The quantum numbers $J^{PC}=1^{++}$ of the $X(3872)$ and the proximity of its mass to the $D^{*0}{\overline{D}}^0$ threshold imply that it is either a loosely bound hadronic molecule whose constituents are a superposition of $D^{*0}{\overline{D}}^0$ and $D^0{\overline{D}}^{*0}$ or it is a virtual state of charm mesons. The line shapes of the $X(3872)$ can discriminate between these two possibilities. At energies within a few MeV of the $D^{*0}{\overline{D}}^0$ threshold, the lines shapes of the $X$ produced in $B\to K$ transitions are determined by its binding energy and its width. Their normalizations are determined by a short-distance constant that is different for $B^{+}\to K^{+}$ and $B^0\to K^0$. At energies comparable to the 8 MeV splitting between the $D^{*0}{\overline{D}}^0$ and $D^{*+}{D}^{-}$ thresholds, the charged meson channels $D^{*+}{D}^{-}$ and $D^{+}{D}^{*-}$ have a significant effect on the line shapes of the $X$. We calculate the line shapes taking into account the resonant coupling between the charged and neutral $1^{++}$ channels. The line shapes and their normalizations depend on one additional scattering parameter and two additional short-distance constants associated with the $B\to K$ transitions. The line shapes of the $X$ resonance depend on its decay channel; they are different for $J/\psi {\pi }^{+}{\pi }^{-}$, $J/\psi {\pi }^{+}{\pi }^{-}{\pi }^0$, and $D^0{\overline{D}}^0{\pi }^0$. The line shapes are also different for $X$ produced in $B^{+}$ decays and in $B^0$ decays. Some conceptual errors in previous work on this problem are pointed out.

We study the transverse target spin dependence of the cross section for inclusive electron-nucleon scattering with unpolarized beam. Such dependence is absent in the one-photon exchange approximation (Christ-Lee theorem) and arises only in higher orders of the QED expansion, from the interference of one-photon and absorptive two-photon exchange amplitudes as well as from real photon emission (bremsstrahlung). We demonstrate that the transverse spin-dependent two-photon exchange cross section is free of QED infrared and collinear divergences. We argue that in DIS kinematics the transverse spin dependence should be governed by a “partonlike” mechanism in which the two-photon exchange couples mainly to a single quark. We calculate the normal spin asymmetry in an approximation where the dominant contribution arises from quark-helicity flip due to interactions with nonperturbative vacuum fields (constituent quark picture) and is proportional to the quark transversity distribution in the nucleon. Such helicity-flip processes are not significantly Sudakov-suppressed if the infrared scale for gluon emission in the photon-quark subprocess is of the order of the chiral symmetry breaking scale, ${\mu }_{\mathrm{chiral}}^2\gg {\Lambda }_{\mathrm{QCD}}^2$. We estimate the asymmetry in the kinematics of the planned Jefferson Lab Hall A experiment to be of the order ${10}^{-4}$, with different sign for proton and neutron. We also comment on the spin dependence in the limit of soft high-energy scattering.

We explore the signature of the extra dimension in the Hawking radiation in a rotating Kaluza-Klein black hole with squashed horizons. Comparing with the spherical case, we find that the rotating parameter brings richer physics. We obtain the appropriate size of the extra dimension which can enhance the Hawking radiation and may open a window to detect the extra dimensions.

It has been shown that generalized Einstein-Aether theories may lead to significant modifications to the nonrelativistic limit of the Einstein equations. In this paper we study the effect of a general class of such theories on the Solar System. We consider corrections to the gravitational potential in negative and positive powers of distance from the source. Using measurements of the perihelion shift of Mercury and time delay of radar signals to Cassini, we place constraints on these corrections. We find that a subclass of generalized Einstein-Aether theories is compatible with these constraints.

The minimal supersymmetric standard model (MSSM) is plagued by two major fine-tuning problems: the $\mu$-problem and the proton decay problem. We present a simultaneous solution to both problems within the framework of a $U(1{)}^{\prime }$-extended MSSM (UMSSM), without requiring $R$-parity conservation. We identify several classes of phenomenologically viable models and provide specific examples of $U(1{)}^{\prime }$ charge assignments. Our models generically contain either lepton number violating or baryon number violating renormalizable interactions, whose coexistence is nevertheless automatically forbidden by the new $U(1{)}^{\prime }$ gauge symmetry. The $U(1{)}^{\prime }$ symmetry also prohibits the potentially dangerous and often ignored higher-dimensional proton decay operators such as $QQQL$ and $U^c{U}^c{D}^c{E}^c$ which are still allowed by $R$-parity. Thus, under minimal assumptions, we show that once the $\mu$-problem is solved, the proton is sufficiently stable, even in the presence of a minimum set of exotics fields, as required for anomaly cancellation. Our models provide impetus for pursuing the collider phenomenology of $R$-parity violation within the UMSSM framework.

