We propose a new mechanism to produce a fermion mass hierarchy dynamically in a model with a single generation of fermions. A five-dimensional gauge theory on an interval with point interactions (zero-width branes) takes responsibility for realizing three generations and each massless zero mode localizes at boundaries of the segments on the extra dimension. An extra dimension coordinate-dependent vacuum expectation value of a scalar field makes large differences in overlap integrals of the localized zero modes and then an exponential fermion mass hierarchy can appear. The positions of the point interactions control the magnitude of the fermion mass hierarchy and are determined by the minimization condition of the Casimir energy. As a result of the minimization of the Casimir energy, an exponential mass hierarchy appears dynamically. We also discuss the stability of the extra dimension.

We construct an effective hadronic model including ${\mathrm{\Lambda }}_c(2595)$, ${\mathrm{\Lambda }}_c(2625)$, ${\mathrm{\Lambda }}_b(5912)$, and ${\mathrm{\Lambda }}_b(5920)$, regarding them as chiral partners to ${\mathrm{\Sigma }}_c(2455)$, ${\mathrm{\Sigma }}_c(2520)$, ${\mathrm{\Sigma }}_b$, and ${\mathrm{\Sigma }}_b^{*}$, respectively, with respecting the chiral symmetry and heavy-quark spin-flavor symmetry. We determine the model parameters from the experimental data for relevant masses and decay widths of ${\mathrm{\Sigma }}_c^{(*)}$ and ${\mathrm{\Lambda }}_c(2595)$. Then, we study the decay widths of ${\mathrm{\Lambda }}_c(2625)$, ${\mathrm{\Lambda }}_b(5912)$, and ${\mathrm{\Lambda }}_b(5920)$. We find that, although the decay of ${\mathrm{\Lambda }}_c(2595)$ is dominated by the resonant contribution through ${\mathrm{\Sigma }}_c(2455)$, nonresonant contributions are important for ${\mathrm{\Lambda }}_c(2625)$, ${\mathrm{\Lambda }}_b(5912)$, and ${\mathrm{\Lambda }}_b(5920)$, which reflects the chiral partner structure. We also study the radiative decays of the baryons, and show that each of their widths is determined from the radiative decay width of their chiral partners.

The recent precision measurement of the relative yield of $D^{+}{D}^{-}$ and $D^0{\overline{D}}^0$ meson pairs at the $\psi (3770)$ peak in $e^{+}{e}^{-}$ annihilation is about 3.7 sigma away from a straightforward theoretical estimate. It is argued that combined with an even more significant deviation of a similar ratio for the $B$ mesons at the $\mathrm{\Upsilon }(4S)$ peak, this provides an insight into the structure of heavy mesons and requires both a form factor, corresponding to their finite “size,” and a strong interaction between the mesons in the isovector state $I^G(J^P)=1^{+}(1^{-})$. It is also argued that the data for the $D$ and $B$ mesons are possibly compatible with the heavy quark limit of the same meson-antimeson strong interaction in both systems.

Computing polynomial form of the colored HOMFLY-PT for nonarborescent knots obtained from three or more strand braids is still an open problem. One of the efficient methods suggested for the three-strand braids relies on the eigenvalue hypothesis which uses the Yang-Baxter equation to express the answer through the eigenvalues of the $\mathcal{R}$ matrix. In this paper, we generalize the hypothesis to higher number of strands in the braid where commuting relations of non-neighboring $\mathcal{R}$ matrices are also incorporated. By solving these equations, we determine the explicit form for $\mathcal{R}$ matrices and the inclusive Racah matrices in terms of braiding eigenvalues (for matrices of size up to 6 by 6). For comparison, we briefly discuss the highest weight method for four-strand braids carrying fundamental and symmetric rank two $S{U}_q(N)$ representation. Specifically, we present all the inclusive Racah matrices for representation [2] and compare with the matrices obtained from eigenvalue hypothesis.

