Motivated by recent attempts to find nontrivial infrared fixed points in 4-dimensional lattice gauge theories, we discuss the extension of the renormalization group transformations to complex coupling spaces for $O(N)$ models on $L\times L$ lattices, in the large-$N$ limit. We explain the Riemann sheet structure and singular points of the finite $L$ mappings between the mass gap and the ’t Hooft coupling. We argue that the Fisher’s zeros appear on “strings” ending approximately near these singular points. We show that for the spherical model at finite $N$ and $L$, the density of states is stripwise polynomial in the complex energy plane. We compare finite volume complex flows obtained from the rescaling of the ultraviolet cutoff in the gap equation and from the two-lattice matching. In both cases, the flows are channelled through the singular points and end at the strong coupling fixed points, however strong scheme dependence appear when the Compton wavelength of the mass gap is larger than the linear size of the system. We argue that the Fisher’s zeros control the global properties of the complex flows. We briefly discuss the implications for perturbation theory, proofs of confinement, and searches for nontrivial infrared fixed points in models beyond the standard model.

The coefficients determining the dilepton decay angular distribution of vector particles obey certain positivity constraints and a rotation-invariant identity. These relations are a direct consequence of the covariance properties of angular momentum eigenstates and are independent of the production mechanism. The Lam-Tung relation can be derived as a particular case, simply recognizing that the Drell-Yan dilepton is always produced transversely polarized with respect to one or more quantization axes. The dilepton angular distribution continues to be characterized by a frame-independent identity also when the Lam-Tung relation is violated. Moreover, the violation can be easily characterized by measuring a one-dimensional distribution depending on one shape coefficient.

We report that, unlike most inclusive quarkonium-production processes, the production rate for $pp\to J/\psi +{\rm Y}+X$ dominantly depends on two not well-known long-distance nonrelativistic QCD matrix elements, $⟨O_8^{J/\psi }({}^{3}S_1)⟩$ and $⟨O_8^{{\rm Y}}({}^{3}S_1)⟩$ at leading order in the strong coupling constant, which account for the transition probabilities of the color-octet spin-triplet heavy-quark-antiquark pairs $c{\overline{c}}_8({}^{3}S_1)\to J/\psi$ and $b{\overline{b}}_8({}^{3}S_1)\to {\rm Y}$, respectively. With the integrated luminosity $\sim 100{\mathrm{fb}}^{-1}$ at the center-of-momentum energy $\sqrt{s}=14\mathrm{TeV}$ we expect that approximately 1900 $pp\to J/\psi +{\rm Y}+X$ events can be observed at the CERN Large Hadron Collider by tagging muon pairs, which are enough to probe to the color-octet mechanism. The forthcoming measurement may provide a useful constraint to resolve the decade-old puzzle for the polarization of prompt $J/\psi$ at the Fermilab Tevatron. If corresponding measured rate is significantly less than the prediction, it may imply that the current values for the color-octet matrix elements are overestimated.

We discuss kinematical correlations between charged leptons from semileptonic decays of open charm/bottom leptons produced in the Drell-Yan mechanism as well as some other mechanisms not included so far in the literature in proton-proton scattering at Brookhaven National Laboratory (BNL) Relativistic Heavy Ion Collider (RHIC). The distributions of charm and bottom quarks/antiquarks are calculated in the framework of the $k_t$-factorization approach. For this calculation we use different unintegrated parton distributions from the literature. The hadronization of heavy quarks is done with the help of well-known fragmentation functions. Uncertainties of our predictions related to heavy quark masses, factorization, and renormalization scales as well as due to the choice of fragmentation model are also discussed. We use semileptonic decay functions found by fitting recent semileptonic data obtained by the CLEO and BABAR collaborations. The Drell-Yan processes were calculated including transverse momenta of quarks and antiquarks, using the Kwieciński parton distributions. We have also taken into consideration reactions initiated by purely QED ${\gamma }^{*}{\gamma }^{*}$ fusion in elastic and inelastic $pp$ collisions as well as a recently proposed diffractive mechanism of exclusive charm-anticharm production. The contribution of the latter mechanism is rather small. We get a good description of the dilepton invariant mass spectrum measured recently by the PHENIX Collaboration and present predictions for the dilepton pair transverse momentum distribution as well as the distribution in the azimuthal angle between electron and positron.