We present a theoretical study of the radiative pion photoproduction on the nucleon ($\gamma N\to \pi N{\gamma }^{\prime }$) in the $\Delta$-resonance region, with the aim to determine the magnetic dipole moment (MDM) of the ${\Delta }^{+}(1232)$. The study is done within the framework of chiral effective-field theory, where the expansion is performed (to next-to-leading order) in the $\delta$ power-counting scheme, an extension of chiral perturbation theory to the $\Delta$-resonance energy region. We present the results for the absorptive part of the $\Delta$ MDM, as well as perform a sensitivity study of the dependence of $\gamma N\to \pi N{\gamma }^{\prime }$ observables on the real part of the $\Delta$ MDM. We find that an asymmetry for circular polarization of the photon beam may provide a model-independent way to measure the $\Delta$ MDM.

The resummed differential thrust rate in $e^{+}{e}^{-}$ annihilation is calculated using soft-collinear effective theory (SCET). The resulting distribution in the two-jet region ($T\sim 1)$ is found to agree with the corresponding expression derived by the standard approach. A matching procedure to account for finite corrections at $T<1$ is then described. There are two important advantages of the SCET approach. First, SCET manifests a dynamical seesaw scale $q=p^2/Q$ in addition to the center-of-mass energy $Q$ and the jet mass scale $p\sim Q\sqrt{(1-T)}$. Thus, the resummation of logs of $p/q$ can be cleanly distinguished from the resummation of logs of $Q/p$. Second, finite parts of loop amplitudes appear in specific places in the perturbative distribution: in the matching to the hard function, at the scale $Q$, in matching to the jet function, at the scale $p$, and in matching to the soft function, at the scale $q$. This allows for a consistent merger of fixed order corrections and resummation. In particular, the total NLO $e^{+}{e}^{-}$ cross section is reproduced from these finite parts without having to perform additional infrared regulation.

The decay $b\to s\nu \overline{\nu }$ is discussed in the minimal supersymmetric standard model with general flavor mixing for squarks, at large $\tan \beta$. In this case, in addition to the chargino loop contributions which were analyzed in previous studies, $\tan \beta$-enhanced contributions from the gluino and charged Higgs boson loops might become sizable compared with the standard model contribution, at least in principle. However, it is demonstrated that the experimental bounds on the new physics contributions to the radiative decay $b\to s\gamma$ should strongly constrain these contributions to $b\to s\nu \overline{\nu }$, especially on the gluino contribution. We also briefly comment on a possible constraint from the $B_s\to {\mu }^{+}{\mu }^{-}$ decay.

The nonet symmetry scheme seems to describe rather well the masses and $\eta -{\eta }^{\prime }$ mixing angle of the ground state pseudoscalar mesons. It is expected that nonet symmetry should also be valid for the matrix elements of the pseudoscalar density operators which play an important role in charmless two-body $B$ decays with $\eta$ or ${\eta }^{\prime }$ in the final state. Starting from the divergences of the $SU(3)$ octet and singlet axial vector currents, we show that nonet symmetry for the pseudoscalar mass term implies nonet symmetry for the pseudoscalar density operators. In this nonet symmetry scheme, we find that the branching ratio $B\to PP$, $PV$ with $\eta$ in the final state agrees well with data, while those with ${\eta }^{\prime }$ are underestimated, but by increasing the $B\to {\eta }^{\prime }$ form factor by 40%–50%, one could explain the tree-dominated $B^{-}\to {\pi }^{-}{\eta }^{\prime }$ and $B^{-}\to {\rho }^{-}{\eta }^{\prime }$ measured branching ratios. With this increased form factor and with only a moderate annihilation contribution, we are able to obtain $62\times {10}^{-6}$ for the penguin-dominated $B^{-}\to K^{-}{\eta }^{\prime }$ branching ratios, quite close to the measured value. This supports the predicted value for the $B\to {\eta }^{\prime }$ form factor in PQCD and light-cone sum rules approach. A possible increase by 15% of $⟨0|\overline{s}i{\gamma }_{5}s|s\overline{s}⟩$ for ${\eta }_0$ would bring the predicted $B^{-}\to K^{-}{\eta }^{\prime }$ branching ratio to $69.375\times {10}^{-6}$, very close to experiment.

