Lattice QCD calculations of scattering phase shifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed Lüscher’s formula for extracting these quantities at lowest order. As the calculations become more ambitious, higher-order relations are required. In this study we derive higher-order quantization conditions and introduce a method to transparently cross-check our results. This is an important step given the involved derivations of these formulas. We derive quantization conditions up to $\ell =5$ partial waves in both cubic and elongated geometries, and for states with zero and nonzero total momentum. All 45 quantization conditions we include here (22 in cubic box, 23 in elongated box) pass our cross-check test.

We determine the leading order mesonic ($B_0$ and $F_0$) and baryonic ($m_0$, $D$ and $F$) SU(3) chiral perturbation theory low energy constants from lattice QCD. We employ gauge ensembles with $N_f=3$ (i.e., $m_u=m_d=m_s$) nonperturbatively improved Wilson fermions at six distinct values of the lattice spacing in the range $a\approx (0.039–0.098)\mathrm{fm}$, which constitute a subset of the coordinated lattice simulations (CLS) gauge ensembles. The pseudoscalar meson mass $M_{\pi }$ ranges from around 430 MeV down to 240 MeV and the linear spatial lattice extent $L$ from $6.4M_{\pi }^{-1}$ to $3.3M_{\pi }^{-1}$, where $L{M}_{\pi }\ge 4$ for the majority of the ensembles. This allows us to perform a controlled extrapolation of all the low energy constants to the chiral, infinite volume and continuum limits. We find the SU(3) chiral condensate and $F_0$ to be smaller than their SU(2) counterparts while the Gell-Mann–Oakes–Renner parameters $B_0\approx B$ are similar. Regarding baryonic LECs, we obtain $F/D=0.612_{(12)}^{(14)}$.

We report on a two-flavor lattice QCD study of the $B_s\to D_s$ and $B_s\to D_s^{*}$ transitions parametrized, in the heavy quark limit, by the form factors $\mathcal{G}$, and $h_{A_1}$, $h_{A_2}$, and $h_{A_3}$, respectively. In the search for New Physics through tests of lepton flavor universality, $B_s$ decay channels are complementary to the $B$ decays widely studied at $B$ factories and LHCb, while on the theory side they can be better controlled than the $B_c$ and ${\mathrm{\Lambda }}_b$ decays. The purpose of this exploratory two-flavor study is, in preparation for future analyses of lattice QCD simulations with $N_f>2$ and physical quark masses, to gain experience on a suitable method for a lattice extraction of form factors associated with $b\to c$ currents that may yield tighter control over systematic effects like contamination from excited states and cutoff effects. We obtain the zero-recoil values ${\mathcal{G}}^{B_s\to D_s}(1)=1.03(14)$ and $h^{B_s\to D_s^{*}}(1)=0.85(16)$.

We present the first lattice-QCD calculation of the form factors governing the charm-baryon semileptonic decays ${\mathrm{\Lambda }}_c\to {\mathrm{\Lambda }}^{*}(1520){\ell }^{+}{\nu }_{\ell }$. As in our previous calculation of the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}^{*}(1520)$ form factors, we work in the ${\mathrm{\Lambda }}^{*}(1520)$ rest frame, but here we use four different heavy-baryon momenta instead of just two. Because of the lower mass of the ${\mathrm{\Lambda }}_c$, the moderately sized momenta used here are sufficient to determine the form factors in the full kinematic range of the semileptonic decay. We also update the analysis of our lattice results for the ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}^{*}(1520)$ and ${\mathrm{\Lambda }}_b\to {\mathrm{\Lambda }}_c^{*}(2595,2625)$ form factors by imposing exact relations among the different form factors at zero recoil that follow from rotational symmetry. Imposing these relations ensures the correct behavior of the angular observables near the endpoint.

The Burkhardt-Cottingham (BC) sum rule connects the twist-3 light-cone parton distribution function (PDF) $g_T(x)$ to the twist-2 helicity PDF $g_1(x)$. The chiral-odd counterpart of the BC sum rule relates the twist-3 light-cone PDF $h_L(x)$ to the twist-2 transversity PDF $h_1(x)$. These BC-type sum rules can also be derived for the corresponding quasi-PDFs. We perform a perturbative check of the BC-type sum rules in the quark target model and the Yukawa model, by going beyond the ultraviolet (UV) divergent terms. We employ dimensional regularization (DR) and cutoff schemes to regulate UV divergences, and show that the BC-type sum rules hold for DR, while they are generally violated when using a cutoff. This violation can be traced back to the breaking of rotational invariance. We find corresponding results for the sum rule relating the mass of the target to the twist-3 PDF $e(x)$. Moreover, we supplement our analytical results with numerical calculations.

