We prove the existence and give a construction procedure of Euclidean-invariant exact solutions to the Wetterich equation [Phys. Lett. B 301, 90 (1993)] in $d>2$ dimensions satisfying the naive boundary condition of a massive and interacting real scalar ${\varphi }^4$ theory in the ultraviolet limit as well as a generalized free theory in the infrared limit. The construction produces the momentum-dependent correlation functions to all orders through an iterative scheme, based on a self-consistent ansatz for the four-point function. The resulting correlators are bounded at all regulator scales, and we determine explicit bounds capturing the asymptotics in the UV and IR limits. Furthermore, the given construction principle may be extended to other systems and might become useful in the study of general properties of exact solutions.

We formulate four-dimensional $\mathcal{N}=1$ supersymmetric nonlinear sigma models on Hermitian symmetric spaces with higher derivative terms, free from the auxiliary field problem and the Ostrogradski’s ghosts, as gauged linear sigma models. We then study Bogomol’nyi-Prasad-Sommerfield equations preserving $1/2$ or $1/4$ supersymmetries. We find that there are distinct branches, that we call canonical ($F=0$) and noncanonical ($F\ne 0$) branches, associated with solutions to auxiliary fields $F$ in chiral multiplets. For the $\mathbb{C}{P}^N$ model, we obtain a supersymmetric $\mathbb{C}{P}^N$ Skyrme-Faddeev model in the canonical branch while in the noncanonical branch the Lagrangian consists of solely the $\mathbb{C}{P}^N$ Skyrme-Faddeev term without a canonical kinetic term. These structures can be extended to the Grassmann manifold $G_{M,N}=SU(M)/[SU(M-N)\times SU(N)\times U(1)]$. For other Hermitian symmetric spaces such as the quadric surface $Q^{N-2}=SO(N)/[SO(N-2)\times U(1)])$, we impose F-term (holomorphic) constraints for embedding them into $\mathbb{C}{P}^{N-1}$ or Grassmann manifold. We find that these constraints are consistent in the canonical branch but yield additional constraints on the dynamical fields, thus reducing the target spaces in the noncanonical branch.

We propose a covariant entropy bound in gravitational theories beyond general relativity (GR), using Wald entropy or its extension instead of Bekenstein-Hawking entropy. We first extend the proof of the bound known in four-dimensional GR to $D$-dimensional GR, $f(R)$ gravity, and canonical scalar-tensor theory. We then consider Einstein-Gauss-Bonnet (EGB) gravity as a more nontrivial example and, under a set of reasonable assumptions, prove the bound in the GR branch of spherically symmetric configurations. As a corollary, it is shown that under the null and dominant energy conditions, the generalized second law holds in the GR branch of spherically symmetric configurations of EGB gravity at the fully nonlinear level.

We investigate the Noether symmetries of the Lagrangian for the stationary rotating Banados, Teitelboim, and Zanelli (BTZ)–type three-dimensional spacetimes in the $f(R)$ theory of gravity. A detailed analysis of Noether symmetries of ($2+1$)-dimensional rotating BTZ-type black hole spacetime model is presented. Applying the Noether symmetry approach, the first integrals (constants of motion) for each of the Noether symmetries are obtained to look for the exact solutions. After solving the first integral equations depending on the form of the function $f(R)$, we derived some new ($2+1$)-dimensional rotating BTZ-type black hole solutions. We discussed the physical implications of the derived exact solutions. The thermodynamical properties of the obtained BTZ-type black hole solutions are analyzed by making use of the mass $M$ and the angular momentum $J$ in terms of $r_{\pm }$, where $r_{+}$ is the event horizon and $r_{-}$ is the inner horizon. Further, it is shown that thermodynamic quantities obey the first law, and the Smarr-like formulas of the solutions we found are obtained.

Galaxy bispectrum is a promising probe of inflationary physics in the early Universe as a measure of primordial non-Gaussianity (PNG), whereas its signal-to-noise ratio is significantly affected by the mode coupling due to nonlinear gravitational growth. In this paper, we examine the standard reconstruction method of linear cosmic mass density fields from nonlinear galaxy density fields to decorrelate the covariance in redshift-space galaxy bispectra. In particular, we evaluate the covariance of the bispectrum for massive-galaxy-sized dark matter halos with reconstruction by using 4000 independent $N$-body simulations. Our results show that the bispectrum covariance for the postreconstructed field approaches the Gaussian prediction at scale of $k<0.2h{\mathrm{Mpc}}^{-1}$. We also verify the leading-order PNG-induced bispectrum is not affected by details of the reconstruction with perturbative theory. We then demonstrate the constraining power of the postreconstructed bispectrum for PNG at redshift of approximately 0.5. Further, we perform a Fisher analysis to make a forecast of PNG constraints by galaxy bispectra including anisotropic signals. Assuming a massive galaxy sample in the Sloan Digital Sky Survey Baryon Oscillation Spectroscopic Survey, we find that the postreconstructed bispectrum can constrain the local, equilateral, and orthogonal types of PNG with $\mathrm{\Delta }{f}_{\mathrm{NL}}\sim 13$, 90, and 42, respectively, improving the constraints with the prereconstructed bispectrum by a factor of 1.3–3.2. In conclusion, the reconstruction plays an essential role in constraining various types of PNG signatures with a level of $\mathrm{\Delta }{f}_{\mathrm{NL}}\lesssim 1$ from the galaxy bispectrum based on upcoming galaxy surveys.

