The typical velocity of a heavy quark in a quarkonium is a widely used quantity, in this paper, based on the relativistic Bethe-Salpeter equation method, we calculate the average values $\overline{|\mathit{q}{|}^n}$ and $\overline{|\mathit{v}{|}^n}\equiv v^n$ of a heavy quark in a $S$ wave or $P$ wave quarkonium rest frame, where $\mathit{q}$ and $\mathit{v}$ are the three dimensional momentum and velocity, $n=1$, 2, 3, 4. For a charm quark in $J/\psi$, we obtained $v_{J/\psi }=0.46$, $v_{J/\psi }^2=0.26$, $v_{J/\psi }^3=0.18$, and $v_{J/\psi }^4=0.14$, for a bottom quark in $\mathrm{\Upsilon }(1S)$, $v_{\mathrm{\Upsilon }(1S)}=0.24$, $v_{\mathrm{\Upsilon }(1S)}^2=0.072$, $v_{\mathrm{\Upsilon }(1S)}^3=0.025$, and $v_{\mathrm{\Upsilon }(1S)}^4=0.010$. The values indicate that $v^n>v^{n_1}·v^{n_2}$, where $n_1+n_2=n$, which is correct for all the charmonia and bottomonia. Our results also show the poor convergence if we make the speed expansion in charmonium system, but good for bottomonium. Based on the $v^n$ values and the following obtained relations $v_{4S}^n>v_{3S}^n>v_{2S}^n>v_{1S}^n$, $v_{4P}^n>v_{3P}^n>v_{2P}^n>v_{1P}^n$, and $v_{mP}^n>v_{mS}^n$ ($n$, $m=1$, 2, 3, 4), we conclude that highly excited quarkonia have larger relativistic corrections than those of the corresponding low excited and ground states, and there are large relativistic corrections in charmonium system.

Future lepton colliders such as the Circular Electron Positron Collider (CEPC) and FCC (Future Circular Collider)-ee would run as high-luminosity $Z$-boson factories, which offer a unique opportunity to study long-lived particles which couple to Z bosons. In order to exemplify this particular advantage, in this work, we consider one benchmark physics scenario where the long-lived lightest neutralinos pair $({\tilde{\chi }}_1^0{\tilde{\chi }}_1^0)$ is produced from $Z$ decays in the context of the R-parity-violating supersymmetry. Our analysis indicates that when assuming $\mathrm{BR}(Z\to {\tilde{\chi }}_1^0{\tilde{\chi }}_1^0)={10}^{-3}$ and $m_{{\tilde{\chi }}_1^0}\sim 40\mathrm{GeV}$, the model parameter ${\lambda }_{112}^{\prime }/m_{\tilde{f}}^2$ can be discovered down to as low as $\sim 1.5\times {10}^{-14}$ $(3.9\times {10}^{-14}){\mathrm{GeV}}^{-2}$ at the FCC-ee (CEPC) with center-of-mass energy $\sqrt{s}=91.2\mathrm{GeV}$ and $150(16){\mathrm{ab}}^{-1}$ integrated luminosity. These limits exceed the projected sensitivity reaches of the ATLAS experiment at the high-luminosity Large Hadron Collider (LHC) and the proposed LHC experiments with far detectors (AL3X, CODEX-b, FASER, and MATHUSLA).

We revisit scalar leptoquark pair production at hadron colliders. Apart from QCD contributions, we include the lepton $t$-channel exchange diagrams relevant in the light of the recent $B$-flavor anomalies. We evaluate all contributions at next-to-leading order in QCD and resum, in the threshold regime, soft-gluon radiation at next-to-next-to-leading-logarithmic accuracy. All corrections are found equally relevant. Our predictions consist of the most precise leptoquark cross section calculations available to date and are necessary for the best exploitation of leptoquark LHC searches.

