We study the tetraquark state with $I^G{J}^{PC}=0^{+}{1}^{-+}$ in the QCD sum rule. We exhaust all possible flavor structures by using a diquark-antidiquark construction and find that the flavor structure $(\overline{\mathbf{3}}\otimes \overline{\mathbf{6}})\oplus (\mathbf{6}\otimes \mathbf{3})$ is preferred. There are altogether four independent currents which have the quark contents $qs\overline{q}\overline{s}$. By using both the Shifman-Vainshtein-Zakharov sum rule and the finite energy sum rule, these currents lead to mass estimates around 1.8–2.1 GeV, where the uncertainty is due to the mixing of two single currents. Its possible decay modes are $S$-wave $b_1(1235)\eta$ and $b_1(1235){\eta }^{\prime }$, and $P$-wave $KK$, $\eta \eta$, $\eta {\eta }^{\prime }$, and ${\eta }^{\prime }{\eta }^{\prime }$, etc. The decay width is around 150 MeV through a rough estimation.

In a five-dimensional model with one universal extra dimension, signals for a pair of $n=1$ Kaluza-Klein excitations could be easily observed at a future $e^{+}{e}^{-}$ collider if the process in question is kinematically allowed. However, these signals would prove difficult to distinguish from those predicted in other models, such as those with an extended gauge symmetry or supersymmetry. A much better power of discrimination is provided by the fact that the same machine could also produce the $n=2$ gauge bosons ${\gamma }_2$ and $Z_2$ as resonances in fermion pair production without any upgrade in the collision energy $\sqrt{s}$. Assuming a fixed $\sqrt{s}$—as is expected at upcoming $e^{+}{e}^{-}$ machines—we investigate the role of beam radiation in helping to excite such resonances through radiative returns. We then show how these resonances could yield unambiguous signals for a universal extra dimension, if taken in conjunction with the production of $Z_1$ pairs, identified by their decays to leptons and missing transverse energy.

The set of rigidly rotating solutions to the relativistic string equation with subluminal azimuthal velocity has recently been reported by Ogawa et al. This set, together with a second set of rigidly rotating strings with superluminal azimuthal velocity, was reported in earlier papers by Burden and Tassie, and independently by Embacher. We believe the second set is also physically relevant to modelling cosmic strings. We write both sets of rigidly rotating string solutions in the aligned standard gauge and give a geometrical interpretation.

We analyze the classical moduli spaces of supersymmetric vacua of 3D $\mathcal{N}=2$ Chern-Simons quiver gauge theories. We show quite generally that the moduli space of the 3D theory always contains a baryonic branch of a parent 4D $\mathcal{N}=1$ quiver gauge theory, where the 4D baryonic branch is determined by the vector of 3D Chern-Simons levels. In particular, starting with a 4D quiver theory dual to a 3-fold singularity, for certain general choices of Chern-Simons levels this branch of the moduli space of the corresponding 3D theory is a 4-fold singularity. Our results lead to a simple general method, using existing 4D techniques, for constructing candidate 3D $\mathcal{N}=2$ superconformal Chern-Simons quivers with ${\mathrm{AdS}}_4$ gravity duals. As simple, but nontrivial, examples, we identify a family of Chern-Simons quiver gauge theories which are candidate ${\mathrm{AdS}}_4/{\mathrm{CFT}}_3$ duals to an infinite class of toric Sasaki-Einstein seven-manifolds with explicit metrics.

We discuss $2d$ duality transformations in the classical ${\mathrm{AdS}}_5\times S^5$ superstring and their effect on the integrable structure. $T$-duality along four directions in the Poincaré parametrization of ${\mathrm{AdS}}_5$ maps the bosonic part of the superstring action into itself. On the bosonic level, this duality may be understood as a symmetry of the first-order (phase space) system of equations for the coset components of the current. The associated Lax connection is invariant modulo the action of an $\mathfrak{s}\mathfrak{o}(2,4)$-automorphism. We then show that this symmetry extends to the full superstring, provided one supplements the transformation of the bosonic components of the current with a transformation on the fermionic ones. At the level of the action, this symmetry can be seen by combining the bosonic duality transformation with a similar one applied to part of the fermionic superstring coordinates. As a result, the full superstring action is mapped into itself, albeit in a different $\kappa$-symmetry gauge. One implication is that the dual model has the same superconformal symmetry group as the original one, and this may be seen as a consequence of the integrability of the superstring. The invariance of the Lax connection under the duality implies a map on the full set of conserved charges that should interchange some of the Noether (local) charges with hidden (nonlocal) ones and vice versa.

