In this work, we study the classical and quantum properties of the unique commutative Lorentz-covariant connection for loop quantum gravity. This connection has been found after solving the second-class constraints inherited from the canonical analysis of the Holst action without the time gauge. We show that it has the property of lying in the conjugacy class of a pure $\mathfrak{s}\mathfrak{u}(2)$ connection, a result which enables one to construct the kinematical Hilbert space of the Lorentz-covariant theory in terms of the usual SU(2) spin-network states. Furthermore, we show that there is a unique Lorentz-covariant electric field, up to trivial and natural equivalence relations. The Lorentz-covariant electric field transforms under the adjoint action of the Lorentz group, and the associated Casimir operators are shown to be proportional to the area density. This gives a very interesting algebraic interpretation of the area. Finally, we show that the action of the surface operator on the Lorentz-covariant holonomies reproduces exactly the usual discrete SU(2) spectrum of time-gauge loop quantum gravity. In other words, the use of the time gauge does not introduce anomalies in the quantum theory.

We study the general class of gravitational field theories constructed on the basis of scale invariance (and therefore absence of any mass parameters) and invariance under transverse diffeomorphisms, which are the 4-volume conserving coordinate transformations. We show that these theories are equivalent to a specific type of scalar-tensor theories of gravity (invariant under all diffeomorphisms) with a number of properties, making them phenomenologically interesting. They contain, in addition to the dimensionless coupling constants of the original theory, an arbitrary dimensionful parameter ${\Lambda }_0$. This parameter is associated with an integration constant of the equations of motion, similar to the arbitrary cosmological constant appearing in unimodular gravity. We focus on the theories where Newton’s constant and the electroweak scale emerge from the spontaneous breaking of scale invariance and are unrelated to ${\Lambda }_0$. The massless particle spectrum of these theories contains the graviton and a new particle—dilaton. For ${\Lambda }_0=0$, the massless dilaton has only derivative couplings to matter fields and the bounds on the existence of a 5th force are easily satisfied. As for the matter fields, we determine the conditions leading to a renormalizable low-energy theory. If ${\Lambda }_0\ne 0$, scale invariance is broken. The arbitrary constant ${\Lambda }_0$ produces a “run-away” potential for the dilaton. As a consequence, the dilaton can act as a dynamical dark energy component. We elucidate the origin of the cosmological constant in the class of theories under consideration and formulate the condition leading to its absence. If this condition is satisfied, dark energy is purely dynamical and associated to the dilaton.

In this work, we study the effects of field space curvature on scalar field perturbations around an arbitrary background field trajectory evolving in time. Nontrivial imprints of the “heavy” directions on the low-energy dynamics arise when the vacuum manifold of the potential does not coincide with the span of geodesics defined by the sigma model metric of the full theory. When the kinetic energy is small compared to the potential energy, the field traverses a curve close to the vacuum manifold of the potential. The curvature of the path followed by the fields can still have a profound influence on the perturbations, as modes parallel to the trajectory mix with those normal to it if the trajectory turns sharply enough. We analyze the dynamical mixing between these nondecoupled degrees of freedom and deduce its nontrivial contribution to the low-energy effective theory for the light modes. We also discuss the consequences of this mixing for various scenarios where multiple scalar fields play a vital role, such as inflation and low-energy compactifications of string theory.

In recent papers, we have established the existence of gauge-invariant decomposition of nucleon spin, each term of which can be related to known high-energy deep-inelastic-scattering observables. A subtlety remains, however, for the intrinsic spin part of gluons at the quantum level. In fact, it was sometimes claimed that the evolution of gluon spin depends on the gauge choice and its physical interpretation makes sense only in the light-cone gauge. In the present paper, we will demonstrate explicitly that the gluon spin operator appearing in our decomposition evolves gauge-independently and that it properly reproduces the familiar evolution equation for the 1st moments of polarized quark and gluon distributions obtained with the Altarelli-Parisi method, which cannot directly be checked by the standard operator expansion method.

In combination with supersymmetry, flavor symmetry may relate quarks with leptons, even in the absence of a grand-unification group. We propose an $SU(3)\times SU(2)\times U(1)$ model where both supersymmetry and the assumed $A_4$ flavor symmetries are softly broken, reproducing well the observed fermion mass hierarchies and predicting: (i) a relation between down-type quarks and charged lepton masses, and (ii) a correlation between the Cabibbo angle in the quark sector and the reactor angle ${\theta }_{13}$ characterizing $CP$ violation in neutrino oscillations.

