We calculate threshold corrections to the running gauge and Yukawa couplings in the cxceptional supersymmetric standard model (${\mathrm{E}}_6\mathrm{SSM}$) and analyze the more precise and reliable mass spectra in a constrained model (${\mathrm{CE}}_6\mathrm{SSM}$). Full expressions for the corrections are provided and the implementation into a spectrum generator is described. We find a dramatic reduction in the matching scale dependency of the masses of many states and observe a significant adjustment of the correlation of low-scale physical masses and high-scale parameters. Still, in substantial regions of parameter space the mass of the lightest Higgs is compatible with the new boson discovered at the LHC and the model satisfies limits from collider searches for squark, gluinos, and $Z^{\prime }$ bosons. We study the implications for gauge coupling unification from a new dependency of the spectrum on so-called survival Higgs fields which cannot be addressed without the inclusion of the threshold corrections.

We present improved results for the $B$ and $D$ meson spectrum from lattice QCD including the effect of $u/d$, $s$ and $c$ quarks in the sea. For the $B$ mesons the highly improved staggered quark action is used for the sea and light valence quarks and nonrelativistic QCD for the $b$ quark including $\mathcal{O}({\alpha }_s)$ radiative corrections to many of the Wilson coefficients for the first time. The $D$ mesons use the highly improved staggered quark action for both valence quarks on the same sea. We find $M_{B_s}-M_B=84(2)\mathrm{MeV}$, $M_{B_s}=5.366(8)\mathrm{GeV}$, $M_{B_c}=6.278(9)\mathrm{GeV}$, $M_{D_s}=1.9697(33)\mathrm{GeV}$, and $M_{D_s}-M_D=101(3)\mathrm{MeV}$. Our results for the $B$ meson hyperfine splittings are $M_{B^{*}}-M_B=50(3)\mathrm{MeV}$, $M_{B_s^{*}}-M_{B_s}=52(3)\mathrm{MeV}$, in good agreement with existing experimental results. This demonstrates that our perturbative improvement of the nonrelativistic QCD chromomagnetic coupling works for both heavyonium and heavy-light mesons. We predict $M_{B_c^{*}}-M_{B_c}=54(3)\mathrm{MeV}$. We also present first results for the radially excited $B_c$ states as well as the orbitally excited scalar $B_{c0}^{*}$ and axial-vector $B_{c1}$ mesons.

An analysis of the pion mass and pion decay constant is performed using mixed-action lattice QCD calculations with domain-wall valence quarks on ensembles of rooted, staggered $n_f=2+1$ configurations generated by the MILC Collaboration. Calculations were performed at two lattice spacings of $b\approx 0.125\mathrm{fm}$ and $b\approx 0.09\mathrm{fm}$, at two strange quark masses, multiple light quark masses, and a number of lattice volumes. The ratios of light quark to strange quark masses are in the range $0.1\le m_l/m_s\le 0.6$, while pion masses are in the range $235\lesssim m_{\pi }\lesssim 680\mathrm{MeV}$. A two-flavor chiral perturbation theory analysis of the lattice QCD calculations constrains the Gasser-Leutwyler coefficients ${\overline{l}}_3$ and ${\overline{l}}_4$ to be ${\overline{l}}_3=4.04(40)(\genfrac{}{}{0ex}{}{73}{55})$ and ${\overline{l}}_4=4.30(51)(\genfrac{}{}{0ex}{}{84}{60})$. All systematic effects in the calculations are explored, including those from the finite lattice space-time volume, the finite lattice spacing, and the finite fifth dimension in the domain-wall quark action. A consistency is demonstrated between a chiral perturbation theory analysis at fixed lattice spacing combined with a leading order continuum extrapolation, and the mixed-action chiral perturbation theory analysis which explicitly includes the leading order discretization effects. Chiral corrections to the pion decay constant are found to give $f_{\pi }/f=1.062(26)(\genfrac{}{}{0ex}{}{42}{40})$ where $f$ is the decay constant in the chiral limit, and when combined with the experimental determination of $f_{\pi }$ results in a value of $f=122.8(3.0)(\genfrac{}{}{0ex}{}{4.6}{4.8})\mathrm{MeV}$. The most recent scale setting by the MILC Collaboration yields a postdiction of $f_{\pi }=128.2(3.6)(\genfrac{}{}{0ex}{}{4.4}{6.0})(\genfrac{}{}{0ex}{}{1.2}{3.3})\mathrm{MeV}$ at the physical pion mass. A detailed error analysis indicates that precise calculations at lighter pion masses is the single most important systematic to address to improve upon the present work.

