The state space of a generic string bit model is spanned by $N\times N$ matrix creation operators acting on a vacuum state. Such creation operators transform in the adjoint representation of the color group $U(N)$ [or $SU(N)$ if the matrices are traceless]. We consider a system of $b$ species of bosonic bits and $f$ species of fermionic bits. The string, emerging in the $N\to \infty$ limit, identifies $P^{+}=mM\sqrt{2}$ where $M$ is the bit number operator and $P^{-}=H\sqrt{2}$ where $H$ is the system Hamiltonian. We study the thermal properties of this string bit system in the case $H=0$, which can be considered the tensionless string limit: the only dynamics is restricting physical states to color singlets. Then the thermal partition function $\mathrm{Tr}{e}^{-\beta mM}$ can be identified, putting $x=e^{-\beta m}$, with a generating function ${\chi }_0^{bf}(x)$, for which the coefficient of $x^n$ in its expansion about $x=0$ is the number of color singlets with bit number $M=n$. This function is a purely group theoretic object, which is well studied in the literature. We show that at $N=\infty$ this system displays a Hagedorn divergence at $x=1/(b+f)$ with ultimate temperature $T_H=m/\ln (b+f)$. The corresponding function for finite $N$ is perfectly finite for $0<x<1$, so the $N=\infty$ system exhibits a phase transition at temperature $T_H$ which is absent for any finite $N$. We demonstrate that the low temperature phase is unstable above $T_H$. The lowest-order $1/N$ asymptotic correction, for $x\to 1$ in the high temperature phase, is computed for large $N$. Remarkably, this is related to the number of labeled Eulerian digraphs with $N$ nodes. Systematic methods to extend our results to higher orders in $1/N$ are described.

We reconsider the renormalizability of topological Yang-Mills field theories in (anti-)self-dual Landau gauges. By employing algebraic renormalization techniques, we show that there is only one independent renormalization. Moreover, due to the rich set of Ward identities, we are able to obtain some important exact features of the (connected and one-particle irreducible) two-point functions. Specifically, we show that all two-point functions are tree-level exact.

In this paper we continue our program of computing Casimir self-entropies of idealized electrical bodies. Here we consider an electromagnetic $\delta$-function sphere (“semitransparent sphere”) whose electric susceptibility has a transverse polarization with arbitrary strength. Dispersion is incorporated by a plasma-like model. In the strong-coupling limit, a perfectly conducting spherical shell is realized. We compute the entropy for both low and high temperatures. The transverse electric self-entropy is negative as expected, but the transverse magnetic self-entropy requires ultraviolet and infrared renormalization (subtraction), and, surprisingly, is only positive for sufficiently strong coupling. Results are robust under different regularization schemes. These rather surprising findings require further investigation.

Recently, spin-one wave functions in four dimensions that are conformal primaries of the Lorentz group $SL(2,\mathbb{C})$ were constructed. We compute low-point, tree-level gluon scattering amplitudes in the space of these conformal primary wave functions. The answers have the same conformal covariance as correlators of spin-one primaries in a $2d$ CFT. The Britto–Cachazo–Feng–Witten (BCFW) recursion relation between three- and four-point gluon amplitudes is recast into this conformal basis.

We extend the idea of unimodular gravity to the modified $f(R,T)$ theories. A new class of cosmological solutions, that the unimodular constraint on the metric imposes on the $f(R,T)$ theories, is studied. This extension is done in both Jordan and Einstein frames. We show that while the Lagrange multiplier (that imposes the unimodular constraint on the action) depends on the cosmic time in Jordan frame and therefore, can act as an evolving scalar field in the universe history, in the Einstein frame it acts as a cosmological constant. Then a general reconstruction method is used to realize an explicit form of the unimodular $f(R,T)$ corresponding to a given cosmological solution. By adopting a specific form of $f(R,T)$, the issue of cosmological inflation is studied in this setup. To see the observational viability of this model, a numerical analysis on the model parameter space is done in the background of Planck2015 observational data.

