Wald’s entropy formula allows one to find the entropy of black holes’ event horizon within any diffeomorphism invariant theory of gravity. When applied to general relativity, the formula yields the Bekenstein-Hawking result but, for any other gravitational action that departs from the Hilbert action, the resulting entropy acquires an additional multiplicative factor that depends on the global geometry of the background spacetime. On the other hand, the generalized uncertainty principle (GUP) has extensively been recently used to investigate corrections to the Bekenstein-Hawking entropy formula, with the conclusion that the latter always comes multiplied by a factor that depends on the area of the event horizon. We show, by considering the case of an $f(R)$-modified gravity, that the usual black hole entropy derivation based on the GUP might be modified in such a way that the two methods yield the same corrections to Bekenstein-Hawking formula. The procedure turns out to be an interesting method for seeking modified gravity theories. Two different versions of the GUP are used, and it is found that only one of them yields a viable modified gravity model. Conversely, it is possible to find a general formulation of the GUP that would reproduce Wald entropy formula for any $f(R)$ theory of gravity.

The formulation of quasilocal conformal Killing horizons (CKH) is extended to include rotation. This necessitates that the horizon be foliated by 2-spheres which may be distorted. Matter degrees of freedom which fall through the horizon are represented by a real scalar field. We show that these rotating CKHs also admit a first law in differential form.

We discuss how the assumption of variable equation of state (EoS) allows the elimination of the instability at equilibrium throat radius $a_0=3M$ featured by previous Schwarzschild thin-shell wormhole models. Unobstructed stability regions are found for three choices of variable EoS. Two of these EoS entail linear stability at every equilibrium radius. Particularly, the thin shell remains stable as $a_0$ approaches the Schwarzschild radius $2M$. A perturbative analysis of the wormhole equation of motion is carried out in the case of variable Chaplygin EoS. The squared proper angular frequency ${\omega }_0^2$ of small throat oscillations is linked with the second derivative of the thin-shell potential. In various situations ${\omega }_0^2$ remains positive and bounded in the limit $a_0\to 2M$.

Massive bigravity, a theoretically consistent modification of general relativity with an additional dynamical rank-two tensor, successfully describes the observed accelerated expansion of the Universe without a cosmological constant. Recent analyses of perturbations around a cosmological background have revealed power law instabilities in both scalar and tensor perturbations, motivating an analysis of the initial conditions, evolution, and cosmological observables to determine the viability of these theories. In this paper we focus on the tensor sector and study a primordial stochastic gravitational wave background in massive bigravity. The phenomenology can differ from standard general relativity due to nontrivial mixing between the two linearized tensor fluctuations in the theory, only one of which couples to matter. We study perturbations about two classes of cosmological solutions in bigravity, computing the tensor contribution to the temperature anisotropies in the cosmic microwave background radiation and the present stochastic gravitational wave background. The result is strongly dependent on the choice of cosmological background and initial conditions. One class of background solution generically displaying tremendous growth in the amplitude of large-wavelength gravitational waves, while the other remains observationally indistinguishable from standard general relativity for a wide variety of initial conditions. We analyze the initial conditions for tensor modes expected in an inflationary cosmology, finding again that there is a strong dependence on the assumed background. For one choice of background, the semiclassical theory is beyond the perturbative regime. For the other choice, inflation generically yields initial conditions that, when evolved, give rise to a stochastic background observationally indistinguishable from standard general relativity.

If observations confirm BICEP2’s claim of a tensor-scalar ratio $r\approx 0.2$ on CMB scales, then the inflationary consistency relation $n_t=-r/8$ predicts a small negative value for the tensor spectral index $n_t$. We show that future CMB polarization experiments should be able to confirm this prediction at several sigma. We also show how to properly extend the consistency relation to solar system scales, where the primordial gravitational wave density ${\mathrm{\Omega }}_{\mathrm{gw}}$ could be measured by proposed experiments such as the Big Bang Observer. This would provide a far more stringent test of the consistency relation and access much more detailed information about the early Universe.

We describe a class of modified gravity theories that deform general relativity in a way that breaks time reversal invariance and, very mildly, locality. The algebra of constraints, local physical degrees of freedom, and their linearized equations of motion, are unchanged, yet observable effects may be present on cosmological scales, which have implications for the early history of the universe. This is achieved in the Hamiltonian framework, in a way that requires the constant mean curvature gauge conditions and is, hence, inspired by shape dynamics.