Two theoretical descriptions of exclusive diffractive jets and Higgs production at the LHC were implemented into the FPMC generator: the Khoze, Martin, Ryskin model and the Cudell, Hernández, Ivanov, Dechambre exclusive model. We then study the uncertainties. We compare their predictions to the CDF measurement and discuss the possibility of constraining the exclusive Higgs production at the LHC with early measurements of exclusive jets. We show that the present theoretical uncertainties can be reduced with such data by a factor of 5.

We propose a new method to determine at what transverse momenta particle production in high-energy $pp$ collisions is governed by hard parton-parton processes. Using information on the transverse spatial distribution of partons obtained from hard exclusive processes in $ep/\gamma p$ scattering, we evaluate the impact parameter distribution of $pp$ collisions with a hard parton-parton process as a function of $p_T$ of the produced parton (jet). We find that the average $pp$ impact parameters in such events depend very weakly on $p_T$ in the range $2<p_T<\mathrm{\text{few}}100\mathrm{GeV}$, while they are much smaller than those in minimum-bias inelastic collisions. The impact parameters in turn govern the observable transverse multiplicity in such events (in the direction perpendicular to the trigger particle or jet). Measuring the transverse multiplicity as a function of $p_T$ thus provides an effective tool for determining the minimum $p_T$ for which a given trigger particle originates from a hard parton-parton process. Additional tests of the proposed geometric correlations are possible by measuring the dependence on the trigger rapidity. Various strategies for implementing this method are outlined.

We propose a duality between the 2d ${\mathcal{W}}_N$ minimal models in the large $N$ ’t Hooft limit, and a family of higher spin theories on ${\mathrm{AdS}}_3$. The 2d conformal field theories (CFTs) can be described as Wess-Zumino-Witten coset models, and include, for $N=2$, the usual Virasoro unitary series. The dual bulk theory contains, in addition to the massless higher spin fields, two complex scalars (of equal mass). The mass is directly related to the ’t Hooft coupling constant of the dual CFT. We give convincing evidence that the spectra of the two theories match precisely for all values of the ’t Hooft coupling. We also show that the renormalization group flows in the 2d CFT agree exactly with the usual AdS/CFT prediction of the gravity theory. Our proposal is in many ways analogous to the Klebanov-Polyakov conjecture for an ${\mathrm{AdS}}_4$ dual for the singlet sector of large $N$ vector models.

The Polyakov loop of an operator in the antisymmetric representation in $\mathcal{N}=4$ supersymmetric Yang-Mills theory on spacial ${\mathbb{R}}^3$ is calculated, to leading order in $1/N$ and at large ’t Hooft coupling, by solving the saddle point equations of the corresponding quantum impurity model. Agreement is found with previous results from the supergravity dual, which is given by a $D5$-brane in an asymptotically ${\mathrm{AdS}}_5\times S^5$ black brane background. It is shown that the azimuth angle, at which the dual $D5$-brane wraps the $S^5$, is related to the spectral asymmetry angle in the spectral density associated with the Green’s function of the impurity fermions. Much of the calculation also applies to the Polyakov loop on spacial $S^3$ or $H^3$.