Extending our previous studies, we perform high-resolution simulations of inspiraling binary neutron stars in numerical relativity. We thoroughly carry through a convergence study in our currently available computational resources with the smallest grid spacing of $\approx 63–86$ meter for the neutron-star radius 10.9–13.7 km. The estimated total error in the gravitational-wave phase is of order 0.1 rad for the total phase of $\gtrsim 210\mathrm{rad}$ in the last $\sim 15–16$ inspiral orbits. We then compare the waveforms (without resolution extrapolation) with those calculated by the latest effective-one-body formalism (tidal SEOBv2 model referred to as TEOB model). We find that for any of our models of binary neutron stars, the waveforms calculated by the TEOB formalism agree with the numerical-relativity waveforms up to $\approx 3\mathrm{ms}$ before the peak of the gravitational-wave amplitude is reached: For this late inspiral stage, the total phase error is $\lesssim 0.1\mathrm{rad}$. Although the gravitational waveforms have an inspiral-type feature for the last $\sim 3\mathrm{ms}$, this stage cannot be well reproduced by the current TEOB formalism, in particular, for neutron stars with large tidal deformability (i.e., lager radius). The reason for this is described.

The present work deals with the dynamical system investigation of interacting dark energy models (quintessence and phantom) in the framework of loop quantum cosmology by taking into account a broad class of self-interacting scalar field potentials. The main reason for studying potentials beyond the exponential type is to obtain additional critical points which can yield more interesting cosmological solutions. The stability of critical points and the asymptotic behavior of the phase space are analyzed using dynamical system tools and numerical techniques. We study two classes of interacting dark energy models and consider two specific potentials as examples: the hyperbolic potential and the inverse power-law potential. We find a rich and interesting phenomenology, including the avoidance of big rip singularities due to loop quantum effects, smooth and nonlinear transitions from matter domination to dark energy domination, and finite periods of phantom domination with dynamical crossing of the phantom barrier.

We explore the relationship between features in the Planck 2015 temperature and polarization data, shifts in the cosmological parameters, and features from inflation. Residuals in the temperature data from the best-fit power-law $\mathrm{\Lambda }\mathrm{CDM}$ model at low multipole $\ell \lesssim 40$ are mainly responsible for the high $H_0$ and low ${\sigma }_8{\mathrm{\Omega }}_m^{1/2}$ values when comparing the $\ell <1000$ portion to the full data set. These same residuals are better fit to inflationary features with a $1.9\sigma$ preference for running of the running of the tilt or a stronger 99% C.L. local significance preference for a sharp drop in power around $k=0.004{\mathrm{Mpc}}^{-1}$, relieving the internal tension with $H_0$. At $\ell >1000$, the same in-phase acoustic residuals that drive the global $H_0$ constraints and appear as a lensing anomaly also favor running parameters which allow even lower $H_0$, but not once lensing reconstruction is considered. Polarization spectra are intrinsically highly sensitive to these parameter shifts, and even more so in the Planck 2015 TE data due to an anomalous suppression in power at $\ell \approx 165$, which disfavors the best-fit $H_0$ $\mathrm{\Lambda }\mathrm{CDM}$ solution by more than $2\sigma$, and high $H_0$ value at almost $3\sigma$. Current polarization data also slightly enhance the significance of a sharp suppression of large-scale power but leave room for large improvements in the future with cosmic variance limited $E$-mode measurements.

In the wake of recent measurements of the decays $B_c^{+}\to J/\psi D_s^{+}$ and $B_c^{+}\to J/\psi D_s^{*+}$ performed by the LHCb and ATLAS collaborations, we recalculate their branching fractions in the framework of the covariant confined quark model. We compare the obtained results with available experimental data, our previous findings, and numbers from other approaches.