Inspiraling supermassive black hole binary systems with high orbital eccentricity are important sources for space-based gravitational wave observatories like the Laser Interferometer Space Antenna. Eccentricity adds orbital harmonics to the Fourier transform of the gravitational wave signal, and relativistic pericenter precession leads to a three-way splitting of each harmonic peak. We study the parameter estimation accuracy for such waveforms with different initial eccentricity, using the Fisher matrix method and a Monte Carlo sampling of the initial binary orientation. The eccentricity improves the parameter estimation by breaking degeneracies between different parameters. In particular, we find that the source localization precision improves significantly for higher-mass binaries due to eccentricity. The typical sky position errors are $\sim 1\mathrm{deg}$ for a nonspinning, ${10}^7{M}_{\odot }$, equal-mass binary at redshift $z=1$, if the initial eccentricity 1 yr before merger is $e_0\sim 0.6$. Pericenter precession does not affect the source localization accuracy significantly, but it does further improve the mass and eccentricity estimation accuracy systematically by a factor of 3–10 for masses between ${10}^6{M}_{\odot }$ and ${10}^7{M}_{\odot }$ for $e_0\sim 0.3$.

We derive the axial Ward identity for lattice QCD with domain-wall fermions and from which we obtain a formula for the residual mass (45) and (46) that can be used to measure the chiral symmetry breaking due to the finite extension $N_s$ in the fifth dimension. Furthermore, we obtain an upper bound for the residual mass in lattice QCD with the optimal domain-wall fermion.

The relativistic corrections to the color-octet $J/\psi$ hadroproduction at the Tevatron and LHC are calculated up to $\mathcal{O}(v^2)$ in nonrelativistic QCD factorization frame. The short distance coefficients are obtained by matching full QCD with NRQCD results for the partonic subprocess $g+g\to J/\psi ({}^{1}S_0^{[8]},{}^{3}S_1^{[8]},{}^{3}P_J^{[8]})+g$, $q+\overline{q}\to J/\psi ({}^{1}S_0^{[8]},{}^{3}S_1^{[8]},{}^{3}P_J^{[8]})+g$ and $g+q(\overline{q})\to J/\psi ({}^{1}S_0^{[8]},{}^{3}S_1^{[8]},{}^{3}P_J^{[8]})+q(\overline{q})$. The short distance coefficient ratios of relativistic correction to leading order for color-octet states ${}^{1}S_0^{[8]}$, ${}^{3}S_1^{[8]}$, and ${}^{3}P_J^{[8]}$ at large $p_T$ are approximately $-5/6$, $-11/6$, and $-31/30$, respectively, for each subprocess, and it is $1/6$ for color-singlet state ${}^{3}S_1^{[1]}$. If the higher order long distance matrix elements are estimated through velocity scaling rule with adopting $v^2=0.23$ and the lower order long distance matrix elements are fixed, the leading order cross sections of color-octet states are reduced by about a factor of 20–40% at large $p_T$ at both the Tevatron and the LHC. Comparing with QCD radiative corrections to color-octet states, relativistic correction is ignored along with $p_T$ increasing. Using long distance matrix elements extracted from the fit to $J/\psi$ production at the Tevatron, we can find the unpolarization cross sections of $J/\psi$ production at the LHC taking into account both QCD and relativistic corrections are changed by about 20–50% of that considering only QCD corrections. These results indicate that relativistic corrections may play an important role in $J/\psi$ production at the Tevatron and the LHC.