Hadrons and their distributions are the most direct observables in experiments, which would shed light on the nonperturbative mystery of quantum chromodynamics. As the result, any new hadron will challenge our current knowledge on the one hand, and provide additional inputs on the other hand. The fully heavy $cc\overline{c}\overline{c}$ system observed by LHCb recently opened a new era for hadron physics. We first extract the internal structure of the fully heavy tetraquarks directly from the experimental data, within the compact tetraquark picture. By fitting to the di-$J/\psi$ lineshape, we find that the $X(6900)$ is only the cusp effect from the $J/\psi \psi (3770)$ channel. In addition, there is also a cusp slightly below 6.8 GeV stemming from the $J/\psi {\psi }^{\prime }$ channel. The two $0^{++}$ tetraquarks behave as two resonances above the di-${\eta }_c$ and di-$J/\psi$ threshold, respectively. The $2^{++}$ state is a bound state below the di-$J/\psi$ threshold. Furthermore, we find that the $X_{0^{++}}(6035)$ shows a significant structure in the di-${\eta }_c$ lineshape even after the coupled channel effect. This is an unique feature which can distinguish compact $cc\overline{c}\overline{c}$ tetraquark from the loosely hadronic molecules.

We investigate the sensitivity with which two angles of the flat unitarity triangle, defined by $V_{ub}^{*}{V}_{us}+V_{cb}^{*}{V}_{cs}+V_{tb}^{*}{V}_{ts}=0$, can possibly be measured directly at FCC-ee. We show that the measured errors on the angle ${\alpha }_s=\arg (-V_{ub}^{*}{V}_{us}/V_{tb}^{*}{V}_{ts})$ and ${\beta }_s=\arg (-V_{tb}^{*}{V}_{ts}/V_{cb}^{*}{V}_{cs})$ should be better than 0.4° and 0.035°, respectively. These measurements, combined with the measurement of the third angle ${\gamma }_s=\arg (-V_{cb}^{*}{V}_{cs}/V_{ub}^{*}{V}_{us})$, discussed in a different paper, will contribute to probing the consistency of the $CP$ sector of the Standard Model further with an unprecedented level of accuracy.

Black holes and Buchdahl stars are identified respectively by $\mathrm{\Phi }(R)=1/2,4/9$, where $g_{tt}=1–2\mathrm{\Phi }(R)$ for a spherically-symmetric static metric. We investigate the maximum force for black holes and Buchdahl stars when one of the participating objects is charged and/or rotating while the other is neutral and nonrotating. It turns out that the maximum force between two Schwarzschild objects is universal, given in terms of the fundamental constant velocity of light and the gravitational constant in general relativity (GR) in the usual four-dimensional spacetime. In general this feature uniquely picks out the pure Lovelock gravity (having only one $N$th order term in action which includes GR in the linear order $N=1$) and the dimensional spectrum, $D=3N+1$, where $N$ is degree of the Lovelock polynomial action.

This study revisits the absorption and scattering process by which a massless scalar field impinges on a charged-dilatonic black hole. First, we review the classical analysis to obtain the deflection angle and the differential scattering cross section in terms of the mass, electric charge and dilatonic charge. Then, using the partial wave method, we determine the total absorption cross section numerically in terms of the decoupling parameter called $M\omega$, finding that the amplitude of the dilatonic black hole is lower than the Reissner-Nordström one for mild frequencies. In the high-frequency limit, the absorption cross section exhibits two different complex behaviors; the fine structure and the hyperfine structure. For the differential scattering cross section, smaller values of $M\omega$ lead to more significant amplitudes; the opposite scenario is obtained by increasing the charge-to-mass ratio. To fully grasp the main properties of the charged dilatonic black hole, we consider a different framework where the compact object is impinged by a charged massive scalar field. The superradiant effect is lessened for intermediate frequency concerning the Reissner-Nordström case. However, this effect does not necessarily imply the existence of any dynamical instability. In order to trigger the superradiant instability, unstable modes must remain trapped outside the event horizon with a mechanism based on the reflecting-mirror boundary conditions. In this way, a charged scalar field plus a charged black hole configure a charged black hole bomb. We provide an analytic formula (lower bound) for the values of the charge field, which can trigger this superradiant instability. We extend this minimal setup by considering the dilaton perturbations while freezing the other degree of freedom. The new perturbation scheme enhances the superradiance scattering and reduces the lower bound of the charge-to-mass ratio to develop a superradiant instability.

