A definition of “dynamical generation,” a hotly debated topic at present, is proposed and its implications are discussed. This definition, in turn, leads to a method allowing one to distinguish, in principle, tetraquark and molecular states. The different concept of “dynamical reconstruction” is also introduced and applies to the generation of preexisting mesons (quark-antiquark, glueballs, …) via unitarization methods applied to low-energy effective Lagrangians. Large-$N_c$ arguments play an important role in all these investigations. A simple toy model with two scalar fields is introduced to elucidate these concepts. The large-$N_c$ behavior of the parameters is chosen in order that the two scalar fields behave as quark-antiquark mesons. When the heavier field is integrated out, one is left with an effective Lagrangian with the lighter field only. A unitarization method applied to the latter allows one to “reconstruct” the heavier “quarkoniumlike” field, which was previously integrated out. It is shown that a Bethe-Salpeter analysis is capable of reproducing the preformed quark-antiquark state, and that the corresponding large-$N_c$ behavior can be brought in agreement with the expected large-$N_c$ limit; this is a subtle and interesting issue on its own. However, when only the lowest term of the effective Lagrangian is retained, the large-$N_c$ limit of the reconstructed state is not reproduced: Instead of the correct large-$N_c$ quarkonium limit, it fades out as a molecular state would do. Implications of these results are presented: It is proposed that axial-vector, tensor, and (some) scalar mesons just above 1 GeV, obtained via the Bethe-Salpeter approach from the corresponding low-energy, effective Lagrangian in which only the lowest term is kept, are quarkonia states, in agreement with the constituent quark model, although they might fade away as molecular states in the large-$N_c$ limit.

The partial decay widths of positive parity baryons belonging to $\mathbf{56}$-plets of $SU(6)$ are analyzed in the framework of the $1/N_c$ expansion. The channels considered are those with emission of a single $\pi$, $K$, or $\overline{K}$ meson, and the analysis is carried out to subleading order in $1/N_c$ and to first order in $SU(3)$ symmetry breaking. The results for the multiplet $[\mathbf{56},0^{+}]$, to which the Roper resonance belongs, indicate a poor description of the widths at leading order, requiring important next to leading order corrections. For the multiplet $[\mathbf{56},2^{+}]$, the $P$ wave decays in the nonstrange sector are well described at leading order, while the $F$ wave decays require the next to leading order corrections, which turn out to be of natural magnitude. $SU(3)$ breaking effects are poorly determined, because only few decays with a $K$ meson in the final state are established, and their widths are not known with sufficient accuracy.

We develop a framework to study the exclusive two-body decays of bottomonium into two charmed mesons and apply it to study the decays of the $C$-even bottomonia. Using a sequence of effective field theories, we take advantage of the separation between the scales contributing to the decay processes, $2m_b\gg m_c\gg {\Lambda }_{\mathrm{QCD}}$. We prove that, at leading order in the EFT power counting, the decay rate factorizes into the convolution of two perturbative matching coefficients and three nonperturbative matrix elements, one for each hadron. We calculate the relations between the decay rate and nonperturbative bottomonium and $D$-meson matrix elements at leading order, with next-to-leading log resummation. The phenomenological implications of these relations are discussed.

In the type-I seesaw model the size of mixing between light and heavy neutrinos, $\nu$ and $N$, respectively, is of order the square root of their mass ratio, $(m_{\nu }/m_N{)}^{1/2}$, with only one generation of the neutrinos. Since the light-neutrino mass must be less than an eV or so, the mixing would be very small, even for a heavy-neutrino mass of order a few hundred GeV. This would make it unlikely to test the model directly at the LHC, as the amplitude for producing the heavy neutrino is proportional to the mixing size. However, it has been realized for some time that, with more than one generation of light and heavy neutrinos, the mixing can be significantly larger in certain situations. In this paper we explore this possibility further and consider specific examples in detail in the context of type-I seesaw. We study its implications for the single production of the heavy neutrinos at the LHC via the main channel $q{\overline{q}}^{\prime }\to W^{*}\to lN$ involving an ordinary charged lepton $l$. We then extend the discussion to the type-III seesaw model, which has richer phenomenology due to presence of the charged partners of the heavy neutrinos, and examine the implications for the single production of these heavy leptons at the LHC. In the latter model the new kinds of solutions that we find also make it possible to have sizable flavor-changing neutral-current effects in processes involving ordinary charged leptons.