This paper describes the performance and sensitivity to neutrino mixing parameters of a Magnetised Iron Neutrino Detector at a Neutrino Factory with a neutrino beam created from the decay of 10 GeV muons. Specifically, it is concerned with the ability of such a detector to detect muons of the opposite sign to those stored (wrong-sign muons) while suppressing contamination of the signal from the interactions of other neutrino species in the beam. A new, more realistic simulation and analysis, which improves the efficiency of this detector at low energies, has been developed using the GENIE neutrino event generator and the GEANT4 simulation toolkit. Low-energy neutrino events down to 1 GeV were selected, while reducing backgrounds to the ${10}^{-4}$ level. Signal efficiency plateaus of $\sim 60\%$ for ${\nu }_{\mu }$ and $\sim 70\%$ for ${\overline{\nu }}_{\mu }$ events were achieved starting at $\sim 5\mathrm{GeV}$. Contamination from the ${\nu }_{\mu }\to {\nu }_{\tau }$ oscillation channel was studied for the first time and was found to be at the level between 1% and 4%. Full response matrices are supplied for all the signal and background channels from 1 GeV to 10 GeV. The sensitivity of an experiment involving a Magnetised Iron Neutrino Detector detector of 100 ktons at 2000 km from the Neutrino Factory is calculated for the case of ${sin}^{2}2{\theta }_{13}\sim {10}^{-1}$. For this value of ${\theta }_{13}$, the accuracy in the measurement of the $CP$-violating phase is estimated to be $\Delta {\delta }_{CP}\sim 3°–5°$, depending on the value of ${\delta }_{CP}$, the $CP$ coverage at $5\sigma$ is 85% and the mass hierarchy would be determined with better than $5\sigma$ level for all values of ${\delta }_{CP}$.

We report a measurement of the process $\gamma {\gamma }^{*}\to {\pi }^0$ with a $759{\mathrm{fb}}^{-1}$ data sample recorded with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. The pion transition form factor, $F(Q^2)$, is measured for the kinematical region $4{\mathrm{GeV}}^2\lesssim Q^2\lesssim 40{\mathrm{GeV}}^2$, where $-Q^2$ is the invariant-mass squared of a virtual photon. The measured values of $Q^2|F(Q^2)|$ agree well with the previous measurements below $Q^2\simeq 9{\mathrm{GeV}}^2$ but do not exhibit the rapid growth in the higher $Q^2$ region seen in another recent measurement, which exceeds the asymptotic QCD expectation by as much as 50%.

Tendex and vortex fields, defined by the eigenvectors and eigenvalues of the electric and magnetic parts of the Weyl curvature tensor, form the basis of a recently developed approach to visualizing spacetime curvature. In analogy to electric and magnetic fields, these fields are coordinate-dependent. However, in a further analogy, we can form invariants from the tendex and vortex fields that are invariant under coordinate transformations, just as certain combinations of the electric and magnetic fields are invariant under coordinate transformations. We derive these invariants, and provide a simple, analytical demonstration for nonspherically symmetric slices of a Schwarzschild spacetime.

We show that the simple extension of the method of obtaining the general exact solution for the cosmological model with the exponential scalar-field potential to the case when the dust is present fails, and we discuss the reasons of this puzzling phenomenon.

In this work we explore $1+1$-dimensional $p$-wave superconductors using the probe D-brane construction. Specifically, we choose three intersecting D-brane models: D1/D5, D2/D4, and D3/D3 systems. According to the dilaton running behavior, we denote the former two systems as nonconformal models and the last system as conformal. We find that all three models are qualitatively similar in describing superconducting condensate as well as some basic features (such as the gap formation and DC superconductivity) of superconducting conductivity. There also exist some differences among the three models as far as the AC conductivity is concerned. Specifically, for D3/D3 model there is no peak at nonzero frequency for the imaginary part of the conductivity, which is present in the nonconformal models; their asymptotic behaviors are different—for D1/D5 the real part of the AC conductivity approaches one at large frequency limit, for D2/D4 it slowly goes to a certain nonzero constant smaller than one, and for D3/D3 it goes to zero. We find that the profile of the AC conductivity for the D1/D5 system is very similar to that of higher dimensional $p$-wave superconductors.

