We study multifield tunneling using exact solutions for additive potentials. We introduce a binomial potential with noninteger powers that could be considered a generalization of the 4D Fubini instanton potential. Using scaling arguments, we show that for multifield potentials taller and wider barriers may still lead to a smaller bounce action.

The generalized spectral dimension $D_S(T)$ provides a powerful tool for comparing different approaches to quantum gravity. In this work, we apply this formalism to the classical spectral actions obtained within the framework of almost-commutative geometry. Analyzing the propagation of spin-0, spin-1 and spin-2 fields, we show that a nontrivial spectral dimension arises already at the classical level. The effective field theory interpretation of the spectral action yields plateau structures interpolating between a fixed spin-independent $D_S(T)=d_S$ for short and $D_S(T)=4$ for long diffusion times $T$. Going beyond effective field theory the spectral dimension is completely dominated by the high-momentum properties of the spectral action, yielding $D_S(T)=0$ for all spins. Our results support earlier claims that high-energy bosons do not propagate.

In general, there are differences between Lagrangian and Hamiltonian approaches at the same post-Newtonian (PN) order in a coordinate system under a coordinate gauge. They are from truncation of higher-order PN terms. They do not affect qualitative and quantitative results of the two approaches for a weak gravitational system such as the Solar System. Nevertheless, they may make the two approaches have somewhat or completely different dynamical qualitative features of integrability and nonintegrability (or order and chaos) for a strong gravitational field. Even if the two approaches have the same qualitative features, they have different quantitative results when the distances among compact objects are appropriately small. For a relativistic circular restricted three-body problem with the 1PN contribution from the circular motion of the primaries, although the two 1PN Lagrangian and Hamiltonian approaches are nonintegrable, their dynamics are somewhat nonequivalent for a small quantity of separations between the primaries when the initial conditions and other parameters are given. Particularly for comparable mass compact binaries with two arbitrary spins and spin effects restricted to the leading-order spin-orbit interaction, as an important example of extremely strong gravitational fields, the 2PN Arnowitt–Deser–Misner Lagrangian formulation is always nonintegrable and can be chaotic under some appropriate conditions because its equivalent higher-order PN canonical Hamiltonian includes many spin-spin couplings resulting in the absence of a fifth integral in a ten-dimensional phase space and is not integrable. However, the 2PN Arnowitt–Deser–Misner Hamiltonian is integrable and nonchaotic due to the presence of five constants of motion in the ten-dimensional phase space.

We consider the general scalar-tensor gravity without derivative couplings. By rescaling of the metric and reparametrization of the scalar field, the theory can be presented in different conformal frames and parametrizations. In this work we argue that while due to the freedom to transform the metric and the scalar field, the scalar field itself does not carry a physical meaning (in a generic parametrization), there are functions of the scalar field and its derivatives which remain invariant under the transformations. We put forward a scheme to construct these invariants, discuss how to formulate the theory in terms of the invariants, and show how the observables like parametrized post-Newtonian parameters and characteristics of the cosmological solutions can be neatly expressed in terms of the invariants. In particular, we describe the scalar field solutions in Friedmann-Lemaître-Robertson-Walker cosmology in Einstein and Jordan frames and explain their correspondence despite the approximate equations turning out to be linear and nonlinear in different frames.

Using a solution-generating method, we derive an exact solution of the Einstein’s field equations in five dimensions describing multiblack hole configurations. More specifically, this solution describes systems of nonextremal static black holes with Kaluza-Klein asymptotics. As expected, we find that, in general, there are conical singularities in between the Kaluza-Klein black holes that cannot be completely eliminated. Notwithstanding the presence of these conical singularities, such solutions still exhibit interesting thermodynamical properties. By choosing an appropriate set of thermodynamic variables we show that the entropy of these objects still obeys the Bekenstein-Hawking law for spaces with Kaluza-Klein asymptotics. This extends the previously known thermodynamic description of asymptotically flat spaces with conical singularities to general spaces with Kaluza-Klein asymptotics with conical singularities. Finally, we obtain a charged generalization of this multiblack hole solution in the general Einstein-Maxwell-Dilaton theory and show how to recover the extremal multiblack hole solution as a particular case.

