We generalize previous studies on the extension of Goldstone’s theorem from Hermitian to non-Hermitian quantum field theories with Abelian symmetries to theories possessing a glocal non-Abelian symmetry. We present a detailed analysis for a non-Hermitian field theory with two complex two component scalar fields possessing an $SU(2)$ symmetry and indicate how our findings extend to the general case. In the PT-symmetric regime (parity and time-reversal) and at the standard exceptional point the Goldstone theorem is shown to apply, although different identification procedures need to be employed. At the zero exceptional points the Goldstone boson can not be identified. Comparing our approach, based on the pseudo-Hermiticity of the model, to an alternative approach that utilizes surface terms to achieve compatibility for the non-Hermitian system, we find that the explicit forms of the Goldstone boson fields are different.

Within the framework of $f(R)=R+\alpha R^2$ gravity, we study realistic models of neutron stars, using equations of state compatible with the LIGO constraints, i.e., APR4, MPA1, SLy, and WW1. By numerically solving modified Tolman-Oppenheimer-Volkoff equations, we investigate the mass-radius relation in both metric and torsional $f(R)=R+\alpha R^2$ gravity models. In particular, we observe that torsion effects decrease the compactness and total mass of neutron star with respect to the general relativity predictions, therefore mimicking the effects of a repulsive massive field. The opposite occurs in the metric theory, where mass and compactness increase with $\alpha$, thus inducing an excess of mass that overtakes the standard general relativity limit. We also find that the sign of $\alpha$ must be reversed whether one considers the metric theory (positive) or torsion (negative) to avoid blowing up solutions. This could draw an easy test to either confirm or discard one or the other theory by determining the sign of parameter $\alpha$.

In this paper, we use a suitable conformal rescaling to construct static and rotating regular black holes in conformal massive gravity. The new metric is characterized by the mass $M$, the “scalar charge” $Q$, the angular momentum parameter $a$, the “hair parameter” $\lambda$, and the conformal scale factor encoded in the parameter $L$. We explore the shadow images and the deflection angles of relativistic massive particles in the spacetime geometry of a rotating regular black hole. For $\lambda \ne 0$ and $Q>0$, the shadow is larger than the shadow of a Kerr black hole. In particular, if $\lambda <0$, the shadow radius increases considerably. For $\lambda \ne 0$ and $Q<0$, the shadow is smaller than the shadow of a Kerr black hole. Additionally, we put observational constraints on the parameter $Q$ using the latest Event Horizon Telescope observation of the supermassive black hole M87*. Lastly, using the Gauss-Bonnet theorem, we show that the deflection angle of massive particles is strongly affected by the parameter $L$. The deflection angle might be used to distinguish rotating regular black holes from rotating singular black holes.

We propose a new paradigm for the thermal production of dark matter in the early Universe, in which dark-matter particles acquire their mass and freeze out spontaneously from the thermal bath after a dark phase transition takes place. The decoupling arises because the dark-matter particles become suddenly nonrelativistic and not because of any decay channel becoming kinematically close. We propose a minimal scenario in which a scalar and a fermionic dark matter are in thermal equilibrium with the standard-model bath. We compute the finite temperature corrections to the scalar potential and identify a region of the parameter space where the fermionic dark-matter mass spontaneously jumps over the temperature when the dark phase transition happens. We explore the phenomenological implications of such a model in simple cases and show that the annihilation cross section of dark-matter particles has to be larger by more than 1 order of magnitude as compared to the usual constant-mass weakly interacting massive particle scenario in order to accommodate the correct relic abundance. We show that in the spontaneous freeze out regime a TeV-scale fermionic dark matter that annihilates into leptons through $s$-wave processes can be accessible to detection in the near future.

We consider chaotic inflation models with a pseudoscalar field containing the general couplings to the four-form flux. The four-form mixing with the pseudoscalar field induces a quadratic potential for inflaton while the coexisting four-form mixing with graviton generates a nonminimal gravity coupling for inflaton. The shift symmetry is respected by the derived inflaton couplings, and it is broken spontaneously only by the fixed four-form flux. We discuss the success of inflationary predictions and robustness against higher order terms. Finally, the built-in reheating mechanism is also addressed.