The heavy-light mesons are studied within the framework of Dyson-Schwinger equations of QCD. Inspired by the axial-vector Ward-Takahashi identity resulting from the chiral symmetry, we propose a truncation scheme beyond the ladder approximation without introducing any additional parameters. For the pseudoscalar and vector heavy-light mesons, the obtained mass spectrum has the level of relative errors at 5% compared with experimental data and lattice-QCD results. For the leptonic decay constants, our results are comparable with those from experiments and/or lattice QCD. For some channels, the discrepancies are sizable but significantly smaller than those using the equal spacing rule. The truncation scheme proposed in this work is simple and could be improved and applied to study other open flavor hadrons including both mesons and baryons.

We investigate $P$-wave bottom baryons of the $SU(3)$ flavor ${\mathbf{6}}_F$, and systematically study their $D$-wave decays into ground-state bottom baryons and pseudoscalar mesons. Together with [H. X. Chen et al., Phys. Rev. D 91, 054034 (2015); Q. Mao et al., Phys. Rev. D 92, 114007 (2015); H. X. Chen et al., Phys. Rev. D 95, 094008 (2017); H. M. Yang et al.,Eur. Phys. J. C 80, 80 (2020)], a rather complete study is performed on both mass spectra and decay properties of $P$-wave bottom baryons, using the method of QCD sum rules and light-cone sum rules within the framework of heavy quark effective theory. Among all the possibilities, we find four ${\mathrm{\Sigma }}_b$, four ${\mathrm{\Xi }}_b^{\prime }$, and six ${\mathrm{\Omega }}_b$ baryons, with limited widths and so capable of being observed. Their masses, mass splittings within the same multiplets, and decay properties are extracted (summarized in Table VI) for future experimental searches.

We present a computation of next-to-next-to-leading-order (NNLO) QCD corrections to the production of a Higgs boson in association with a $W$ boson at the LHC followed by the decay of the Higgs boson to a $b\overline{b}$ pair. At variance with previous NNLO QCD studies of the same process, we treat $b$ quarks as massive. An important advantage of working with massive $b$ quarks is that it makes the use of flavor jet algorithms unnecessary and allows us to employ conventional jet algorithms to define $b$ jets. We compare NNLO QCD descriptions of the associated $WH(b\overline{b})$ production with massive and massless $b$ quarks and also contrast them with the results provided by parton showers. We find $\mathcal{O}(5\%)$ differences in fiducial cross sections computed with massless and massive $b$ quarks. We also observe that much larger differences between massless and massive results, as well as between fixed-order and parton-shower results, can arise in selected kinematic distributions.

The form factors of ${\gamma }^{*}N\to \mathrm{\Delta }(1600)$ transition is calculated within the light-cone sum rules assuming that ${\mathrm{\Delta }}^{+}(1600)$ is the first radial excitation of $\mathrm{\Delta }(1232)$. The $Q^2$ dependence of the magnetic dipole ${\tilde{G}}_M(Q^2)$, electric quadrupole ${\tilde{G}}_E(Q^2)$, and Coulomb quadrupole ${\tilde{G}}_c(Q^2)$ form factors are investigated. Moreover, the $Q^2$ dependence of the ratios $R_{\mathrm{EM}}=-\frac{{\tilde{G}}_E(Q^2)}{{\tilde{G}}_M(Q^2)}$ and $R_{\mathrm{SM}}=-\frac{1}{4m_{\mathrm{\Delta }(1600)}^2}\sqrt{4m_{\mathrm{\Delta }(1600)}^2{Q}^2+(m_{\mathrm{\Delta }(1600)}^2-Q^2-m_N^2{)}^2}\frac{{\tilde{G}}_c(Q^2)}{{\tilde{G}}_M(Q^2)}$ are studied. Finally, our predictions on ${\tilde{G}}_M(Q^2)$, ${\tilde{G}}_E(Q^2)$, and ${\tilde{G}}_C(Q^2)$ are compared with the results of other theoretical approaches.