In models like axion monodromy, temporal features during inflation which are not associated with its ending can produce scalar, and to a lesser extent, tensor power spectra where deviations from scale-free power law spectra can be as large as the deviations from scale invariance itself. Here the standard slow-roll approach breaks down since its parameters evolve on an $e$-folding scale $\mathrm{\Delta }N$ much smaller than the $e$-folds to the end of inflation. Using the generalized slow-roll approach, we show that the expansion of observables in a hierarchy of potential or Hubble evolution parameters comes from a Taylor expansion of the features around an evaluation point that can be optimized. Optimization of the leading-order expression provides a sufficiently accurate approximation for current data as long as the power spectrum can be described over the well-observed few $e$-folds by the local tilt and running. Standard second-order approaches, often used in the literature, ironically are worse than leading-order approaches due to inconsistent evaluation of observables. We develop a new optimized next-order approach which predicts observables to ${10}^{-3}$ even for $\mathrm{\Delta }N\sim 1$ where all parameters in the infinite hierarchy are of comparable magnitude. For models with $\mathrm{\Delta }N\ll 1$, the generalized slow-roll approach provides integral expressions that are accurate to second order in the deviation from scale invariance. Their evaluation in the monodromy model provides highly accurate explicit relations between the running oscillation amplitude, frequency, and phase in the curvature spectrum and parameters of the potential.

The present article is an endeavor to look into some fruitful frameworks based on “bimaximal” (BM) neutrino mixing from a model-independent stand. The possibilities involving the correction or attenuation of the original BM mixing matrix followed by grand-unified-theory-inspired charged-lepton correction are invoked. The “symmetry basis,” thus, constructed accentuates some interesting facets such as a modified quark lepton complementarity relation, ${\theta }_{12}+{\theta }_c\approx \frac{\pi }{4}-{\theta }_{13}\cos (n\pi -{\delta }_{CP})$, a possible linkup between neutrino and charged-lepton sectors, ${\theta }_{13}^{\nu }={\theta }_{12}^l\sim \mathcal{O}({\theta }_C)$, or that between neutrinos and quarks, ${\theta }_{13}^{\nu }={\theta }_C$. The study vindicates the relevance of the bimaximal mixing as a first approximation.

We perform a lattice study of charmonium-like mesons with $J^{\mathrm{PC}}=1^{++}$ and three quark contents $\overline{c}c\overline{d}u$, $\overline{c}c(\overline{u}u+\overline{d}d)$ and $\overline{c}c\overline{s}s$, where the later two can mix with $\overline{c}c$. This simulation with $N_f=2$ and $m_{\pi }\simeq 266\mathrm{MeV}$ aims at the possible signatures of four-quark exotic states. We utilize a large basis of $\overline{c}c$, two-meson and diquark-antidiquark interpolating fields, with diquarks in both antitriplet and sextet color representations. A lattice candidate for $X(3872)$ with $I=0$ is observed very close to the experimental state only if both $\overline{c}c$ and $D{\overline{D}}^{*}$ interpolators are included; the candidate is not found if diquark-antidiquark and $D{\overline{D}}^{*}$ are used in the absence of $\overline{c}c$. No candidate for neutral or charged $X(3872)$, or any other exotic candidates are found in the $I=1$ channel. We also do not find signatures of exotic $\overline{c}c\overline{s}s$ candidates below 4.2 GeV, such as $Y(4140)$. Possible physics and methodology related reasons for that are discussed. Along the way, we present the diquark-antidiquark operators as linear combinations of the two-meson operators via the Fierz transformations.

We investigate low-energy fluctuations in the real kink crystal phase of dense quark matter within the Nambu–Jona-Lasinio model. The modulated chiral condensate breaks both the translational symmetry and chiral symmetry spontaneously, which leads to the appearance of phonons and pions that are dominant degrees of freedom in the infrared. Using the Ginzburg–Landau expansion near the Lifshitz point, we derive elastic free energies for phonons and pions in dependence on the temperature and chemical potential. We show that the one-dimensional modulation is destroyed by thermal fluctuations of phonons at nonzero temperature and compute the exponent that characterizes the anisotropic algebraic decay of quasicondensate correlations at long distance. We also estimate finite-volume effects on the stability of the real kink crystal and briefly discuss the possibility of its existence in neutron stars.

