We perform an $n_f=2+1$ lattice study of a number of channels where past claims exist in the literature for the existence of strong-interaction-stable light-heavy tetraquarks. We find no evidence for any such deeply bound states, beyond the $J^P=1^{+}$, $I=0$ $ud\overline{b}\overline{b}$ and $I=1/2$ $\ell s\overline{b}\overline{b}$ states already identified in earlier lattice studies. We also describe a number of systematic improvements to our previous lattice studies, including working with larger $m_{\pi }L$ to better suppress possible finite volume effects, employing extended sinks to better control excited-state contamination, and expanding the number of operators used in the GEVP analyses. Our results also allow us to rule out several phenomenological models which predict significant tetraquark binding in channels where no such binding is found.

The forward Compton amplitude describes the process of virtual photon scattering from a hadron and provides an essential ingredient for the understanding of hadron structure. As a physical amplitude, the Compton tensor naturally includes all target mass corrections and higher twist effects at a fixed virtuality, $Q^2$. By making use of the second-order Feynman-Hellmann theorem, the nucleon Compton tensor is calculated in lattice QCD at an unphysical quark mass across a range of photon momenta $3\lesssim Q^2\lesssim 7{\mathrm{GeV}}^2$. This allows for the $Q^2$ dependence of the low moments of the nucleon structure functions to be studied in a lattice calculation for the first time. The results demonstrate that a systematic investigation of power corrections and the approach to parton asymptotics is now within reach.

The formalism for uniform description of the Drell-Yan transverse-momentum spectrum is presented in a framework of high-energy factorization, which smoothly interpolates between Collins-Soper-Sterman formalism at $|{\mathbf{q}}_T|\ll Q$ and usual collinear parton model at $|{\mathbf{q}}_T|\sim Q\ll \sqrt{S}$. The new formula for deriving unintegrated parton distribution functions (UPDFs) from collinear ones is introduced, which leads to excellent description of the shape of $Z$-boson $|{\mathbf{q}}_T|$-spectrum at high energies up to $|{\mathbf{q}}_T|/\sqrt{S}\simeq 0.02$. Description of normalized $|{\mathbf{q}}_T|$-distributions at low energies is achieved via the fit of nonperturbative parameters of quark UPDFs. Reasonable description of angular distributions of leptons in the dilepton center-of-mass frame is also obtained with new UPDFs.

We revisit the isospin-breaking and electromagnetic corrections to the decay ${\tau }^{-}\to {\pi }^{-}{\pi }^0{\nu }_{\tau }$, which allow its use as input in the two-pion contribution to the (leading-order) hadronic vacuum polarization part of the muon anomalous magnetic moment. We extend a previous resonance chiral Lagrangian analysis, which included those operators saturating the next-to-leading-order chiral low-energy constants, by including the contributions appearing at the next order. As a result, we improve agreement between the two-pion tau decay and $e^{+}{e}^{-}$ data and reduce the discrepancy between experiment and the Standard Model prediction of $a_{\mu }$ (using $\tau$ input) to the approximately $2\sigma$ level.

The Curci-Ferrari model has been shown to provide a good grasp on pure Yang-Mills correlation functions in the Landau gauge, already at one-loop order. In a recent work, the robustness of these results has been tested by evaluating the two-loop corrections to the gluon and ghost propagators. We pursue this systematic investigation by computing the ghost-antighost-gluon vertex to the same accuracy in a particular kinematic configuration that makes the calculations simpler. Because both the parameters of the model and the normalizations of the fields have already been fixed in a previous work, the present calculation represents both a pure prediction and a stringent test of the approach. We find that the two-loop results systematically improve the comparison to Monte Carlo simulations as compared to earlier one-loop results. The improvement is particularly significative in the SU(3) case where the predicted ghost-antighost-gluon vertex is in very good agreement with the data. The same comparison in the SU(2) case is not as good, however. This may be due to the presence of a larger coupling constant in the infrared in that case although we note that a similar mismatch has been quoted in nonperturbative continuum approaches. Despite these features of the SU(2) case, it is possible to find sets of parameters fitting both the propagators and the ghost-antighost-gluon vertex to a reasonable accuracy.

