Higher derivative extensions of Einstein’s general relativity are commonly viewed as alternative and effective theories of gravity, not just due to the fact that these arise naturally in the string theory approach to gravity, but mainly for their use in cosmology to generate geometric dark energy models. In a recent paper [Phys. Rev. Lett. 114, 171601 (2015)] Lü et al. used numerical methods to obtain static, spherically symmetric and asymptotically flat black hole solutions in vacuum Einstein-Weyl gravity and showed that these are different than the Schwarzschild black hole. Inspired by the absence of any no-hair theorem for Einstein-Weyl gravity, in this paper we derive numerical examples of black hole solutions with massive scalar hair, and study the effect of the scalar field on the black hole structure. We limit ourselves to static and spherically symmetric solutions which are asymptotically flat such that the scalar field is regular on the horizon and vanishes at infinity.

Massive gravities in anti–de Sitter spacetime can be viewed as effective dual field theories of different phases of condensed matter systems with broken translational symmetry such as solids, (perfect) fluids, and liquid crystals. Motivated by this fact, we explore the black hole chemistry (BHC) of these theories and find a new range of novel phase transitions close to realistic ones in ordinary physical systems. We find that the equation of state of topological black holes (TBHs) at their inflection point(s) in $d$-dimensional spacetime reduces to a polynomial equation of degree ($d-4$), which yields up to $n=(d-4)$ critical points. As a result, for (neutral) TBHs, we observe triple-point phenomena with the associated first-order phase transitions (in $d\ge 7$), and a new phenomenon we call an $N$-fold reentrant phase transition, in which several ($N$) regions of thermodynamic phase space exhibit distinct reentrant phase transitions, with associated virtual triple points and zeroth-order phase transitions (in $d\ge 8$), as well as Van der Waals transitions (in $d\ge 5$) and reentrant (in $d\ge 6$) behavior. We conclude that BHC in higher-dimensional massive gravity is very likely to offer further new surprises.

We propose a step-by-step manual for the construction of alternative theories of gravity, perturbatively as well as nonperturbatively. The construction is guided by no more than two fundamental principles that we impose on the gravitational dynamics: invariance under spacetime diffeomorphisms and causal compatibility with given matter dynamics, provided that spacetime is additionally endowed with matter fields. The developed framework then guides the computation of the most general, alternative theory of gravity that is consistent with the two fundamental requirements. Utilizing this framework we recover the cosmological sector of general relativity solely from assuming that spacetime is a spatially homogeneous and isotropic metric manifold. On top of that, we explicitly test the perturbative framework by deriving the most general third-order expansion of a metric theory of gravity that is causally compatible with a Klein-Gordon scalar field. Thereby we recover the perturbative expansion of general relativity. To demonstrate how new physics emerges from our approach, we finally construct the most comprehensive third-order expansion of a theory of gravity that supports general (not necessarily Maxwellian) linear electrodynamics.

We study the nonadiabatic cosmological production of ultralight dark matter (ULDM) under a minimal set of assumptions: a free ultralight real scalar as a spectator field in its Bunch-Davies vacuum state during inflation and instantaneous reheating into a radiation dominated era. For ULDM fields minimally coupled to gravity, nonadiabatic particle production yields a distribution function peaked at low comoving momentum ${\mathcal{N}}_k\propto 1/k^3$. The infrared behavior is a remnant of the infrared enhancement of light minimally coupled fields during inflation. We obtain the full energy momentum tensor, show explicitly its equivalence with the fluid-kinetic one in the adiabatic regime, and extract the abundance, equation of state, and free-streaming length (cutoff in the matter power spectrum). Taking the upper bound on the scale of inflation from Planck, the ULDM saturates the dark matter abundance for $m\simeq 1.5\times {10}^{-5}\mathrm{eV}$ with an equation of state parameter $w\simeq {10}^{-14}$ and a free-streaming length ${\lambda }_{\mathrm{fs}}\simeq 70\mathrm{pc}$. Thus this cosmologically produced ULDM yields a cold dark matter particle. We argue that the abundance from nonadiabatic production yields a lower bound on generic ULDM and axionlike particles that must be included in any assessment of ULDM as a dark matter candidate.

