitable for easy incorporation into standard supernova codes. In this paper, we derive generalized Boltzmann equations for quasiclassical, real-valued phase-space densities that retain all the standard oscillation phenomenology, including the matter-enhanced resonant flavor conversion (Mikheev-Smirnov-Wolfenstein effect), neutrino self-interactions, and the interplay between decohering matter coupling and flavor oscillations. With this formalism, any code(s) that can now handle the solution of the classical Boltzmann or transport equation can easily be generalized to include neutrino oscillations in a quantum-physically consistent fashion.

We study a noncommutative nonrelativistic fermionic field theory in $2+1$ dimensions coupled to the Chern-Simons field. We perform a perturbative analysis of the model and show that up to one loop the ultraviolet divergences are canceled and the infrared divergences are eliminated by the noncommutative Pauli term.

We derive the renormalized Schwinger-Dyson equations for the one- and two-point functions in the auxiliary field formulation of Coleman, Jackiw, and Politzer [S. Coleman, R. Jackiw, and H. D. Politzer, Phys. Rev. D 10, 2491 (1974).] for $\lambda {\varphi }^4$ field theory, to order $1/N$, in the 2PI-$1/N$ expansion. We show that the renormalization of the broken-symmetry theory depends only on the counter terms of the symmetric theory with $\varphi =0$, as discussed in our previous paper [F. Cooper, B. Mihaila, and J. F.Dawson, Phys. Rev. D 70, 105008 (2004).]. We find that the 2PI-$1/N$ expansion violates the Goldstone theorem at order $1/N$. In using the $O(4)$ model as a low energy effective field theory of pions to study the time evolution of disoriented chiral condensates one has to explicitly break the $O(4)$ symmetry to give the physical pions a nonzero mass. In this effective theory, we expect that the additional small contribution to the pion mass due to the violation of the Goldstone theorem in the 2PI-$1/N$ equations to be unimportant for an adequate description of the phenomenology.

We demonstrate the impact that present lepton flavor and CP violation data—neutrino oscillations, baryon asymmetry of the universe, flavor violations in charged lepton decays and lepton electric dipole moments—have on supersymmetric seesaw theories by analyzing the class of models based on a $U(1)$ flavor symmetry. The fermion $U(1)$ charges are determined to a large extent by the data, the flavor patterns being naturally defined through their choice. The selected models generically predict $\mu \to e\gamma$ within the reach of the projected experiments, which could be sensitive enough to exclude the whole class of them. By now, the present sensitivity to $\mu \to e\gamma$ already provides stringent bounds on the contribution of the seesaw couplings to the lepton electric dipole moments.

In this article, we study rotating cosmological models with domain wall in the context of general relativity. For this purpose we consider domain walls with strange quark matter and normal matter in the nonstatic and stationary Gödel universes with cosmological constant. We solve Einstein’s field equations by using equation of state for strange quark matter and normal matter. Also, we discuss the features of obtained solutions.

We explore whether KamLAND and solar data may end up inconsistent when analyzed in terms of neutrino oscillations. If this turned out to be the case, one would be led to conclude that there is more new physics, besides neutrino masses and mixing, in the leptonic sector. On the other hand, given that KamLAND and solar data currently agree when analyzed in terms of two-flavor neutrino oscillations, one is able to place nontrivial bounds on several manifestations of new physics. In particular, we compute how well a combined KamLAND and solar data analysis is able to constrain a specific form of violation of CPT invariance by placing a very stringent upper bound on $|\Delta m^2-\Delta {\overline{m}}^2|<1.1\times {10}^{-4}{\mathrm{eV}}^2$ at the three sigma confidence level ($m$ refers to neutrinos, $\overline{m}$ to antineutrinos). We also estimate upper bounds on ${sin}^2\theta -{sin}^2\overline{\theta }$. These are quite poor due to the fact that matter effects are almost irrelevant at KamLAND, which leads to an intrinsic inability to distinguish whether the antineutrino mixing angle is on the light ($\overline{\theta }<\pi /4$) or dark side of the parameter space ($\overline{\theta }>\pi /4$). We briefly discuss whether this ambiguity can be resolved by future long-baseline ${\overline{\nu }}_e\leftrightarrow {\overline{\nu }}_{e,\mu }$ searches.

Neutrino oscillation data indicate the presence of a 2-3 symmetry for the left-handed neutrinos. We show that this symmetry between the second and third generations cannot be extended to include the charged leptons, no matter what basis we use. We point out that if this symmetry is also independently valid for the right-handed neutrinos, then the active neutrino spectrum is inverted, with $m_3=0$. This conclusion remains valid even when the left-handed 2-3 symmetry is broken by a nonmaximal atmospheric mixing angle ${\theta }_{23}$, or a nonzero reactor angle ${\theta }_{13}$. As previously shown by Mohapatra, Nasri, and Yu, such a symmetry also gives rise to interesting consequences on the leptogenesis asymmetry parameter ${ϵ}_1$.

Gauge theory with light flavor quark is studied by embedding a D7 brane in a deconfinement phase background newly constructed. We find a phase transition by observing a jump of the vacuum expectation value of the quark bilinear and also of the derivative of D7 energy at a critical temperature. For the model considered here, we also study quark-antiquark potential to see some possible quark-bound states and other physical quantities in the deconfinement phase.

