Grand gauge-Higgs unification of five-dimensional SU(6) gauge theory on an orbifold $S^1/Z_2$ with localized gauge kinetic terms is discussed. The Standard Model (SM) fermions on the boundaries and some massive bulk fermions coupling to the SM fermions on the boundary are introduced. Taking the power-law running contributions from the bulk fields into account, perturbative gauge coupling unification is shown to be realized at around ${10}^{14}\mathrm{GeV}$, which is a few orders smaller than the unification scale of four-dimensional grand unified theories.

In order to understand the puzzle of the free energy of an individual quark in QCD, we explicitly construct ensembles with quark numbers $N_V\ne 0\text{mod}3$, corresponding to nonzero triality in a finite subvolume $V$ on the lattice. We first illustrate the basic idea in an effective Polyakov-loop theory for the heavy-dense limit of QCD and then extend the construction to full lattice QCD, where the electric center flux through the surface of $V$ has to be fixed at all times to account for Gauss’s law. This requires introducing discrete Fourier transforms over closed center-vortex sheets around the spatial volume $V$ between all subsequent time slices and generalizes the construction of ’t Hooft’s electric fluxes in the purge gauge theory. We derive this same result from a dualization of the Wilson fermion action and from the transfer-matrix formulation with a local ${\mathbb{Z}}_3$-Gauss law to restrict the dynamics to sectors with the required center charge in $V$.

We study the 2+1-dimensional XY model at nonzero chemical potential $\mu$ on deformed integration manifolds, with the aim of alleviating its sign problem. We investigate several proposals for the deformations and considerably improve on the severity of the sign problem with respect to standard reweighting approaches. We present numerical evidence that the reduction of the sign problem is exponential both in ${\mu }^2$ and in the spatial volume. We also present a new approach to the optimization procedure based on reweighting that sensibly reduces its computational cost.

The universal fragmentation functions of gluon into the flavored quarkonia $B_c$ and (polarized) $B_c^{*}$ are computed within NRQCD factorization framework at the lowest order in velocity expansion and strong coupling constant. It is mandatory to invoke the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi renormalization program to render the NRQCD short-distance coefficients UV finite in a pointwise manner. The calculation is facilitated with the sector decomposition method, with the final results presented with high numerical accuracy. This knowledge is useful to enrich our understanding toward the large-$p_T$ behavior of $B_c^{(*)}$ production at LHC experiment.

We develop a model for the production of the $P_c$ states observed at LHCb in ${\mathrm{\Lambda }}_b\to J/\psi p{K}^{-}$ decays. With fewer parameters than other approaches, we obtain excellent fits to the $J/\psi p$ invariant mass spectrum, capturing both the prominent peaks, and broader features over the full range of invariant mass. A distinguishing feature of our model is that whereas $P_c(4312)$, $P_c(4380)$, and $P_c(4440)$ are resonances with ${\mathrm{\Sigma }}_c^{(*)}{\overline{D}}^{(*)}$ constituents, the nature of $P_c(4457)$ is quite different, and can be understood either as a ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ threshold cusp, a ${\mathrm{\Lambda }}_c(2595)\overline{D}$ enhancement due to the triangle singularity, or a ${\mathrm{\Lambda }}_c(2595)\overline{D}$ resonance. We propose experimental measurements that can discriminate among these possibilities. Unlike in other models, our production mechanism respects isospin symmetry and the empirical dominance of color-enhanced processes in weak decays, and additionally gives a natural explanation for the overall shape of the data. Our model is consistent with experimental constraints from photoproduction and ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c{\overline{D}}^{(*)0}{K}^{-}$ decays and it does not imply the existence of partner states whose apparent absence in experiments is unexplained in other models.