If new physics were capable of pushing the neutrino-nucleon inelastic cross section 3 orders of magnitude beyond the standard model prediction, then ultrahigh energy (UHE) neutrinos would have already been observed at neutrino observatories. We use such a constraint to reveal information on the scale of noncommutativity (NC) ${\Lambda }_{\mathrm{NC}}$ in noncommutative gauge field theories where neutrinos possess a tree-level coupling to photons in a generation-independent manner. In the energy range of interest (${10}^{10}$ to ${10}^{11}\mathrm{GeV}$), the $\theta$ expansion ($|\theta |\sim 1/{\Lambda }_{\mathrm{NC}}^2$) and, therefore, the perturbative expansion, in terms of ${\Lambda }_{\mathrm{NC}}$, retains no longer its meaningful character, forcing us to resort to those NC field theoretical frameworks involving the full $\theta$ resummation. Our numerical analysis of the contribution to the process coming from the photon exchange impeccably pins down a lower bound on ${\Lambda }_{\mathrm{NC}}$ to be as high as 900 (450) TeV, depending on the estimates for the cosmogenic neutrino flux. If, on the other hand, one considers a surprising recent result that occurred in Pierre Auger Observatory data, that UHE cosmic rays are mainly composed of highly ionized Fe nuclei, then our bounds get weaker, due to the diminished cosmic neutrino flux. Nevertheless, we show that, even for the very high fraction of heavy nuclei in primary UHE cosmic rays, our method may still yield remarkable bounds on ${\Lambda }_{\mathrm{NC}}$, typically always above 200 TeV. Albeit, in this case, one encounters a maximal value for the Fe fraction, from which any useful information on ${\Lambda }_{\mathrm{NC}}$ can be drawn, delimiting thus the applicability of our method.

I derive the distribution of energy and momentum transmitted from a fast parton to a medium of thermalized quarks, or the source term, in perturbative thermal field theory directly from the quark energy-momentum tensor. The fast parton is coupled to the medium by adding an interaction term to the Lagrangian. The thermal expectation value of the energy-momentum tensor source term is then evaluated using standard Feynman rules at finite temperature. It is found that local excitations, which are important for exciting an observable Mach cone structure, fall sharply as a function of the energy of the fast parton. This may have implications for the trigger $p_T$ dependence of measurements of azimuthal dihadron particle correlations in heavy-ion collisions. In particular, a conical emission pattern would be less likely to be observed for increasing trigger $p_T$. I show that the results presented in this paper can be generalized to more realistic modeling of fast parton propagation, such as through a time-dependent interaction term, in future studies.

We study the asymptotic behavior of the quasinormal modes (QNMs) of $w$-mode pulsations of compact stars in the high-frequency regime. We observe that both the axial and polar $w$-mode QNMs attain similar asymptotic behaviors in spite of the fact that they are described by two totally different differential equation systems. We obtain robust asymptotic formulas relating $w$-mode QNMs of different polarities and different angular momenta. To explore the physical reason underlying such similarity, we first derive a high-frequency approximation for the polar $w$-mode oscillations to unify the descriptions for both cases. Then, we develop WKB-type analyses for them and quantitatively explain the observed asymptotic behaviors for polytropic stars and quark stars. We also point out that such asymptotic behaviors for realistic stars are strongly dependent on the equation of state near the stellar surface.

We study the response of a rotating monopole detector that is coupled to a massless scalar field which is described by a nonlinear dispersion relation in flat spacetime. Since it does not seem to be possible to evaluate the response of the rotating detector analytically, we resort to numerical computations. Interestingly, unlike the case of the uniformly accelerated detector that has been considered recently, we find that defining the transition probability rate of the rotating detector poses no difficulties. Further, we show that the response of the rotating detector can be computed exactly (albeit, numerically) even when it is coupled to a field that is governed by a nonlinear dispersion relation. We also discuss the response of the rotating detector in the presence of a cylindrical boundary on which the scalar field is constrained to vanish. While superluminal dispersion relations hardly affect the standard results, we find that subluminal dispersion relations can lead to relatively large modifications.