We analyze the final release of the Planck satellite data to constrain the gravitational lensing potential in a model-independent manner. The amount of lensing determined from the smoothing of the acoustic peaks in the temperature and polarization power spectra is $2\sigma$ too high when compared with the measurements using the lensing reconstruction and $2.8\sigma$ too high when compared with $\mathrm{\Lambda }\mathrm{CDM}$ expectation based on the “unlensed” portion of the temperature and polarization power spectra. The largest change from the previous data release is the $\mathrm{\Lambda }\mathrm{CDM}$ expectation, driven by improved constraints to the optical depth to reionization. The anomaly still is inconsistent with actual gravitational lensing, given that the lensing reconstruction constraints are discrepant independent of the model. Within the context of $\mathrm{\Lambda }\mathrm{CDM}$, improvements in its parameter constraints from lensing reconstruction bring this tension to $2.1\sigma$ and from further adding baryon acoustic oscillation and Pantheon supernova data to a marginally higher $2.2\sigma$. Once these other measurements are included, marginalizing this lensinglike anomaly cannot substantially resolve tensions with low-redshift measurements of $H_0$ and $S_8$ in $\mathrm{\Lambda }\mathrm{CDM}$, $\mathrm{\Lambda }\mathrm{CDM}+N_{\mathrm{eff}}$, or $\mathrm{\Lambda }\mathrm{CDM}+\sum m_{\nu }$; furthermore, the artificial strengthening of constraints on $\sum m_{\nu }$ is less than 20%.

The rotational kinematic Sunyaev-Zeldovich (rkSZ) signal, imprinted on the cosmic microwave background (CMB) by the gaseous halos (spinning “atmospheres”) of foreground galaxies, would be a novel probe of galaxy formation. Although the signal is too weak to detect in individual galaxies, we analyze the feasibility of its statistical detection via stacking CMB data on many galaxies for which the spin orientation can be estimated spectroscopically. We use an “optimistic” model, in which fully ionized atmospheres contain the cosmic baryon fraction and spin at the halo’s circular velocity $v_{\mathrm{circ}}$, and a more realistic model, based on hydrodynamical simulations, with multiphase atmospheres spinning at a fraction of $v_{\mathrm{circ}}$. We incorporate realistic noise estimates into our analysis. Using low-redshift galaxy properties from the MaNGA spectroscopic survey (with median halo mass of $6.6\times {10}^{11}{M}_{\odot }$), and CMB data quality from Planck, we find that a $3\sigma$ detection would require a $\mathrm{few}\times {10}^4$ galaxies, even in the optimistic model. This is too high for current surveys, but upcoming higher-angular resolution CMB experiments will significantly reduce the requirements: stacking CMB data on galaxy spins in a $\sim 10$ ${\mathrm{deg}}^2$ can rule out the optimistic models, and $\approx 350{\mathrm{deg}}^2$ will suffice for a $3\sigma$ detection with ACT. As a proof-of-concept, we stacked Planck data on the position of $\approx \mathrm{2,000}$ MaNGA galaxies, aligned with the galaxies’ projected spin, and scaled to their halos’ angular size. We rule out average temperature dipoles larger than $\approx 1.9\mu \mathrm{K}$ around field spiral galaxies.

We analyze a new numerical relativity dataset of spinning but nonprecessing binary black holes on eccentric orbits, with eccentricities from approximately 0.1 to 0.5, with dimensionless spins up to 0.75 included at mass ratios $q=m_1/m_2=(1,2)$, and further nonspinning binaries at mass ratios $q=(1.5,3,4)$. A comparison of the final mass and spin of these simulations with noneccentric data extends previous results in the literature on circularization of eccentric binaries to the spinning case. For the $(l,m)=(2,2)$ spin-weighted spherical harmonic mode, we construct eccentric hybrid waveforms that connect the numerical relativity data to a post-Newtonian description for the inspiral, and we discuss the limitations in the current knowledge about post-Newtonian theory which complicate the generation of eccentric hybrid waveforms. We also perform a Bayesian parameter estimation study, quantifying the parameter biases introduced when using three different quasicircular waveform models to estimate the parameters of highly eccentric binary systems. We find that the used aligned-spin quasicircular model including higher order modes produces lower bias in certain parameters than the nonprecessing quasicircular model without higher order modes and the quasicircular precessing model.