Finite-temperature corrections to the effective potential and the energy-momentum tensor of a scalar field are computed in a perturbed Minkoswki spacetime. We consider the explicit mode decomposition of the field in the perturbed geometry and obtain analytical expressions in the nonrelativistic and ultrarelativistic limits to first order in scalar metric perturbations. In the static case, our results are in agreement with previous calculations based on the Schwinger-DeWitt expansion which indicate that thermal effects in a curved spacetime can be encoded in the local Tolman temperature at leading order in perturbations and in the adiabatic expansion. We also study the shift of the effective potential minima produced by thermal corrections in the presence of static gravitational fields. Finally, we discuss the dependence on the initial conditions set for the mode solutions.

We generalize the covariant Tolman-Oppenheimer-Volkoff equations proposed in Carloni and Vernieri [Phys. Rev. D 97, 124056 (2018).]. to the case of static and spherically symmetric spacetimes with anisotropic sources. The extended equations allow a detailed analysis of the role of the anisotropic terms in the interior solution of relativistic stars and lead to the generalization of some well-known solutions of this type. We show that, like in the isotropic case, one can define generating theorems for the anisotropic Tolman-Oppenheimer-Volkoff equations. We also find that it is possible to define a reconstruction algorithm able to generate a double infinity of interior solutions. Among these, we derive a class of solutions that can represent “quasi-isotropic” stars.

We construct a covariant version of the Tolman-Oppenheimer-Volkoff equations in the case of isotropic sources. The new equations make evident the mathematical problems in the determination of interior solutions of relativistic stellar objects. Using a reconstruction algorithm, we find two physically interesting generalizations of previously known stellar interior solutions. The variables that we use also allow an easier formulation of known generating theorems for solutions associated to relativistic stellar objects.

We report a gravitational $BF$-type action principle propagating two (complex) degrees of freedom that, besides the gauge connection and the $B$ field, only employs an additional Lagrange multiplier. The action depends on two parameters and remarkably is polynomial in the $B$ field. For a particular choice of the involved parameters the action provides an alternative description of (complex) general relativity with a nonvanishing cosmological constant, whereas another choice corresponds to anti-self-dual gravity. Generic values of the parameters produce “close neighbors” of general relativity, although there is a peculiar choice of the parameters that leads to a Hamiltonian theory with two scalar constraints. Given the nontrivial form of the resulting scalar constraint for these models, we consider a more general setting where the scalar constraint is replaced with an arbitrary analytic function of some fundamental variables and show that the Poisson algebra involving this constraint together with the Gauss and vector constraints of the Ashtekar formalism closes, thus generating an infinite family of gravitational models that propagate the same number of degrees of freedom as general relativity.

A Hamiltonian analysis of models given by a three-form field with a generic potential coupled to general relativity in four dimensions is performed. This kind of field is naturally present in string theory and cosmological scenarios. In particular, the action that is considered has been extensively used during the last years to propose inflationary and dark-energy models. Nevertheless, in order to keep the discussion as generic as possible, neither symmetries nor a specific form of the potential for the three-form field is imposed. Interesting and relevant results about the number of dynamical degrees of freedom of these models are obtained. In addition, an analogy with a weakly coupled scalar field is discussed. Finally, as a particular example of this generic framework, a homogeneous and isotropic cosmological case is presented.

We find neutral and charged black brane solutions with axion fields in the context of a conformally coupled gravitational theory in four dimensions. These solutions describe anti–de Sitter (AdS) black branes supported by axion fields that break translational invariance at the boundary, which provides momentum dissipation. The conformally coupled scalar field is regular inside and outside the event horizon and there is no need for any self-interaction, obtaining in this way solutions without fine-tuned parameters. We analyze the thermodynamics of our solutions considering the effects of the axionic charges. In asymptotically AdS configurations, the axionic and electric charges are related, implying vanishing scalar field contributions to the mass. The rotating solution is obtained by means of a Lorentz boost having angular momentum sustained by the axion parameter. We compute the holographic DC conductivity and we show how it is affected by the inclusion of the conformal scalar field, which provides a temperature-independent behavior. Finally, we include a $k$-essence term that modifies the DC conductivity and provides more general behaviors.