Certain exact relations among transverse momentum dependent parton distribution functions due to QCD equations of motion turn into approximate ones upon the neglect of pure twist-3 terms. On the basis of available data from HERMES, we test the practical usefulness of one such “Wandzura-Wilczek-type approximation,” namely, of that connecting $h_{1L}^{\perp (1)a}(x)$ to $h_L^a(x)$, and discuss how it can be further tested by future CLAS and COMPASS data.

The production of ($b\overline{c}$)-quarkonium (${\overline{B}}_c$ meson and its excited states) or ($c\overline{b}$)-quarkonium ($B_c$ meson and its excited states) via top quark $t$ or top antiquark $\overline{t}$ decays, $t\to (b\overline{c})+c+W^{+}$ or $\overline{t}\to (c\overline{b})+\overline{c}+W^{-}$, respectively, is studied within the framework of NRQCD. In addition to the production of the two color-singlet $S$-wave states $|(b\overline{c})({}^{1}S_0{)}_{\mathbf{1}}⟩$ or $|(c\overline{b})({}^{1}S_0{)}_{\mathbf{1}}⟩$ and $|(b\overline{c})({}^{3}S_1{)}_{\mathbf{1}}⟩$ or $|(c\overline{b})({}^{3}S_1{)}_{\mathbf{1}}⟩$, the production of the $P$-wave excited $(b\overline{c})$ or $(c\overline{b})$ states, i.e. the four color-singlet $P$-wave states $|(b\overline{c})({}^{1}P_1{)}_{\mathbf{1}}⟩$ or $|(c\overline{b})({}^{1}P_1{)}_{\mathbf{1}}⟩$, and $(b\overline{c})({}^{3}P_J{)}_{\mathbf{1}}⟩$ or $(c\overline{b})({}^{3}P_J{)}_{\mathbf{1}}⟩$ (with $J=(1,2,3)$), is also studied. According to the velocity scaling rule of NRQCD, for the production of $P$-wave excited states the contributions from the two color-octet components $|(b\overline{c})({}^{1}S_0{)}_{\mathbf{8}}⟩$ or $|(c\overline{b})({}^{1}S_0{)}_{\mathbf{8}}⟩$ and $|(b\overline{c})({}^{3}S_1{)}_{\mathbf{8}}⟩$ or $|(c\overline{b})({}^{3}S_1{)}_{\mathbf{8}}⟩$ are also taken into account. We quantitatively discuss the possibility and the advantages in experimental studies of $B_c$ or ${\overline{B}}_c$ meson and its excited states via the indirect production at LHC in high luminosity runs and at LHC possible upgraded versions such as SLHC, DLHC, TLHC, etc. in the future.

We consider modified $f(R)$ gravity which may unify $R^m$ early-time inflation with late-time $\Lambda \mathrm{CDM}$ epoch. It is shown that such a model passes the local tests (Newton law, stability of Earth-like gravitational solution, very heavy mass for additional scalar degree of freedom) and suggests the realistic alternative for general relativity. Various scenarios for the future evolution of $f(R)$ $\Lambda \mathrm{CDM}$ era are discussed.

We apply the method of Banerjee and Kulkarni [R. Banerjee and S. Kulkarni, Phys. Rev. D 77, 024018 (2008).] to provide a derivation of Hawking radiation from the Garfinkle-Horowitz-Strominger (stringy) black hole which falls in the class of the most general spherically symmetric black holes ($\sqrt{-g}\ne 1$) and also the nonextremal D1-D5 black hole using only covariant gravitational anomalies.

The Ashtekar-Barbero constraints for general relativity with fermions are derived from the Einstein-Cartan canonical theory rescaling the state functional of the gravity-spinor coupled system by the exponential of the Nieh-Yan functional. A one parameter quantization ambiguity naturally appears and can be associated with the Immirzi parameter.

We explore the properties of test-particle orbits in bumpy spacetimes—stationary, reflection-symmetric, asymptotically flat solutions of Einstein equations that have a non-Kerr (anomalous) higher-order multipole-moment structure but can be tuned arbitrarily close to the Kerr metric. Future detectors should observe gravitational waves generated during inspirals of compact objects into supermassive central bodies. If the central body deviates from the Kerr metric, this will manifest itself in the emitted waves. Here, we explore some of the features of orbits in non-Kerr spacetimes that might lead to observable signatures. As a basis for this analysis, we use a family of exact solutions proposed by Manko and Novikov which deviate from the Kerr metric in the quadrupole and higher moments, but we also compare our results to other work in the literature. We examine isolating integrals of the orbits and find that the majority of geodesic orbits have an approximate fourth constant of the motion (in addition to the energy, angular momentum, and rest mass) and the resulting orbits are triperiodic to high precision. We also find that this fourth integral can be lost for certain orbits in some oblately deformed Manko-Novikov spacetimes, leading to ergodic motion. However, compact objects will probably not end up on these chaotic orbits in nature. We compute the location of the innermost stable circular orbit (ISCO) and find that the behavior of an orbit in the approach to the ISCO can be qualitatively different depending on whether the location of the ISCO is determined by the onset of an instability in the radial or vertical direction. Finally, we compute periapsis and orbital-plane precessions for nearly circular and nearly equatorial orbits in both the strong and weak field, and discuss weak-field precessions for eccentric equatorial orbits.