We discuss the properties of the effective-one-body (EOB) multipolar gravitational waveform emitted by nonspinning black-hole binaries of masses $\mu$ and $M$ in the extreme-mass-ratio limit $\mu /M=\nu \ll 1$. We focus on the transition from quasicircular inspiral to plunge, merger, and ringdown. We compare the EOB waveform to a Regge-Wheeler-Zerilli waveform computed using the hyperboloidal layer method and extracted at null infinity. Because the EOB waveform keeps track analytically of most phase differences in the early inspiral, we do not allow for any arbitrary time or phase shift between the waveforms. The dynamics of the particle, common to both wave-generation formalisms, is driven by a leading-order $\mathcal{O}(\nu )$ analytically resummed radiation reaction. The EOB and the Regge-Wheeler-Zerilli waveforms have an initial dephasing of about $5\times {10}^{-4}\mathrm{rad}$ and maintain then a remarkably accurate phase coherence during the long inspiral ($\sim 33$ orbits), accumulating only about $-2\times {10}^{-3}\mathrm{rad}$ until the last stable orbit, i.e. $\Delta \varphi /\varphi \sim -5.95\times {10}^{-6}$. We obtain such accuracy without calibrating the analytically resummed EOB waveform to numerical data, which indicates the aptitude of the EOB waveform for studies concerning the Laser Interferometer Space Antenna. We then improve the behavior of the EOB waveform around merger by introducing and tuning next-to-quasicircular corrections in both the gravitational wave amplitude and phase. For each multipole we tune only four next-to-quasicircular parameters by requiring compatibility between EOB and Regge-Wheeler-Zerilli waveforms at the light ring. The resulting phase difference around the merger time is as small as $\pm 0.015\mathrm{rad}$, with a fractional amplitude agreement of 2.5%. This suggest that next-to-quasicircular corrections to the phase can be a useful ingredient in comparisons between EOB and numerical-relativity waveforms.

We study inhomogeneous solutions of a $3+1$-dimensional Einstein-Maxwell–scalar theory. Our results provide a holographic model of superconductivity in the presence of a charge density wave sourced by a modulated chemical potential. We find that below a critical temperature $T_c$ superconducting stripes develop. We show that they are thermodynamically favored over the normal state by computing the grand canonical potential. We investigate the dependence of $T_c$ on the modulation’s wave vector, which characterizes the inhomogeneity. We find that it is qualitatively similar to that expected for a weakly coupled Bardeen-Cooper-Schrieer theory, but we point out a quantitative difference. Finally, we use our solutions to compute the conductivity along the direction of the stripes.

We perform simulations of general relativistic rotating stellar core collapse and compute the gravitational waves (GWs) emitted in the core-bounce phase of three representative models via multiple techniques. The simplest technique, the quadrupole formula (QF), estimates the GW content in the spacetime from the mass-quadrupole tensor only. It is strictly valid only in the weak-field and slow-motion approximation. For the first time, we apply GW extraction methods in core collapse that are fully curvature based and valid for strongly radiating and highly relativistic sources. These techniques are not restricted to weak-field and slow-motion assumptions. We employ three extraction methods computing (i) the Newman-Penrose (NP) scalar ${\Psi }_4$, (ii) Regge-Wheeler-Zerilli-Moncrief master functions, and (iii) Cauchy-characteristic extraction (CCE) allowing for the extraction of GWs at future null infinity, where the spacetime is asymptotically flat and the GW content is unambiguously defined. The latter technique is the only one not suffering from residual gauge and finite-radius effects. All curvature-based methods suffer from strong nonlinear drifts. We employ the fixed-frequency integration technique as a high-pass waveform filter. Using the CCE results as a benchmark, we find that finite-radius NP extraction yields results that agree nearly perfectly in phase, but differ in amplitude by $\sim 1\%–7\%$ at core bounce, depending on the model. Regge-Wheeler-Zerilli-Moncrief waveforms, while, in general, agreeing in phase, contain spurious high-frequency noise of comparable amplitudes to those of the relatively weak GWs emitted in core collapse. We also find remarkably good agreement of the waveforms obtained from the QF with those obtained from CCE. The results from QF agree very well in phase and systematically underpredict peak amplitudes by $\sim 5\%–11\%$, which is comparable to the NP results and is certainly within the uncertainties associated with core collapse physics.