We studied the effect of a strong magnetic field ($B$) on the electrical conductivity of hot quark matter. The electrical conductivity is a key transport coefficient determining the time dependence and strength of magnetic fields generated in a relativistic heavy-ion collision. A magnetic field induces Hall anisotropic conduction, phase-space Landau-level quantization and, if sufficiently strong, interferes with prominent QCD phenomena such as dynamical quark mass generation, likely affecting the quark matter electrical conductivity, which depends strongly on the quark masses. To address these issues, we used a quasiparticle description of quark matter in which the electric charge carriers are constituent quarks with temperature- and magnetic-field-dependent masses predicted by a Nambu–Jona-Lasinio model. The model accurately describes recent lattice QCD results showing magnetic catalysis at low temperatures and inverse magnetic catalysis at temperatures close to the pseudocritical temperature ($T_{\mathrm{pc}}$) of the QCD phase transition. We found that the magnetic field increases the conductivity component parallel to it and decreases the transverse component, in qualitative agreement with recent lattice QCD results. In addition, we found that (1) the space anisotropy of the conductivity increases with $B$, (2) the longitudinal conductivity increases due to phase-space Landau-level quantization, (3) a lowest Landau level approximation behaves poorly for temperatures close to $T_{\mathrm{pc}}$, and (5) inverse magnetic catalysis leaves a distinctive signal in all components of the conductivity, a prominent peak at $T_{\mathrm{pc}}$. Our study adds to the existing body of work on the hot quark matter electrical conductivity by incorporating nontrivial temperature and magnetic field effects on dynamical mass generation. Our results are useful both for studies employing magnetohydrodynamics simulations of heavy-ion collisions and for getting insight on lattice QCD results.

We construct QCD sum rules for nonperturbative studies without assuming the quark-hadron duality for the spectral density at low energy on the hadron side. Instead, both resonance and continuum contributions to the spectral density are solved with the operator-product-expansion input on the quark side by treating sum rules as an inverse problem. This new formalism does not involve the continuum threshold, does not require the Borel transformation and stability analysis, and can be extended to extract properties of excited states. Taking the two-current correlator as an example, we demonstrate that the series of $\rho$ resonances can emerge in our formalism, and the decay constants $f_{\rho (770)}(f_{\rho (1450)},f_{\rho (1700)},f_{\rho (1900)})\approx 0.22$ (0.19, 0.14, 0.14) GeV for the masses $m_{\rho (770)}(m_{\rho (1450)},m_{\rho (1700)},m_{\rho (1900)})\approx 0.78$ (1.46, 1.70, 1.90) GeV are determined. We also show that the decay width ${\mathrm{\Gamma }}_{\rho (770)}\approx 0.17\mathrm{GeV}$ can be obtained by substituting a Breit-Wigner parametrization for the $\rho (770)$ pole on the hadron side. It is observed that quark condensates of dimension-six on the quark side are crucial for establishing those $\rho$ resonances. Handling the conventional sum rules with the duality assumption as an inverse problem, we find that the multiple pole sum rules widely adopted in the literature do not describe the $\rho$ excitations reasonably. The precision of our theoretical outcomes can be improved systematically by including higher-order and higher-power corrections on the quark side. Broad applications of this formalism to abundant low energy QCD observables are expected.

The off-shell Higgs production in $pp\to ZZ$ at LHC provides at present the most direct measurement of the Higgs width in the absence of beyond the standard model contributions. Here, we analyze the impact of anomalous $Z$ couplings to fermions on the Higgs width determination. We show that, despite these couplings being strongly constrained by the available electroweak precision data, they can substantially affect the Higgs width determination at the LHC Runs 2 and 3. Conversely, in larger integrated luminosities runs, such as those foreseen at the high luminosity LHC and high energy LHC setups, the effect of such anomalous interactions in the Higgs width measurement is minimal.

Understanding the role of charge density wave (CDW) in high-temperature superconductivity is a longstanding challenge in condensed matter physics. We construct a holographic superconductor model in which the $U(1)$ symmetry is spontaneously broken only due to the presence of CDWs, rather than previously known free charges with constant density. Below the critical temperature of superconductivity, CDW phase and superconducting phase coexist, which is also justified by the numerical results of optical conductivity. The competitive and cooperative relations between CDW phase and superconducting phase are observed. This work supports the opinion that the appearance of pseudo-gap in CDW phase promotes the prepairing of electrons as well as holes such that the formation of superconductivity benefits from the presence of CDW.