Inspired by the updated information on $\mathrm{\Omega }(2012)$ by the Belle Collaboration, we conduct a study of all possible $S$-wave pentaquark systems with quark contents $sssq\overline{q},q=u$, $d$ in a chiral quark model with the help of Gaussian expansion method. Channel coupling is also considered. The real-scaling method (stabilization method) is employed to identify and check the bound states and the genuine resonances. In addition, the decay widths of all resonances are given. The results show that $\mathrm{\Omega }(2012)$ can be interpreted as a ${\mathrm{\Xi }}^{*}\overline{K}$ molecular state with quantum number of $I{J}^P=0(\frac{3}{2}{)}^{-}$. Another bound state $\mathrm{\Omega }\pi$ with $I{J}^P=1(\frac{3}{2}{)}^{-}$ is also found. Other resonances are obtained: ${\mathrm{\Xi }}^{*}{\overline{K}}^{*}$ with $I{J}^P=0(\frac{1}{2}{)}^{-}$ and $0(\frac{3}{2}{)}^{-}$. These pentaquark states is expected to be further verified in future experiments.

We study the decays of ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c(\to B_{n}f){\ell }^{-}\overline{\nu }$ with $\ell =e$, $\mu$, $\tau$, where $B_n$ and $f$ are the daughter baryon and the rest of the particles in ${\mathrm{\Lambda }}_c$ cascade decays, respectively. In particular, we examine the full angular distributions with polarized ${\mathrm{\Lambda }}_b$ and lepton mass effects, in which the time-reversal asymmetries are identified. We concentrate on the decay modes of ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c(\to p{K}^{-}{\pi }^{+}){\ell }^{-}\overline{\nu }$ to demonstrate their experimental feasibility. We show that the observables associated with the time-reversal asymmetries are useful to search for new physics as they vanish in the standard model. We find that they are sensitive to the right-handed current from new physics, and possible to be observed at LHCb.

We study nonanalytic terms, which cannot be written in the form of any positive integer power of field-dependent mass squared, in effective potential at finite temperature in one-loop approximation for a real scalar field on the $D$-dimensional spacetime, $S_{\tau }^1\times R^{D-(p+1)}\times {\prod }_{i=1}^p{S}_i^1$. The effective potential can be recast into the integral form in the complex plane by using the integral representation for the modified Bessel function of the second kind and the analytical extension for multiple mode summations. The pole structure of the mode summations is clarified and all the nonanalytic terms are obtained by the residue theorem. We find that the effective potential has a nonanalytic term when the dimension of the flat Euclidean space, $D-(p+1)$ is odd. There appears only one nonanalytic term for the given values of $D$ and $p$, for which the nonanalytic term exists.

We calculate the scalar self-force experienced by a scalar point-charge orbiting a Kerr black hole along $r\theta$-resonant geodesics. We use the self-force to calculate the averaged rate of change of the charge’s orbital energy $⟨\dot{E}⟩$, angular momentum $⟨{\dot{L}}_z⟩$, and Carter constant $⟨\dot{Q}⟩$, which together capture the leading-order adiabatic, secular evolution of the point-charge. Away from resonances, only the dissipative (time antisymmetric) components of the self-force contribute to $⟨\dot{E}⟩$, $⟨{\dot{L}}_z⟩$, and $⟨\dot{Q}⟩$. We demonstrate, using a new numerical code, that during $r\theta$ resonances conservative (time symmetric) scalar perturbations also contribute to $⟨\dot{Q}⟩$ and, thus, help drive the adiabatic evolution of the orbit. Furthermore, we observe that the relative impact of these conservative contributions to $⟨\dot{Q}⟩$ is particularly strong for eccentric $2:3$ resonances. These results provide the first conclusive numerical evidence that conservative scalar perturbations of Kerr spacetime are nonintegrable during $r\theta$ resonances.

In modified theories of gravity, higher curvature terms may be added to the Einstein-Hilbert action. Conventionally, the effects of the higher curvature terms on the black hole thermodynamics are rather difficult to obtain. In this paper, we show that, at least at the first order level, the corrections to the thermodynamics of the Schwarzschild black hole can be easily obtained, without solving the modified black hole metric. We examine some specific examples, which produces the known results in the literature, as well as those previously unknown. Furthermore, we find some nonperturbative exact results by generalizing the first-order analysis. In particular, a novel relation between the Euclidean integrals of the Einstein-Hilbert term and the higher curvature terms is found and proved.