We construct matrix models for the deconfining phase transition in $SU(N)$ gauge theories, without dynamical quarks, at a nonzero temperature $T$. We generalize models with zero and one free parameter to study a model with two free parameters: besides perturbative terms $\sim T^4$, we introduce terms $\sim T^2$ and $\sim T^0$. The two $N$-dependent parameters are determined by fitting to data from numerical simulations on the lattice for the pressure, including the latent heat. Good agreement is found for the pressure in the semi quark gluon plasma, which is the region from $T_c$, the critical temperature, to about $\sim 4T_c$. Above $\sim 1.2T_c$, the pressure is a sum of a perturbative term, $\sim +T^4$, and a simple nonperturbative term, essentially just a constant times $\sim -T_c^2{T}^2$. For the pressure, the details of the matrix model only enter within a very narrow window, from $T_c$ to $\sim 1.2T_c$, whose width does not change significantly with $N$. Without further adjustment, the model also agrees well with lattice data for the ’t Hooft loop. This is notable, because in contrast to the pressure, the ’t Hooft loop is sensitive to the details of the matrix model over the entire semi quark gluon plasma. For the (renormalized) Polyakov loop, though, our results disagree sharply with those from the lattice. Matrix models provide a natural and generic explanation for why the deconfining phase transition in $SU(N)$ gauge theories is of first order not just for three, but also for four or more, colors. Lastly, we consider gauge theories where there is no strict order parameter for deconfinement, such as for a $G(2)$ gauge group. To agree with lattice measurements, in the $G(2)$ matrix model, it is essential to add terms that generate complete eigenvalue repulsion in the confining phase.

We investigated chiral symmetry and $U_A(1)$ anomaly at finite temperature by applying the functional renormalization group to the $SU(3)$ linear sigma model. Expanding the local potential around the classical fields, we derived the flow equations for the renormalization parameters. In the chiral limit, the flow equation for the chiral condensate is decoupled from the others and can be analytically solved. The Goldstone theorem is guaranteed in vacuum and at finite temperature, and the two phase transitions for the chiral and $U_A(1)$ symmetry restoration happen at the same critical temperature. In the general case with explicit chiral symmetry breaking, the two symmetries are partially and slowly restored, and the scalar and pseudoscalar meson masses are controlled by the restoration in the limit of high temperature.

It is shown that in a scale-invariant relativistic field theory, any field ${\psi }_n$ belonging to the $(j,0)$ or $(0,j)$ representations of the Lorentz group and with dimensionality $d=j+1$ is a free field. For other field types there is no value of the dimensionality that guarantees that the field is free. Conformal invariance is not used in the proof of these results, but it gives them a special interest; as already known and as shown here in the appendix, the only fields in a conformal field theory that can describe massless particles belong to the $(j,0)$ or $(0,j)$ representations of the Lorentz group and have dimensionality $d=j+1$. Hence in conformal field theories massless particles are free.

Recently, an interesting indication for a dark matter signal in the form of a narrow line, or maybe two lines and/or an internal bremsstrahlung feature, has been found in analyses of public data from the Fermi-LAT satellite detector. As recent analyses have also shown that there is little sign of extra contributions to continuum photons, it is natural to investigate leptophilic interacting massive particle models. We show that a model of radiatively generated neutrino masses may have the properties needed to explain the Fermi-LAT structure around 130 GeV. This model was proposed some 10 years ago, and predicted a clearly observable $\gamma$-ray signal in the Fermi-LAT (then GLAST) detector. Here, we update and improve that analysis, and show as an example that a right-handed neutrino of mass 135 GeV should give rise to three conspicuous effects: a broad internal bremsstrahlung bump with maximum around 120 GeV, a $2\gamma$ line around 135 GeV, and a $Z\gamma$ line at 119.6 GeV (neglected in the previous work). These features together give a good fit to the 130 GeV structure, given the present energy resolution of the Fermi-LAT data. An attractive feature of the model is that the particle physics properties are essentially fixed, once the relic density and the mass of the right-handed neutrino dark matter particle have been set. Puzzling features of the data at present are a slight displacement of the signal from the galactic center, and a needed boost factor of order 5–15. This presents interesting challenges for numerical simulations including both baryons and dark matter on scales of 100 pc, and perhaps a need to go beyond the simplest halo models. With upcoming experiments having better energy resolution, or with future Fermi-LAT data, the double-peak structure with a definite predicted ratio of the strengths of the two lines and the internal bremsstrahlung feature should be seen, if this model is correct. With the planned satellite GAMMA-400, a striking fingerprint of this dark matter candidate should then appear.

