Nonperturbative determinations of the renormalization group (RG) $\beta$ function are crucial to understand properties of gauge-fermion systems at strong coupling and connect lattice simulations and the perturbative ultraviolet regime. Choosing well-understood, QCD-like systems with SU(3) gauge group and either six or four fundamental flavors, we investigate their step-scaling $\beta$ function. In both cases we push the simulations to the boundary of chiral symmetry breaking and study the regime $g_{\mathrm{GF}}^2\lesssim 8.2$ with six, and $g_{\mathrm{GF}}^2\lesssim 6.6$ with four flavors. We carefully consider the lattice discretization errors by comparing three different gradient flows (GF), and for each flow three operators to estimate the renormalized finite volume coupling. We also consider the tree level improvement of the coupling. Noteworthy outcome is that nonperturbatively determined $\beta$ functions sits between the universal 2-loop result and the 3-loop gradient flow scheme prediction. At strong coupling the renormalized coupling runs significantly slower than the 2-loop prediction.

The $X(6900)$ resonance, recently discovered in the double-$J/\psi$ channel at the LHCb experiment, has spurred intensive interest in unraveling the nature of the fully charmed tetraquark state. The aim of this paper is to present a model-independent framework to study the inclusive production of this novel species of exotic hadrons, the resonances composed of four heavy quark (commonly referred to as $T_{4c}$), at large $p_T$ in hadron colliders. Appealing to asymptotic freedom and the fact $m_c\gg {\mathrm{\Lambda }}_{\mathrm{QCD}}$, we propose that the universal gluon-to-$T_{4c}$ fragmentation function, can be decomposed into the product of the perturbatively calculable short-distance coefficients and the long-distance nonrelativistic QCD (NRQCD) matrix elements. We compute the short-distance coefficient at lowest order in ${\alpha }_s$ and velocity expansion. Adopting the phenomenological four-body wave functions at the origin to roughly estimate those not-yet-known NRQCD matrix elements, and applying the standard QCD factorization theorem, we predict the differential production rates for the $T_{4c}$ ($0^{++}$ and $2^{++}$) at large $p_T$ in $pp$ collision, which eagerly awaits the confrontation with the future LHC experiments.

We used a diffusion Monte Carlo technique to describe the properties of fully heavy compact arrangements (no dibaryon molecules) including six quarks and no antiquarks within the framework of a constituent quark model. Only arrangements whose wavefunctions were eigenvectors of $L^2$ with eigenvalue $\ell =0$ were taken into account, what means that we only considered the subset of all the possible color-spin combinations that make the total wavefunctions antisymmetric with respect to the interchange of any two quarks of the same type. In all cases, the masses of the six-quark arrangements are larger than the ones corresponding to the sum of any of the two baryons we can split them into, but smaller than the ones for a set of six isolated quarks, i.e., all them are bound systems. The analysis of their structure indicates that all the hexaquarks considered in this work are compact objects, except the $cccbbb$, that appears to be a loose association of two baryons for all the possible spin values.

The semi-inclusive electroproduction of exotic hadrons, including the $T_{cc}$, $P_{cs}$, and hidden-charm baryon-antibaryon states, is explored under the assumption that they are $S$-wave hadronic molecules of a pair of charmed hadrons. We employ the Monte Carlo event generator Pythia to produce the hadron pairs and then bind them together to form hadronic molecules. With the use of such a production mechanism, the semi-inclusive electroproduction rates are estimated at the order-of-magnitude level. Our results indicate that a larger number of $P_{cs}$ states and ${\mathrm{\Lambda }}_c{\overline{\mathrm{\Lambda }}}_c$ molecules can be produced at the proposed electron-ion colliders in China (EicC) and the US (EIC). The results also suggest that the $T_{cc}$ states and other hidden-charm baryon-antibaryon states can be searched for at EIC. Besides, the potential 24-GeV upgrade of the Continuous Beam Accelerator Facility at the Thomas Jefferson National Accelerator Facility can play an important role in the search for the hidden-charm tetraquark and pentaquark states due to its high luminosity.

Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders will require three-loop electroweak and mixed electroweak-QCD corrections to single-particle production and decay processes and two-loop electroweak corrections to pair-production processes. This article presents a new seminumerical approach to multiloop multiscale Feynman integrals calculations which will be able to fill the gap between rigid experimental demands and theory. The approach is based on differential equations with boundary terms specified at Euclidean kinematic points. These Euclidean boundary terms can be computed numerically with high accuracy using sector decomposition or other numerical methods. They are then mapped to the physical kinematic configuration by repeatedly solving the differential equation system in terms of series solutions. An automatic and general method is proposed for constructing a basis of master integrals such that the differential equations are finite. The approach also provides a prescription for the analytic continuation across physical thresholds. Our implementation is able to deliver 8 or more digits of precision, and has a built-in mechanism for checking the accuracy of the obtained results. Its efficacy is illustrated with state-of-the-art examples for three-loop self-energy and vertex integrals and two-loop box integrals.

We use $\mathcal{N}=2^{*}$ and cascading gauge theory holographic models to extract the general features of the gravitational susceptibility $\kappa$ of strongly coupled nonconformal quark-gluon plasma. We show that in theories with a relevant coupling constant the gravitational susceptibility is renormalization scheme dependent. We propose to use its temperature derivative, i.e., $\frac{d\kappa }{d\ln T}$, as a scheme-independent characteristic of a quark gluon plasma. Although $\kappa$ is a thermodynamic quantity, its critical behavior can be drastically distinct in the vicinity of seemingly identical thermal phase transitions.

We study the canonical quantization of a massless charged scalar field on a Reissner-Nordström black hole background. Our aim is to construct analogs of the standard Boulware, Unruh and Hartle-Hawking quantum states which can be defined for a neutral scalar field, and to explore their physical properties by computing differences in expectation values of the scalar field condensate, current and stress-energy tensor operators between two quantum states. Each of these three states has a non-time-reversal-invariant past and future charged field generalization, whose properties are similar to those of the corresponding past and future states for a neutral scalar field on a Kerr black hole. In addition, we present some tentative, time-reversal-invariant, equilibrium states. The first is a “Boulware”-like state which is as empty as possible at both future and past null infinity. Second, we posit a “Hartle-Hawking”-like state which may correspond to a thermal distribution of particles. The construction of both these latter states relies on the use of nonstandard commutation relations for the creation and annihilation operators pertaining to superradiant modes.

Noether’s first and second theorems both imply conserved currents that can be identified as an energy-momentum tensor (EMT). The first theorem identifies the EMT as the conserved current associated with global spacetime translations, while the second theorem identifies it as a conserved current associated with local spacetime translations. This work obtains an EMT for quantum electrodynamics and quantum chromodynamics through the second theorem, which is automatically symmetric in its indices and invariant under the expected symmetries [e.g., Becchi-Rouet-Stora-Tyutin (BRST) invariance] without the need for introducing an ad hoc improvement procedure.

We investigate how GWs pass through the spacetime of a Schwarzschild black hole using time-domain numerical simulations. Our work is based on the perturbed $3+1$ Einstein’s equations up to the linear order. We show explicitly that our perturbation equations are covariant under infinitesimal coordinate transformations. Then we solve a symmetric second-order hyperbolic wave equation with a spatially varying wave speed. As the wave speed in our wave equation vanishes at the horizon, our formalism can naturally avoid boundary conditions at the horizon. Our formalism also does not contain coordinate singularities and, therefore, does not need regularity conditions. Then, based on our code, we simulate both finite and continuous initially plane-fronted wave trains passing through the Schwarzschild black hole. We find that for the finite wave train, the wave zone of GWs is wildly twisted by the black hole. While for the continuous wave train, unlike geometric optics, GWs cannot be sheltered by the black hole. A strong beam and an interference pattern appear behind the black hole along the optical axis. Moreover, we find that the back-scattering due to the interaction between GWs and the background curvature is strongly dependent on the direction of the propagation of the trailing wavefront relative to the black hole. Finally, for a realistic input waveform generated by binary black holes, we find that the lensed waveform in the merger and ringdown phases is much longer than that of the input waveform due to the effect of back-scattering.