The CMS Collaboration at the CERN LHC has searched for the $t$-channel single top quark production using the spin correlation of the $t$-channel. The signal extraction and cross section measurement rely on the angular distribution of the charged lepton in the top quark decays, the angle between the charged lepton momentum and top spin in the top rest frame. The behavior of the angular distribution is a distinct slope for the $t$-channel single top (signal) while it is flat for the backgrounds. In this Brief Report, we investigate the contributions which this spin correlation may receive from a two-Higgs doublet model, a top-color assisted technicolor (TC2) and the noncommutative extension of the standard model.

In the heavy quark limit, a doubly heavy baryon is regarded as composed of a heavy diquark and a light quark. We establish the Bethe-Salpeter equations for the heavy diquarks and the doubly heavy baryons, respectively, to leading order in a $1/m_Q$ expansion. The Bethe-Salpeter equations are solved numerically under the covariant instantaneous approximation with the kernels containing scalar confinement and one-gluon-exchange terms. The masses for the heavy diquarks and the doubly heavy baryons are obtained, and the nonleptonic decay widths for the doubly heavy baryons emitting a pseudoscalar meson are calculated within the model.

The ${\Omega }^{-}$ has an extremely long lifetime, and is the most stable of the baryons with spin $3/2$. Therefore the ${\Omega }^{-}$ magnetic moment is very accurately known. Nevertheless, its electric quadrupole moment was never measured, although estimates exist in different formalisms. In principle, lattice QCD simulations provide at present the most appropriate way to estimate the ${\Omega }^{-}$ form factors, as function of the square of the transferred four-momentum, $Q^2$, since it describes baryon systems at the physical mass for the strange quark. However, lattice QCD form factors, and in particular $G_{E2}$, are determined at finite $Q^2$ only, and the extraction of the electric quadrupole moment, $Q_{{\Omega }^{-}}=G_{E2}(0)\frac{e}{2M_{\Omega }}$, involves an extrapolation of the numerical lattice results. In this work, we reproduce the lattice QCD data with a covariant spectator quark model for ${\Omega }^{-}$ which includes a mixture of $S$ and two $D$ states for the relative quark-diquark motion. Once the model is calibrated, it is used to determine $Q_{{\Omega }^{-}}$. Our prediction is $Q_{{\Omega }^{-}}=(0.96\pm 0.02)\times {10}^{-2}e{\mathrm{fm}}^2$ [$G_{E2}(0)=0.680\pm 0.012$].

We calculate the differential cross section for the unpolarized semi-inclusive deeply inelastic scattering process $e^{-}+N\to e^{-}+q+X$ in leading order of perturbative QCD and up to twist-4 in power corrections and study, in particular, the azimuthal asymmetry $⟨\cos 2\varphi ⟩$. The final results are expressed in terms of transverse momentum dependent parton matrix elements of the target nucleon up to twist-4. We also apply it to $e^{-}+A\to e^{-}+q+X$ and illustrate numerically the nuclear dependence of the azimuthal asymmetry $⟨\cos 2\varphi ⟩$ by using a Gaussian ansatz for the transverse momentum dependent parton matrix elements.

The Dirac nature of the gauginos (and also the Higgsinos) can be realized in $R$-symmetric supersymmetry models. In this class of models, the Dirac bino (or wino) with a small mixture of the Dirac Higgsinos is a good dark matter candidate. When the seesaw mechanism with Higgs triplet superfields is implemented to account for the neutrino masses and mixing, the leptogenesis driven by the heavy triplet decay is shown to produce not only the matter-antimatter asymmetry, but also the asymmetric relic density of the Dirac gaugino dark matter. The dark matter mass turns out to be controlled by the Yukawa couplings of the heavy Higgs triplets, and it can be naturally at the weak scale for a mild hierarchy of the Yukawa couplings.