We study the spectrum of semiclassical rotating strings in de Sitter space and its consistency. Even though a naive extrapolation of the linear Regge trajectory on flat space implies a violation of the Higuchi bound (a unitarity bound on the mass of higher-spin particles in de Sitter space), the curved space effects turn out to modify the trajectory to respect the bound. Interestingly, as a consequence of accelerated expansion, there exists a maximum spin for each Regge trajectory, which is helpful to make the spectrum consistent with the Higuchi bound, but at the same time, it could be an obstruction to stringy UV completion based on an infinite higher-spin tower. By pushing further this observation, we demonstrate that the vacuum energy $V$ inflating the Universe has to be bounded by the string scale $M_s$ as $V\lesssim M_s^4$, if UV completion is achieved with the leading Regge trajectory of higher spin states up to the 4D Planck scale. Its application to inflation in the early Universe implies an upper bound on the tensor-to-scalar ratio, $r\lesssim 0.01\times (M_s/{10}^{16}\mathrm{GeV}{)}^4$, which is within the scope of the near future CMB experiments. We also discuss another possibility that UV completion is achieved by multiple Regge trajectories.

The star product usually associated with the Snyder model of noncommutative geometry is nonassociative, and this property prevents the construction of a proper Hopf algebra. It is however possible to introduce a well-defined Hopf algebra by including the Lorentz generators and their conjugate momenta into the algebra. In this paper, we study the realizations of this extended Snyder spacetime, and obtain the coproduct and twist and the associative star product in a Weyl-ordered realization, to first order in the noncommutativity parameter. We then extend our results to the most general realizations of the extended Snyder spacetime, always up to first order.

An example of a consistent theory with massive higher spin fields is constructed in flat space-time of dimension three. The action is written in the light-cone gauge. The theory has certain stringlike features, e.g., its spectrum is unbounded in spin and mass; the theory admits Chan-Paton factors. The quartic and the higher tree-level amplitudes vanish, which softens the UV behavior at the loop level and provides a new mechanism of how massive higher spin states can resolve the quantum gravity problem.

We holographically calculate two-point functions in the pseudoconformal universe, an early universe alternative to inflation. The pseudoconformal universe can be modeled as a defect conformal field theory, where the reheating surface is a codimension-1 spacelike defect that breaks the conformal algebra to a de Sitter subalgebra. The dual spacetime geometries are domain walls with de Sitter symmetry in an asymptotically anti–de Sitter spacetime. We compute two-point functions of scalars and stress tensors by solving the linearized equations for scalar and tensor fluctuations about these backgrounds.

We develop a nonperturbative functional framework for computing real-time correlation functions in strongly correlated systems. The framework is based on the spectral representation of correlation functions and dimensional regularization. Therefore, the nonperturbative spectral renormalization setup here respects all symmetries of the theories at hand. In particular, this includes space-time symmetries, as well as internal symmetries such as chiral symmetry, and gauge symmetries. Spectral renormalization can be applied within general functional approaches such as the functional renormalization group, Dyson-Schwinger equations, and two- or $n$-particle irreducible approaches. As an application, we compute the full, nonperturbative, spectral function of the scalar field in the ${\varphi }^4$-theory in $2+1$ dimensions from spectral Dyson-Schwinger equations. We also compute the $s$-channel spectral function of the full ${\varphi }^4$-vertex in this theory.

We propose a $1/N$ expansion of Starobinsky and Yokoyama’s effective stochastic approach for light quantum fields on superhorizon scales in de Sitter spacetime. We explicitly compute the spectrum and the eigenfunctions of the Fokker-Planck operator for a $\mathrm{O}(N)$-symmetric theory with quartic self-interaction at leading and next-to-leading orders in this expansion. We obtain simple analytical expressions valid in various nonperturbative regimes in terms of the interaction coupling constant.