We perform several consistency tests between different phases of binary black hole dynamics; the inspiral, the merger, and the ringdown on the gravitational wave events GW150914 and GW170814. To perform these tests we excise the data explicitly in the time domain to avoid any spectral leakage between the different phases using gating and inpainting method. We estimate the posterior distributions on the mass and spin of the initial black holes and the final black hole separately and independently from the different phases in frequency-domain. We also compute the initial areas of the two individual black holes and the final area from the parameters describing the remnant black hole. This facilitates a test of Hawking’s black hole area theorem. We use different waveform models to quantify systematic waveform uncertainties for the area increase law with the two events. We find that these errors may lead to overstating the confidence with which the area theorem is confirmed. For example, we find $>99\%$ agreement with the area theorem for GW150914 if a damped sinusoid consisting of a single mode is used at merger to estimate the final area. This is because this model overestimates the final mass. Including an overtone of the dominant mode decreases the confidence to $\sim 94\%$; using a full merger-ringdown model further decreases the confidence to $\sim 85–90\%$. We find that comparing the measured change in area to the expected change in area yields a more robust test, as it also captures over estimates in the change of area. We find good agreement with GR when applying this test to GW150914 and GW170814.

Black holes in certain modified gravity theories that contain a scalar field coupled to curvature invariants are known to possess (monopole) scalar hair while non-black-hole spacetimes (like neutron stars) do not. Therefore, as a neutron star collapses to a black hole, scalar hair must grow until it settles to the stationary black hole solution with (monopole) hair. In this paper, we study this process in detail and show that the growth of scalar hair is tied to the appearance and growth of the event horizon (before an apparent horizon forms), which forces scalar modes that would otherwise (in the future) become divergent to be radiated away. We prove this result rigorously in general first for a large class of modified theories, and then we exemplify the results by studying the temporal evolution of the scalar field in scalar Gauss-Bonnet gravity in two backgrounds: (i) a collapsing Oppenheimer-Snyder background, and (ii) a collapsing neutron star background. In case (i), we find an exact scalar field solution analytically, while in case (ii) we solve for the temporal evolution of the scalar field numerically, with both cases supporting the conclusion presented above. Our results suggest that the emission of a burst of scalar field radiation is a necessary condition for black hole formation in a large class of modified theories of gravity.

We study the coupled dark energy model constructed from the general conformal transformation in which the coefficient of the conformal transformation depends on both the scalar field and its kinetic term. Under this conformal transformation, the action for subclass of degenerate higher-order scalar-tensor (DHOST) theories is related to the Einstein-Hilbert action. The evolution of the background universe has the scaling fixed point which corresponds to acceleration of the universe at late time. For the choices of parameters which make the late-time scaling point stable, the fixed point corresponding to $\varphi$-matter-dominated-era ($\varphi \mathrm{MDE}$) is a saddle point, and the universe can evolve from radiation dominated epoch through $\varphi \mathrm{MDE}$ before reaching the scaling point at late time with the cosmological parameters which satisfy the observational bound. During the $\varphi \mathrm{MDE}$, the effective equation of state parameter is slightly positive, so that one of possible mechanisms for alleviating the $H_0$ tension can be achieved. In this coupled dark energy model, the effective gravitational coupling for dark matter perturbations on small scales can be smaller than that in the $\mathrm{\Lambda }\mathrm{CDM}$ model. Therefore a growth rate of the dark matter perturbations is suppressed compared with the $\mathrm{\Lambda }\mathrm{CDM}$ model, which implies that the ${\sigma }_8$ tension could be alleviated.

Realizing the inflationary epoch driven by a pseudo-Nambu Goldstone boson could ensure the coveted flatness, and the sub-Planckian scales related to the dynamics of the paradigm. In this work, we have taken the most general form of such a scenario: Goldstone Inflation, proposed in Croon et al. [High Energy Phys. Nucl. Phys. 10 (2015) 020], and studied the model in Einstein-Gauss-Bonnet (EGB) gravity. Natural inflation, which is a limiting case of this model, is also studied here. The specific form of the EGB coupling gives ample opportunity to study the rich phenomenology associated with inflation as well as the reheating epoch. Predicted values of the inflationary observables, tensor to scalar ratio ($r$), and spectral index ($n_s$) are in good agreement with the recent observations from Planck’18. Thus, in the framework of EGB one can resurrect the model, which otherwise needs quite a bit of fine tuning or diversion from the canonical domain as studied in Bhattacharya and Gangopadhyay [Phys. Rev. D 101, 023509 (2020)], to survive in the standard cold inflationary scenario. Finally, the era of reheating is studied for different choices of model parameters.

