The excitation curve of $e^{+}{e}^{-}$ annihilation into four charged pions in the $\rho (770)$ region is calculated using three existing models with $\rho$ mesons and pions in intermediate states supplemented by Feynman diagrams with the $a_1(1260)\pi$ intermediate states. A two-term phenomenological Lagrangian of the $a_1\rho \pi$ interaction is used. The mixing angle is determined by fitting the $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ cross section data of the Novosibirsk CMD-2 Collaboration and also its combination with the low-energy part of the BABAR Collaboration data. It is shown that the inclusion of the $a_1\pi$ intermediate states succeeds in obtaining a good agreement with the data on both cross section and the ${\rho }^0\to {\pi }^{+}{\pi }^{-}{\pi }^{+}{\pi }^{-}$ decay width. When moving to energies above 1 GeV, the $\rho (1450)$ and $\rho (1700)$ resonances are taken into account to get excellent agreement with the BABAR data over the full energy range up to 4.5 GeV.

In chiral models with SU(3) group structure, baryon decuplet, and octet magnetic moments are evaluated by constructing their sum rules to yield theoretical predictions. In these sum rules we exploit six experimentally known baryon magnetic moments. Sum rules for flavor components and strange form factors of the octet and decuplet magnetic moments and decuplet-to-octet transition magnetic moments are also investigated.

We study the effects of moderately strong magnetic fields on the properties of color-flavor locked color superconducting quark matter in the framework of the Nambu-Jona-Lasinio model. We find that the energy gaps, which describe the color superconducting pairing as well as the magnetization, are oscillating functions of the magnetic field. Also, we observe that the oscillations of the magnetization can be so strong that homogeneous quark matter becomes metastable for a range of parameters. We suggest that this points to the possibility of magnetic domains or other types of magnetic inhomogeneities in the quark cores of magnetars.

The most general covariant gauge fixing Lagrangian is considered for a spin-two gauge theory in the context of the Faddeev-Popov procedure. In general, five parameters characterize this gauge fixing. Certain limiting values for these parameters give rise to a spin-two propagator that is either traceless or transverse, but for no values of these parameters is this propagator simultaneously traceless and transverse. Having a traceless-transverse propagator ensures that only the physical degrees of freedom associated with the tensor field propagate, and hence it is analogous to the Landau gauge in electrodynamics. To obtain such a traceless-transverse propagator, a gauge fixing Lagrangian which is not quadratic must be employed; this sort of gauge fixing Lagrangian is not encountered in the usual Faddeev-Popov procedure. It is shown that when this nonquadratic gauge fixing Lagrangian is used, two fermionic and one bosonic ghosts arise. As a simple application we discuss the energy-momentum tensor of the gravitational field at finite temperature.

We construct $\mathrm{N}=1$ supersymmetry in $4+2$ dimensions compatible with the theoretical framework of 2T physics field theory and its gauge symmetries. The fields are arranged into $4+2$-dimensional chiral and vector supermultiplets, and their interactions are uniquely fixed by supersymmetry (SUSY) and 2T-physics gauge symmetries. Many $3+1$ spacetimes emerge from $4+2$ by gauge fixing. Gauge degrees of freedom are eliminated as one comes down from $4+2$ to $3+1$ dimensions without any remnants of Kaluza-Klein modes. In a special gauge, the remaining physical degrees of freedom, and their interactions, coincide with ordinary $\mathrm{N}=1$ supersymmetric field theory in $3+1$ dimensions. In this gauge, SUSY in $4+2$ is interpreted as superconformal symmetry $\mathrm{SU}(2,2|1)$ in $3+1$ dimensions. Furthermore, the underlying $4+2$ structure imposes some interesting restrictions on the emergent $3+1$ SUSY field theory, which could be considered as part of the predictions of 2T-physics. One of these is the absence of the troublesome renormalizable $CP$ violating $\mathrm{F}\star \mathrm{F}$ terms. This is good for curing the strong $CP$ violation problem of QCD. An additional feature is that the superpotential is required to have no dimensionful parameters. To induce phase transitions, such as SUSY or electroweak symmetry breaking, a coupling to the dilaton is needed. This suggests a common origin of phase transitions that is driven by the vacuum value of the dilaton and needs to be understood in a cosmological scenario as part of a unified theory that includes the coupling of supergravity to matter. Another interesting aspect of the proposed theory is the possibility to utilize the inherent 2T gauge symmetry to explore dual versions of the $\mathrm{N}=1$ theory in $3+1$ dimensions, such as the minimal supersymmetric standard model (MSSM) and its duals. This is expected to reveal nonperturbative aspects of ordinary 1T field theory.