Theories of scalars and gravity, with nonminimal interactions, $\sim (M_P^2+F({\varphi }_i))R+L({\varphi }_i)$, have graviton exchange induced contact terms. These terms arise in single particle reducible diagrams with vertices, $\propto q^2$, that cancel the Feynman propagator denominator, $1/q^2$, and are familiar in various other physical contexts. In gravity these lead to additional terms in the action such as $\sim F({\varphi }_i)T_{\mu }^{\mu }({\varphi }_i)/M_P^2$ and $F({\varphi }_i){\partial }^{2}F({\varphi }_i)/M_P^2$. The contact terms are equivalent to induced operators obtained by a Weyl transformation that removes the nonminimal interactions, leaving a minimal Einstein-Hilbert gravitational action. This demonstrates explicitly the equivalence of different representations of the action under Weyl transformations, both classically and quantum mechanically. To avoid such “hidden contact terms” one is compelled to go to the minimal Einstein-Hilbert representation.

In this work we investigate the matrix elements of the energy-momentum tensor for massless on-shell states in four-dimensional unitary, local, and Poincaré covariant quantum field theories. We demonstrate that these matrix elements can be parametrized in terms of covariant multipoles of the Lorentz generators, and that this gives rise to a form factor decomposition in which the helicity dependence of the states is factorized. Using this decomposition we go on to explore some of the consequences for conformal field theories, deriving the explicit analytic conditions imposed by conformal symmetry, and using examples to illustrate that they uniquely fix the form of the matrix elements. We also provide new insights into the constraints imposed by the existence of massless particles, showing in particular that massless free theories are necessarily conformal.

The physical principles of causality and unitarity put strong constraints on the analytic structure of the flat-space S matrix. In particular, these principles give rise to the Steinmann relations, which require that the double discontinuities of scattering amplitudes in partially overlapping momentum channels vanish. Conversely, at cosmological scales, the imprint of causality and unitarity is in general less well understood—the wavefunction of the Universe lives on the future spacelike boundary, and has all time evolution integrated out. In the present work, we show how the flat-space Steinmann relations emerge from the structure of the wavefunction of the Universe, and derive similar relations that apply to the wavefunction itself. This is done within the context of scalar toy models whose perturbative wavefunction has a first-principles definition in terms of cosmological polytopes. In particular, we use the fact that the scattering amplitude is encoded in the scattering facet of cosmological polytopes, and that cuts of the amplitude are encoded in the codimension-one boundaries of this facet. As we show, the flat-space Steinmann relations are thus implied by the nonexistence of codimension-two boundaries at the intersection of the boundaries associated with pairs of partially overlapping channels. Applying the same argument to the full cosmological polytope, we also derive Steinmann-type constraints that apply to the full wavefunction of the Universe. These arguments show how the combinatorial properties of cosmological polytopes lead to the emergence of flat-space causality in the S matrix, and provide new insights into the analytic structure of the wavefunction of the Universe.

We have discovered a new type of scalarized charged black holes in a surprisingly simple system: an Einstein-Maxwell-Klein-Gordon field theory where the three fields couple nonminimally through a Horndeski vector-tensor term. In addition to hairy charged black holes, this system exhibits Horndeski-Reissner-Nordstrom solutions and ordinary Reissner-Nordstrom ones which bifurcate to the scalarized solutions. There exist also vector-tensor black hole solutions which possess central curvature singularities although their metric components are finite there, and also solutions with naked singularities producing regular metric components everywhere around them. We analyze the solutions and present their main features.

We compute spin-orbit effects in the equations of motion, binding energy, and energy loss of binary systems of compact objects at the next-to-leading order in the post-Newtonian approximation in the effective field theory (EFT) framework. We then use these quantities to compute the evolution of the orbital frequency and accumulated orbital phase including spin-orbit effects beyond the dominant order. To obtain the results presented in this paper, we make use of known ingredients in the EFT literature, such as the potential and the multipole moments with spin effects at next-to-leading order, and which are given in the linearized harmonic gauge and with the spins in the locally flat frame. We also obtain the correction to the center-of-mass frame caused by spin-orbit effects at next-to-leading order. We demonstrate the equivalence between our EFT results and those which were obtained elsewhere using different formalisms. The results presented in this paper provide us with the final ingredients for the construction of theoretical templates for gravitational waves including next-to-leading order spin-orbit effects, which will be presented in a future publication.