The mechanism of electroweak symmetry breaking (EWSB) will be directly scrutinized soon at the CERN Large Hadron Collider. We analyze the LHC potential to look for new vector bosons associated with the EWSB sector, presenting a possible model independent approach to search for these new spin-1 resonances. We show that the analyses of the processes $pp\to {\ell }^{+}{\ell }^{\prime -}{\mathrm{E̸}}_T$, ${\ell }^{\pm }jj{\mathrm{E̸}}_T$, ${\ell }^{\prime \pm }{\ell }^{+}{\ell }^{-}{\mathrm{E̸}}_T$, ${\ell }^{\pm }jj{\mathrm{E̸}}_T$, and ${\ell }^{+}{\ell }^{-}jj$ (with $\ell$, ${\ell }^{\prime }=e$ or $\mu$ and $j=\mathrm{\text{jet}}$) have a large reach at the LHC and can lead to the discovery or exclusion of many EWSB scenarios such as Higgsless models.

$D_s$ mesons are investigated in a semiclassic flux tube model where the spin-orbit interaction is taken into account. Spectrum of $D$-wave $D_s$ is predicted. The predicted spectrum is much lower than most previous predictions. Analysis of some $D_s$ candidates is made. $D_{sJ}(2632{)}^{+}$ may be a $1^{-}$ $j^P={\frac{3}{2}}^{-}$ or 1 ${}^{3}D_1$) orbitally excited $D_s$ meson if it really exists. $D_{s1}(2700{)}^{\pm }$ is very possibly the first radially excited $1^{-}$ ($j^P={\frac{1}{2}}^{-}$ or 2 ${}^{3}S_1$) $D_s$ meson [the first radial excitation of $D_s^{\star \pm }(2112{)}^0$]. $D_{sJ}^{\star }(2860{)}^{+}$ should be a $3^{-}$ ($j^P={\frac{5}{2}}^{-}$ or 1 ${}^{3}D_3$) orbitally excited $D_s$ meson, and $D_{sJ}(3040{)}^{+}$ is the first radially excited $1^{+}$ ($j^P={\frac{1}{2}}^{+}$) $D_s$ meson. Our conclusions are consistent with the latest BABAR experiment.

It has recently been pointed out by Finn that the long-standing derivation of the response of an interferometric gravitational wave detector contains several errors. Here I point out that a contemporaneous derivation of the gravitational wave response for spacecraft doppler tracking and pulsar timing avoids these pitfalls, and when adapted to describe interferometers, recovers a simplified version of Finn’s derivation. This simplified derivation may be useful for pedagogical purposes.

Various Hamiltonian formulations of $f(\mathcal{R})$ gravity can be found in the literature. Some authors follow the Ostrogradsky treatment of higher derivative theories and introduce as extra variables first order time derivatives of the metric (typically the extrinsic curvature). Some others take advantage of the conformal equivalence of $f(\mathcal{R})$ theory with Einstein’s gravity coupled to a scalar field and introduce as an extra variable the scalar curvature $\mathcal{R}$ itself, which includes second time derivatives of the metric. We show that, contrarily to some claims, these formulations are related by canonical transformations.

In this paper we initiate the study of spontaneous symmetry breaking in $3+1$ dimensional rotating, charged, asymptotically AdS black holes. The theory living on their boundary, $\mathbb{R}\times S^2$, has the interpretation of a $2+1$ dimensional rotating holographic superconductor. We study the appearance of a marginal mode of the condensate as the temperature is decreased. We find that the transition temperature depends on the rotation. At temperatures just below $T_c$, the transition temperature at zero rotation, there exists a critical value of the rotation, which destroys the superconducting order. This behavior is analogous to the emergence of a critical applied magnetic field and we show that the superconductor in fact produces the expected London field in the planar limit.

We will show that the ADM $3+1$ evolution equations, for a zero shift vector, arise naturally from the equations for the second variation of arclength.