In this paper we study the one-loop evolution equation of the Higgs quartic coupling $\lambda$ in the minimal universal extra dimension model, and find that there are certain bounds on the extra dimension due to the singularity and vacuum stability conditions of the Higgs sector. In the range $250\mathrm{GeV}\sim R^{-1}\sim 80\mathrm{TeV}$ of the compactification radius, we notice that for a given initial value $\lambda (M_Z)$, there is an upper limit on $R^{-1}$ for a Higgs mass of $183\mathrm{GeV}\sim m_H(M_Z)\sim 187\mathrm{GeV}$; where any other compactification scales beyond that have been ruled out for theories where the evolution of $\lambda$ does not develop a Landau pole and become divergent in the whole range (that is, from the electroweak scale to the unification scale). Likewise, in the range of the Higgs mass $152\mathrm{GeV}\sim m_H(M_Z)\sim 157\mathrm{GeV}$, for an initial value $\lambda (M_Z)$, we are led to a lower limit on $R^{-1}$; any other compactification scales below that will be ruled out for theories where the evolution of $\lambda$ does not become negative and destabilize the vacuum between the electroweak scale and the unification scale. For a Higgs mass in the range $157\mathrm{GeV}<m_H(M_Z)<183\mathrm{GeV}$, the evolution of $\lambda$ is finite and the theory is valid in the whole range (from the electroweak scale to the unification scale) for $250\mathrm{GeV}\sim R^{-1}\sim 80\mathrm{TeV}$.

The tetramixing of pseudoscalar mesons $\pi$-$\eta$-${\eta }^{\prime }$-${\eta }_c$ and vector mesons $\omega$-$\rho$-$\varphi$-$J/\psi$ are studied in the light-cone constituent quark model, and such mixing of four mesons provides a natural source for the intrinsic charm $c\overline{c}$ components of light mesons. By mixing with the light mesons, the charmonium states $J/\psi$ and ${\eta }_c$ could decay into light mesons more naturally, without introducing gluons or a virtual photon as intermediate states. Thus, the introduction of light quark components into $J/\psi$ is helpful to reproduce the new experimental data of $J/\psi$ decays. The mixing matrices and the $Q^2$ behaviors of the transition form factors are also calculated and compared with experimental data.

We report the first observation of the decay $D^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e$ in two analyses, which combined provide a branching fraction of $\mathcal{B}(D^{+}\to {\eta }^{\prime }{e}^{+}{\nu }_e)=(2.16\pm 0.53\pm 0.07)\times {10}^{-4}$. We also provide an improved measurement of $\mathcal{B}(D^{+}\to \eta e^{+}{\nu }_e)=(11.4\pm 0.9\pm 0.4)\times {10}^{-4}$, provide the first form factor measurement, and set the improved upper limit $\mathcal{B}(D^{+}\to \varphi e^{+}{\nu }_e)<0.9\times {10}^{-4}$ (90%C.L.).

We investigate the marginally stable modes of the scalar (vector) perturbations in the AdS soliton background coupled to electric field. In the probe limit, we find that the marginally stable modes can reveal the onset of the phase transitions of this model. The critical chemical potentials obtained from this approach are in good agreement with the previous numerical or analytical results.

We study the one-loop low-energy effective action for the higher-derivative superfield gauge theory coupled to chiral matter.

Using a solution generating technique based on the symmetries of the dimensionally reduced Lagrangian we derive two exact solutions of the Einstein-Maxwell-Dilaton field equations in five dimensions. More specifically, these solutions describe general systems of a nonextremally charged static asymptotically flat black bi/di-ring. We compute their conserved charges and investigate some of their properties. As expected, we find that in general there are conical singularities in between the black rings and for the static solutions considered here they cannot be completely eliminated.

The brane-world cosmological model in higher-dimensional spacetime with a bulk scalar field is investigated. We derive the $(4+n)$-dimensional gravitational field equations for the scalar field on the $(3+n)$-brane in a $(5+n)$-dimensional bulk with Einstein gravity plus a self-interacting scalar field. The $(4+n)$-dimensional gravitational field equations can be formulated to standard form with the extra component. Using this formalism we study the Kaluza-Klein brane cosmology. We derive the Friedmann equation and a possible energy leak out of the brane into the bulk. We present some exact solutions corresponding to vacuum brane and matter on the brane.

By using the Bousso geometrical covariant procedure we consider in this paper the holographic principle as applied to asymptotic Friedmann-Robertson-Walker space-times whose vacuum dark energy is due to the presence of a quintessential dark and phantom-energy scalar field with constant equation of state $p=\omega \rho$, both for $w>-1$ and $w<-1$. We have obtained the positions of the optimal screen for each case, deriving for them moreover expressions for the future event horizon and hence holographic dark-energy models of the Li and Huang and Li types, which are compared with the most consistent results derived from the covariant Bousso procedure. It is also seen that one of the two obtained holographic screens is placed on the big rip hypersurface in the phantom-energy case, both for the covariant holographic formalism and holographic phantom models. Consistency of fundamental theories is analyzed in the light of the largest physical regions allowed by the existence of a holographic screen in the future.

