In this paper two tracker solutions for the conformally coupled quintessence model is obtained. The first solution is determined by dividing the evolution of the Universe into matter- and dark-energy-dominated epochs and then the allowed bound on the equation of state parameter is obtained, such that a tracker behavior results. For the other solution, the quintessence potential is assumed to be a linear combination of two exponential functions, allowing us to find an exact solution that can be a tracker by adjusting some parameters.

The study of neutrinoless double beta decays of nuclei and hyperons requires the calculation of hadronic matrix elements of local four-quark operators that change the total charge by two units $\Delta Q=2$. Using a low energy effective Lagrangian that induces these transitions, we compute these hadronic matrix elements in the framework of the Massachussetts Institute of Technology bag model. As an illustrative example we evaluate the amplitude and transition rate of ${\Sigma }^{-}\to p{e}^{-}{e}^{-}$, a decay process that violates lepton number by two units ($\Delta L=2$). The relevant matrix element is evaluated without assuming the usual factorization approximation of the four-quark operators and the results obtained in both approaches are compared.

We consider lattice gauge theories at strong coupling with gauge group $U(N_C)$, or $SU(N_C)$ restricted to the meson sector, and coupled to $N_F$ flavors of fundamental representation staggered fermions. We study the formation of a chiral condensate by means of resummation of a hopping expansion. Different classes of graphs become dominant as the parameter ($N_F/N_C$) is varied. By performing graph resummation we obtain an equation for determining the condensate as a function of ($N_F/N_C$) and mass $m$. For values of ($N_F/N_C$) below a critical value, one reproduces the well-known result of the existence of a nonvanishing condensate solution in the $m=0$ limit. Above the critical ($N_F/N_C$) value, however, no such solution exists, its abrupt disappearance indicating a first-order transition to a chirally symmetric phase with composite (colorless) excitation spectrum.

The form factors of weak decays of $B_s$ mesons to ground state $D_s^{(*)}$ mesons as well as to their radial $D_s^{(*)}(2S)$ and orbital $D_{sJ}^{(*)}$ excitations are calculated in the framework of the relativistic quark model based on the quasipotential approach. All relativistic effects, including contributions of intermediate negative-energy states and boosts of the meson wave functions, are consistently taken into account. As a result, the form factors are determined in the whole kinematical range without additional phenomenological parametrizations and extrapolations. On this basis, semileptonic decay branching fractions are calculated. Two-body nonleptonic $B_s$ decays are considered within the factorization approximation. The obtained results agree well with available experimental data.

The LHCb Collaboration has recently observed two narrow baryon resonances with beauty. Their masses and decay modes look consistent with the quark model orbitally excited states ${\Lambda }_b(5912)$ and ${\Lambda }_b^{*}(5920)$, with quantum numbers $J^P=1/2^{-}$ and $3/2^{-}$, respectively. We predict the existence of these states within a unitarized meson-baryon coupled-channel dynamical model, which implements heavy-quark spin symmetry. Masses, quantum numbers and couplings of these resonances to the different meson-baryon channels are obtained. We find that the resonances ${\Lambda }_b^0(5912)$ and ${\Lambda }_b^0(5920)$ are heavy-quark spin symmetry partners, which naturally explains their approximate mass degeneracy. Corresponding bottom-strange baryon resonances are predicted at ${\Xi }_b(6035.4)$ ($J^P=\frac{1}{2}\genfrac{}{}{0ex}{}{{\mathrm{}}^{-}}{}$) and ${\Xi }_b(6043.3)$ ($J^P=\frac{3}{2}\genfrac{}{}{0ex}{}{{\mathrm{}}^{-}}{}$). The two ${\Lambda }_b$ and two ${\Xi }_b$ resonances complete a multiplet of the combined symmetry SU(3)-flavor times heavy-quark spin.