In modified theories of gravity, the potentials appearing in the Schrödinger-like equations that describe perturbations of nonrotating black holes are also modified. In this paper we ask: can these modifications be constrained with high-precision gravitational-wave measurements of the black hole’s quasinormal mode frequencies? We expand the modifications in a small perturbative parameter regulating the deviation from the general-relativistic potential, and in powers of $M/r$. We compute the quasinormal modes of the modified potential up to quadratic order in the perturbative parameter. Then we use Markov-chain Monte Carlo methods to recover the coefficients in the $M/r$ expansion in an “optimistic” scenario where we vary them one at a time, and in a “pessimistic” scenario where we vary them all simultaneously. In both cases, we find that the bounds on the individual parameters are not robust. Because quasinormal mode frequencies are related to the behavior of the perturbation potential near the light ring, we propose a different strategy. Inspired by Wentzel-Kramers-Brillouin (WKB) theory, we demonstrate that the value of the potential and of its second derivative at the light ring can be robustly constrained. These constraints allow for a more direct comparison between tests based on black hole spectroscopy and observations of black hole “shadows” by the Event Horizon Telescope and future instruments.

A proper time observable for a quantum clock is introduced and it is found that the proper time read by one clock conditioned on another clock reading a different proper time obeys classical time dilation in accordance with special relativistic kinematical time dilation. Here, we extend this proposal to a weak gravitational field in order to investigate whether the weak equivalence principle holds for quantum matter. We find that for general quantum states the quantum time dilation in a weak gravitational field obeys a similar gravitational time dilation found in classical relativity. However, unlike the special relativistic case, the time dilation involves the external time (a background coordinate time at the observer on the Earth) as well as the proper times of two clocks. We also investigate a quantum time dilation effect induced by a clock in a superposition of wave packets localized in momentum space or in position space and propose the setup to observe the gravitational effect in the quantum interference effect in the time dilation.

Using mock data for the Hubble diagrams of type Ia supernovae (SNIa) and quasars (QSOs) generated based on the standard model of cosmology, and using the least-squares method based on the Markov-Chain-Monte-Carlo (MCMC) algorithm, we first put constraints on the cosmographic parameters in the context of the various model-independent cosmographic methods reconstructed from the Taylor 4th and 5th order expansions and the Padé (2,2) and (3,2) polynomials of the Hubble parameter, respectively. We then reconstruct the distance modulus in the framework of cosmographic methods and calculate the percentage difference between the distance modulus of the cosmographic methods and that of the standard model. The percentage difference is minimized when the Padé approximation is used which means that the Padé cosmographic method is sufficiently suitable for reconstructing the distance modulus even at high-redshifts. In the next step, using the real observational data for the Hubble diagrams of SNIa, QSOs, gamma-ray-bursts (GRBs), and observations from baryon acoustic oscillations (BAO) in two sets of the low-redshift combination ($\mathrm{SNIa}+\mathrm{QSOs}+\mathrm{GRBs}+\mathrm{BAO}$) embracing the redshift range of $0.01<z<2.26$ and the high-redshift combination ($\mathrm{SNIa}+\mathrm{QSOs}+\mathrm{GRBs}$) which covers a redshift range of $0.01<z<5.5$, we put observational constraints on the cosmographic parameters of the Padé cosmography and also the standard model. Our analysis indicates that Padé cosmographic approaches do not reveal any cosmographic tension between the standard model and the observational data. We also confirm this result, using the statistical AIC criteria. Finally, we put the cosmographic method in the redshift-bin data and find a larger value of ${\mathrm{\Omega }}_{m0}$ extracted from $s_0$ parameter compared with those of the $q_0$ parameter and Planck-$\mathrm{\Lambda }\mathrm{CDM}$ values.

We introduce a second-order stochastic effective theory for light scalar fields in de Sitter spacetime, extending the validity of the stochastic approach beyond the massless limit and demonstrating how it can be used to compute long-distance correlation functions nonperturbatively. The parameters of the second-order stochastic theory are determined from quantum field theory through a perturbative calculation, which is valid if the self-interaction parameter $\lambda$ satisfies $\lambda \ll m^2/H^2$, where $m$ is the scalar and $H$ is the Hubble rate. Therefore, it allows stronger self-interactions than conventional perturbation theory, which is limited to $\lambda \ll m^4/H^4$ by infrared divergences. We demonstrate the applicability of the second-order stochastic theory by comparing its results with perturbative quantum field theory and overdamped stochastic calculations, and discuss the prospects of improving its accuracy with a full one-loop calculation of its parameters.