Understanding a behavior of galaxy biasing is crucial for future galaxy redshift surveys. One aim is to measure the baryon acoustic oscillations (BAOs) within the precision of a few percent level. Using 30 large cosmological $N$-body simulations for a standard $\Lambda \mathrm{CDM}$ cosmology, we study the halo biasing over a wide redshift range. We compare the simulation results with theoretical predictions proposed by Matsubara [T. Matsubara, Phys. Rev. D 78, 083519 (2008).] which naturally incorporate the halo bias and redshift-space distortions into their formalism of perturbation theory with a resummation technique via the Lagrangian picture. The power spectrum and correlation function of halos obtained from Lagrangian resummation theory (LRT) well agree with $N$-body simulation results on scales of BAOs. Especially nonlinear effects on the baryon acoustic peak of the halo correlation function are accurately explained both in real and redshift space. We find that nonlinearity and scale dependence of bias are fairly well reproduced by 1-loop LRT up to $k=0.35h{\mathrm{Mpc}}^{-1}$ ($z=2$ and 3) within a few percent level in real space and up to $k=0.1h{\mathrm{Mpc}}^{-1}$ ($z=2$) and $0.15h{\mathrm{Mpc}}^{-1}$ ($z=3$) in redshift space. Thus, the LRT is very powerful for accurately extracting cosmological information in upcoming high redshift BAO surveys.

We introduce a small correction term, $\delta M_{\nu }$, in the neutrino sector and examine whether a large ${\theta }_{13}$ and an almost maximal ${\theta }_{23}$ can simultaneously be obtained starting from the tri-bimaximal neutrino mixing. It is found that one can easily gain ${\theta }_{13}\simeq 10°$, which is favored by the recent T2K experiment, by taking account of the enhancement due to the degeneracy among three neutrino masses. We also find that $(\delta M_{\nu }{)}_{22}=(\delta M_{\nu }{)}_{33}$ is a key condition for ${\theta }_{23}\simeq 45°$.

Symmetry breaking patterns of the $U(n{)}_L\times U(n{)}_R$ symmetric meson model are investigated in a formulation involving three auxiliary composite fields. The effective potential is constructed at leading order in the $1/n$ expansion for a condensate belonging to the center of the $U(n)$ group. A wide region is found in the coupling space, where, in addition to the condensate proportional to the unit matrix, also metastable minima exist even in the chiral limit, in which a further breakdown of the diagonal $U_V(n)$ symmetry to $U_V(n-1)$ is realized. Application of a moderate external field conjugate to this component of the order parameter changes this state into the true ground state of the system.

We have systematically studied the $S$-wave pseudoscalar meson and heavy vector meson scattering lengths to the third order with the chiral perturbation theory, which will be helpful to reveal their strong interaction. For comparison, we have presented the numerical results of the scattering lengths (1) in the framework of the heavy meson chiral perturbation theory and (2) in the framework of the infrared regularization. The chiral expansion converges well in some channels.

This work is the first check of gauge invariance for nonperturbative calculations in light-front QED. To quantize QED in an arbitrary covariant gauge, we use a light-front analog of the equal-time Stueckelberg quantization. Combined with a Pauli-Villars regularization, where massive, negative-metric photons and fermions are included in the Lagrangian, we are then able to construct the light-front QED Hamiltonian and the associated mass eigenvalue problem in a Fock-space representation. The formalism is applied to the dressed-electron state, with a Fock-space truncation to include at most one photon. From this eigenstate, we compute the anomalous magnetic moment. The result is found to be gauge independent, to an order in $\alpha$ consistent with the truncation.

The QCD evolution of the pion distribution amplitude (DA) ${\varphi }_{\pi }(x,Q^2)$ is computed for several commonly used models. Our analysis includes the nonperturbative form predicted by light-front holographic QCD, thus combining the nonperturbative bound state dynamics of the pion with the perturbative ERBL evolution of the pion DA. We calculate the meson-photon transition form factors for the ${\pi }^0$, $\eta$ and ${\eta }^{\prime }$ using the hard-scattering formalism. We point out that a widely-used approximation of replacing $\varphi (x,(1-x)Q)$ with $\varphi (x,Q)$ in the calculations will unjustifiably reduce the predictions for the meson-photon transition form factors. It is found that the four models of the pion DA discussed give very different predictions for the $Q^2$ dependence of the meson-photon transition form factors in the region of $Q^2>30{\mathrm{GeV}}^2$. More accurate measurements of these transition form factors at the large $Q^2$ region will be able to distinguish different models of the pion DA. The rapid growth of the large $Q^2$ data for the pion-photon transition form factor reported by the BABAR Collaboration is difficult to explain within the current framework of QCD. If the BABAR data for the pion-photon transition form factor is confirmed, it could indicate physics beyond-the-standard model, such as a weakly coupled elementary $C=+$ axial vector or pseudoscalar $z^0$ in the few GeV domain, an elementary field which would provide the coupling ${\gamma }^{*}\gamma \to z^0\to {\pi }^0$ at leading twist. Our analysis thus indicates the importance of additional measurements of the pion-photon transition form factor at large $Q^2$.