We calculate next-to-leading-order corrections to exclusive processes in the $k_T$ factorization theorem, taking $\pi {\gamma }^{*}\to \gamma$ as an example. Partons off shell by $k_T^2$ are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the $k_T$-dependent hard kernel as their difference. The gauge invariance of the hard kernel is then proven to all orders by induction. The light-cone singularities in the $k_T$-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. This regularization introduces a factorization-scheme dependence into the hard kernel, which can be minimized in the standard way. Both the large double logarithms ${ln}^2{k}_T$ and ${ln}^{2}x$, $x$ being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function and organized by the $k_T$ resummation and the latter absorbed into a jet function and organized by the threshold resummation. The next-to-leading-order corrections are found to be only a few percent for $\pi {\gamma }^{*}\to \gamma$, if setting the factorization scale to the momentum transfer from the virtual photon.

We formulate a theory for an $N=4$ supersymmetric Yang-Mills multiplet in a nonadjoint representation $R$ of $SO(\mathcal{N})$, as an important application of our recently proposed model for $N=1$ supersymmetry. This system is obtained by dimensional reduction from an $N=1$ supersymmetric Yang-Mills multiplet in a nonadjoint representation in ten dimensions. The consistency with supersymmetry requires that a nonadjoint representation $R$ with the indices $i,j,\dots$ satisfy the three conditions ${\eta }^{ij}={\delta }^{ij}$, $(T^I{)}^{ij}=-(T^I{)}^{ji}$, and $(T^I{)}^{[ij|}(T^I{)}^{|k]l}=0$ for the metric ${\eta }^{ij}$ and the generators $T^I$, which are the same as the $N=1$ case.

We consider $\mathcal{N}=1$ supersymmetric quantum chromodynamics (SQCD) with the gauge group $\mathrm{U}(N_c)$ and $N_c+N$ quark flavors. $N_c$ flavors are massless; the corresponding squark fields develop (small) vacuum expectation values (VEVs) on the Higgs branch. Extra $N$ flavors are endowed with small (and equal) mass terms. We study this theory through its Seiberg’s dual: $\mathrm{U}(N)$ gauge theory with $N_c+N$ flavors of “dual quark” fields plus a gauge-singlet mesonic field $M$. The original theory is referred to as “quark theory” while the dual one is termed “monopole theory.” The suggested mild deformation of Seiberg’s procedure changes the dynamical regime of the monopole theory from infrared free to asymptotically free at large distances. We show that, upon condensation of the dual quarks, the dual theory supports non-Abelian flux tubes (strings). Seiberg’s duality is extended beyond purely massless states to include light states on both sides. Being interpreted in terms of the quark theory, the monopole-theory flux tubes are supposed to carry chromoelectric fields. The string junctions—confined monopole-theory monopoles—can be viewed as “constituent quarks” of the original quark theory. We interpret closed strings as glueballs of the original quark theory. Moreover, there are string configurations formed by two junctions connected by a pair of different non-Abelian strings. These can be considered as constituent quark mesons of the quark theory.

We consider a massless, minimally coupled scalar with a quartic self-interaction which is released in Bunch-Davies vacuum in the locally de Sitter background of an inflating universe. It was shown, in this system, that quantum effects can induce a temporary phase of superacceleration, causing a violation of the weak energy condition on cosmological scales. In this paper, we investigate the system’s stability by studying the behavior of linearized perturbations in the quantum-corrected effective field equation at one- and two-loop order. We show that the amplitude of the quantum-corrected mode function is reduced in time, starting from its initial classical (Bunch-Davies) value. This implies that the linear perturbations do not grow; hence, the model is stable. The decrease in the amplitude is in agreement with the system developing a positive (growing) mass squared due to quantum processes. The induced mass, however, remains perturbatively small and does not go tachyonic. This ensures the stability.

We investigate the matching of eigenvalue densities of Wilson loops in $SU(N)$ lattice gauge theory: the eigenvalue densities in $1+1$, $2+1$, and $3+1$ dimensions are nearly identical when the traces of the loops are equal. We show that the matching is present to at least second order in the strong-coupling expansion and also to second order in perturbation theory. We find that in the continuum limit there is matching at all values of the trace for bare Wilson loops. We confirm numerically that there is matching in these limits and find that there are small violations away from them. We discuss the implications for the bulk transitions and for nonanalytic gap formation at $N=\infty$ in $2+1$ and $3+1$ dimensions.