We derive a lower bound on the merger rate of primordial black hole (PBH) binaries by estimating the maximal fraction of binaries that were perturbed between formation in the early Universe and merger, and computing a conservative merger rate of perturbed binaries. This implies robust constraints on the PBH abundance in the range $1–100M_{\odot }$. We further show that LIGO/Virgo design sensitivity has the potential to reach the PBH mass range of $10^{-2}–10^3{M}_{\odot }$. The constraint from the merger rate of perturbed binaries is stronger if PBHs are initially spatially clustered.

The Affleck-Dine mechanism in its simplest form provides baryogenesis from the out-of-equilibrium evolution of a complex scalar field with a simple renormalizable potential. We show that such a model supplemented by nonminimal coupling to gravity can also provide inflation, consistent with Planck constraints, simultaneously with the generation of the baryon asymmetry. The predictions of the model include significant tensor-to-scalar ratio and possibly baryon isocurvature fluctuations. The reheating temperature is calculable, making the model fully predictive. We require color triplet scalars for reheating and transferring the primordial baryon asymmetry to quarks; these could be observable at colliders. They can also be probed at higher scales by searches for quark compositeness in dijet angular distributions, and flavor-changing neutral current effects.

We investigate the quantum channel consisting of two localized quantum systems that communicate through a scalar quantum field. We choose a scalar field rather than a tensor or vector field, such as the electromagnetic field, in order to isolate the situation where the qubits are carried by the field amplitudes themselves rather than, for example, by encoding qubits in the polarization of photons. We find that suitable protocols for this type of quantum channel require the careful navigation of several constraints, such as the no-cloning principle, the strong Huygens principle and the tendency of short field-matter couplings to be entanglement breaking. We nonperturbatively construct a protocol for such a quantum channel that possesses maximal quantum capacity.

We analyze the electroweak phase transition at finite temperature in a model of gauge-Higgs unification where the fermion mass hierarchy including top quark mass, a viable electroweak symmetry breaking, and an observed Higgs mass are successfully reproduced. To study the phase transition, we employ the $\zeta$ function regularization method which is a well-known technique because the Kaluza-Klein mass spectrum is not determined exactly. Applying to our model of gauge-Higgs unification, the strong first order phase transition is realized in our model.

We determine the anomaly associated with an arbitrary scaling of the fields in a quantum gauge theory without making use of the Fujikawa method. We show that this anomaly is dependent on the spin term present in the action and at one loop can be directly extracted from the spin contribution to the one loop effective action. Our results can be readily applied to any gauge theory, supersymmetric or not, and agree with a previous determination for supersymmetric gauge theories based on the Fujikawa method.

The strongest upper bounds on the axion mass come from astrophysical observations like the neutrino burst duration of SN1987A, which depends on the axion couplings to nucleons, or the white-dwarf cooling rates and red-giant evolution, which involve the axion-electron coupling. It has been recently argued that in variants of Dine-Fischler-Srednicki-Zhitnitsky (DFSZ) models with generation-dependent Peccei-Quinn charges an approximate axion-nucleon decoupling can occur, strongly relaxing the SN1987A bound. However, as in standard DFSZ models, the axion remains in general coupled to electrons, unless an ad hoc cancellation is engineered. Here we show that axion-electron decoupling can be implemented without extra tunings in DFSZ-like models with three Higgs doublets. Remarkably, the numerical value of the quark mass ratio $m_u/m_d\sim 1/2$ is crucial to open up this possibility.

We present an in-depth analysis of a recently proposed Standard Model extension with a complete fourth generation of quarks and leptons, which are vectorlike with respect to the Standard Model gauge group and charged under a new spontaneously broken vectorlike $\mathrm{U}(1{)}^{\prime }$ gauge symmetry. The model is designed to explain the known muon anomalies, i.e., the observed deviations from Standard Model predictions in the anomalous magnetic moment of the muon, $\mathrm{\Delta }{a}_{\mu }$, and in $b\to s{\ell }^{+}{\ell }^{-}$ processes. We perform a global ${\chi }^2$ analysis of the data with 65 model parameters and including 98 observables. We find many points with ${\chi }^2$ per degree of freedom $\le 1$. The vectorlike leptons and the new heavy $Z^{\prime }$ are typically much lighter than a TeV and would, thus, be eminently visible at the HL-LHC.