We search for $J/\psi$ radiative decays into a weakly interacting neutral particle, namely an invisible particle, using the $J/\psi$ produced through the process $\psi (3686)\to {\pi }^{+}{\pi }^{-}J/\psi$ in a data sample of $(448.1\pm 2.9)\times {10}^6\psi (3686)$ decays collected by the BESIII detector at BEPCII. No significant signal is observed. Using a modified frequentist method, upper limits on the branching fractions are set under different assumptions of invisible particle masses up to $1.2\mathrm{GeV}/c^2$. The upper limit corresponding to an invisible particle with zero mass is $7.0\times {10}^{-7}$ at the 90% confidence level.

This paper reports the first simultaneous measurement of the double differential muon neutrino charged-current cross section on oxygen and carbon without pions in the final state as a function of the outgoing muon kinematics, made at the ND280 off-axis near detector of the T2K experiment. The ratio of the oxygen and carbon cross sections is also provided to help validate various models’ ability to extrapolate between carbon and oxygen nuclear targets, as is required in T2K oscillation analyses. The data are taken using a neutrino beam with an energy spectrum peaked at 0.6 GeV. The extracted measurement is compared with the prediction from different Monte Carlo neutrino-nucleus interaction event generators, showing particular model separation for very forward-going muons. Overall, of the models tested, the result is best described using local Fermi gas descriptions of the nuclear ground state with RPA suppression.

We study the three-body decay of the newly observed bottom baryon ${\mathrm{\Lambda }}_b^{*}(6072)$ by LHCb; ${\mathrm{\Lambda }}_b^{*}(6072)\to {\mathrm{\Lambda }}_b\pi \pi$. Its mass about 500 MeV above the ground state ${\mathrm{\Lambda }}_b$ and a broad width imply that the state could be an analogue of the Roper resonance of the nucleon $N(1440)$. In terms of sequential processes going through ${\mathrm{\Sigma }}_b$ and ${\mathrm{\Sigma }}_b^{*}$, we find that the observed invariant mass distribution is reproduced assuming its spin and parity $J^P=1/2^{+}$. We discuss that the ratio of the two sequential processes and angular correlation of two pions are useful for the determination of spin and parity. We suggest further studies for the Roper resonance analogue in various flavor contents, raising an interesting and important question in baryon spectroscopy.

We show that in an asymptotically flat space where an S-matrix can be defined, dual supertranslations leave all its matrix elements invariant and the Hilbert space of asymptotic states factorizes into distinct superselection sectors, labeled by their dual supertranslation charges. These results suggest that dual supertranslation may be interpreted as a redundant gauge symmetry of asymptotically flat spacetimes. This would allow to recast general relativity as a theory of diffeomorphisms possessing an additional asymptotic gauge symmetry. We then use the conjectured dual supertranslation gauge symmetry to construct a gravitational equivalent of the Wu-Yang monopole solution. The metric describing the solution is defined using two overlapping patches on the celestial sphere. The solution is regular on each one of the patches separately and differentiable in the overlap region, where the two descriptions are identical by virtue of a dual supertranslation gauge transformation. Our construction provides an alternative to Misner’s interpretation of the Taub-NUT metric. In particular, we find that using our approach, the Taub-NUT metric can be made regular everywhere on the celestial sphere and at the same time it is devoid of closed timelike curves, provided that the bound $\frac{m}{\ell }\le \sqrt{\frac{5}{27}}$ on the ratio of mass to NUT charge is obeyed.