There is a growing expectation that the gravitational wave detectors will start probing the stochastic gravitational wave backgrounds in the following years. We explore the spectral shapes of gravitational waves induced to second order by scalar perturbations and presumably have been produced in the early Universe. We calculate the gravitational wave spectra generated during radiation and kination eras together with the associated primordial black hole counterpart. We employ power spectra for the primordial curvature perturbation generated by $\alpha$-attractors and nonminimal derivative coupling inflation models as well as Gaussian and delta-type shapes. We demonstrate the ability of the tensor modes to constrain the spectrum of the primordial curvature perturbations and discriminate among inflationary models. Gravitational wave production during kination and radiation eras can also be distinguished by their spectral shapes and amplitudes.

Cosmological data provide a powerful tool in the search for physics beyond the Standard Model (SM). An interesting target are light relics, new degrees of freedom which decoupled from the SM while relativistic. Nearly massless relics contribute to the radiation energy budget, and are commonly parametrized as variations in the effective number $N_{\mathrm{eff}}$ of neutrino species. Additionally, relics with masses greater than ${10}^{-4}\mathrm{eV}$ become nonrelativistic before today, and thus behave as matter instead of radiation. This leaves an imprint in the clustering of the large-scale structure of the Universe, as light relics have important streaming motions, mirroring the case of massive neutrinos. Here we forecast how well current and upcoming cosmological surveys can probe light massive relics. We consider minimal extensions to the SM by both fermionic and bosonic relic degrees of freedom. By combining current and upcoming cosmic-microwave-background and large-scale-structure surveys, we forecast the significance at which each light massive relic, with different masses and temperatures, can be detected. We find that a very large coverage of parameter space will be attainable by upcoming experiments, opening the possibility of exploring uncharted territory for new physics beyond the SM.

A promising avenue to measure the total, and potentially individual, mass of neutrinos consists of leveraging cosmological datasets, such as the cosmic microwave background and surveys of the large-scale structure of the Universe. In order to obtain unbiased estimates of the neutrino mass, however, many effects ought to be included. Here we forecast, via a Markov chain Monte Carlo likelihood analysis, whether measurements by two galaxy surveys, DESI and Euclid, when added to the CMB-S4 experiment, are sensitive to two effects that can alter neutrino-mass measurements. The first is the slight difference in the suppression of matter fluctuations that each neutrino-mass hierarchy generates at fixed total mass. The second is the growth-induced scale-dependent bias of haloes produced by massive neutrinos. We find that near-future surveys can distinguish hierarchies with the same total mass only at the $1\sigma$ level; thus, while these are poised to deliver a measurement of the sum of neutrino masses, they cannot significantly discern the mass of each individual neutrino in the foreseeable future. We further find that neglecting the growth-induced scale-dependent bias induces up to a $1\sigma$ overestimation of the total neutrino mass, and we show how to absorb this effect via a redshift-dependent parametrization of the scale-independent bias.

The existing constraints from particle colliders reveal a suspicious but nonlethal metastability for our current electroweak vacuum of Higgs potential in the standard model of particle physics, which is, however, disfavored in the early Universe if the inflationary Hubble scale is larger than the instability scale when Higgs quartic self-coupling runs into negative value. Alternative to previous trials of acquiring a positive effective mass-squared from Higgs quadratic couplings to Ricci scalar or inflaton field, we propose a third approach to stabilize the Higgs potential in the early Universe by regarding Higgs as chameleon coupled to inflaton alone without conflicting to the present constraints on either Higgs or chameleon.

In the current work an equation of state model with a first-order phase transition for astrophysical applications is presented. The model is based on a two-phase approach for quark-hadron phase transitions, which leads by construction to a first-order phase transition. The resulting model has already been successfully used in several astrophysical applications, such as cold neutron stars, core-collapse supernova explosions and binary neutron star mergers. Main goal of this work is to present the details of the model, discuss certain features and eventually publish it in a tabulated form for further use.