In this work we provide a bosonized version of the Thirring model in $2+1$ dimensions in the case of single fermion species, where we do not have the benefit of large $N$ expansion. In this situation there are very few analytical methods to extract nonperturbative information. Meanwhile, nontrivial behavior is expected to take place precisely in this regime. To establish the bosonization of the Thirring model, we consider a deformation of a basic fermion-boson duality relation in $2+1$ dimensions. The bosonized model interpolates between the ultraviolet and infrared regimes, passing several consistency checks and recovering the usual bosonization relation of the web of dualities in the infrared limit. In addition the duality predicts the existence of a nontrivial ultraviolet fixed point in the Thirring model.

The observation of lepton flavor violating processes at colliders could be a clear signal of a nonminimal neutrino sector. We define a 5-parameter model with a pair of TeV fermion singlets and arbitrary mixings with the three active neutrino flavors. Then we analyze several flavor violating transitions ($\ell \to {\ell }^{\prime }\gamma$, ${\ell }^{\prime }{\ell }^{\prime \prime }{\overline{\ell }}^{\prime \prime \prime }$, or $\mu -e$ conversions in nuclei) and $Z\to \overline{\ell }{\ell }^{\prime }$ decays induced by the presence of heavy neutrinos. In particular, we calculate all the one-loop contributions to these processes and present their analytic expressions. We focus on the genuine effects of the heavy Majorana masses, comparing the results in that case with the ones obtained when the two heavy neutrinos define a Dirac field. Finally, we use our results to update the bounds on the heavy-light mixings in the neutrino sector.

We provide a dynamical mechanism for the generation of the Cabibbo-Kobayashi-Maskawa matrix in the context of a recently proposed model of flavor. The framework, based on the paradigm that Yukawa couplings are effective low energy couplings generated radiatively by dark sector interactions, is here extended to include a new scalar field which plays the role of a dark flavon. Being singlet under the Standard Model gauge group but charged under the $U(1)$ symmetry of the dark sector, this particle sources new two- and three-loop diagrams that result in off-diagonal Yukawa interactions, thereby providing a simple explanation for the observed structure of the Cabibbo-Kobayashi-Maskawa (CKM) matrix. By using an effective parametrization of these new loop contributions, we show that the CKM matrix elements can be correctly reproduced for perturbative values of the involved couplings. New implications for dark matter phenomenology are briefly outlined.

We extend the recently proposed $SU(5)\times {\mathcal{T}}_{13}$ model for the asymmetric texture to the up-type quark and seesaw sectors. The hierarchical up-type quark masses are generated from higher-dimensional operators involving family-singlet Higgses, gauge-singlet familons, and vectorlike messengers. The complex-tribimaximal seesaw mixing arises from the vacuum structure of a minimal number of familons, resulting in an alignment between the Yukawa and Majorana matrices of the seesaw formula. Introducing four right-handed neutrinos, normal ordering of the light neutrino masses is obtained, with $m_{{\nu }_1}=27.6\mathrm{meV}$, $m_{{\nu }_2}=28.9\mathrm{meV}$ and $m_{{\nu }_3}=57.8\mathrm{meV}$. Their sum almost saturates Planck’s cosmological upper bound (120 meV). The right-handed neutrino masses are expressed in terms of two parameters for a particular choice of familon vacuum alignment. We predict the $\cancel{CP}$ Jarlskog-Greenberg invariant to be $|\mathcal{J}|=0.028$, consistent with the current Particle Data Group (PDG) estimate, and Majorana invariants $|{\mathcal{I}}_1|=0.106$ and $|{\mathcal{I}}_2|=0.011$. A sign ambiguity in the model parameters leads to two possibilities for the invariant mass parameter $|m_{\beta \beta }|$: 13.02 or 25.21 meV, both within an order of magnitude of the most rigorous experimental upper limit (61–165 meV).

We present a minimal model of fermionic dark matter (DM), where a singlet Dirac fermion can interact with the Standard Model (SM) particles via the torsion field of gravitational origin. In general, torsion can be realized as an antisymmetric part of the affine connection associated with the spacetime diffeomorphism symmetry and thus can be thought of as a massive axial vector field. Because of its gravitational origin, the torsion field couples to all the fermion fields including the DM with equal strength, which makes the model quite predictive. The DM is naturally stable without any imposition of ad hoc symmetry, e.g., ${\mathcal{Z}}_2$. Apart from producing the correct thermal abundance, a singlet fermion can easily evade the stringent bounds on the spin-independent DM-nucleon direct detection cross section due to its axial nature. However, in the allowed parameter space, strong bounds can be placed on the torsion mass and its couplings to fermions from the recent LHC searches. Assuming a nonuniversal torsion-DM and torsion-SM coupling, smaller values of torsion masses may become allowed. In both cases we also study the reach of spin-dependent direct detection searches of the DM.