Four-dimensional Yang-Mills theory formulated through an action on twistor space has a larger gauge symmetry than the usual formulation, which in previous work was shown to allow a simple gauge transformation between textbook perturbation theory and the Cachazo-Svrček-Witten rules. In this paper we study nonsupersymmetric twistor Yang-Mills theory at loop level using the background field method. For an appropriate partial quantum field gauge choice it is shown that the calculation of the effective action is equivalent to (the twistor lift of) the calculation in ordinary Yang-Mills theory in the Chalmers and Siegel formulation to all orders in perturbation theory. A direct consequence is that the twistor version of Yang-Mills theory is just as renormalizable in this particular gauge. As applications an explicit calculation of the Yang-Mills beta function and some preliminary investigations into using the formalism to calculate S-matrix elements at loop level are presented. In principle the technique described in this paper generates consistent quantum completions of the Cachazo-Svrček-Witten rules. However, by inherent limitations of the partial gauge choice employed here, this offers in its current form mainly simplifications for tree-level forestry. The method is expected to be applicable to a wide class of four-dimensional gauge theories.

We introduce a new attractor mechanism to find the entropy for spherically symmetric extremal black holes. The key ingredient is to find a two-dimensional dilaton gravity with the dilaton potential $V(\varphi )$. The condition of an attractor is given by ${\nabla }^2\varphi =V({\varphi }_0)$ and ${\overline{R}}_2=-V^{\prime }({\varphi }_0)$, and for a constant dilaton $\varphi ={\varphi }_0$, these are also used to find the location of the degenerate horizon $r=r_e$ of an extremal black hole. As a nontrivial example, we consider an extremal regular black hole obtained from the coupled system of Einstein gravity and nonlinear electrodynamics. The desired Bekenstein-Hawking entropy is successfully recovered from the generalized entropy formula combined with the 2D dilaton gravity, while the entropy function approach does not work for obtaining this entropy.

Kination dominated quintessence models of dark energy have the intriguing feature that the relic abundance of thermal cold dark matter can be significantly enhanced compared to the predictions from standard cosmology. Previous treatments of such models do not include a realistic embedding of inflationary initial conditions. We remedy this situation by constructing a viable inflationary model in which the inflaton and quintessence field are the same scalar degree of freedom. Kination domination is achieved after inflation through a strong push or “kick” of the inflaton, and sufficient reheating can be achieved depending on model parameters. This allows us to explore both model-dependent and model-independent cosmological predictions of this scenario. We find that measurements of the B-mode cosmic microwave background polarization can rule out this class of scenarios almost model independently. We also discuss other experimentally accessible signatures for this class of models.

We present the phenomenology of antisymmetric rank-2 tensor unparticle operator ${\mathcal{O}}_{\mathcal{U},\mathcal{A}}^{\mu \nu }$ with scaling dimension $d_{\mathcal{U}}$. We consider the physical effects of operator $O_{\mathcal{U},\mathcal{A}}^{\mu \nu }$ in $Z^0$ boson invisible decays $Z^0\to \mathcal{U}$, $Z^0\to b\overline{b}$ channel, the electroweak precision observable $S$ parameter, and the muon anomalous magnetic dipole moment. The $Z^0$ boson invisible decay gives a very stringent constraint in the $({\Lambda }_{\mathcal{U}},M_{\mathcal{U}})$ plane, and only small $r\equiv {\Lambda }_{\mathcal{U}}/M_{\mathcal{U}}\lesssim 0.1$ is favored, when ${\Lambda }_{\mathcal{U}}$ is order of several 100 GeV. When the phenomenological parameter $\mu$, which parameterizes the scale invariance breaking, goes to 0, the $S$ parameter and the muon $(g-2)$ diverge for $1<d_{\mathcal{U}}<2$, while for nonzero $\mu$, there will be constraints on $({\Lambda }_{\mathcal{U}},M_{\mathcal{U}})$ which are more stringent than those obtained from collider experiments.