Black holes with masses $\approx 1M_{\odot }$ cannot be produced via stellar evolution. A popular scenario of their formation involves transmutation of neutron stars—by accumulation of dark matter triggering gravitational collapse in the star centers. We show that this scenario can be realized in the models of bosonic dark matter despite the apparently contradicting requirements on the interactions of dark matter particles: on the one hand, they should couple to neutrons strongly enough to be captured inside the neutron stars, and on the other, their loop-induced self-interactions impede collapse. Observing that these conflicting conditions are imposed at different scales, we demonstrate that models with efficient accumulation of dark matter can be deformed at large fields to make unavoidable its subsequent collapse into a black hole. Workable examples include weakly coupled models with bent infinite valleys.

The Landau-Lifshitz equation is obtained from the Lorentz-Abraham-Dirac equation through “reduction of order.” It is the first in a divergent series of approximations that, after resummation, eliminate runaway solutions. Using Borel plane and transseries analysis we explain why this is, and show that a nonperturbative formulation of reduction of order can retain runaway solutions. We also apply transseries analysis to solutions of the Lorentz-Abraham-Dirac equation, essentially treating them as expansions in both time and a coupling. Our results illustrate some aspects of such expansions under changes of variables and limits.

We explore a novel approach to compute the force between a static quark and a static antiquark with lattice gauge theory directly. The approach is based on expectation values of Wilson loops or Polyakov loops with chromoelectric field insertions. We discuss theoretical and technical aspects in detail, in particular, how to perform their finite multiplicative renormalization and their evaluation using a multilevel algorithm. We also compare the numerical results for the static force to the corresponding results obtained in the traditional way, i.e., by computing first the static potential and then taking the derivative.

We study the interactions of a static quark-antiquark pair at nonzero temperature using realistic $2+1$ flavor lattice QCD calculations. The study consists of two parts. The first investigates the properties of Wilson line correlators in Coulomb gauge and compares to predictions of hard-thermal loop perturbation theory. As a second step we extract the spectral functions underlying the correlators using four conceptually different methods: spectral function fits, a hard-thermal-loop-inspired fit for the correlation function, Padé rational approximation and the Bayesian reconstruction. We find that our high-statistics Euclidean lattice data are amenable to different hypotheses for the shapes of the spectral function and we compare the implications of each analysis method for the existence and properties of a well-defined ground state spectral peak.

We perform a Langevin simulation of the $O(4)$ critical point, which lies in the dynamic universality class of “model G.” This is the dynamic universality class of the chiral phase transition in QCD with two massless flavors. The axial charge and the order parameter ${\varphi }_a=(\sigma ,\overrightarrow{\pi })$ exhibit a rich dynamical interplay, which reflects the qualitative differences in the hydrodynamic effective theories above and below $T_c$. From the axial charge correlators on the critical line we extract a dynamical critical exponent of $\zeta =1.47\pm 0.01(\text{stat.})$, which is compatible with the theoretical expectation of $\zeta =d/2$ (with $d=3$) when systematic errors are taken into account. At low temperatures, we quantitatively match the $O(4)$ simulations to the superfluid effective theory of soft pions.

We study the tomographic applications of a new phenomenon we dub “jet drift”—the deflection of high-energy particles and jets toward the direction of a flowing medium—to the quark-gluon plasma produced in heavy-ion collisions. While the physics of jet drift is quite general, for specificity we consider the case of photon-jet production at midrapidity. Beginning with the simplest possible model, a large slab of uniformly flowing plasma, we systematically introduce the geometrical elements of a heavy-ion collision in a simple optical Glauber model. We find that the moving medium causes the jet to drift in the direction of the flow, bending its trajectory and leaving detailed signatures of the flow pattern in the distribution of $\gamma +\text{jet}$ acoplanarities. In the elliptical geometries produced in noncentral collisions, this drift effect leads to a strong geometry coupling which persists despite the addition of event-by-event fluctuations in the jet production point, impact parameter, and acoplanarity. We propose a new observable to measure the jet drift effect through the correlation of $\gamma +\text{jet}$ acoplanarities with the elliptic flow of soft particles. Preliminary estimates suggest this correlation may be studied at sPHENIX and the LHC.