We present the first numerical study of the ultraviolet dynamics of nonasymptotically free gauge-fermion theories at large number of matter fields. As test bed theories, we consider non-Abelian SU(2) gauge theories with 24 and 48 Dirac fermions on the lattice. For these numbers of flavors, asymptotic freedom is lost, and the theories are governed by a Gaussian fixed point at low energies. In the ultraviolet, they can develop a physical cutoff and therefore be trivial, or achieve an interacting safe fixed point and therefore be fundamental at all energy scales. We demonstrate that the gradient flow method can be successfully implemented and applied to determine the renormalized running coupling when asymptotic freedom is lost. Additionally, we prove that our analysis is connected to the Gaussian fixed point as our results nicely match with the perturbative beta function. Intriguingly, we observe that it is hard to achieve large values of the renormalized coupling on the lattice. This might be an early sign of the existence of a physical cutoff and imply that a larger number of flavors is needed to achieve the safe fixed point. A more conservative interpretation of the results is that the current lattice action is unable to explore the deep ultraviolet region where safety might emerge. Our work constitutes an essential step toward determining the ultraviolet fate of nonasymptotically free gauge theories.

Topological insulators in odd dimensions are characterized by topological numbers. We prove the well-known relation between the topological number given by the Chern character of the Berry curvature and the Chern-Simons level of the low energy effective action for a general class of Hamiltonians bilinear in the fermion with general U(1) gauge interactions including nonminimal couplings by an explicit calculation. A series of Ward-Takahashi identities are crucial to relate the Chern-Simons level to a winding number, which could then be directly reduced to Chern character of Berry curvature by carrying out the integral over the temporal momenta.

We determine the leading Fock state light front wave functions (LFWFs) of the pion and kaon via light front projections of the covariant Bethe-Salpeter wave function. Using these LFWFs we study the multidimensional images of the valence quarks in the pion and kaon that are provided by their generalized parton distribution functions (GPDs) and transverse momentum dependent parton distribution functions (TMDs). Moments of the GPDs are taken to obtain the electromagnetic and gravitational form factors of the pion and kaon, and comparisons to available experimental and lattice data are made. Highlights from this study include predictions that the mean-squared impact parameter for the quarks in the pion and kaon are: $⟨{\mathit{b}}_T^2{⟩}_u^{\pi }=0.11{\mathrm{fm}}^2$, $⟨{\mathit{b}}_T^2{⟩}_s^K=0.08{\mathrm{fm}}^2$, and $⟨{\mathit{b}}_T^2{⟩}_u^K=0.13{\mathrm{fm}}^2$, and therefore the $s$ quark in the kaon is much closer to the center of transverse momentum than the $u$ quark. From the electromagnetic and gravitational form factors we find that the light-cone energy radii are about 60% smaller than the light-cone charge radii for each quark sector in the pion and kaon. A quantitative measure of the importance of the leading Fock state is obtained via comparison with a full Dyson-Schwinger equations calculation (containing an infinite tower of Fock states) for the pion form factor.

The massive two-dimensional Nambu–Jona-Lasinio model with isospin (isoNJL) is reconsidered in the large $N_c$ limit. We continue the exploration of its phase diagram by constructing missing first-order phase boundaries. At zero temperature, a phase boundary in the plane of baryon and isospin chemical potentials separates the vacuum from a crystal phase. We derive it from the baryon spectrum of the isoNJL model which, in turn, is obtained via a numerical Hartree-Fock (HF) calculation. At finite temperature, a first-order phase boundary sheet is found using a thermal HF calculation. It interpolates smoothly between the zero temperature phase boundary and the perturbative sheet. The calculations remain tractable owing to the assumption that the charged pion condensate vanishes. In that case, most of the calculations can be done with methods developed in the past for solving the massive one-flavor NJL model.