The generalized Weyl transform of index $\alpha$ is used to implement the time-slice definition of the phase space path integral yielding the Feynman kernel in the case of noncommutative quantum mechanics. As expected, this representation for the Feynman kernel is not unique but labeled by the real parameter $\alpha$. We succeed in proving that the $\alpha$-dependent contributions disappear at the limit where the time slice goes to zero. This proof of consistency turns out to be intricate because the Hamiltonian involves products of noncommuting operators originating from the noncommutativity. The antisymmetry of the matrix parametrizing the noncommutativity plays a key role in the cancellation mechanism of the $\alpha$-dependent terms.

We consider the cosmological constraints on theories in which there exists a nontrivial coupling between the dark matter sector and the sector responsible for the acceleration of the universe, in light of the most recent supernovae, large scale structure and cosmic microwave background data. For a variety of models, we show that the strength of the coupling of dark matter to a quintessence field is constrained to be less than 7% of the coupling to gravity. We also show that long-range interactions between fermionic dark matter particles mediated by a light scalar with a Yukawa coupling are constrained to be less than 5% of the strength of gravity at a distance scale of 10 Mpc. We show that all of the models we consider are quantum mechanically weakly coupled, and argue that some other models in the literature are ruled out by quantum mechanical strong coupling.

We study the impact of cosmological parameters’ uncertainties on estimates of the primordial non-Gaussianity (NG) parameter $f_{\mathrm{NL}}$ in local and equilateral models of non-Gaussianity. We show that propagating these errors increases the $f_{\mathrm{NL}}$ $1\sigma$ uncertainty by a term $\delta f_{\mathrm{NL}}^{\mathrm{local}}/f_{\mathrm{NL}}^{\mathrm{local}}\simeq 16\%$ for WMAP and $\delta f_{\mathrm{NL}}^{\mathrm{local}}/f_{\mathrm{NL}}^{\mathrm{local}}\simeq 5\%$ for Planck in the local case, whereas for equilateral configurations the correction terms are $\delta f_{\mathrm{NL}}^{\mathrm{equil}}/f_{\mathrm{NL}}^{\mathrm{equil}}\simeq 14\%$ and $\delta f_{\mathrm{NL}}^{\mathrm{equil}}/f_{\mathrm{NL}}^{\mathrm{equil}}\simeq 4\%$, respectively. If we assume for $f_{\mathrm{NL}}^{\mathrm{local}}$ a central value $⟨f_{\mathrm{NL}}^{\mathrm{local}}⟩\simeq 60$, according to recent WMAP 5-year estimates, we obtain for Planck a final correction $\Delta f_{\mathrm{NL}}^{\mathrm{local}}\simeq 3$. Although not dramatic, this correction is at the level of the expected estimator uncertainty for Planck, and should then be taken into account when quoting the significance of an eventual future detection. In current estimates of $f_{\mathrm{NL}}$ the cosmological parameters are held fixed at their best-fit values. We finally note that the impact of uncertainties in the cosmological parameters on the final $f_{\mathrm{NL}}$ error bar would become totally negligible if the parameters were allowed to vary in the analysis and then be marginalized over.

We consider the Higgs sector of multi-Higgs-doublet models in the presence of simple symmetries relating the various fields. We construct basis-invariant observables which may in principle be used to detect these symmetries for any number of doublets. A categorization of the symmetries into classes is required, which we perform in detail for the case of two and three Higgs doublets.