It was recently demonstrated that small black holes can act as seeds for nucleating decay of the metastable Higgs vacuum, dramatically increasing the tunneling probability. Any primordial black hole lighter than $4.5\times {10}^{14}\mathrm{g}$ at formation would have evaporated by now, and in the absence of new physics beyond the standard model, would therefore have entered the mass range in which seeded decay occurs, however, such true vacuum bubbles must percolate in order to completely destroy the false vacuum; this depends on the bubble number density and the rate of expansion of the universe. Here, we compute the fraction of the universe that has decayed to the true vacuum as a function of the formation temperature (or equivalently, mass) of the primordial black holes, and the spectral index of the fluctuations responsible for their formation. This allows us to constrain the mass spectrum of primordial black holes given a particular Higgs potential and conversely, should we discover primordial black holes of definite mass, we can constrain the Higgs potential parameters.

We analyze the classical configurations of a bootstrapped Newtonian potential generated by homogeneous spherically symmetric sources in terms of a quantum coherent state. We first compute how the mass and mean wavelength of these solutions scale in terms of the number of quanta in the coherent state. We then note that the classical relation between the ADM mass and the proper mass of the source naturally gives rise to a generalized uncertainty principle (GUP) for the size of the gravitational radius in the quantum theory. Consistency of the mass and wavelength scalings with this GUP requires the compactness remains at most of order one even for black holes, and the corpuscular predictions are thus recovered, with the quantized horizon area expressed in terms of the number of quanta in the coherent state. Our findings could be useful for analyzing the classicalization of gravity in the presence of matter and the avoidance of singularities in the gravitational collapse of compact sources.

We investigate the three-dimensional (3D) motion of a test particle in the gravitational field generated by a nonspherical compact object endowed with a mass quadrupole moment, described by the Erez-Rosen metric, and a radiation field, including the general relativistic Poynting-Robertson (PR) effect, coming from a rigidly rotating spherical emitting source located outside of the compact object. We derive the equations of motion for test particles influenced by such radiation field, recovering the two-dimensional (2D) description, and the weak-field approximation. This dynamical system admits the existence of a critical hypersurface, region where gravitational and radiation forces balance. Selected test particle orbits for different set of input parameters are displayed. The possible configurations on the critical hypersurfaces can be either latitudinal drift toward the equatorial ring or suspended orbits. We discuss about the existence of multiple hypersurface solutions through a simple method to perform the calculations. We graphically prove also that the critical hypersurfaces are stable configurations within the Lyapunov theory.

We investigate the thermodynamics of dyonic hairy black holes in flat spacetime when the asymptotic value of the scalar field is not fixed. We use the quasilocal formalism of Brown and York and corresponding boundary terms that make the variational principle well defined to prove that the scalar charges do not contribute to the first law of thermodynamics. We also provide a unified picture of obtaining exact solutions by comparing two different methods and discuss in detail the ansatz used in each coordinate system and the relation between them.

I provide a derivation of some characteristic effects of Milgrom’s modified Newtonian dynamics (MOND) from a fractional version of Newton’s theory based on the fractional Poisson equation. I employ the properties of the fractional Laplacian to investigate the features of the fundamental solution of the proposed model. The key difference between MOND and the fractional theory introduced here is that the latter is an inherently linear theory, featuring a characteristic length scale $\ell$, whilst the former is ultimately nonlinear in nature and it is characterized by an acceleration scale $a_0$. Taking advantage of the Tully-Fisher relation, as the fractional order $s$ approaches $3/2$, I then connect the length scale $\ell$, emerging from this modification of Newton’s gravity, with the critical acceleration $a_0$ of MOND. Finally, implications for galaxy rotation curves of a variable-order version of the model are discussed.

Theories with an infinite number of derivatives are described by nonlocal Lagrangians for which the standard Hamiltonian formalism cannot be applied. Hamiltonians of special types of nonlocal theories can be constructed by means of the ($1+1$)-dimensional Hamiltonian formalism. In this paper, we consider a simple scalar field model inspired by the infinite derivative gravity and study its reduced phase space by using this formalism. Assuming the expansion of the solutions in the coupling constant, we compute the perturbative Hamiltonian and the symplectic 2-form. We also discuss an example of a theory leading to an infinite-dimensional reduced phase space for a different choice of the form factor.