We propose a model of inflation driven by the relaxation of an initially Planckian cosmological constant due to diffusion. The model can generate a (approximately) scale invariant spectrum of (adiabatic) primordial perturbations with the correct amplitudes and red tilt without an inflaton. The inhomogeneities observable in the cosmic microwave background (CMB) arise from those associated with the fundamental Planckian granularity that are imprinted into the standard model Higgs scalar fluctuations during the inflationary phase. The process admits a semiclassical interpretation and avoids the trans-Planckian problem of standard inflationary scenarios based on the role of vacuum fluctuations. The deviations from scale invariance observed in the CMB are controlled by the self-coupling constant of the Higgs scalar of the standard model of particle physics. The thermal production of primordial black holes can produce the amount of cold dark matter required by observations. For natural initial conditions set at the Planck scale the amplitude and tilt of the power spectrum of perturbations observed at the CMB depend only on known parameters of the standard model such as the self-coupling of the Higgs scalar and its mass.

Deviations from the blackbody spectral energy distribution of the cosmic microwave background (CMB) are a precise probe of physical processes active both in the early Universe (such as those connected to particle decays and inflation) and at later times (e.g., reionization and astrophysical emissions). Limited progress has been made in the characterization of these spectral distortions after the pioneering measurements of the FIRAS instrument on the COBE satellite in the early 1990s, which mainly targeted the measurement of their average amplitude across the sky. Since at present no follow-up mission is scheduled to update the FIRAS measurement, in this work we reanalyze the FIRAS data and produce a map of $\mu$-type spectral distortion across the sky. We provide an updated constraint on the $\mu$ distortion monopole $|⟨\mu ⟩|<47\times {10}^{-6}$ at 95% confidence level that sharpens the previous FIRAS estimate by a factor of $\sim 2$. We also constrain primordial non-Gaussianities of curvature perturbations on scales $10\lesssim k\lesssim 5\times {10}^4$ through the cross-correlation of $\mu$ distortion anisotropies with CMB temperature and, for the first time, the full set of polarization anisotropies from the Planck satellite. We obtain upper limits on $f_{\mathrm{NL}}\lesssim 3.6\times {10}^6$ and on its running $n_{\mathrm{NL}}\lesssim 1.4$ that are limited by the FIRAS sensitivity but robust against galactic and extragalactic foreground contaminations. We revisit previous similar analyses based on data of the Planck satellite and show that, despite their significantly lower noise, they yield similar or worse results to ours once all the instrumental and astrophysical uncertainties are properly accounted for. Our work is the first to self-consistently analyze data from a spectrometer and demonstrate the power of such instrument to carry out this kind of science case with reduced systematic uncertainties.

A new definition of the electromagnetic spatial densities for a spin-$1/2$ system is proposed and worked out in the zero average momentum frame and in moving frames. The obtained results are compared with the traditional definition of the densities in terms of the three-dimensional Fourier transforms of the electromagnetic form factors in the Breit frame.