We consider an infrared truncated massive minimally coupled scalar field with a quartic self-interaction $\lambda {\phi }^4$ in the locally de Sitter background of an inflating universe. We compute the quantum-corrected two-point correlation function of the scalar analytically at one- and two-loop order. The one-loop correlator at a fixed comoving separation asymptotes to zero in the massive case but grows like $-\lambda {\ln }^2(a)$ at late times in the massless limit, where $a$ is the cosmic scale factor. For a fixed physical distance, on the other hand, it grows like $-\lambda {\ln }^3(a)$ at late times in the massless limit. This growth is severely suppressed in the massive case. In fact, the one-loop correlator asymptotes effectively to zero for masses larger than half the expansion rate. We use our quantum-corrected correlation function to compute the stochastic contributions to the power spectrum, spectral index, and running of the spectral index. The spectrum of fluctuations of a massive scalar is red tilted at tree and one-loop order. As the mass decreases, so does the tilt. In the massless limit, although the tilt vanishes at tree order, the one-loop correction still induces a red tilt. Thus, the amplitudes of scalar field fluctuations—massive or massless—grow toward the larger scales. We also compute the variance of the field variation at tree and one-loop order. The one-loop variance implies that the tree-order result decreases when quantum corrections are included. Hence, the actual effect that any local observer perceives in the field strength as fluctuations happen does not deviate from the average effect as much as the tree-order variance implies.

Black holes in general relativity are characterized by their trapping horizon, a one-way membrane that can be crossed only inwards. The existence of trapping horizons in astrophysical black holes can be tested observationally using a reductio ad absurdum argument, replacing black holes by horizonless configurations with a physical surface and looking for inconsistencies with electromagnetic and gravitational wave observations. In this approach, the radius of the horizonless object is always larger than but arbitrarily close to the position where the horizon of a black hole of the same mass would be located. Upper bounds on the radius of these alternatives have been provided using electromagnetic observations (in the optical/IR band) of astronomical sources at the center of galaxies, but lower bounds were lacking, leaving unconstrained huge regions of parameter space. We show here that lower bounds on the radius of horizonless objects that do not develop trapping horizons can be placed using observations of accreting systems. This result is model independent and relies only on the local notion of causality dictated by the spacetime geometry around the horizonless object. These observational bounds reduce considerably the previously allowed parameter space, boosting the prospects of establishing the existence of trapping horizons using electromagnetic observations.

The anomalous dimension of spin-$1/2$ baryon operators in QCD is derived at leading $1/N_f$ order using the minimal subtraction scheme. A residual ambiguity, originating from the presence of evanescent operators in dimensional regularization, is parametrized by a function of the renormalized coupling. Our result is shown to agree with previous two- and three-loop calculations performed in two different renormalization schemes.

The measurements of $R_K$ and $R_{K^{*}}$ provide hints for the violation of lepton universality. However, it is generally difficult to explain the $R_{K^{*}}$ measurement in the low $q^2$ range, $0.045\le q^2\le 1.1{\mathrm{GeV}}^2$. Light mediators offer a solution by making the Wilson coefficients $q^2$ dependent. We check if new lepton nonuniversal interactions mediated by a scalar ($S$) or vector particle ($Z^{\prime }$) of mass between 10–200 MeV can reproduce the data. We find that a 25 MeV $Z^{\prime }$ with a $q^2$-dependent $b-s$ coupling and that couples to the electron but not the muon can explain all three anomalies in conjunction with other measurements. A similar 25 MeV $S$ provides a good fit to all relevant data except $R_{K^{*}}$ in the low $q^2$ bin. A 25 MeV $Z^{\prime }$ with a $q^2$-dependent $b-s$ coupling and that couples to the muon but not the electron provides a good fit to the combination of the $R_K$ and $R_{K^{*}}$ data, but does not fit $R_{K^{*}}$ in the low $q^2$ bin well.