In the Palatini action of general relativity, the connection and the metric are treated as independent dynamical variables. Instead of assuming a relation between these quantities, the desired relation between them is derived through the Euler-Lagrange equations of the Palatini action. In this manuscript we construct an extended Palatini action, where we do not assume any a priori relationship between the connection, the covariant metric tensor, and the contravariant metric tensor. Instead we treat these three quantities as independent dynamical variables. We show that this action reproduces the standard Einstein field equations depending on a single metric tensor. We further show that in vacuum and in the absence of cosmological constant this theory has an enhanced symmetry.

We investigate the parameter space of two-field inflation models where inflation terminates via a first-order phase transition causing nucleation of bubbles. Such models experience a tension from the need to ensure nearly scale-invariant density perturbations, while avoiding a near scale-invariant bubble size distribution which would conflict observations. We perform an exact analysis of the different regimes of the models, where the energy density of the inflaton field ranges from being negligible as compared to the vacuum energy to providing most of the energy for inflation. Despite recent microwave anisotropy results favoring a spectral index less than 1, we find that there are still viable models that end with bubble production and can match all available observations. As a by-product of our analysis, we also provide an up-to-date assessment of the viable parameter space of Linde’s original second-order hybrid model across its full parameter range.

We study the propagation of the scalar modes around a Friedmann-Lemaître-Robertson-Walker universe for general modifications of gravity in the presence of a real scalar field. In general, there will be two propagating scalar perturbation fields, which will have in total 4 degrees of freedom. Two of these degrees will have a superluminal propagation—with $k$-dependent speed of propagation—whereas the other two will have the speed of light. Therefore, the scalar degrees of freedom do not modify the general feature of modified gravity models: the appearance of modes whose frequency depends on the second power of the modulus of the wave vector. Constraints are given and special cases are discussed.

The two kinds of indirect $CP$ violation in neutral meson systems are related, in the absence of new weak phases in decay. The result is a model-independent expression relating $CP$ violation in mixing, $CP$ violation in the interference of decays with and without mixing, and the meson mass and width differences. It relates the semileptonic and time-dependent $CP$ asymmetries, and pairs of time-dependent $CP$ asymmetries in $D^0$ decays to non-$CP$ eigenstates. $CP$ violation in the interference of decays with and without mixing is related to the mixing parameters of relevance to model building: the off-diagonal mixing matrix elements $|M_{12}|$, $|{\Gamma }_{12}|$, and ${\varphi }_{12}\equiv \arg (M_{12}/{\Gamma }_{12})$. Incorporating this relation into a fit to the $D^0-{\overline{D}}^0$ mixing data implies a level of sensitivity to $|{\varphi }_{12}^D|$ of 0.10 (rad) at $1\sigma$. The formalism is extended to include new weak phases in decay, and in ${\Gamma }_{12}$. The phases are highly constrained by direct $CP$ violation measurements. Consequently, the bounds on $|{\varphi }_{12}^D|$ are not significantly altered, and the effects of new weak phases in decay could be difficult to observe at a high luminosity flavor factory ($D^0$) or at the LHC ($B_s$) via violations of the above relations, unlike in direct $CP$ violation.

We discuss inhomogeneous ground states of the Nambu–Jona-Lasinio and quark-meson model within mean-field approximation and their possible existence in the respective phase diagrams. For this purpose we focus on lower-dimensional modulations and point out that known solutions in the $2+1$ and $1+1$ dimensional (chiral) Gross-Neveu model can be lifted to the to the $3+1$ dimensional Nambu–Jona-Lasinio model. This is worked out in detail for one-dimensional modulations and numerical results for the phase diagrams are presented. Focus is put on the critical point and on vanishing temperatures. As an interesting result the first order transition line in the phase diagram of homogeneous phases gets replaced by an inhomogeneous phase which is bordered by two second order transition lines.