We discuss in detail and from the geometrical point of view the issues of gauge invariance and Lorentz covariance raised by the approach proposed recently by Chen et al. to the proton spin decomposition. We show that the gauge invariance of this approach follows from a mechanism similar to the one used in the famous Stueckelberg trick. Stressing the fact that the Lorentz symmetry does not force the gauge potential to transform as a Lorentz four-vector, we show that the Chen et al. approach is Lorentz covariant provided that one uses the suitable Lorentz transformation law. We also make an attempt to summarize the present situation concerning the proton spin decomposition. We argue that the ongoing debates concern essentially the physical interpretation and are because of the plurality of the adopted pictures. We discuss these different pictures and propose a pragmatic point of view.

A $D$-like meson resonance with mass around 2.9 GeV has been found in the $DK\overline{K}$ system using two independent and different model calculations based on (1) QCD sum rules and (2) solution of Fadeev equations with input interactions obtained from effective field theories built by considering both chiral and heavy quark symmetries. The QCD sum rules have been used to study the $D_{s^{*}0}(2317)\overline{K}$ and $D{f}_0(980)$ molecular currents. A resonance of mass 2.926 GeV is found with the $D{f}_0(980)$ current. Although a state in the $D_{s^{*}0}(2317)\overline{K}$ current is also obtained, with mass around 2.9 GeV, the coupling of this state is found to be two times weaker than the one formed in $D{f}_0(980)$. On the other hand, few-body equations are solved for the $DK\overline{K}$ system and its coupled channels with the input $t$ matrices obtained by solving Bethe-Salpeter equations for the $DK$, $D\overline{K}$, and $K\overline{K}$ subsystems. In this study a $D$-like meson with mass 2.890 GeV and full width $\sim 55\mathrm{MeV}$ is found to get dynamically generated when $DK\overline{K}$ gets reorganized as $D{f}_0(980)$. However, no clear signal appears for the $D_{s^{*}0}(2317)\overline{K}$ configuration. The striking similarity between the results obtained in the two different models strongly indicates the existence of a $D{f}_0(980)$ molecule with mass nearly 2.9 GeV.

In the light of the discovery of a 126 GeV Standard-Model-like Higgs boson at the LHC, we evaluate the achievable accuracies for direct measurements of the width, mass, and the $s$-channel resonant production cross section of the Higgs boson at a proposed muon collider. We find that with a beam energy resolution of $R=0.01\%$ (0.003%) and integrated luminosity of $0.5{\mathrm{fb}}^{-1}$ ($1{\mathrm{fb}}^{-1}$), a muon collider would enable us to determine the Standard-Model-like Higgs width to $\pm 0.35\mathrm{MeV}$ ($\pm 0.15\mathrm{MeV}$) by combining two complementary channels of the $W{W}^{*}$ and $b\overline{b}$ final states. A non-Standard-Model Higgs with a broader width is also studied. The unparalleled accuracy potentially attainable at a muon collider would test the Higgs interactions to a high precision.

We calculate the diffuse intensityof cosmic ray (CR) nuclei and their secondaries in the boron-carbon ($\mathrm{B}/\mathrm{C}$) group produced by supernova remnants (SNRs). The trajectories of charged particles in the SNRs are modeled as a random walk in the test particle approximation. Secondary production by CRs colliding with gas in the SNR is included as a Monte Carlo process, while we use GALPROP to account for the propagation and interactions of CRs in the Galaxy. In the vicinity of a source, we find an approximately constant $\mathrm{B}/\mathrm{C}$ ratio as a function of energy. As a result, the $\mathrm{B}/\mathrm{C}$ ratio at the Earth does not rise with energy, but flattens instead in the high-energy limit. This prediction will be tested soon by the AMS-2 Collaboration.