We consider the nuclear scattering cross section for the exciting dark matter (XDM) model. In XDM, the weakly interacting massive particles (WIMPs) couple to the standard model only via an intermediate light scalar which mixes with the Higgs: this leads to a suppression in the nuclear scattering cross section relative to models in which the WIMPs couple to the Higgs directly. We estimate this suppression factor to be of order ${10}^{-5}$. The elastic nuclear scattering cross section for XDM can also be computed directly: we perform this computation for XDM coupled to the Higgs sector of the standard model and find a spin-independent cross section in the order of $4\times {10}^{-13}\mathrm{pb}$ in the decoupling limit, which is not within the range of any near-term direct detection experiments. However, if the XDM dark sector is instead coupled to a two-Higgs-doublet model, the spin-independent nuclear scattering cross section can be enhanced by up to 4 orders of magnitude for large $\tan \beta$, which should be observable in the upcoming SuperCDMS and ton-scale xenon experiments.

The sensitivity of observables in radiative decays $\psi (2S)\to \gamma {\chi }_{c1,2}\to \gamma \gamma J/\psi$ to quadrupole (M2) admixtures in the dominant electric dipole (E1) transitions is explored. Emphasis is placed on distributions in a single angle, and several examples are given.

We investigate the possible measurement of parity-violating spin asymmetries in jet pair production in proton-proton collisions at the Brookhaven Relativistic Heavy Ion Collider (RHIC), with the goal to constrain longitudinally polarized quark and antiquark distribution functions. A measurable asymmetry could be observed in the vicinity of the massive weak $W$ boson resonance, where the parity-violating signal appears above the parity-conserving background and is enhanced by interference of the strong and electroweak production amplitudes. We discuss the potential for such measurements, perhaps the first opportunity to measure a parity-violating asymmetry in proton-proton collisions at RHIC. Sensitivity of this measurement to the polarization of down-type antiquarks is demonstrated.

We investigate the azimuthal asymmetry $v_2$ of produced pions in $pp$ and $pA$ collisions at both the Relativistic Heavy Ion Collider and CERN SPS energies. In our approach, based on the perturbative QCD parton model and the light-cone QCD-dipole formalism, the azimuthal asymmetry results from a correlation between the color-dipole orientation and the impact parameter of the collision. We introduce the color-dipole orientation within an improved Born approximation and the saturation model which satisfies available deep inelastic scattering data, showing that the azimuthal asymmetry of partons and pions is very sensitive to the choice of the model, and that it is reduced in the saturation model. We find that $v_2$ of quarks and gluons in parton-nucleus collisions have very different patterns. The azimuthal asymmetry of gluons in gluon-nucleus collisions can be negative at small transverse momentum, and can change sign and become positive at high transverse momentum. The azimuthal asymmetry of quarks in quark-nucleus collisions is positive at all values of transverse momentum. We find that the azimuthal anisotropy $v_2$ of produced pions in both $pp$ and $pA$ collisions is positive, albeit rather small.

In this paper the interaction of high energy neutrinos with weak gravitational fields is briefly explored. The form of the graviton-neutrino vertex is motivated from Lorentz and gauge invariance and the nonrelativistic interpretations of the neutrino-gravitational form factors are obtained. We comment on the renormalization conditions, the preservation of the weak equivalence principle and the definition of the neutrino mass radius. We associate the neutrino-gravitational form factors with specific angular momentum states. Based on Feynman diagrams, spin-statistics, $CP$ invariance and symmetries of the angular momentum states in the graviton-neutrino vertex, we deduce differences between the Majorana and Dirac cases. It is then proved that in spite of the theoretical differences between the two cases, as far as experiments are considered, they would be virtually indistinguishable for any space-time geometry satisfying the weak-field condition. We then calculate the transition gravitational form factors for the neutrino by evaluating the relevant Feynman diagrams at 1-loop and estimate a neutrino transition mass radius. The form factor is seen to depend on the momentum transfer very weakly. It is also seen that the neutrino transition mass radius is smaller than the typical neutrino charge radius by a couple of orders of magnitude.