It has been pointed out that the recent BABAR data on the $\pi {\gamma }^{*}\to \gamma$ transition form factor $F_{\pi \gamma }(Q^2)$ at low (high) momentum transfer squared $Q^2$ indicate an asymptotic (flat) pion distribution amplitude. These seemingly contradictory observations can be reconciled in the perturbative QCD approach based on the $k_T$ factorization theorem: the increase of the measured $Q^2{F}_{\pi \gamma }(Q^2)$ for $Q^2>10{\mathrm{GeV}}^2$ is explained by convoluting a $k_T$ dependent hard kernel with a flat pion distribution amplitude, $k_T$ being a parton transverse momentum. The low $Q^2$ data are accommodated by including the resummation of ${\alpha }_s{ln}^{2}x$, with $x$ being a parton momentum fraction, which provides a strong suppression at the end points of $x$. The next-to-leading-order correction to the pion transition form factor is found to be less than 20% in the considered range of $Q^2$.

We show that HERA data for the inclusive structure function $F_2(x,Q^2)$ at small Bjorken-$x$ and $Q^2$ can be reasonably well described by a color-dipole model with an anti-de Sitter space/conformal field theory (AdS/CFT)-inspired dipole-proton cross section. The model contains only three free parameters fitted to data. In our AdS/CFT-based parameterization the saturation scale varies in the range of $1÷3\mathrm{GeV}$ becoming independent of energy/Bjorken-$x$ at very small $x$. This leads to the prediction of $x$ independence of the $F_2$ and $F_L$ structure functions at very small $x$. We provide predictions for $F_2$ and $F_L$ in the kinematic regions of future experiments. We discuss the limitations of our approach and its applicability region, and argue that our AdS/CFT-based model of nonperturbative physics could be viewed as complementary to the perturbative description of data based on saturation/color glass condensate physics.

The exclusive reaction $\gamma p\to p{\pi }^{+}{\pi }^{-}$ was studied in the photon energy range 3.0–3.8 GeV and the momentum transfer range $0.4<-t<1.0{\mathrm{GeV}}^2$. Data were collected with the CLAS detector at the Thomas Jefferson National Accelerator Facility. In this kinematic range, the integrated luminosity was about $20{\mathrm{pb}}^{-1}$. The reaction was isolated by detecting the ${\pi }^{+}$ and proton in CLAS, and reconstructing the ${\pi }^{-}$ via the missing-mass technique. Moments of the di-pion decay angular distributions were derived from the experimental data. Differential cross sections for the $S$, $P$, and $D$-waves, in the $M_{{\pi }^{+}{\pi }^{-}}$ mass range 0.4–1.4 GeV, were derived performing a partial wave expansion of the extracted moments. Beside the dominant contribution of the $\rho (770)$ meson in the $P$-wave, evidence for the $f_0(980)$ and the $f_2(1270)$ mesons was found in the $S$ and $D$-waves, respectively. The differential production cross sections $d\sigma /dt$ for individual waves in the mass range of the above-mentioned mesons were extracted. This is the first time the $f_0(980)$ has been measured in a photoproduction experiment.

We study the foliation of a $D$-dimensional spherically symmetric black-hole spacetime with $D\ge 5$ by two kinds of one-parameter families of maximal hypersurfaces: a reflection-symmetric foliation with respect to the wormhole slot and a stationary foliation that has an infinitely long trumpetlike shape. As in the four-dimensional case, the foliations by the maximal hypersurfaces avoid the singularity irrespective of the dimensionality. This indicates that the maximal slicing condition will be useful for simulating higher-dimensional black-hole spacetimes in numerical relativity. For the case of $D=5$, we present analytic solutions of the intrinsic metric, the extrinsic curvature, the lapse function, and the shift vector for the foliation by the stationary maximal hypersurfaces. These data will be useful for checking five-dimensional numerical-relativity codes based on the moving puncture approach.

Although there is no known meaningful notion of the energy density of the gravitational field in general relativity, a few notions of quasilocal energy of gravity associated to extended but finite domains have been proposed. In this paper, the notions of quasilocal energy are studied in the framework of loop quantum gravity, in order to see whether these notions can be carried out at quantum level. Two basic quasilocal geometric quantities are quantized, which lead to well-defined operators in the kinematical Hilbert space of loop quantum gravity. We then use them as basic building blocks to construct different versions of quasilocal energy operators. The operators corresponding to Brown-York energy, Liu-Yau energy, Hawking energy, and Geroch energy are obtained, respectively. The virtue of the Geroch energy operator is that it is beneficial for us to derive a rather general entropy-area relation and thus a holographic principle from loop quantum gravity.