We investigate the enhancement in the $D^0{\overline{D}}^0{\pi }^0$ final state with the mass $M=3875.2\pm {0.7}_{-1.6}^{+0.3}\pm 0.8\mathrm{MeV}$ found recently by the Belle Collaboration in the $B\to K{D}^0{\overline{D}}^0{\pi }^0$ decay and test the possibility that this is yet another manifestation of the well-established resonance $X(3872)$. We perform a combined Flattè analysis of the data for the $D^0{\overline{D}}^0{\pi }^0$ mode and for the ${\pi }^{+}{\pi }^{-}J/\psi$ mode of the $X(3872)$. Only if the $X(3872)$ is a virtual state in the $D^0{\overline{D}}^{*0}$ channel do the data on the new enhancement comply with those on the $X(3872)$. In our fits, the mass distribution in the $D^0{\overline{D}}^{*0}$ mode exhibits a peak at 2–3 MeV above the $D^0{\overline{D}}^{*0}$ threshold, with a distinctive non-Breit-Wigner shape.

The flavor conversion of supernova neutrinos can lead to observable signatures related to the unknown neutrino parameters. As one of the determinants in dictating the efficiency of resonant flavor conversion, the local density profile near the Mikheyev-Smirnov-Wolfenstein (MSW) resonance in a supernova environment is, however, not so well understood. In this analysis, variable power-law functions are adopted to represent the independent local density profiles near the locations of resonance. It is shown that the uncertain matter density profile in a supernova, the possible neutrino mass hierarchies, and the undetermined 1-3 mixing angle would result in six distinct scenarios in terms of the survival probabilities of ${\nu }_e$ and ${\overline{\nu }}_e$. The feasibility of probing the undetermined neutrino mass hierarchy and the 1-3 mixing angle with the supernova neutrinos is then examined using several proposed experimental observables. Given the incomplete knowledge of the supernova matter profile, the analysis is further expanded to incorporate the Earth matter effect. The possible impact due to the choice of models, which differ in the average energy and in the luminosity of neutrinos, is also addressed in the analysis.

In this paper we study the influence of radiation reaction (RR) forces on the dynamics of centrifugally accelerated particles. It is assumed that the particles move along magnetic field lines anchored in the rotating central object. The common “bead-on-the-wire” approximation is used. The solutions are found and analyzed for cases when the form of the prescribed trajectory (rigidly rotating field line) is approximated by: (a) straight line, and (b) Archimedes spiral. Dynamics of neutral and charged particles are compared with the emphasis on the role of RR forces in the latter case. It is shown that for charged particles there exist locations of stable equilibrium. It is demonstrated that for particular initial conditions RR forces cause centripetal motion of the particles: their “falling” on the central rotating object. It is found that in the case of Archimedes spiral both neutral and charged particles can reach infinity where their motion has asymptotically force-free character. The possible importance of these processes for the acceleration of relativistic, charged particles by rotating magnetospheres in the context of the generation of nonthermal, high-energy emission of AGN and pulsars is discussed.

We study analytically the intermediate and late-time behavior of the massive scalar field in the background of static spherically symmetric brane black hole solutions. The intermediate asymptotic behavior of the scalar field reveals the dependence on the field’s parameter mass as well as the multipole moment $l$, while the late-time behavior has the power-law decay rate independent of those factors.

Inflation near a maximum of the potential is studied when nonlocal derivative operators are included in the inflaton Lagrangian. Such terms can impose additional sources of friction on the field. For an arbitrary spacetime geometry, these effects can be quantified in terms of a local field theory with a potential whose curvature around the turning point is strongly suppressed. This implies that a prolonged phase of slow-roll inflation can be achieved with potentials that are otherwise too steep to drive quasiexponential expansion. We illustrate this mechanism within the context of $p$-adic string theory.

We present a new method for computing the best approximation to a Killing vector on closed 2-surfaces that are topologically $S^2$. When solutions of Killing’s equation do not exist, this method is shown to yield results superior to those produced by existing methods. In addition, this method appears to provide a new tool for studying the horizon geometry of distorted black holes.

We study the evolution of a neutral $K$ meson prepared as an incoherent equal mixture of $K^0$ and ${\overline{K}}^0$. Denoting the density matrix by $\rho (t)=\frac{1}{2}N(t)[\mathbb{1}+\overrightarrow{\zeta }(t)·\overrightarrow{\sigma }]$, the norm of the state $N(t)$ is found to decrease monotonically from one to zero, while the magnitude of the Stokes vector $|\overrightarrow{\zeta }(t)|$ increases monotonically from zero to one. This property qualifies these observables as arrows of time. Requiring monotonic behavior of $N(t)$ for arbitrary values of ${\gamma }_L$, ${\gamma }_S$, and $\Delta m$ yields a bound on the $CP$-violating overlap $\delta =⟨K_L|K_S⟩$, which is similar to, but weaker than, the known unitarity bound. A similar requirement on $|\overrightarrow{\zeta }(t)|$ yields a new bound, ${\delta }^2<\frac{1}{2}(\frac{\Delta \gamma }{\Delta m})\sinh (\frac{3\pi }{4}\frac{\Delta \gamma }{\Delta m})$ which is particularly effective in limiting the $CP$-violating overlap in the $B^0\mathrm{\text{−}}{\overline{B}}^0$ system. We obtain the Stokes parameter ${\zeta }_3(t)$ which shows how the average strangeness of the beam evolves from zero to $\delta$. The evolution of the Stokes vector from $|\overrightarrow{\zeta }|=0$ to $|\overrightarrow{\zeta }|=1$ has a resemblance to an order parameter of a system undergoing spontaneous symmetry breaking.