Using multiple tracers of large-scale structure allows to evade the limitations imposed by sampling variance for some parameters of interest in cosmology. We demonstrate the optimal way of carrying out a multitracer analysis in a galaxy redshift survey by considering the principal components of the shot noise matrix from two-point clustering statistics. We show how to construct two tracers that maximize the benefits of sampling variance and shot noise cancellation using optimal weights. On the basis of high-resolution $N$-body simulations of dark matter halos we apply this technique to the analysis of redshift-space distortions and demonstrate how constraints on the growth rate of structure formation can be substantially improved. The primary limitations are nonlinear effects, which cause significant biases in the method already at scales of $k<0.1h{\mathrm{Mpc}}^{-1}$, suggesting the need to develop nonlinear models of redshift-space distortions in order to extract the maximum information from future redshift surveys. Nonetheless we find gains of a factor of a few in constraints on the growth rate achievable when merely the linear regime of a galaxy survey like EUCLID is considered.

As a first step toward developing a reaction model that enables a comprehensive description of neutrino-nucleon reactions in the nucleon resonance region, we have applied for the first time a dynamical coupled-channels model, which successfully describes $\pi N$, $\gamma N\to \pi N$, $\eta N$, $\pi \pi N$, $K\Lambda$, and $K\Sigma$ reactions up to $W=2\mathrm{GeV}$, to predict the neutrino-induced meson production reactions with $\Delta S=0$ at the forward-angle limit. This has been achieved by relating the divergence of the axial current matrix elements at $Q^2=0$ to the $\pi N\to X$ reaction amplitudes through the partially conserved axial current hypothesis. We present the contributions from each of the $\pi N$, $\eta N$, $\pi \pi N$, $K\Lambda$, and $K\Sigma$ channels to the $F_2$ structure function at the $Q^2\to 0$ limit up to $W=2\mathrm{GeV}$.

We solve the Bethe-Salpeter equation for a system of a heavy quark-antiquark pair interacting with a Poincare invariant generalization of screened linear confining potential. In order to get a reliable description the Lorentz scalar confining interaction is complemented by the effective one gluon exchange. Within the presented model we reasonably reproduce all known radial excitations of the vector charmonia. We have found that $J/\Psi$ is the only charmonium left below naive quark-antiquark threshold $2m_c$, while the all excited states are situated above this threshold. We develop a method which is able to provide a solution of full four dimensional Bethe-Salpeter equation for the all excited states. We discuss the consequences of the use of the free propagators for calculation of excited states above the threshold. The Bethe-Salpeter string breaking scale $\mu \simeq 350\mathrm{MeV}$ appears to be relatively larger then the one defined in various potential models $\mu \simeq 150\mathrm{MeV}$.

We study the physics potential of the 8 TeV LHC (LHC-8) to discover, during its 2012 run, a large class of extended gauge models or extradimensional models whose low-energy behavior is well represented by an $SU(2{)}^2\otimes U(1)$ gauge structure. We analyze this class of models and find that, with a combined integrated luminosity of $40–60{\mathrm{fb}}^{-1}$ at the LHC-8, the first new Kaluza-Klein mode of the $W$ gauge boson can be discovered up to a mass of about 370–400 GeV when produced in association with a $Z$ boson.