We present results of the first lattice QCD calculation of three-flavored heavy dibaryons both in the flavor-symmetric and in the antisymmetric channels. These dibaryons have spin zero, and the three-flavored states are constructed using various possible combinations of quark flavors with at least one of them as the charm ($c$) or the bottom ($b$) quark i.e., namely, ${\mathcal{H}}_c(cudcud)$, ${\mathcal{H}}_b(budbud)$, ${\mathcal{H}}_{bcs}(bcsbcs)$, ${\mathcal{H}}_{csl}(cslcsl)$n,m, ${\mathcal{H}}_{bsl}(bslbsl)$ and ${\mathcal{H}}_{bcl}(bclbcl)$; $l\in u$, $d$. We compute the ground state masses of these dibaryons and the calculations are performed on three $N_f=2+1+1$ HISQ gauge ensembles of the MILC Collaboration, with lattice spacings $a=0.1207$, 0.0888 and 0.0582 fm. A relativistic overlap action is employed for the valence light and charm quarks and a nonrelativistic QCD Hamiltonian with improved coefficients is used for the bottom quarks. Unlike the doubly heavy tetraquarks, deuteron-like heavy dibaryons and dibaryons with only bottom quarks, for which lattice QCD calculations have predicted deeply bound strong-interactions-stable states, for these ${\mathcal{H}}_c(cudcud)$, ${\mathcal{H}}_b(budbud)$, ${\mathcal{H}}_{csl}(cslcsl)$, ${\mathcal{H}}_{bsl}(bslbsl)$ dibaryons we do not find any such deeply bound state at the physical quark masses. However, for ${\mathcal{H}}_{bcs}(bcsbcs)$, our results indicate the presence of an energy level $29\pm 24\mathrm{MeV}$ below the lowest two-baryon elastic threshold, which could be relevant for its future experimental searches. Moreover, we find that the energy difference between the lowest state and the lowest elastic threshold, which could well be interpreted as the binding energy for such heavy dibaryons (${\mathcal{H}}_{bcl}$), increases with the increase of quark masses ($m_l>m_s$). Taken together, our findings indicate the possibility of the existence of the physical ${\mathcal{H}}_{bcs}$ dibaryon while all other physical three-flavored dibaryons are much closer to their thresholds suggesting either they are weakly bound or unbound, resolving which requires further detail study. Our results also point that the binding of a dibaryon configuration becomes stronger with the increase of its valence quark masses which suggests an interesting aspect of strong interaction dynamics at multiple scales.

Efficient quantum simulation protocols for any quantum theories demand efficient protection protocols for its underlying symmetries. This task is nontrivial for gauge theories as it involves local symmetry/invariance. For non-Abelian gauge theories, protecting all the symmetries generated by a set of mutually noncommuting generators, is particularly difficult. In this paper, a global symmetry-protection protocol is proposed. Using the novel loop-string-hadron formalism of non-Abelian lattice gauge theory, we numerically demonstrate that all of the local symmetries get protected even for large time by this global symmetry protection scheme. With suitable protection strength, the dynamics of a ($1+1$)-dimensional SU(2) lattice gauge theory remains confined in the physical Hilbert space of the theory even in presence of explicit local symmetry violating terms in the Hamiltonian that may occur in both analog and digital simulation schemes as an error. The whole scheme holds for SU(3) gauge theory as well.

The $SU(2)$ unitary matrix $U$ employed in chiral descriptions of hadronic low-energy processes has both exponential and analytic representations, related by $U=\exp [i\mathit{\tau }·\widehat{\mathit{\pi }}\theta ]=\cos \theta I+i\mathit{\tau }·\widehat{\mathit{\pi }}\sin \theta$, where $\mathit{\tau }$ are Pauli matrices and $\mathit{\pi }=({\pi }_1,{\pi }_2,{\pi }_3)$ is the pion field. One extends this result to the $SU(3)$ unitary matrix by deriving an analytic expression which, for Gell-Mann matrices $\mathit{\lambda }$, reads $U=\exp [i\mathit{v}·\mathit{\lambda }]=[(F+\frac{2}{3}G)I+(H\widehat{\mathit{v}}+\frac{1}{\sqrt{3}}G\widehat{\mathit{b}})·\mathit{\lambda }]+i[(Y+\frac{2}{3}Z)I+(X\widehat{\mathit{v}}+\frac{1}{\sqrt{3}}Z\widehat{\mathit{b}})·\mathit{\lambda }]$, with $v_i=[v_1,\cdots v_8]$, $b_i=d_{ijk}{v}_j{v}_k$, and factors $F,\dots ,Z$ written in terms of elementary functions depending on $v=|\mathit{v}|$ and $\eta =2d_{ijk}{\widehat{v}}_i{\widehat{v}}_j{\widehat{v}}_k/3$. This result does not depend on the particular meaning attached to the variable $\mathit{v}$ and the analytic expression is used to calculate explicitly the associated left and right forms. When $\mathit{v}$ represents pseudoscalar meson fields, the classical limit corresponds to $⟨0|\eta |0⟩\to \eta \to 0$ and yields the cyclic structure $U=\{[\frac{1}{3}(1+2\cos v)I+\frac{1}{\sqrt{3}}(-1+\cos v)\widehat{\mathit{b}}·\mathit{\lambda }]+i(\sin v)\widehat{\mathit{v}}·\mathit{\lambda }\}$, which gives rise to a tilted circumference with radius $\sqrt{2/3}$ in the space defined by $I$, $\widehat{\mathit{b}}·\mathit{\lambda }$, and $\widehat{\mathit{v}}·\mathit{\lambda }$. For the sake of completeness, the axial transformations of the analytic matrix are also evaluated explicitly.