In the paper, we make a comprehensive study of the hadroproduction of the $B_c(B_c^{*})$ meson via the gluon-gluon fusion mechanism at the RHIC and LHC colliders. Total and differential cross sections via the proton-nucleus ($p\text{−}\mathrm{N}$) and nucleus-nucleus (N-N) collision modes have been discussed under various collision energies. To compare with those via the proton-proton collision mode at the LHC, we observe that a sizable number of $B_c(B_c^{*})$-meson events can also be produced via the $p\text{−}\mathrm{N}$ and N-N collision modes at the RHIC and LHC. If assuming the spin-triplet $B_c^{*}$ meson directly decays to the spin-singlet $B_c$ meson with 100% probability, $1.2\times {10}^5$ and $4.7\times {10}^5$ $B_c$-meson events can be produced via the $p\text{−}\mathrm{Au}$ and Au-Au collision modes at the RHIC in one operation year, and $5.8\times {10}^6$ and $4.6\times {10}^6$ $B_c$-meson events can be produced via the $p\text{−}\mathrm{Pb}$ and Pb-Pb collision modes at the LHC in one operation year.

We study the $\mathrm{\Upsilon }(1S)$ radiative decays to $\gamma {\pi }^{+}{\pi }^{-}$ and $\gamma K^{+}{K}^{-}$ using data recorded with the BABAR detector operating at the SLAC PEP-II asymmetric-energy $e^{+}{e}^{-}$ collider at center-of-mass energies at the $\mathrm{\Upsilon }(2S)$ and $\mathrm{\Upsilon }(3S)$ resonances. The $\mathrm{\Upsilon }(1S)$ resonance is reconstructed from the decay $\mathrm{\Upsilon }(nS)\to {\pi }^{+}{\pi }^{-}\mathrm{\Upsilon }(1S)$, $n=2$, 3. Branching fraction measurements and spin-parity analyses of $\mathrm{\Upsilon }(1S)$ radiative decays are reported for the $\mathrm{I}=0$ $S$-wave and $f_2(1270)$ resonances in the ${\pi }^{+}{\pi }^{-}$ mass spectrum, the $f_2^{\prime }(1525)$ and $f_0(1500)$ in the $K^{+}{K}^{-}$ mass spectrum, and the $f_0(1710)$ in both.

We discuss the branching structure of the quantum-gravitational wave function that describes the evaporation of a black hole. A global wave function which initially describes a classical Schwarzschild geometry is continually decohered into distinct semiclassical branches by the emission of Hawking radiation. The laws of quantum mechanics dictate that the wave function evolves unitarily, but this unitary evolution is only manifest when considering the global description of the wave function; it is not implemented by time evolution on a single semiclassical branch. Conversely, geometric notions like the position or smoothness of a horizon only make sense on the level of individual branches. We consider the implications of this picture for probes of black holes by classical observers in definite geometries, like those involved in the Almheiri-Marolf-Polchinski-Sully construction. We argue that individual branches can describe semiclassical geometries free of firewalls, even as the global wave function evolves unitarily. We show that the pointer states of infalling detectors that are robust under Hamiltonian evolution are distinct from, and incompatible with, those of exterior detectors stationary with respect to the black hole horizon, in the sense that the pointer bases are related to each other via nontrivial transformations that mix the system, apparatus, and environment. This result describes a Hilbert-space version of black hole complementarity.

We consider the description of form factors of local and Wilson line operators (Reggeon amplitudes) in $\mathcal{N}=4$ Supersymmetric Yang-Mills theory within the framework of four-dimensional ambitwistor string theory. We present the explicit expressions for string composite operators corresponding to stress-tensor operator supermultiplet and Wilson line operator insertion. It is shown that corresponding tree level string correlation functions correctly reproduce previously obtained Grassmannian integral representations. As a by-product we derive four-dimensional tree-level scattering equation representations for the mentioned form factors and formulate a simple gluing procedure used to relate operator form factors with on-shell amplitudes.