The International Gamma-Ray Astrophysics Laboratory ($INTEGRAL$) satellite has yielded unprecedented measurements of the soft gamma-ray spectrum of our Galaxy. Here we use those measurements to set constraints on dark matter (DM) that decays or annihilates into photons with energies $E\approx 0.02–2\mathrm{MeV}$. First, we revisit the constraints on particle DM that decays or annihilates to photon pairs. In particular, for decaying DM, we find that previous limits were overstated by roughly an order of magnitude. Our new, conservative analysis finds that the DM lifetime must satisfy $\tau \gtrsim 5\times {10}^{26}\mathrm{s}\times (m_{\chi }/\mathrm{MeV}{)}^{-1}$ for DM masses $m_{\chi }=0.054–3.6\mathrm{MeV}$. For MeV-scale DM that annihilates into photons $INTEGRAL$ sets the strongest constraints to date. Second, we target ultralight primordial black holes (PBHs) through their Hawking radiation. This makes them appear as decaying DM with a photon spectrum peaking at $E\approx 5.77/(8\pi G{M}_{\mathrm{PBH}})$, for a PBH of mass $M_{\mathrm{PBH}}$. We use the $INTEGRAL$ data to demonstrate that, at 95% C.L., PBHs with masses less than $1.2\times {10}^{17}\mathrm{g}$ cannot comprise all of the DM, setting the tightest bound to date on ultralight PBHs.

In this work, we provide updated constraints on coupled dark energy (CDE) cosmology with Peebles-Ratra (PR) potential and constant coupling strength $\beta$. This modified gravity scenario introduces a fifth force between dark matter particles, mediated by a scalar field that plays the role of dark energy. The mass of the dark matter particles does not remain constant, but changes with time as a function of the scalar field. Here we focus on the phenomenological behavior of the model, and assess its ability to describe updated cosmological datasets that include the Planck 2018 cosmic microwave background (CMB) temperature, polarization and lensing, baryon acoustic oscillations, the Pantheon compilation of supernovae of Type Ia, data on $H(z)$ from cosmic chronometers, and redshift-space distortions. We also study the impact of the local measurement of $H_0$ from SH0ES and the strong-lensing time delay data from the H0LICOW Collaboration on the parameter that controls the strength of the interaction in the dark sector. We find a peak corresponding to a coupling $\beta >0$ and to a potential parameter $\alpha >0$, more or less evident depending on the dataset combination. We show separately the impact of each dataset and remark that CMB lensing is especially the one dataset that shifts the peak the most towards $\mathrm{\Lambda }\mathrm{CDM}$. When a model selection criterion based on the full Bayesian evidence is applied, however, $\mathrm{\Lambda }\mathrm{CDM}$ is still preferred in all cases, due to the additional parameters introduced in the CDE model.

Gravitational waves from binary black holes that are gravitationally lensed can be distorted by small microlenses along the line of sight. Microlenses with masses of a few tens of solar masses, and that are close to a critical curve in the lens plane, can introduce a time delay of a few milliseconds. Such a time delay would result in distinctive interference patterns in the gravitational wave that can be measured with current experiments such as LIGO/Virgo. We consider the particular case of primordial black holes with masses between 5 and 50 solar masses acting as microlenses. We study the effect of a population of primordial black holes constituting a fraction of the dark matter, and contained in a macrolens (galaxy or cluster), over gravitational waves that are being lensed by the combined effect of the macrolens plus microlenses. We find that, at the typical magnifications expected for observed gravitational wave events, the fraction of dark matter in the form of compact microlenses, such as primordial black holes, can be constrained to the percent level. Similarly, if a small percentage of the dark matter is in the form of microlenses with a few tens of solar masses, at sufficiently large magnification factors, all gravitational waves will show interference effects. These effects could have an impact on the inferred parameters. The effect is more important for macroimages with negative parity, which usually arrive after the macroimages with positive parity.