The smallness of the 1–3 lepton mixing angle ${\theta }_{13}$ and of the neutrino mass-squared-difference ratio $\Delta m_{12}^2/\Delta m_{23}^2$ can be understood as the departure from a common limit where they both vanish. We discuss in general the conditions for realizing the mass degeneracy of a pair of neutrinos and show that the vanishing of a $CP$ violating phase is needed. We find that the discrete quaternion group $Q$ of eight elements is the simplest family symmetry which correlates the smallness of $\Delta m_{12}^2$ to the value of ${\theta }_{13}$. In such a model we predict $0.12\lesssim \sin {\theta }_{13}\lesssim 0.2$ if the ordering of the neutrino mass spectrum is normal, and $\sin {\theta }_{13}\lesssim 0.12$ if it is inverted.

If the LHC experiments discover new particles that couple to the standard model fermions, then measurements by ATLAS and CMS can contribute to our understanding of the flavor puzzles. We demonstrate this statement by investigating a scenario where extra SU(2)-singlet down-type quarks are within the LHC reach. By measuring masses, production cross sections, and relative decay rates, minimal flavor violation (MFV) can in principle be excluded. Conversely, these measurements can probe the way in which MFV applies to the new degrees of freedom. Many of our conclusions are valid in a much more general context than this specific extension of the standard model.

In the Randall-Sundrum model, setting the ratio of up- and down-quark masses $m_u/m_d\ll 1$, relevant to the strong $CP$ problem, does not require chiral symmetry or fine-tuning, due to exponential bulk fermion profiles. We point out that such geometric suppression of the mass of a fermion magnifies the masses of its corresponding Kaluza-Klein (KK) states. In this sense, these KK states act as “microscopes” for probing light quark and lepton masses. In simple realizations, this hypothesis can be testable at future colliders, like the LHC, by measuring the spectrum of level-1 KK fermions. The microscope can then provide an experimental test for the vanishing of $m_u$ in the ultraviolet, independently of nonperturbative determinations, by lattice simulations or other means, at hadronic scales. We also briefly comment on application of our microscope idea to other fermions, such as the electron and neutrinos.

We compute charmonium spectral functions in 2-flavor QCD on anisotropic lattices using the maximum entropy method. Our results suggest that the S-waves ($J/\psi$ and ${\eta }_c$) survive up to temperatures close to $2T_c$, while the P-waves (${\chi }_{c0}$ and ${\chi }_{c1}$) melt away below $1.2T_c$.

If the quantum numbers of the $X(3872)$ are $J^{PC}=1^{++}$, the measurement of its mass implies that it is either a loosely bound hadronic molecule whose constituents are a superposition of the charm mesons pairs $D^{*0}{\overline{D}}^0$ and $D^0{\overline{D}}^{*0}$ or else it is a virtual state of these charm mesons. Its binding energy is small enough that the decay width of a constituent $D^{*0}$ or ${\overline{D}}^{*0}$ has a significant effect on the line shapes of the $X$ resonance. We develop a simple approximation to the line shapes that takes into account the effect of the $D^{*0}$ width as well as inelastic scattering channels of the charm mesons. We carry out a simultaneous fit to the line shapes in the $J/\psi {\pi }^{+}{\pi }^{-}$ and $D^0{\overline{D}}^0{\pi }^0$ channels measured in the decays $B^{+}\to K^{+}+X$ by the Belle Collaboration. The best fit corresponds to the $X(3872)$ being a bound state just below the $D^{*0}{\overline{D}}^0$ threshold, but a virtual state just above the $D^{*0}{\overline{D}}^0$ threshold is not excluded.

We present an exact method to study four-quark systems based on the hyperspherical harmonics formalism. We apply it to several physical systems of interest containing two heavy and two light quarks using different quark-quark potentials. Our conclusions mark the boundaries for the possible existence of compact, nonmolecular, four-quark bound states. While $QQ\overline{n}\overline{n}$ states may be stable in nature, the stability of $Q\overline{Q}n\overline{n}$ states would imply the existence of quark correlations not taken into account by simple quark dynamical models.