$B^0–{\overline{B}}^0$ entanglement offers a conceptual alternative to the single charged $B$-decay asymmetry for the measurement of the direct $CP$-violating $\gamma /{\varphi }_3$ phase. With $f=J/\mathrm{\Psi }{K}_L,J/\mathrm{\Psi }{K}_S$ and $g=(\pi \pi {)}^0,({\rho }_L{\rho }_L{)}^0$, the 16 time-ordered double-decay rate intensities to $(f,g)$ depend on the relative phase between the $f$- and $g$-decay amplitudes given by $\gamma$ at tree level. Several constraining consistencies appear. An intrinsic accuracy of the method at the level of $\pm 1°$ could be achievable at Belle-II with an improved determination of the penguin amplitude to $g$ channels from existing facilities.

This article presents the first measurement of the interaction between charm hadrons and nucleons. The two-particle momentum correlations of $\mathrm{p}{\mathrm{D}}^{-}$ and ${\overline{\mathrm{p}}\mathrm{D}}^{+}$ pairs are measured by the ALICE Collaboration in high-multiplicity pp collisions at $\sqrt{s}=13\mathrm{TeV}$. The data are compatible with the Coulomb-only interaction hypothesis within $(1.1–1.5)\sigma$. The level of agreement slightly improves if an attractive nucleon $(\mathrm{N})\overline{\mathrm{D}}$ strong interaction is considered, in contrast to most model predictions which suggest an overall repulsive interaction. This measurement allows for the first time an estimation of the 68% confidence level interval for the isospin $\mathrm{I}=0$ inverse scattering length of the $\mathrm{N}\overline{\mathrm{D}}$ state $f_{0,\mathrm{I}=0}^{-1}\in [-0.4,0.9]{\mathrm{fm}}^{-1}$, assuming negligible interaction for the isospin $\mathrm{I}=1$ channel.

We report the results of the first search for the decay $B_s^0\to {\eta }^{\prime }{K}_S^0$ using $121.4{\mathrm{fb}}^{-1}$ of data collected at the $\mathrm{\Upsilon }(5S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^{+}{e}^{-}$ collider. We observe no signal and set a 90% confidence-level upper limit of $8.16\times {10}^{-6}$ on the $B_s^0\to {\eta }^{\prime }{K}_S^0$ branching fraction.

The sensitivity and the frequency bandwidth of third-generation gravitational-wave detectors are such that the Newtonian noise (NN) signals produced by atmospheric turbulence could become relevant. We build models for atmospheric NN that take into account finite correlation times and inhomogeneity along the vertical direction, and are therefore accurate enough to represent a reliable reference tool for evaluating this kind of noise. We compute the NN spectral density from our models and compare it with the expected sensitivity curve of the Einstein Telescope (ET) with the xylophone design. The noise signal decays exponentially for small values of the frequency and the detector’s depth, followed by a power law for large values of the parameters. We find that, when the detector is built at the Earth’s surface, the NN contribution in the low-frequency band is above the ET sensitivity curve for strong wind. Building the detector underground is sufficient to push the noise signal under the ET sensitivity curve, but the decrement is close to marginal for strong wind. In light of the slow decay with depth of the NN, building the detector underground could be only partially effective as passive noise mitigation.