The energy dependence of the cross sections for electromagnetic diffractive processes can be well described by a single power, $W^{\delta }$. For $J/\psi$ photoproduction this holds in the range from 20 GeV to 2 TeV. This feature is most easily explained by a single pole in the angular momentum plane which depends on the scale of the process, at least in a certain range of values of the momentum transfer. It is shown that this assumption allows a unified description of all electromagnetic elastic diffractive processes. We also discuss an alternative model with an energy-dependent dipole cross section, which is compatible with the data up to 2 TeV and which shows an energy behavior typical for a cut in the angular momentum plane.

We formulate a framework to determine the mass of glueball states of the Landau gauge Yang-Mills theory in the continuum. To this end we derive a Bethe-Salpeter equation for two gluon bound states including the effects of Faddeev-Popov ghosts. We construct a suitable approximation scheme such that the interactions in the bound state equation match a corresponding successful approximation of the Dyson-Schwinger equations for the Landau gauge ghost and gluon propagators. Based upon a recently obtained solution for the propagators in the complex momentum plane we obtain results for the mass of the $0^{++}$ and $0^{-+}$ glueballs. In the scalar channel we find a mass value in agreement with lattice gauge theory.

We examine the constraints on the two-Higgs-doublet model (2HDM) due to the stability of the scalar potential and absence of Landau poles at energy scales below the Planck scale. We employ the most general 2HDM that incorporates an approximately Standard Model (SM) Higgs boson with a flavor aligned Yukawa sector to eliminate potential tree-level Higgs-mediated flavor changing neutral currents. Using basis independent techniques, we exhibit regimes of the 2HDM parameter space with a 125 GeV SM-like Higgs boson that is stable and perturbative up to the Planck scale. Implications for the heavy scalar spectrum are exhibited.

We critically review the assumption that no new physics is acting in tree-level $B$-meson decays and study the consequences for the ultimate precision in the direct determination of the Cabibbo-Kobayashi-Maskawa (CKM) angle $\gamma$. In our exploratory study we find that sizeable universal new physics contributions, $\mathrm{\Delta }{C}_{1,2}$, to the tree-level Wilson coefficients $C_{1,2}$ of the effective Hamiltonian describing weak decays of the $b$ quark are currently not excluded by experimental data. In particular, we find that $\mathrm{Im}\mathrm{\Delta }{C}_1$ and $\mathrm{Im}\mathrm{\Delta }{C}_2$ can easily be of order $\pm 10\%$ without violating any constraints from data. Such a size of new physics effects in $C_1$ and $C_2$ corresponds to an intrinsic uncertainty in the CKM angle $\gamma$ of the order of $|\delta \gamma |\approx 4°$, which is slightly below the current experimental precision. The accuracy in the determination of $\gamma$ can be improved by putting stronger constraints on the tree-level Wilson coefficients, in particular $C_1$. To this end we suggest a more refined theoretical study as well as more precise measurements of the observables that currently provide the strongest bounds on hypothetical new weak phases in $C_1$ and $C_2$. We note that the semileptonic $CP$ asymmetries seem to have the best prospect for improving the bound on the weak phase in $C_1$.

We consider $\tau$-lepton mass effects in the cascade decays $H\to Z(\to {\ell }^{+}{\ell }^{-})+Z^{*}(\to {\tau }^{+}{\tau }^{-})$ and $H\to W^{-}(\to {\ell }^{-}{\overline{\nu }}_{\ell })+W^{+*}(\to {\tau }^{+}{\nu }_{\tau })$. Since the scale of the problem is set by the off-shellness $q^2$ of the respective gauge bosons in the limits $(m_{\ell }+m_{{\ell }^{\prime }}{)}^2\le q^2\le (m_H-m_{W,Z}{)}^2$ and not by $m_{W,Z}^2$, lepton-mass effects are non-negligible for the $\tau$ modes in particular close to the threshold of the off-shell decays. Lepton-mass effects show up in the rate and in the three-fold joint angular decay distribution for the decays. Nonzero lepton masses lead to leptonic helicity-flip contributions which in turn can generate novel angular dependencies in the respective three-fold angular decay distributions. Lepton-mass effects are more pronounced in the $H\to Z(\to \ell \ell )Z^{*}(\to \tau \tau )$ mode which, in part, is due to the fact that the ratio of lepton helicity-flip/nonflip contributions in the decay $Z^{*}\to {\ell }^{+}{\ell }^{-}$ is four times larger than in the decay $W^{+*}\to {\ell }^{+}\nu$. Overall the inclusion of $\tau$ mass effects leads to a 3.97% reduction in the leptonic $H\to Z{Z}^{*}$ rate. Lepton mass effects are quite pronounced for $q^2$ values from threshold up to $\sim 200{\mathrm{GeV}}^2$. For example, at $q^2=50{\mathrm{GeV}}^2$ the transverse–longitudinal–scalar helicity composition of the off-shell $Z$–boson changes from $0.06:0.94:0$ to $0.04:0.65:0.31$ for the $\tau$ lepton. This has observational consequences for the angular decay distributions of the final-state leptons. We also briefly consider the corresponding off-shell–off-shell decays $H\to Z^{*}(\to {\ell }^{+}{\ell }^{-})+Z^{*}(\to {\tau }^{+}{\tau }^{-})$ and $H\to W^{-*}(\to {\ell }^{-}{\overline{\nu }}_{\ell })+W^{+*}(\to {\tau }^{+}{\nu }_{\tau })$.