High-temperature resummed perturbation theory is plagued by poor convergence properties. The problem appears for theories with bosonic field content such as QCD, QED or scalar theories. We calculate the pressure as well as other thermodynamic quantities at high temperature for a scalar one-component field theory, solving a three-loop 2PI effective action numerically without further approximations. We present a detailed comparison with the two-loop approximation. One observes a strongly improved convergence behavior as compared to perturbative approaches. The renormalization employed in this work extends previous prescriptions, and is sufficient to determine all counterterms required for the theory in the symmetric as well as the spontaneously broken phase.

We present a simple method for applying excision boundary conditions for the relativistic Euler equations. This method depends on the use of reconstruction-evolution methods, a standard class of high-resolution shock-capturing methods. We test three different reconstruction schemes, namely, total variation diminishing, piecewise parabolic method (PPM) and essentially nonoscillatory. The method does not require that the coordinate system is adapted to the excision boundary. We demonstrate the effectiveness of our method using tests containing discontinuities, static test fluid solutions with black holes, and full dynamical collapse of a neutron star to a black hole. A modified PPM scheme is introduced because of problems arisen when matching excision with the original PPM reconstruction scheme.

We discuss critical gravitational collapse on the threshold of apparent horizon formation as a model both for the discussion of global aspects of critical collapse and for numerical studies in a compactified context. For our matter model we choose a self-gravitating massless scalar field in spherical symmetry, which has been studied extensively in the critical collapse literature. Our evolution system is based on Bondi coordinates, the mass-function is used as an evolution variable to ensure regularity at null infinity. We compute radiation quantities like the Bondi mass and news-function and find that they reflect the discretely self-similar (DSS) behavior. Surprisingly, the period of radiation at null infinity is related to the formal result for the leading quasinormal mode of a black hole with rapidly decreasing mass. Furthermore, our investigations shed some light on global versus local issues in critical collapse, and the validity and usefulness of the concept of null infinity when predicting detector signals.

We present a unified parametrization of quark and lepton mixing matrices. By using some simple relations between the mixing angles of quarks and leptons, i.e., the quark-lepton complementarity, we parametrize the lepton mixing matrix with the Wolfenstein parameters $\lambda$ and $A$ of the quark mixing matrix. It is shown that the Wolfenstein parameter $\lambda$ can measure both the deviation of the quark mixing matrix from the unit matrix, and the deviation of the lepton mixing matrix from the exactly bimaximal mixing pattern.

Recently, it was argued that new-physics (NP) effects in $B$ decays can be approximately parametrized in terms of a few quantities. As a result, $CP$ violation in the $B$ system allows one not only to detect the presence of NP, but also to measure its parameters. This will allow a partial identification of the NP, before its production at high-energy colliders. In this paper, we examine three methods for measuring NP parameters. The first uses a technique involving both $\overline{b}\to \overline{s}$ and $\overline{b}\to \overline{d}$ penguin $B$ decays. Depending on which pair of decays is used, the theoretical error is in the range $5–15\%$. The second involves a comparison of $B\to \pi K$ and $B\to \pi \pi$ decays. Although the theoretical error is large ($\gtrsim 25\%$), the method can be performed now, with presently available data. The third is via a time-dependent angular analysis of $B\to V_1{V}_2$ decays. In this case, there is no theoretical error, but the technique is experimentally challenging, and the method applies only to those NP models whose weak phase is universal to all NP operators. A reliable identification of the NP will involve the measurement of the NP parameters in many different ways, and with as many $B$ decay modes as possible, so that it will be important to use all of these methods.

It is pointed out that the heavy singlet neutrinos characteristic of leptogenesis develop asymmetries in the abundances of the two helicity states as a result of the same mechanism that generates asymmetries in the standard lepton sector. Neutrinos and standard leptons interchange asymmetries in collisions with each other. It is shown that an appropriate quantum number, $B-L^{\prime }$, combining baryon, lepton and neutrino asymmetries, is not violated as fast as the standard $B-L$. This suppresses the washout effects relevant for the derivation of the final baryon asymmetry. One presents detailed calculations for the period of neutrino thermal production in the framework of the singlet seesaw mechanism.

We present the calculations of the complete next-to-leading-order (NLO) inclusive total cross sections for pair production of neutral Higgs bosons through $b\overline{b}$ annihilation in the minimal supersymmetric standard model at the CERN Large Hadron Collider. In our calculations, we used both the dimensional regularization scheme and the dimensional reduction scheme and found that the NLO total cross sections in these two schemes are the same. Our results show that the $b\overline{b}$-annihilation contributions can exceed those of $gg$ fusion and $q\overline{q}$ annihilation for $h^0{H}^0$, $A^0{h}^0$, and $A^0{H}^0$ productions when $\tan \beta$ is large. In the case of $\mu >0$, the NLO corrections enhance the leading-order total cross sections significantly, reaching a few tens of percent, while for $\mu <0$, the corrections are relatively small, and are negative in most of parameter space. Moreover, the NLO QCD corrections reduce the dependence of the total cross sections on the renormalization/factorization scale, especially for $\mu <0$. We also used the CTEQ6.1 parton distribution function sets to estimate the uncertainty of leading-order and NLO total cross sections, and found that the uncertainty arising from the choice of parton distribution functions increases with the increasing $m_{A^0}$.