We calculate the $Z$ boson propagator correction, as described by the $S$ parameter, in technicolor theories with extended technicolor interactions included. Our method is to solve the Bethe-Salpeter equation for the requisite current-current correlation functions. Our results suggest that the inclusion of extended technicolor interactions has a relatively small effect on $S$.

We consider pion interactions in an effective field theory of the narrow resonance $X(3872)$, assuming it is a weakly bound molecule of the charm mesons $D^0{\overline{D}}^{*0}$ and $D^{*0}{\overline{D}}^0$. Since the hyperfine splitting of the $D^0$ and $D^{*0}$ is only 7 MeV greater than the neutral pion mass, pions can be produced near threshold and are nonrelativistic. We show that pion exchange can be treated in perturbation theory and calculate the next-to-leading-order correction to the partial decay width $\Gamma [X\to D^0{\overline{D}}^0{\pi }^0]$.

We identify the quantum algebra of position and momentum operators for a quantum system bearing an irreducible representation of the super Poincaré algebra in the $N>1$ and $D=4$ superspace, both in the case where there are no central charges in the algebra, and when they are present. This algebra is noncommutative for the position operators. We use the properties of superprojectors acting on the superfields to construct explicit position and momentum operators satisfying the algebra. They act on the projected wave functions associated to the various supermultiplets with defined superspin present in the representation. We show that the quantum algebra associated to the massive superparticle appears in our construction and is described by a supermultiplet of superspin 0. This result generalizes the construction for $D=4$, $N=1$ reported recently. For the case $N=2$ with central charges, we present the equivalent results when the central charge and the mass are different. For the $\kappa$-symmetric case when these quantities are equal, we discuss the reduction to the physical degrees of freedom of the corresponding superparticle and the construction of the associated quantum algebra.

This paper extends and builds upon the results of [J. L. Bourjaily, arXiv:0704.0444.], in which we described how to use the tools of geometrical engineering to deform geometrically engineered grand unified models into ones with lower symmetry. This top-down unfolding has the advantage that the relative positions of singularities giving rise to the many “low-energy” matter fields are related by only a few parameters which deform the geometry of the unified model. And because the relative positions of singularities are necessary to compute the superpotential, for example, this is a framework in which the arbitrariness of geometrically engineered models can be greatly reduced. In [J. L. Bourjaily, arXiv:0704.0444.], this picture was made concrete for the case of deforming the representations of an $S{U}_5$ model into their standard model content. In this paper we continue that discussion to show how a geometrically engineered $\mathbf{16}$ of $S{O}_{10}$ can be unfolded into the standard model, and how the three families of the standard model uniquely emerge from the unfolding of a single, isolated $E_8$ singularity.

The heat kernel in curved space-time is computed to fourth order in a strict expansion in the number of covariant derivatives. The computation is made for arbitrary non-Abelian gauge and scalar fields and for the Riemann connection in the coordinate sector. The expressions obtained hold for arbitrary tensor representations of the matter field. Complete results are presented for the diagonal matrix elements and for the trace of the heat kernel operator. In addition, Chan’s formula is extended to curved space-time. As a byproduct, the bosonic effective action is also obtained to fourth order.

In this work we study the dynamics of the Universe in $f(R)=\sqrt{R^2-R_0^2}$ modified gravity with the Palatini formalism. We use data from recent observations, such as the supernova type Ia Gold sample and Supernova Legacy Survey data, the size of the baryonic acoustic peak from the Sloan Digital Sky Survey , the position of the acoustic peak from the cosmic microwave background observations, and large-scale structure formation from the 2dFGRS survey, to put constraints on the parameters of the model. To check the consistency of this action, we compare the age of old cosmological objects with the age of the Universe. In the combined analysis with all the observations, we find the parameters of the model as $R_0={6.192}_{-0.177}^{+0.167}\times H_0^2$ and ${\Omega }_m={0.278}_{-0.278}^{+0.273}$.