One of the most important observational constraints on possible models of dark-matter physics exploits the Lyman-$\alpha$ absorption spectrum associated with photons traversing the intergalactic medium. Because these data allow us to probe the linear matter power spectrum with great accuracy down to relatively small distance scales, finding ways of accurately evaluating such Lyman-$\alpha$ constraints across large classes of candidate models of dark-matter physics is of paramount importance. While such Lyman-$\alpha$ constraints have been evaluated for dark-matter models that give rise to relatively simple dark-matter velocity distributions, more complex models—particularly those whose dark-matter velocity distributions stretch across multiple scales—have recently been receiving increasing attention. In this paper, we undertake a study of the Lyman-$\alpha$ constraints associated with general dark-matter velocity distributions. Although such Lyman-$\alpha$ constraints are difficult to evaluate in principle, in practice there currently exist two classes of methods in the literature through which such constraints can be recast into forms which are easier to evaluate and which therefore allow a more rapid determination of whether a given dark-matter model is ruled in or out. Accordingly, we utilize both of these recasts in order to determine the Lyman-$\alpha$ bounds on different classes of dark-matter velocity distributions. We also develop a general method by which the results of these different recasts can be compared. For relatively simple dark-matter velocity distributions, we demonstrate that these two classes of recasts tend to align and give similar results. However, we find that the situation is far more complex for distributions involving multiple velocity scales: while these two classes of recasts continue to yield similar results within certain regions of parameter space, they nevertheless yield dramatically different results within precisely those regions of parameter space which are likely to be phenomenologically relevant. This, then, serves as a cautionary tale regarding the use of such recasts for complex dark-matter velocity distributions.

In the framework of mixed Higgs-Starobinsky inflation, we consider the generation of Abelian gauge fields due to their nonminimal coupling to gravity (in two different formulations of gravity—metric and Palatini). We couple the gauge-field invariants $F_{\mu \nu }{F}^{\mu \nu }$ and $F_{\mu \nu }{\tilde{F}}^{\mu \nu }$ to an integer power of the scalar curvature $R^n$ in Jordan frame and, treating these interactions perturbatively, switch to the Einstein frame where they lead to effective kinetic and axial couplings between gauge fields and inflaton. We determine the power spectra, energy densities, correlation length, and helicality of the generated gauge fields for different values of the nonminimal coupling constants and parameter $n$. We analytically estimate the spectral index $n_B$ of the magnetic power spectrum and show that for $n>1$ it is possible to get the scale-invariant or even red-tilted spectrum for a wide range of modes that implies larger correlation length of the generated fields. On the other hand, the magnitude of these fields typically decreases in time becoming very small in the end of inflation. Thus, it is difficult to obtain both large magnitude and correlation length of the gauge field in the frame of this model.

Boson stars represent a hypothetical exotic type of compact stellar object that may be observed from the gravitational signal of coalescing binaries in current and future gravitational wave (GW) detectors. In this work we show that the moment of inertia $I$, the (dimensionless) angular momentum $\chi$, and the quadrupole moment $Q$ of rotating boson stars obey a universal relation, valid for a wide set of boson star models. Further, the obtained $I-\chi -Q$ relation clearly differs from its famous neutron star counterpart, providing us with an unequivocal diagnostic tool to distinguish boson stars from ordinary compact stars or other celestial bodies in GW observations. Such universal (i.e., model-independent) relations also provide a useful tool to probe the strong gravity regime of general relativity and to constrain the equation of state of matter inside compact stars.