Extra dimensions are a common feature of physics beyond the Standard Model. In a braneworld scenario, local physics on the brane can depend strongly on the brane’s location within the bulk. Generically, the relevant properties of the bulk manifold for the physics on/of the brane are neither local nor global, but depend on the structure of finite regions of the bulk, even for locally homogeneous and isotropic bulk geometries. In a recent work, we considered various mechanisms (in a braneworld context) to stabilize the location of a brane within bulk spaces of nontrivial topology. In this work, we elaborate on and generalize that work by considering additional bulk and brane dimensionalities as well as different boundary conditions on the bulk scalar field that provides a Casimir force on the brane, providing further insight on this effect. In $D=2+1$ ($D=5+1$), we consider both local and global contributions to the effective potential of a 1-brane (4-brane) wrapped around both the two-dimensional hyperbolic horn and the Euclidean cone, which are used as toy models of an extradimensional manifold. We calculate the total energy due to brane tension and elastic energy (extrinsic curvature) as well as that due to the Casimir energy of a bulk scalar satisfying both Dirichlet and Neumann boundary conditions on the brane. In some cases, stable minima of the potential are found that result from the competition of at least two of the contributions. Generically, any one of these effects may be sufficient when the bulk space has less symmetry than the manifolds considered here. We highlight the importance of the Casimir effect for the purpose of brane stabilization.

We propose a new approach to compute correlators of quantum fields in de Sitter space. It is based on nonequilibrium field theory techniques, and exploits de Sitter symmetries so as to partially reduce the number of independent variables of $n$-point functions in a manner that preserves the usefulness of a momentum representation, e.g., for writing spatial convolution integrals as simple products. In this representation, the two-point function of a scalar field only depends on two physical momenta, and the corresponding Schwinger-Dyson evolution equations take the form of momentum flow equations. Moreover, standard diagrammatic rules can be entirely formulated in this representation. The method is suitable for analytical approximations as well as numerical implementations. In forthcoming publications, we apply it to resum infrared logarithmic terms appearing in the perturbative calculation of vertex and correlation functions.

We compute the Casimir energy for a system consisting of a fermion and a pseudoscalar field in the form of a prescribed kink. This model is not exactly solvable and we use the phase shift method to compute the Casimir energy. We use the relaxation method to find the bound states and the Runge-Kutta-Fehlberg method to obtain the scattering wave functions of the fermion in the whole interval of $x$. The resulting phase shifts are consistent with the weak and strong forms of the Levinson theorem. Then, we compute and plot the Casimir energy as a function of the parameters of the pseudoscalar field, i.e., the slope of $\varphi (x)$ at $x=0$ ($\mu$) and the value of $\varphi (x)$ at infinity ($\pm {\theta }_0$). In the graph of the Casimir energy as a function of $\mu$ there is a sharp maximum occurring when the fermion bound state energy crosses the line of $E=0$. Furthermore, this graph shows that the Casimir energy goes to zero for $\mu \to 0$, and also for $\mu \to \infty$ when ${\theta }_0$ is an integer multiple of $\pi$. Moreover, the graph of the Casimir energy as a function of ${\theta }_0$ shows that this energy is on the average an increasing function of ${\theta }_0$ and has a cusp whenever there is a zero fermionic mode. We finally compute the total energy of a system consisting of a valence fermion in the ground state. Most importantly, we show that this energy (the sum of the Casimir energy and the energy of the fermion) is minimum when the background field has winding number one, independent of the details of the background profile. Throughout the paper we compare our results with those of a simple exactly solvable model, where a piecewise linear profile approximates the kink. We find that the kink is an almost reflectionless barrier for the fermions, within the context of our model.

On the basis of the closed-time-path formalism of nonequilibrium quantum field theory, we derive the real-time quantum dynamics of heavy-quark systems. Even though our primary goal is the description of heavy quarkonia, our method allows a unified description of the propagation of single heavy quarks as well as their bound states. To make calculations tractable, we deploy leading-order perturbation theory and consider the nonrelativistic limit. Various dynamical equations, such as the master equation for quantum Brownian motion and the time-evolution equation for heavy-quark and quarkonium forward correlators, are obtained from a single operator: the renormalized effective Hamiltonian. We are thus able to reproduce previous results of perturbative calculations of the drag force and the complex potential simultaneously. In addition, we present stochastic time-evolution equations for the heavy-quark and quarkonium wave function, which are equivalent to the dynamical equations.

Recently, in the Einstein gravity, Majhi and Padmanabhan proposed a straightforward and transparent way of obtaining the Bekenstein-Hawking entropy by using an approach based on the Virasoro algebra and central charge. In this work, we generalize their approach to the modified gravity with higher-curvature corrections and show that their approach can successfully lead to the corresponding Wald entropy in the higher-curvature gravity. Our result shows that the approach is physically general.