We evaluate general-relativistic effects in the motion of stationary self-gravitating accretion disks around a Schwarzschild black hole, assuming the first post-Newtonian (1PN) approximation. There arises an integrability condition that leads to the emergence of two types of general-relativistic corrections to a Newtonian rotation curve. The well-known geometric dragging of frames accelerates rotation, but the hitherto unknown dynamic term, that reflects the disk structure, decelerates rotation. The net result can diminish the Newtonian angular velocity of rotation in a central disk zone, but the geometric dragging of frames dominates in the disk boundary zone. Both effects are nonlinear in nature, and they disappear in the limit of test fluids. Dust disks can only be geometrically dragged, while uniformly rotating gaseous disks are untouched at the 1PN order. General-relativistic contributions can strongly affect rotation periods in Keplerian motion for compact systems.

N-flation is a radiatively stable scenario for chaotic inflation in which the displacements of $N\gg 1$ axions with decay constants $f_1\le \dots \le f_N<M_P$ lead to a super-Planckian effective displacement equal to the Pythagorean sum $f_{\mathrm{Py}}$ of the $f_i$. We show that mixing in the axion kinetic term generically leads to the phenomenon of kinetic alignment, allowing for effective displacements as large as $\sqrt{N}{f}_N\ge f_{\mathrm{Py}}$, even if $f_1,\dots ,f_{N-1}$ are arbitrarily small. At the level of kinematics, the necessary alignment occurs with very high probability, because of eigenvector delocalization. We present conditions under which inflation can take place along an aligned direction. Our construction sharply reduces the challenge of realizing N-flation in string theory.

It is well known that effective potentials can be gauge dependent while their values at extrema should be gauge invariant. Unfortunately, establishing this invariance in perturbation theory is not straightforward, since contributions from arbitrarily high-order loops can be of the same size. We show in massless scalar QED that an infinite class of loops can be summed (and must be summed) to give a gauge-invariant value for the potential at its minimum. In addition, we show that the exact potential depends on both the scale at which it is calculated and the normalization of the fields, but the vacuum energy does not. Using these insights, we propose a method to extract some physical quantities from effective potentials which is self-consistent order by order in perturbation theory, including improvement with the renormalization group.

We present a point-by-point determination of the valence transversity distributions from two different types of processes: single-hadron production and dihadron production, both in semi-inclusive deep inelastic scattering and $e^{+}{e}^{-}$ annihilation. The extraction is based on some simple assumptions and does not require any parametrization. The transversity distributions obtained from Collins effect in single-hadron production and from interference effects in dihadron production are found to be compatible with each other.

We show that the experimental data on $|V_{ub}|$ in various $B$ meson decay modes suggest a possibility of $CP$-violating right-handed current in the $b\to u$ transition. Its consequences in $B\to \pi \pi ,\rho \rho ,DK$ are examined and compared with experimental results in order to clarify possible signals of the $CP$ violation in these decay modes. As a result, we find that the $CP$-violating right-handed current is consistent with current experimental data. Its signal might be discovered by precise $CP$ measurements in future experiments.

By assuming the $Z(4430)$ as a tetraquark state, we study the production of neutral $Z^0(4430)$ by antiproton-proton annihilation through the $s$ channel with the approach of an effective Lagrangian in terms of hadrons. Meanwhile, the background from the $\overline{p}p\to {\psi }^{\prime }{\pi }^0$ process through the $t$ and $u$ channels by exchanging a proton is also considered. It is found that there exists an obvious peak for the production of signal near the $Z(4430)$ threshold. Also discussed is the feasibility of searching for the neutral $Z^0(4430)$ at the PANDA detector, which will be important in promoting a better understanding of the exotic tetraquark candidate, both in theory and through experimentation.