We present the first Monte Carlo based global QCD analysis of spin-averaged and spin-dependent parton distribution functions (PDFs) that includes nucleon isovector matrix elements in coordinate space from lattice QCD. We investigate the degree of universality of the extracted PDFs when the lattice and experimental data are treated under the same conditions within the Bayesian likelihood analysis. For the unpolarized sector, we find rather weak constraints from the current lattice data on the phenomenological PDFs, and difficulties in describing the lattice matrix elements at large spatial distances. In contrast, for the polarized PDFs we find good agreement between experiment and lattice data, with the latter providing significant constraints on the spin-dependent isovector quark and antiquark distributions.

We study the contributions of the kaon pair originating from the resonance $\rho (770)$ for the three-body decays $B\to DK\overline{K}$ by employing the perturbative QCD approach. According to the predictions in this work, the contributions from the intermediate state $\rho (770{)}^0$ are relatively small for the three-body decays such as $B^0\to {\overline{D}}^0{K}^{+}{K}^{-}$, $B_s^0\to {\overline{D}}^0{K}^{+}{K}^{-}$, and $B^{+}\to D_s^{+}{K}^{+}{K}^{-}$, while about 20% of the total three-body branching fraction for $B^{+}\to {\overline{D}}^0{K}^{+}{\overline{K}}^0$ could possibly come from the subprocess $\rho (770{)}^{+}\to K^{+}{\overline{K}}^0$. We also estimate the branching fractions for $\rho (770{)}^{\pm }$ decay into the kaon pair to be about 1%, and that for the neutral $\rho (770)$ decay into $K^{+}{K}^{-}$ or $K^0{\overline{K}}^0$ to be about 0.5%, which will be tested by future experiments.

In the heavy-quark limit, the two heavy quarks in a doubly heavy baryon or a doubly heavy tetraquark are bound by their color-Coulomb potential into a compact diquark. The doubly heavy hadrons are related by the approximate heavy-quark–diquark symmetry of QCD to the heavy hadrons obtained by replacing the heavy diquark by a heavy antiquark. Effective field theories can be used to expand the masses of singly heavy hadrons and doubly heavy hadrons in inverse powers of the heavy-quark masses. The coefficients in the expansions for doubly heavy tetraquarks can be determined from those for heavy mesons, heavy baryons, and doubly heavy baryons using heavy-quark–diquark symmetry. We predict the masses of the ground-state doubly heavy tetraquarks with error bars using as inputs the masses of heavy mesons and heavy baryons measured in experiments and the masses of doubly heavy baryons calculated using lattice QCD. The only doubly heavy tetraquarks predicted to be stable with respect to strong decays are $bb$ tetraquarks with light flavor $\overline{u}\overline{d}$, $\overline{s}\overline{u}$, and $\overline{s}\overline{d}$.

Exotic self-interactions among the Standard Model neutrinos have been proposed as a potential reason behind the tension in the expansion rate, $H_0$, of the universe inferred from different observations. We constrain this proposal using electroweak precision observables, rare meson decays, and neutrinoless double-$\beta$ decay. In contrast to previous works, we emphasize the importance of carrying out this study in a framework with full Standard Model gauge invariance. We implement this first by working with a relevant set of Standard Model effective field theory operators and subsequently by considering a UV completion in the inverse seesaw model. We find that the scenario in which all flavors of neutrinos self-interact universally is strongly constrained, disfavoring a potential solution to the $H_0$ problem in this case. The scenario with self-interactions only among tau neutrinos is the least constrained and can potentially be consistent with a solution to the $H_0$ problem.

The projected reach of direct electroweakino searches at the high luminosity LHC (HL-LHC) ($\sqrt{s}=14\mathrm{TeV}$, $3000{\mathrm{fb}}^{-1}$ LHC) in the framework of simplified models with $R$-parity violating operators, ${\lambda }_{112}^{\prime \prime }{u}^c{d}^c{s}^c$ and ${\lambda }_{113}^{\prime \prime }{u}^c{d}^c{b}^c$, is studied. Four different analysis channels are chosen: $Wh$ mediated $1l+2b+\mathrm{jets}+{\cancel{\mathrm{E}}}_{\mathrm{T}}$, $Wh$ mediated $1l+2\gamma +\mathrm{jets}+{\cancel{\mathrm{E}}}_{\mathrm{T}}$, $WZ$ mediated $3l+\mathrm{jets}+{\cancel{\mathrm{E}}}_{\mathrm{T}}$ and $WZ$ mediated $3l+2b+\mathrm{jets}+{\cancel{\mathrm{E}}}_{\mathrm{T}}$ and the projected exclusion/discovery reach of direct wino searches in these channels is analyzed by performing a detailed cut-based collider analysis. The projected exclusion contour reaches up to 600–700 GeV for a massless binolike ${\chi }_1^0$ from searches in the $Wh$ mediated $1l+2b+\mathrm{jets}+{\cancel{\mathrm{E}}}_{\mathrm{T}}$, $Wh$ mediated $1l+2\gamma +\mathrm{jets}+{\cancel{\mathrm{E}}}_{\mathrm{T}}$ and $WZ$ mediated $3l+\mathrm{jets}+{\cancel{\mathrm{E}}}_{\mathrm{T}}$ channels, while the $WZ$ mediated $3l+2b+\mathrm{jets}+{\cancel{\mathrm{E}}}_{\mathrm{T}}$ search channel is found to have a projected exclusion reach up to 600 GeV for $150\mathrm{GeV}<M_{{\chi }_1^0}<250\mathrm{GeV}$. The baryon number violating simplified scenario considered in this work is found to furnish a weaker projected reach (typically by a factor of $\sim 1/2$) than the $R$-parity conserving (RPC) case. The projected reach at the HL-LHC in these four channels is also recast for realistic benchmark scenarios.