In models of composite Higgs dynamics, new composite pseudoscalars can interact with the Higgs and electroweak gauge bosons via anomalous interactions, stemming from the topological sector of the underlying theory. We show that a future 100 TeV proton-proton collider (FCC-pp) will be able to test this important sector and thus shed light on the strong dynamics which generates the Higgs and other composite states. To elucidate our results, we focus on the topological interactions of a minimal composite Higgs model with a fermionic ultraviolet completion, based on the coset $\mathrm{SU}(4)/\mathrm{Sp}(4)$. We suggest the strategy to test these interactions at the FCC-pp and analyze the expected reach.

We present results for the ratios of mean ($M_B$), variance (${\sigma }_B^2$), skewness ($S_B$) and kurtosis (${\kappa }_B$) of net baryon-number fluctuations obtained in lattice QCD calculations with physical values of light and strange quark masses. Using next-to-leading order Taylor expansions in baryon chemical potential we find that qualitative features of these ratios closely resemble the corresponding experimentally measured cumulant ratios of net proton-number fluctuations for beam energies down to $\sqrt{s_{NN}}\ge 19.6\mathrm{GeV}$. We show that the difference in cumulant ratios for the mean net baryon-number, $M_B/{\sigma }_B^2={\chi }_1^B(T,{\mu }_B)/{\chi }_2^B(T,{\mu }_B)$, and the normalized skewness, $S_B{\sigma }_B={\chi }_3^B(T,{\mu }_B)/{\chi }_2^B(T,{\mu }_B)$, naturally arises in QCD thermodynamics. Moreover, we establish a close relation between skewness and kurtosis ratios, $S_B{\sigma }_B^3/M_B={\chi }_3^B(T,{\mu }_B)/{\chi }_1^B(T,{\mu }_B)$ and ${\kappa }_B{\sigma }_B^2={\chi }_4^B(T,{\mu }_B)/{\chi }_2^B(T,{\mu }_B)$, valid at small values of the baryon chemical potential.

As an effective model corresponding to $Z_3$-symmetric QCD ($Z_3$-QCD), we construct a $Z_3$-symmetric effective Polyakov-line model ($Z_3$-EPLM) by using the logarithmic fermion effective action. Since $Z_3$-QCD tends to QCD in the zero-temperature limit, $Z_3$-EPLM also agrees with the ordinary effective Polyakov-line model (EPLM) there; note that (ordinary) EPLM does not possess $Z_3$ symmetry. Our main purpose is to discuss a sign problem appearing in $Z_3$-EPLM. The action of $Z_3$-EPLM is real when not only the Polyakov line is real but also its $Z_3$ images. This suggests that the sign problem becomes milder in $Z_3$-EPLM than in EPLM. In order to confirm this suggestion, we do lattice simulations for both EPLM and $Z_3$-EPLM by using the reweighting method with the phase quenched approximation. In the low-temperature region, the sign problem is milder in $Z_3$-EPLM than in EPLM. We also propose a new reweighting method. This makes the sign problem very weak in $Z_3$-EPLM.

The electromagnetic properties of the tetraquark state $Z_c(3900)$ are investigated in the diquark-antidiquark picture and its magnetic and quadrupole moments are extracted. To this end, the light-cone QCD sum rule in electromagnetic background field is used. The magnetic and quadrupole moments encode the spatial distributions of the charge and magnetization in the particle. The result obtained for the magnetic moment is quite large and can be measured in future experiments. We obtain a nonzero but small value for the quadrupole moment of $Z_c(3900)$ indicating a nonspherical charge distribution.

The inclusive diffractive quarkonium photoproduction in $pp$ and $pA$ collisions is investigated considering the resolved Pomeron Model to describe the diffractive interaction. We estimate the rapidity and transverse momentum distributions for the $J/\mathrm{\Psi }$, $\mathrm{\Psi }(2S)$ and $\mathrm{\Upsilon }$ photoproduction in hadronic collisions at the LHC and present our estimate for the total cross sections at the Run 2 energies. A comparison with the predictions associated to the exclusive production also is presented. Our results indicate that the inclusive diffractive production is a factor $\gtrsim 10$ smaller than the exclusive one in the kinematical range probed by the LHC.