Enhanced global non-Abelian symmetries at zero coupling in Yang Mills theory play an important role in diagonalizing the two-point functions of multimatrix operators. Generalized Casimirs constructed from the iterated commutator action of these enhanced symmetries resolve all the multiplicity labels of the bases of matrix operators which diagonalize the two-point function. For the case of $U(N)$ gauge theory with a single complex matrix in the adjoint of the gauge group we have a $U(N{)}^{\times 4}$ global symmetry of the scaling operator at zero coupling. Different choices of commuting sets of Casimirs, for the case of a complex matrix, lead to the restricted Schur basis previously studied in connection with string excitations of giant gravitons and the Brauer basis studied in connection with brane-antibrane systems. More generally these remarks can be extended to the diagonalization for any global symmetry group $G$. Schur-Weyl duality plays a central role in connecting the enhanced symmetries and the diagonal bases.

We investigate the construction of five-dimensional supergravity solutions that do not have any triholomorphic $U(1)$ isometries. We construct a class of solutions that in various limits of parameters reduces to many of previously constructed five-dimensional supergravity solutions based on both hyper-Kähler base spaces that can be put into a Gibbons-Hawking form and hyper-Kähler base spaces that cannot be put into a Gibbons-Hawking form. We find a new solution which is over triaxial Bianchi type IX Einstein–hyper-Kähler base space with no triholomorphic $U(1)$ symmetry. One special case of this solution corresponds to a five-dimensional solution based on Eguchi-Hanson type II geometry.

$\widehat{q}$ is the average squared transverse momentum transfer per unit length to a high-energy particle traversing a QCD medium such as a quark-gluon plasma. We find the (UV-regulated) value of $\widehat{q}$ to leading order in the weak coupling limit, ${\alpha }_{\mathrm{s}}(T)\ll 1$. We then use this value to generalize previous analytic results on the gluon bremsstrahlung and pair production rates for massless high-energy particles in a weakly coupled quark-gluon plasma, at next-to-leading logarithmic order.

In this short note, we reduce the $\mathcal{N}=6$, $U(N)\times U(N)$ Chern-Simons gauge theories to $\mathcal{N}=8$, $U(N)$ Yang-Mills gauge theories. This process corresponds to recovering the world-volume theory of $N$ D2-branes from that of $N$ M2-branes in an intermediate energy range. The supersymmetries are enhanced because in this limit the branes localize far away from the orbifold singularity. Our main scheme is exactly in accordance with Mukhi and Papageorgakis’s earlier work, although the Higgs mechanism becomes trickier in the present case. We also speculate on applying the scheme to a large class of new Bagger-Lambert models more generally.

We present a locally $N=1$ supersymmetric model of the dilaton $\phi$ and the two-form tensor (axion) $B_{\mu \nu }$ as compensators without propagation. This is a generalization of our previous model with global $N=1$ supersymmetry to local $N=1$ supersymmetry. The dilaton $\phi$ and the axion $B_{\mu \nu }$ are, respectively, absorbed into the vector $A_{\mu }$ and the three-form tensor $C_{\mu \nu \rho }$, where the latter is dual to the ordinary auxiliary field $D$ in the usual vector multiplet. With local $N=1$ supersymmetry, we have three multiplets: the multiplet of supergravity $(e_{\mu }{}^m,{\psi }_{\mu })$, linear multiplet $(B_{\mu \nu },\chi ,\phi )$, and the vector multiplet $(A_{\mu },\lambda ,C_{\mu \nu \rho })$. We find that the field strengths of $B$ and $C$ need the following particular Chern-Simons terms for consistency with local supersymmetry: $\mathcal{G}\equiv 3dB-6B\mathcal{D}\phi +3mBA+mC$ and $\mathcal{H}=4dC-6BF+4\mathcal{G}A+8C\mathcal{D}\phi -4mCA$. The newly established supergravity couplings provide the supporting evidence of the consistency of our basic system of the dilaton and axion as compensators.

We present a supersymmetric recursion relation for tree-level scattering amplitudes in $\mathcal{N}=4$ super Yang-Mills. Using this recursion relation, we prove that the tree-level $S$ matrix of the maximally supersymmetric theory is covariant under dual superconformal transformations. We further analyze the consequences that the transformation properties of the trees under this symmetry have on those of the loops. In particular, we show that the coefficients of the expansion of generic one-loop amplitudes in a basis of pseudoconformally invariant scalar box functions transform covariantly under dual superconformal symmetry, and in exactly the same way as the corresponding tree-level amplitudes.