We show the prospects of probing neutral-current nonstandard interaction (NSI) in the propagation of atmospheric neutrinos in future large-volume neutrino experiments including DUNE, HK, KNO, and ORCA. For DUNE, we utilize its ability of identifying the tau neutrino event and combine the ${\nu }_{\tau }$ appearance with the ${\nu }_{\mu }$ disappearance. Based on our simulated results, the 10 years of data taking of the atmospheric neutrinos can enormously improve the bounds on the NSI parameters ${ϵ}_{\mu \tau },|{ϵ}_{\mu \mu }-{ϵ}_{\tau \tau }|$, ${ϵ}_{e\mu }$, ${ϵ}_{e\tau }$ and $|{ϵ}_{\mu \mu }-{ϵ}_{ee}|$ by a couple of orders of magnitudes. In addition, we show the expected correlations between the $CP$-violation phase ${\delta }_{CP}$ and the NSI parameters ${ϵ}_{e\mu },{ϵ}_{e\tau }$, and $|{ϵ}_{ee}-{ϵ}_{\mu \mu }|$ and confirm the potentials of DUNE, HK, KNO (combined with HK) in excluding the “No $CP$ violation” hypothesis at $1\sigma$, $2\sigma$, and $3\sigma$, respectively.

Traditionally, lattice QCD computations of generalized parton distributions (GPDs) have been carried out in a symmetric frame, where the transferred momentum is symmetrically distributed between the incoming and outgoing hadrons. However, such frames are inconvenient since they require a separate calculation for each value of the momentum transfer, increasing significantly the computational cost. In this work, by focusing on the quasidistribution approach, we lay the foundation for faster and more effective lattice QCD calculations of GPDs exploiting asymmetric frames, with freedom in the transferred momentum distribution. An important ingredient of our approach is the Lorentz covariant parametrization of the matrix elements in terms of Lorentz-invariant amplitudes, which allows one to relate matrix elements in different frames. We also use this amplitude approach to propose a new definition of quasi-GPDs that is frame independent and, more importantly, may lead to smaller power corrections in the matching relations to the light-cone GPDs. We demonstrate the efficacy of the formalism through numerical calculations using one ensemble of $N_f=2+1+1$ twisted-mass fermions with a clover improvement. The value of the light-quark masses lead to a pion mass of about 260 MeV. Concentrating on the proton, and limiting ourselves to a vanishing longitudinal momentum transfer to the target, we extract the invariant amplitudes from matrix element calculations in both the symmetric and asymmetric frame and obtain results for the twist-2 light-cone GPDs for unpolarized quarks, that is, $H$ and $E$.

We propose to utilize noisy-intermediate-scale-quantum-era quantum devices to compute short distance quantities in ($2+1$)-dimensional QED and to combine them with large volume Monte Carlo simulations and perturbation theory. On the quantum computing side, we perform a calculation of the mass gap in the small and intermediate regime, demonstrating, in the latter case, that it can be resolved reliably. The so obtained mass gap can be used to match corresponding results from Monte Carlo simulations, which can be used eventually to set the physical scale. In this paper we provide the setup for the quantum computation and show results for the mass gap and the plaquette expectation value. In addition, we discuss some ideas that can be applied to the computation of the running coupling. Since the theory is asymptotically free, it would serve as a training ground for future studies of QCD in $3+1$ dimensions on quantum computers.

We present lattice QCD calculations of the valence parton distribution function (PDF) of pion employing next-to-next-leading-order (NNLO) perturbative QCD matching. Our calculations are based on three gauge ensembles of $2+1$ flavor highly improved staggered quarks and Wilson-Clover valance quarks, corresponding to pion mass $m_{\pi }=140\mathrm{MeV}$ at a lattice spacing $a=0.076\mathrm{fm}$ and $m_{\pi }=300\mathrm{MeV}$ at $a=0.04$, 0.06 fm. This enables us to present, for the first time, continuum-extrapolated lattice QCD results for the NNLO valence PDF of the pion at the physical point. Applying leading-twist expansion for renormalization group invariant (RGI) ratios of bilocal pion matrix elements with NNLO Wilson coefficients, we extract second, fourth, and sixth Mellin moments of the PDF. We reconstruct the Bjorken-$x$ dependence of the NNLO PDF from real-space RGI ratios using a deep neural network as well as from momentum-space matrix elements renormalized using a hybrid scheme. All our results are in broad agreement with the results of global fits to the experimental data carried out by the xFitter and JAM collaborations.