Vector-boson scattering (VBS) processes provide particularly promising means for probing the mechanism of electroweak symmetry breaking and to search for new physics in the weak sector. In the environment of a future proton-proton collider operating at a center-of-mass energy of 100 TeV, unprecedented opportunities arise for the investigation of this important class of reactions. We highlight the prominent features of VBS processes in this energy regime and discuss how the VBS signal can be isolated in the presence of a priori large QCD backgrounds. We find excellent opportunities for the analysis of VBS reactions in a kinematic range that is inaccessible to present colliders.

We explore neutrino mass hierarchy determination and $CP$-phase measurement using the multimegaton water Cherenkov detector KM3NeT-Oscillation Research with Cosmics in the Abyss in the Mediterranean sea receiving neutrino beam from the Fermilab Long Baseline Neutrino Facility over a 6900 km baseline. We find that with the proposed beam luminosity of $1.2\times {10}^{21}$ proton on target per year, it will be possible to determine mass hierarchy at $\gtrsim 4\sigma$ confidence level within 1 year in the neutrino mode alone. A combined 1 year in neutrino and 1 year in antineutrino mode can determine hierarchy at $\gtrsim 6\sigma$ confidence level. We also find that a nonzero $CP$ phase can be detected with up to $\sim 1.8\sigma$ significance after 10 years of data taking. We explore degeneracy of neutrino oscillation parameters and uncertainties in detection efficiencies affecting the results.

A measurement of the differential cross sections for a $W$ boson produced in association with jets in the muon decay channel is presented. The measurement is based on 13 TeV proton-proton collision data corresponding to an integrated luminosity of $2.2{\mathrm{fb}}^{-1}$, recorded by the CMS detector at the LHC. The cross sections are reported as functions of jet multiplicity, jet transverse momentum $p_{\mathrm{T}}$, jet rapidity, the scalar $p_{\mathrm{T}}$ sum of the jets, and angular correlations between the muon and each jet for different jet multiplicities. The measured cross sections are in agreement with predictions that include multileg leading-order (LO) and next-to-LO matrix element calculations interfaced with parton showers, as well as a next-to-next-to-LO calculation for the $W$ boson and one jet production.

We consider various forms of action allowing us to describe a perfect fluid in the framework of general relativity. First, we consider a potential motion without pressure. Starting from an action in terms of the current density vector built similarly to the action of a single particle, we build a series of equivalent actions through various changes of variables. The results are then generalized to the cases of motion with vorticity and the presence of pressure. The obtained forms of action are compared to the previously known variants. We discuss the possibilities to use the obtained results to formulate the theories containing a description of a perfect fluid. A new form of action is proposed for mimetic gravity, which allows a motion with vorticity for mimetic matter as a perfect fluid.

The Gödel universe is a homogeneous rotating dust with negative $\mathrm{\Lambda }$ which is a direct product of a three-dimensional pure rotation metric with a line. We would generalize it to higher dimensions for Einstein and pure Lovelock gravity with only one $N$th-order term. For higher-dimensional generalization, we have to include more rotations in the metric, and hence we shall begin with the corresponding pure rotation odd $(d=2n+1)$-dimensional metric involving $n$ rotations, which eventually can be extended by a direct product with a line or a space of constant curvature for yielding a higher-dimensional Gödel universe. The considerations of $n$ rotations and also of constant curvature spaces is a new line of generalization and is being considered for the first time.

We calculate the evolution and gravitational-wave emission of a spinning compact object inspiraling into a substantially more massive (nonrotating) black hole. We extend our previous model for a nonspinning binary [Phys. Rev. D 93, 064024 (2016)] to include the Mathisson-Papapetrou-Dixon spin-curvature force. For spin-aligned binaries we calculate the dephasing of the inspiral and associated waveforms relative to models that do not include spin-curvature effects. We find this dephasing can be either positive or negative depending on the initial separation of the binary. For binaries in which the spin and orbital angular momentum are not parallel, the orbital plane precesses and we use a more general osculating element prescription to compute inspirals.