Indirect searches have the potential to probe scales beyond the realm of direct searches. In this paper, we consider the implications of two parity violating experiments: weak charge of proton $Q_W^p$ and the Caesium atom $Q_W^{Cs}$ on the solutions to lepton flavor nonuniversality violations in the decay of $B$ mesons. Working in a generic implementation of a minimal $Z^{\prime }$ model, we assume the primary contribution being due to the electron to facilitate comparison with the low $q^2$ parity violating experiments. We demonstrate that the conclusion is characterized by different limiting behavior depending on the chirality of the lepton current. The correlation developed in this study demonstrates the effectiveness in studying the synergy between different experiments leading to a deeper understanding of the interpretation of the existing data. It is shown that a possible future improvement in the parity violating experiments can have far reaching implications in the context of direct searches. We also comment on the prospect of addition of the muon to the fits and the role it plays in ameliorating the constraints on models of $Z^{\prime }$. This offers a complimentary understanding of the pattern of the coupling of the new physics to the leptons, strongly suggesting either a muon only or a combination of solutions to the anomalies.

Models with massive vector leptoquarks, resulting from an $SU(4)$ gauge symmetry spontaneously broken at the TeV scale, are of great phenomenological interest given the current “anomalies” in semileptonic $B$ decays. We analyze the relations between low- and high-energy observables in such class of models to next-to-leading order accuracy in the $SU(4)$ gauge coupling $g_4$. For large values of $g_4$, motivated by recent $B$-physics data, one-loop corrections are sizable. The main effect is an enhanced contribution at low energy at fixed on-shell couplings. This result has important implications for current and future high-energy searches of vector leptoquark models.

Following updated and extended measurements of the full angular distribution of the decay ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }(\to p{\pi }^{-}){\mu }^{+}{\mu }^{-}$ by the LHCb collaborations, as well as a new measurement of the $\mathrm{\Lambda }\to p{\pi }^{-}$ decay asymmetry parameter by the BESIII collaboration, we study the impact of these results on searches for nonstandard effects in exclusive $b\to s{\mu }^{+}{\mu }^{-}$ decays. To this end, we constrain the Wilson coefficients ${\mathcal{C}}_9$ and ${\mathcal{C}}_{10}$ of the numerically leading dimension-six operators in the weak effective Hamiltonian, in addition to the relevant nuisance parameters. In stark contrast to previous analyses of this decay mode, the changes in the updated experimental results lead us to find very good compatibility with both the Standard Model and with the $b\to s{\mu }^{+}{\mu }^{-}$ anomalies observed in rare $B$-meson decays. We provide a detailed analysis of the impact of the partial angular distribution, the full angular distribution, and the ${\mathrm{\Lambda }}_b\to \mathrm{\Lambda }{\mu }^{+}{\mu }^{-}$ branching fraction on the Wilson coefficients. In this process, we are also able to constrain the size of the production polarization of the ${\mathrm{\Lambda }}_b$ baryon at LHCb.

We study the feasibility to observe sterile neutrinos with masses in the range $5\mathrm{GeV}<m_N<20\mathrm{GeV}$ at the LHC, using exclusive semileptonic modes involving pions, $W\to \ell N\to \pi \ell \ell$, $2\pi \ell \ell$, and $3\pi \ell \ell$. We thus cover a mass window that is between what can be studied in meson factories and high-energy colliders. We run simulations for these exclusive events, where pions should be distinguished from the background provided the neutrino decay exhibits a vertex displacement from its production point. In a previous work, we have estimated the theoretical rates, and here we analyze the observability of the processes at the LHC, given the fact that exclusive hadronic states may be difficult to identify. We study the sensitivity bounds for the observation and discovery of sterile neutrinos in the above mass range. By the end of run 3, current bounds on heavy-to-light lepton mixings in the lower-mass end ($\sim 5\mathrm{GeV}$) could be improved by about an order of magnitude to $|U_{\ell N}{|}^2\sim 5\times {10}^{-6}$, and the High-Luminosity LHC could reach $|U_{\ell N}{|}^2\lesssim 3\times {10}^{-7}$ in the mass range below 11 GeV. Studying in addition equal-sign and opposite-sign dileptons, the Majorana or Dirac character of the sterile neutrino could be revealed.