In this paper we construct supersymmetric Pati-Salam (PS) models containing the minimal supersymmetric standard model and an invisible axion. The models include two discrete symmetries, ${\mathbb{Z}}_4^R\times {\mathbb{Z}}_N$, which maintain the quality of the accidental Peccei-Quinn (PQ) symmetry and thus the solution to the strong $CP$ problem. We require that the discrete anomaly conditions are satisfied for both ${\mathbb{Z}}_4^R\times G_{\mathrm{PS}}^2$ and ${\mathbb{Z}}_N\times G_{\mathrm{PS}}^2$. The vacuum expectation value of the PQ field spontaneously breaks all the discrete symmetries. R-parity is violated if any of the PQ field(s) has an odd charge under ${\mathbb{Z}}_4^R$. We present two explicit models which we refer to as a minimal model where R-parity violation is extremely suppressed, and a nonminimal model where R-parity violation is significant. In the latter model, the neutralino becomes unstable even if it is the lightest supersymmetric particle (LSP), and, in addition, there are new low-energy vectorlike states. In both examples, R-parity violation is sufficiently suppressed such that the proton is stable.

Inspired by the localization phenomenon in condensed matter systems, we explore constructions in the theory space of multiple scalar fields, in which exponentially suppressed couplings could originate from random parameters. In particular, we find a new class of nonlocal theory space models, in which scalar fields at nonadjacent sites interact with each other but with strengths decaying exponentially with the site separation. Such a model could have very different localization properties, compared to the local theory space scenarios with only nearest-site interactions, based on the original Anderson localization model. More specifically, we find that a particular nonlocal interaction pattern leads to bilocalization of the two lightest eigenstates. Exponential localization (and thus exponentially suppressed couplings) then emerges only and immediately when randomness is introduced, no matter how tiny it is. We discuss variants of the model and possible UV completions as well.

In this paper, we summarize our efforts in simulating Yang-Mills theories coupled to matter fields transforming under the fundamental and adjoint representations of the gauge group. In the context of composite Higgs scenarios, gauge theories with mixed representation fields have been suggested to describe the fundamental interactions well beyond the electroweak unification scale, and they are also closely related to supersymmetric QCD. In addition, they are studied as deformations of theories with pure adjoint matter in the context of adiabatic continuity. We provide some first results for bare parameter tuning and interdependence of the two representations. We also investigate how the chiral symmetry breaking or a conformal scenario can be realized and checked in such theories.

We present a nonperturbative lattice calculation of the form factors which contribute to the amplitudes for the radiative decays $P\to \ell {\overline{\nu }}_{\ell }\gamma$, where $P$ is a pseudoscalar meson and $\ell$ is a charged lepton. Together with the nonperturbative determination of the corrections to the processes $P\to \ell {\overline{\nu }}_{\ell }$ due to the exchange of a virtual photon, this allows accurate predictions at $O({\alpha }_{\mathrm{em}})$ to be made for leptonic decay rates for pseudoscalar mesons ranging from the pion to the $D_s$ meson. We are able to separate unambiguously and nonpertubatively the pointlike contribution, from the structure-dependent, infrared-safe, terms in the amplitude. The fully nonperturbative $O(a)$ improved calculation of the inclusive leptonic decay rates will lead to the determination of the corresponding Cabibbo-Kobayashi-Maskawa matrix elements also at $O({\alpha }_{\mathrm{em}})$. Prospects for a precise evaluation of leptonic decay rates with emission of a hard photon are also very interesting, especially for the decays of heavy $D$ and $B$ mesons for which currently only model-dependent predictions are available to compare with existing experimental data.

A random matrix model for lattice QCD which takes into account the positive definite nature of the Wilson term is introduced. The corresponding effective theory for fixed index of the Wilson Dirac operator is derived to next to leading order. It reveals a new term proportional to the topological index of the Wilson Dirac operator and the lattice spacing. The new term appears naturally in a fixed index spurion analysis. The spurion approach reveals that the term is the first in a new family of such terms and that equivalent terms are relevant for the effective theory of continuum QCD.