Spectroscopic parameters and decay channels of the vector resonance $Y(2175)$ are studied by considering it as a diquark-antidiquark state with the quark content $su\overline{s}\overline{u}$. The mass and coupling of the tetraquark $Y(2175)$ are calculated using the QCD two-point sum rules by taking into account various quark, gluon and mixed condensates up to dimension 15. Partial widths of its strong decays to $\varphi f_0(980)$, $\varphi \eta$, and $\varphi {\eta }^{\prime }$ are computed as well. To this end, we explore the vertices $Y\varphi f_0(980)$, $Y\varphi \eta$, and $Y\varphi {\eta }^{\prime }$, and calculate the corresponding strong couplings by means of the QCD light-cone sum rule method. The coupling $G_{Y\varphi f}$ of the vertex $Y\varphi f_0(980)$ is found using the full version of this method, and by treating the scalar meson $f_0(980)$ as a diquark-antidiquark tetraquark state. The couplings $g_{Y\varphi \eta }$ and $g_{Y\varphi {\eta }^{\prime }}$, however, are calculated by applying the soft-meson approximation to the light-cone sum rule method. Prediction for the mass of the resonance $m_Y=(2173\pm 85)\mathrm{MeV}$ is in excellent agreement with the data of the BABAR Collaboration [Phys. Rev. D 74, 091103 (2006)], and within errors of calculations is compatible with the result reported by BESIII [Phys. Rev. D 91, 052017 (2015)]. The full width ${\mathrm{\Gamma }}_{\mathrm{full}}=(91.1\pm 20.5)\mathrm{MeV}$ of the $Y(2175)$ saturated by its three strong decay channels is in a reasonable agreement with existing experimental data.

The quarks and gluons are confined objects; they cannot be put on the mass shell. It is questionable to apply the Landau equation to study the Feynman diagrams in the QCD sum rules. Furthermore, we carry out the operator product expansion in the deep Euclidean region $p^2\to -\infty$, where the Landau singularities cannot exist. The Landau equation servers as a kinematical equation in the momentum space and is independent on the factorizable and nonfactorizable properties of the Feynman diagrams in the color space. The meson-meson scattering state and tetraquark molecular state both have four valence quarks, which form two color-neutral clusters; we cannot distinguish the contributions based on the two color-neutral clusters in the factorizable Feynman diagrams. Lucha et al. assert that the contributions at the order $\mathcal{O}({\alpha }_s^k)$ with $k\le 1$ in the operator product expansion, which are factorizable in the color space, are exactly canceled out by the meson-meson scattering states at the hadron side, and the tetraquark molecular states begin to receive contributions at the order $\mathcal{O}({\alpha }_s^2)$. Such an assertion is questionable, we refute the assertion in details, and choose an axial-vector current and a tensor current to examine the outcome of the assertion. After a detailed analysis, we observe that the meson-meson scattering states cannot saturate the QCD sum rules, while the tetraquark molecular states can saturate the QCD sum rules. The Landau equation is of no use to study the Feynman diagrams in the QCD sum rules for the tetraquark molecular states; the tetraquark molecular states begin to receive contributions at the order $\mathcal{O}({\alpha }_s^0/{\alpha }_s^1)$ rather than at the order $\mathcal{O}({\alpha }_s^2)$.

Because of the discovery of the hidden-charm pentaquark $P_c$ states by the LHCb Collaboration, the interests in the candidates of hidden-bottom pentaquark $P_b$ states are increasing. They are anticipated to exist as the analogs of the $P_c$ states in the bottom sector and predicted by many models. We give an exploration of searching for a typical $P_b$ in the $\gamma p\to \mathrm{\Upsilon }p$ reaction, which shows a promising potential to observe it at an electron-ion collider. The possibility of searching for $P_b$ in open-bottom channels is also briefly discussed. Meanwhile, the $t$-channel nonresonant contribution, which in fact covers several interesting topics at low energies, is systematically investigated.

The work concerns the quasielastic charged current neutrino-neutron and antineutrino-proton interactions. Single, double, and triple spin asymmetries are computed and analyzed. The spin asymmetries are sensitive to the axial form factor of the nucleon. In particular, the target-recoil double spin asymmetry and the lepton-target-recoil triple spin asymmetry depend strongly on the axial form factor of the nucleon. Indeed, the sign and shape of these components depend on the axial mass parameter. All the asymmetries, except the lepton polarization, are observables well suited to study the nonstandard interactions described by the second-class current contribution.