We study a mechanism to produce the circular polarization of primordial gravitational waves. The circular polarization is generated during the superinflation driven by the Gauss-Bonnet term in the string-inspired cosmology. The instability in the tensor mode caused by the Gauss-Bonnet term and the parity violation due to the gravitational Chern-Simons term are the essential ingredients of the mechanism. We also discuss detectability of the produced circular polarization of gravitational waves. It turns out that the simple model of single-field inflation contradicts cosmic microwave background (CMB) observations. To circumvent this difficulty, we propose a two-field inflation model. In this two-field model, the circular polarization of gravitational waves is created in the frequency range designed by the big-bang observer (BBO) or the deci-hertz gravitational-wave observatory (DECIGO).

We study how the uncertainty in the cosmological parameters impacts on the detection of topological signals, focussing on three cubic torus universes and using three tests: the information content, the $S/N$ statistic, and the Bayesian evidence. We find, within the concordance cosmological model, that 3D torus universes with a size of $\sim 29{\mathrm{Gpc}}^3$ or larger cannot be detected. For the toroidal models that can be detected, the detection significance is primarily influenced by ${\Omega }_{\Lambda }$, which enters both in the noise amplitude due to the Integrated Sachs-Wolfe effect and in the size of the causal horizon which limits the accessible fundamental domain. On large angular scales $\ell <40$, only ${\Omega }_{\Lambda }$ significantly alters the detection for all three estimators considered here.

We discuss a general fourth-order theory of gravity on the brane. In general, the formulation of the junction conditions (except for Euler characteristics such as Gauss-Bonnet term) leads to the higher powers of the delta function and requires regularization. We suggest the way to avoid such a problem by imposing the metric and its first derivative to be regular at the brane, while the second derivative to have a kink, the third derivative of the metric to have a step function discontinuity, and no sooner as the fourth derivative of the metric to give the delta function contribution to the field equations. Alternatively, we discuss the reduction of the fourth-order gravity to the second-order theory by introducing an extra tensor field. We formulate the appropriate junction conditions on the brane. We prove the equivalence of both theories. In particular, we prove the equivalence of the junction conditions with different assumptions related to the continuity of the metric along the brane.

We analyze a toy Swiss-cheese cosmological model to study the averaging problem. In our Swiss-cheese model, the cheese is a spatially flat, matter only, Friedmann-Robertson-Walker solution (i.e., the Einstein-de Sitter model), and the holes are constructed from a Lemaître-Tolman-Bondi solution of Einstein’s equations. We study the propagation of photons in the Swiss-cheese model, and find a phenomenological homogeneous model to describe observables. Following a fitting procedure based on light-cone averages, we find that the expansion scalar is unaffected by the inhomogeneities (i.e., the phenomenological homogeneous model is the cheese model). This is because of the spherical symmetry of the model; it is unclear whether the expansion scalar will be affected by nonspherical voids. However, the light-cone average of the density as a function of redshift is affected by inhomogeneities. The effect arises because, as the universe evolves, a photon spends more and more time in the (large) voids than in the (thin) high-density structures. The phenomenological homogeneous model describing the light-cone average of the density is similar to the $\Lambda \mathrm{CDM}$ concordance model. It is interesting that, although the sole source in the Swiss-cheese model is matter, the phenomenological homogeneous model behaves as if it has a dark-energy component. Finally, we study how the equation of state of the phenomenological homogeneous model depends on the size of the inhomogeneities, and find that the equation-of-state parameters $w_0$ and $w_a$ follow a power-law dependence with a scaling exponent equal to unity. That is, the equation of state depends linearly on the distance the photon travels through voids. We conclude that, within our toy model, the holes must have a present size of about 250 Mpc to be able to mimic the concordance model.

Until recently, dynamical supersymmetry breaking seemed an exceptional phenomenon, involving chiral gauge theories with a special structure. Recently it has become clear that requiring only metastable states with broken supersymmetry leads to a far broader class of theories. In this paper, we extend these constructions still further, finding new classes which, unlike earlier theories, do not have unbroken, approximate $R$ symmetries. This allows construction of new models with low energy gauge mediation.