Transition decay widths by one-pion emissions for excited heavy baryons with a single heavy (charm and bottom) quark are investigated by following the heavy-quark symmetry and its breaking effects at $\mathcal{O}(1/M)$ for a heavy-baryon mass $M$. Based on heavy-baryon effective theory, interaction Lagrangians for the heavy baryons with an axial-vector current induced by a pion are constructed. We show that the transition decay widths in several channels are related up to $\mathcal{O}(1/M)$. The results will be useful in the experimental study of excited heavy baryons.

A recent CMS search for the right-handed gauge boson $W_R$ reports an interesting deviation from the Standard Model. The search has been conducted in the $eejj$ channel and has shown a $2.8\sigma$ excess around $m_{eejj}\sim 2\mathrm{TeV}$. In this work, we explain the reported CMS excess with $\mathcal{R}$-parity violating supersymmetry. We consider resonant selectron and sneutrino production, followed by the three body decays of the neutralino and chargino via an $\mathcal{R}$-parity violating coupling. We fit the excess for slepton masses around 2 TeV. The scenario can further be tested in neutrinoless double beta decay ($0\nu \beta \beta$) experiments. GERDA Phase-II will probe a significant portion of the good-fit parameter space.

Accurate fits to $pp$ and $\overline{p}p$ cross section, data up to Tevatron energies, incorporating the constraints imposed by analyticity and unitarity, successfully predict the results of recent LHC and cosmic ray measurements and suggest that the cross sections approach a black disc limit asymptotically. The approach to the limit is, however, very slow. We present a simple geometric picture which explains these features in a natural way. A “black disc” of logarithmically growing radius is supplemented by a soft “edge” whose properties are invariant with energy. The constancy of the edge results in the prediction that the quantity $({\sigma }^{\mathrm{TOT}}-2{\sigma }^{\mathrm{El}})/\surd {\sigma }^{\mathrm{TOT}}$ approaches a constant at high energy. Using the existing fits, this prediction appears to be verified. The value of the limiting constant allows an estimate of the thickness of the edge, which turns out to be on the order of 1 fm. One thus arrives at a picture where the proton-proton scattering at lower energies is dominated by what becomes the edge, while at higher energies it is dominated by the disc. The crossover between the two regimes is only at $\surd s\ge 10\mathrm{TeV}$, accounting for the slow approach to asymptotic behavior. Some questions as to the nature of the edge are discussed.

A precision measurement of the mass difference between the $D^0$ and $D^{*0}$ mesons has been made using $316{\mathrm{pb}}^{-1}$ of $e^{+}{e}^{-}$ annihilation data taken at $\sqrt{s}=4170\mathrm{MeV}$ using the CLEO-c detector. We obtain $\mathrm{\Delta }M\equiv M(D^{*0})-M(D^0)=142.007\pm 0.015(\text{stat})\pm 0.014(\text{syst})\mathrm{MeV}$, as the average for the two decays, $D^0\to K^{-}{\pi }^{+}$ and $D^0\to K^{-}{\pi }^{+}{\pi }^{-}{\pi }^{+}$. The new measurement of $\mathrm{\Delta }M$ leads to $M(D^{*0})=2006.850\pm 0.049\mathrm{MeV}$, and the currently most precise measurement of the binding energy of the “exotic” meson X(3872) if interpreted as a $D^0{D}^{*0}$ hadronic molecule, $E_b(\mathrm{X}(3872))\equiv M(D^0{D}^{*0})-M(\mathrm{X}(3872))=3\pm 192\mathrm{keV}$.