The $G_{\mathrm{Newton}}\to 0$ limit of Euclidean gravity introduced by Smolin is described by a generally covariant $U(1{)}^3$ gauge theory. In an earlier paper, Tomlin and Varadarajan constructed the quantum Hamiltonian constraint of density weight $4/3$ for this $U(1{)}^3$ theory so as to produce a nontrivial anomaly-free loop quantum gravity type representation of the Poisson bracket between a pair of Hamiltonian constraints. These constructions involved a choice of regulating coordinate patches. The use of these coordinate patches is in apparent conflict with spatial diffeomorphism covariance. In this work we show how an appropriate choice of coordinate patches together with suitable modifications of these constructions results in the diffeomorphism covariance of the continuum limit action of the Hamiltonian constraint operator, while preserving the anomaly-free property of the continuum limit action of its commutator.

The $G_{\mathrm{Newton}}\to 0$ limit of Euclidean gravity introduced by Smolin is described by a generally covariant $U(1{)}^3$ gauge theory. The Poisson-bracket algebra of its Hamiltonian and diffeomorphism constraints is isomorphic to that of gravity. Motivated by recent results in parametrized field theory and by the search for an anomaly-free quantum dynamics for loop quantum gravity, the quantum Hamiltonian constraint of density weight $4/3$ for this $U(1{)}^3$ theory is constructed so as to produce a nontrivial loop quantum gravity type representation of its Poisson brackets through the following steps. First, the constraint at finite triangulation and the commutator between a pair of such constraints are constructed as operators on the “charge” network basis. Next, the continuum limit of the commutator is evaluated with respect to an operator topology defined by a certain space of “vertex smooth” distributions. Finally, the operator corresponding to the Poisson bracket between a pair of Hamiltonian constraints is constructed at finite triangulation in such a way as to generate a “generalized” diffeomorphism and its continuum limit is shown to agree with that of the commutator between a pair of finite-triangulation Hamiltonian constraints. Our results, in conjunction with the recent work of Henderson, Laddha and Tomlin in a ($2+1$)-dimensional context, constitute the necessary first steps toward a satisfactory treatment of the quantum dynamics of this model.

The short gravitational wave signal from the merger of compact binaries encodes a surprising amount of information about the strong-field dynamics of merger into frequencies accessible to ground-based interferometers. In this paper we describe a previously unknown “precession” of the peak emission direction with time, both before and after the merger, about the total angular momentum direction. We demonstrate that the gravitational wave polarization encodes the orientation of this direction to the line of sight. We argue that the effects of polarization can be estimated nonparametrically, directly from the gravitational wave signal as seen along one line of sight, as a slowly varying feature on top of a rapidly varying carrier. After merger, our results can be interpreted as a coherent excitation of quasinormal modes of different angular orders, a superposition which naturally “precesses” and modulates the line-of-sight amplitude. Recent analytic calculations have arrived at a similar geometric interpretation. We suspect the line-of-sight polarization content will be a convenient observable with which to define new high-precision tests of general relativity using gravitational waves. Additionally, as the nonlinear merger process seeds the initial coherent perturbation, we speculate that the amplitude of this effect provides a new probe of the strong-field dynamics during merger. To demonstrate that the ubiquity of the effects we describe, we summarize the postmerger evolution of 104 generic precessing binary mergers. Finally, we provide estimates for the detectable impacts of precession on the waveforms from high-mass sources. These expressions may identify new precessing binary parameters whose waveforms are dissimilar from the existing sample.

A diffusion equation approach to black hole thermodynamics in Euclidean sector is proposed. A diffusion equation for a generic Kerr-Newman black hole in Euclidean sector is derived from the Bloch equation. Black hole thermodynamics is also derived and it is found, in particular, that the entropy of a Kerr-Newman black hole is the same, apart from the logarithmic corrections, as the Bekenstein-Hawking entropy of the black hole.