A search for the pair production of heavy leptons ($N^0,L^{\pm }$) predicted by the type-III seesaw theory formulated to explain the origin of small neutrino masses is presented. The decay channels $N^0\to W^{\pm }{l}^{\mp }$ ($\ell =e,\mu ,\tau$) and $L^{\pm }\to W^{\pm }\nu$ ($\nu ={\nu }_e,{\nu }_{\mu },{\nu }_{\tau }$) are considered. The analysis is performed using the final state that contains two leptons (electrons or muons), two jets from a hadronically decaying $W$ boson and large missing transverse momentum. The data used in the measurement correspond to an integrated luminosity of $20.3{\mathrm{fb}}^{-1}$ of $pp$ collisions at $\sqrt{s}=8\mathrm{TeV}$ collected by the ATLAS detector at the LHC. No evidence of heavy lepton pair production is observed. Heavy leptons with masses below 325–540 GeV are excluded at the 95% confidence level, depending on the theoretical scenario considered.

Exact solutions of the Dirac equation in external electromagnetic background fields are very helpful for understanding nonperturbative phenomena in quantum electrodynamics. However, for the limited set of known solutions, the field often depends on one coordinate only, which could be the time $t$, a spatial coordinate such as $x$ or $r$, or a light-cone coordinate such as $ct-x$. By swapping the roles of known and unknown quantities in the Dirac equation, we are able to generate families of solutions of the Dirac equation in the presence of genuinely space-time dependent electromagnetic fields in $1+1$ and $2+1$ dimensions.

The Schrödinger-Newton (SN) equation describes the effect of self-gravity on the evolution of a quantum system, and it has been proposed that gravitationally induced decoherence drives the system to one of the stationary solutions of the SN equation. However, the equation itself lacks a decoherence mechanism, because it does not possess any stochastic feature. In the present work we derive a stochastic modification of the Schrödinger-Newton equation, starting from the Einstein-Langevin equation in the theory of stochastic semiclassical gravity. We specialize this equation to the case of a single massive point particle, and by using Karolyhazy’s phase variance method, we derive the Diósi-Penrose criterion for the decoherence time. We obtain a (nonlinear) master equation corresponding to this stochastic SN equation. This equation is, however, linear at the level of the approximation we use to prove decoherence; hence, the no-signaling requirement is met. Lastly, we use physical arguments to obtain expressions for the decoherence length of extended objects.

It is shown that the Wilson fermion doubling phenomenon on irregular lattices (simplicial complexes) does exist. This means that the irregular (not smooth) zero or soft modes exist in the case when the “naive fermions” are introduced. The statement is proved on a four-dimensional lattice by means of the Atiyah-Singer index theorem, and then it is extended easily into the cases $D<4$. But there is a fundamental difference between doubled quanta on regular and irregular lattices: in the latter case, the propagator decreases exponentially. This means that the doubled quanta on irregular lattices are “bad” quasiparticles.

In the standard brane world models, the bulk metric ansatz is usually assumed to be factorizable in brane and bulk coordinates. However, it is not self-evident that it is always possible to factorize the bulk metric. Using the gradient expansion scheme, which involves the expansion of bulk quantities in terms of the brane-to-bulk curvature ratio as a perturbative parameter, we explicitly show that metric factorizability is a valid assumption up to second order in the perturbative expansion. We also argue from our result that the same should be true for all orders in the perturbation scheme. We further establish that the nonlocal terms present in the bulk gravitational field equation can be replaced by the radion field; the effective action on the brane thereby obtained resembles the Brans-Dicke theory of gravity.