We define the pion-photon transition distribution amplitudes (TDA) in a field theoretic formalism from a covariant Bethe-Salpeter approach for the determination of the bound state. We apply our formalism to the Nambu–Jona-Lasinio model, as a realistic theory of the pion. The obtained vector and axial TDAs satisfy all features required by general considerations. In particular, sum rules and the polynomiality condition are explicitly verified. We have numerically proved that the odd coefficients in the polynomiality expansion of the vector TDA vanish in the chiral limit. The role of PCAC and the presence of a pion pole are explicitly shown.

The HERMES experiment has measured the transverse polarization of $\Lambda$ and $\overline{\Lambda }$ hyperons produced inclusively in quasireal photoproduction at a positron beam energy of 27.6 GeV. The transverse polarization $P_{\mathrm{n}}^{\Lambda }$ of the $\Lambda$ hyperon is found to be positive while the observed $\overline{\Lambda }$ polarization is compatible with zero. The values averaged over the kinematic acceptance of HERMES are $P_{\mathrm{n}}^{\Lambda }=0.078\pm 0.006(\mathrm{stat})\pm 0.012(\mathrm{syst})$ and $P_{\mathrm{n}}^{\overline{\Lambda }}=-0.025\pm 0.015(\mathrm{stat})\pm 0.018(\mathrm{syst})$ for $\Lambda$ and $\overline{\Lambda }$, respectively. The dependences of $P_{\mathrm{n}}^{\Lambda }$ and $P_{\mathrm{n}}^{\overline{\Lambda }}$ on the fraction $\zeta$ of the beam’s light-cone momentum carried by the hyperon and on the hyperon’s transverse momentum $p_{\mathrm{T}}$ were investigated. The measured $\Lambda$ polarization rises linearly with $p_{\mathrm{T}}$ and exhibits a different behavior for low and high values of $\zeta$, which approximately correspond to the backward and forward regions in the center-of-mass frame of the ${\gamma }^{*}N$ reaction.

We study the dynamics of the first order phase transition in the holographic hard wall model, namely, the Polchinski-Strassler model and come to the conclusion that the phase transition is incomplete in the large N limit with the natural boundary condition. We also consider the string length corrections to both the hard wall model and Witten’s model and find that the interesting transition configuration is preserved under the ${\alpha }^{\prime }$ corrections.

The supersymmetric analog of the Goldberger-Treiman relation plays a critical role in the low energy effective theory of models in which supersymmetry is spontaneously broken in a hidden sector. The interactions that connect the hidden and visible sectors break a global symmetry, which implies that the low energy theory must be constructed consistently in inverse powers of the messenger scale. The Goldberger-Treiman relation determines the couplings of the Goldstino to the visible sector fields. These couplings are fixed by the soft supersymmetry breaking terms within a power counting scheme that is stable under radiative corrections. We describe the power counting of the low energy effective theory, first for a toy model of extended technicolor and then for the supersymmetric standard model. One implication of this work for supersymmetry phenomenology is the observation that Goldstino loops can destabilize the weak scale if the low energy theory is not constructed consistently. Another is that Goldstino loops induce all visible sector operators not forbidden by symmetries. The magnitudes of these operators are determined by the consistent power counting of the low energy effective theory.

Recent work indicates an approach to the formulation of diffeomorphism invariant quantum field theories (qft’s) on the Groenewold-Moyal plane. In this approach to the qft’s, statistics gets twisted and the $S$ matrix in the nongauge qft’s becomes independent of the noncommutativity parameter ${\theta }^{\mu \nu }$. Here we show that the noncommutative algebra has a commutative spacetime algebra as a substructure: the Poincaré, diffeomorphism and gauge groups are based on this algebra in the twisted approach as is known already from the earlier work. It is natural to base covariant derivatives for gauge and gravity fields as well on this algebra. Such an approach will, in particular, introduce no additional gauge fields as compared to the commutative case and also enable us to treat any gauge group [and not just $U(N)$]. Then classical gravity and gauge sectors are the same as those for ${\theta }^{\mu \nu }=0$, but their interactions with matter fields are sensitive to ${\theta }^{\mu \nu }$. We construct quantum noncommutative gauge theories (for arbitrary gauge groups) by requiring consistency of twisted statistics and gauge invariance. In a subsequent paper (whose results are summarized here), the locality and Lorentz invariance properties of the $S$ matrices of these theories will be analyzed, and new nontrivial effects coming from noncommutativity will be elaborated. This paper contains further developments of an earlier paper of ours and a new formulation based on its approach.