A class of models is considered in which the masses only of the third generation of quarks and leptons arise in the tree approximation, while masses for the second and first generations are produced respectively by one-loop and two-loop radiative corrections. So far, for various reasons, these models are not realistic.

We present a real-space renormalization group transformation with continuous scale change to calculate the continuous renormalization group $\beta$ function in nonperturbative lattice simulations. Our method is motivated by the connection between Wilsonian renormalization group and the gradient flow transformation. It does not rely on the perturbative definition of the renormalized coupling and is also valid at nonperturbative fixed points. Although our method requires an additional extrapolation compared to traditional step scaling calculations, it has several advantages which compensates for this extra step even when applied in the vicinity of the perturbative fixed point. We illustrate our approach by calculating the $\beta$ function of 2-flavor QCD and show that lattice predictions from individual lattice ensembles, even without the required continuum and finite volume extrapolations, can be very close to the result of the full analysis. Thus our method provides a nonperturbative framework and intuitive understanding into the structure of strongly coupled systems, in addition to being complementary to existing lattice determinations.

To measure the helicity of a spin-1 meson from the triple vector product of the three-momenta of its decay products, one needs information about the strong phase of the decay amplitude. In this paper, taking $a_1(1260)$ meson as an example, we present a method to extract information about the strong phase from the triple vector product of the pion momenta in the $W\to \nu \tau (\to \nu a_1(\to {\pi }^{\mp }{\pi }^{\mp }{\pi }^{\pm }))$ process, where the $a_1$ helicity is known a priori from electroweak theory. This process is advantageous in that highly boosted $a_1^{-}$ mesons from ${\tau }_L^{-}$ decays have nearly maximal helicity asymmetry and thus most reflect the strong phase. We revisit the theoretical calculation of the $a_1$ meson helicity in the $W\to \nu \tau (\to \nu a_1)$ process. Next, we formulate the differential decay rate of polarized $a_1$ mesons in a manner convenient for the study of the $a_1$ meson helicity asymmetry. Finally, we present the method for extracting information about the strong phase, and assess its feasibility at the LHC.

We consider the associated production of electroweak gauge bosons and charm or beauty quark jets at the LHC using the $k_T$-factorization framework. We apply the transverse momentum dependent (TMD) parton distributions in a proton obtained from the parton branching (PB) method as well as from the Catani-Ciafaloni-Fiorani-Marchesini (CCFM) evolution equation. For the PB approach, our prescription merges the standard leading order $\mathcal{O}(\alpha {\alpha }_s)$ $k_T$-factorization calculations with several tree-level next-to-leading order $\mathcal{O}(\alpha {\alpha }_s^2)$ off-shell production amplitudes. For the CCFM scenario, our consideration is based on the $\mathcal{O}(\alpha {\alpha }_s^2)$ off-shell gluon-gluon fusion subprocess $g^{*}{g}^{*}\to Z/W+Q\overline{Q}$ and some $\mathcal{O}(\alpha {\alpha }_s^2)$ subprocesses involving quark interactions, taken into account in conventional (collinear) QCD factorization. We find that the $W+c$ and $Z+b$ cross sections, calculated within the PB and CCFM-based schemes with the proper choice of leading and next-to-leading subprocesses, are in good agreement with each other, thus establishing a correspondence between these two scenarios. A comparison with the latest LHC experimental data is given and the necessity for the proper off-shell treatment of the production amplitudes in determination of the parameters of the TMD parton density is demonstrated.