The spectral dimension $d_s$ for high energies is calculated using the Relativistic Schrödinger Equation Analytically Continued (RSEAC) instead of the so-called Telegraph’s equation (TE), in both ultraviolet (UV) and infrared (IR) regimens. Regarding the TE, the recent literature presents difficulties related to its stochastic derivation and interpretation, advocating the use of the RSEAC to properly describe the relativistic diffusion phenomena. Taking into account that the Lorentz symmetry is broken in UV regime at Lifshitz point, we show that there exists a degeneracy in very high energies, meaning that both the RSEAC and TE correctly describe the diffusion processes at these energy scales, at least under the spectral dimension criterion. In fact, both the equations yield the same result, namely, $d_s=2$, a dimensional reduction that is compatible with several theories of quantum gravity. This result is reached even when one takes into account a cosmological model, as for example, the de Sitter universe. On the other hand, in the IR regimen, such degeneracy is lifted in favor of the approach via TE, due to the fact that only this equation provides the correct value for $d_s$, which is equal to the actual number of spacetime dimensions, i.e., $d_s=4$, while RSEAC yields $d_s=3$, so that a diffusing particle described by this method experiences a three-dimensional spacetime.

One of the fundamental hypotheses in observational cosmology is the validity of the so-called cosmic distance-duality relation. In this paper, we perform Monte Carlo simulations based on the method developed in Holanda, Gonçalves, and Alcaniz [J. Cosmol. Astropart. Phys. 06 (2012) 022] to answer the following question: what is the number of galaxy clusters observations $N_{\text{crit}}$ needed to check the validity of this relation at a given confidence level? At $2\sigma$, we find that $N_{\text{crit}}$ should be increased at least by a factor of 5 relative to the current sample size if we assume the current observational uncertainty ${\sigma }_{\text{obs}}$. Reducing this latter quantity by a factor of 2, we show that the present amount of data would be already close to the required number to check the validity of the cosmic distance-duality relation at $2\sigma$.

We consider several types of quantum critical phenomena from finite-density gauge-gravity duality which to different degrees lie outside the Landau-Ginsburg-Wilson paradigm. These include: (i) a “bifurcating” critical point, for which the order parameter remains gapped at the critical point, and thus is not driven by soft order parameter fluctuations. Rather it appears to be driven by “confinement” which arises when two fixed points annihilate and lose conformality. On the condensed side, there is an infinite tower of condensed states and the nonlinear response of the tower exhibits an infinite spiral structure; (ii) a “hybridized” critical point which can be described by a standard Landau-Ginsburg sector of order parameter fluctuations hybridized with a strongly coupled sector; (iii) a “marginal” critical point which is obtained by tuning the above two critical points to occur together and whose bosonic fluctuation spectrum coincides with that postulated to underly the “Marginal Fermi Liquid” description of the optimally doped cuprates.

We study, for $SU(2)$ Yang-Mills theories discretized on a lattice, a nonlocal topological order parameter, the center flux $z$. We show that i) well-defined topological sectors classified by ${\pi }_1(SO(3))={\mathbb{Z}}_2$ can only exist in the ordered phase of $z$; ii) depending on the dimension $2\le d\le 4$ and action chosen, the center flux exhibits a critical behavior sharing striking features with the Kosterlitz-Thouless type of transitions, although belonging to a novel universality class; and iii) such critical behavior does not depend on the temperature $T$. Yang-Mills theories can thus exist in two different continuum phases, characterized by an either topologically ordered or disordered vacuum; this reminds us of a quantum phase transition, albeit controlled by the choice of symmetries and not by a physical parameter.

We compute the renormalized vacuum polarization of a massive scalar field in the Hartle-Hawking state on ($2+1$)-dimensional rotating, spacelike stretched black hole solutions to topologically massive gravity, surrounded by a Dirichlet mirror that makes the state well defined. The Feynman propagator is written as a mode sum on the complex Riemannian section of the spacetime, and a Hadamard renormalization procedure is implemented by matching to a mode sum on the complex Riemannian section of a rotating Minkowski spacetime. No analytic continuation in the angular momentum parameter is invoked. Selected numerical results are given, demonstrating the numerical efficacy of the method. We anticipate that this method can be extended to wider classes of rotating black hole spacetimes, in particular to the Kerr spacetime in four dimensions.