We suggest two alternative schemes to predict lepton mixing angles as well as $CP$ violating phases from a discrete flavor symmetry group combined with $CP$ symmetry. In the first scenario, the flavor and $CP$ symmetry is broken to the residual groups of the structure $Z_2\times CP$ in the neutrino and charged lepton sectors. The resulting lepton mixing matrix depends on two free parameters ${\theta }_{\nu }$ and ${\theta }_l$. This type of breaking pattern is extended to the quark sector. In the second scenario, an Abelian subgroup of the flavor group is preserved by the charged lepton mass matrix and the neutrino mass matrix is invariant under a single remnant $CP$ transformation, all lepton mixing parameters are determined in terms of three free parameters ${\theta }_{1,2,3}$. We derive the most general criterion to determine whether two distinct residual symmetries lead to the same mixing pattern if the redefinition of the free parameters ${\theta }_{\nu ,l}$ and ${\theta }_{1,2,3}$ is taken into account. We have studied the lepton mixing patterns arising from the flavor group $S_4$ and $CP$ symmetry which are subsequently broken to all of the possible residual symmetries discussed in this work.

At the LHC, dileptonic events may turn up new physics interacting with quarks and leptons. The poster child for this scenario is a resonant $Z^{\prime }$, much anticipated in ${\ell }^{+}{\ell }^{-}$ invariant mass spectra. However, angular spectra of dileptons may play an equal or stronger role in discovering a nonresonant species. This paper avails their LHC measurements to corner the couplings and masses of leptoquarks (LQs) that can mediate $q\overline{q}\to {\ell }^{+}{\ell }^{-}$ in the $t$ channel and dramatically alter Standard Model (SM) angular spectra. Also derived are constraints from alterations to $m_{\ell \ell }$ distributions. These dilepton probes exploiting the high rates and small uncertainties of the Drell-Yan process, rival or outdo dedicated LHC searches for LQs in single and pair production modes. The couplings of LQs with electronic interactions are best bound today by low-energy measurements of atomic parity violation, but can be probed better by ${\ell }^{+}{\ell }^{-}$ measurements in the high luminosity runs of the LHC, with the angular spectra leading the way. This work also urges the experimental presentation of boost-invariant angular asymmetries that vanish in the SM.

Satisfactory description of data by hydrodynamics-motivated models, as has been reported recently by experimental collaborations at the LHC, confirm “collectivity” in high-multiplicity proton-proton $(pp)$ collisions. Notwithstanding this, a detailed study of high-multiplicity $pp$ data in other approaches or models is essential for better understanding of the specific phenomenon. In this study, the focus is on a pQCD-inspired multiparton interaction (MPI) model, including a color reconnection (CR) scheme as implemented in the Monte Carlo code, PYTHIA8 tune 4C. The MPI with the color reconnection reproduces the dependence of the mean transverse momentum $⟨p_T⟩$ on the charged particle multiplicity $N_{\mathrm{ch}}$ in $pp$ collisions at the LHC, providing an alternate explanation to the signature of “hydrodynamic collectivity” in $pp$ data. It is, therefore, worth exploring how this model responds to other related features of high-multiplicity $pp$ events. This comparative study with recent experimental results demonstrates the limitations of the model in explaining some of the prominent features of the final-state charged particles up to the intermediate-$p_T$ ($p_T<2.0\mathrm{GeV}/c$) range in high-multiplicity $pp$ events.

We evaluate the partial decay widths for the semileptonic ${\mathrm{\Lambda }}_b\to {\overline{\nu }}_{l}l{\mathrm{\Lambda }}_c(2595)$ and ${\mathrm{\Lambda }}_b\to {\overline{\nu }}_{l}l{\mathrm{\Lambda }}_c(2625)$ decays from the perspective that these two ${\mathrm{\Lambda }}_c^{*}$ resonances are dynamically generated from the $DN$ and $D^{*}N$ interaction with coupled channels. We find that the ratio of the rates obtained for these two reactions is compatible with present experimental data and is very sensitive to the $D^{*}N$ coupling, which becomes essential to obtain agreement with experiment. Together with the results obtained for the ${\mathrm{\Lambda }}_b\to {\pi }^{-}{\mathrm{\Lambda }}_c^{*}$ reactions, it gives strong support to the molecular picture of the two ${\mathrm{\Lambda }}_c^{*}$ resonances and the important role of the $D^{*}N$ component neglected in prior studies of the ${\mathrm{\Lambda }}_c(2595)$ from the molecular perspective.

Combining the recently reported electric dipole moment (EDM) of the ${}^{199}\mathrm{Hg}$ atom due to breaking of parity and time-reversal symmetries with the improved relativistic atomic calculations, precise limits on the tensor-pseudotensor (T-PT) electron-nucleus (e-N) coupling coefficient and the nuclear Schiff moment interactions are determined. Using these limits with the nuclear calculations, we infer limits on the EDMs of the neutron and proton as $d_n<2.2\times {10}^{-26}|e|\mathrm{cm}$ and $d_p<2.1\times {10}^{-25}|e|\mathrm{cm}$, respectively, and on the quantum chromodynamics parameter and the combined up- and down-quark chromo-EDMs as $|\overline{\theta }|<1.1\times {10}^{-10}$ and $|{\tilde{d}}_u-{\tilde{d}}_d|<5.5\times {10}^{-27}|e|\mathrm{cm}$, respectively. These are the best limits to date to probe new sources of $CP$ violation beyond the standard model from a diamagnetic atom. The role of a capable many-body method to account for the electron correlation effects to all orders for inferring the above limits has been highlighted. From this analysis, constraints on the T-PT e-N coupling coefficient with a large range of mass of a possible dark matter carrier $\chi$ between the atomic electrons and nucleus are given.

The NEMO-3 experiment measured the half-life of the $2\nu \beta \beta$ decay and searched for the $0\nu \beta \beta$ decay of ${}^{116}\mathrm{Cd}$. Using 410 g of ${}^{116}\mathrm{Cd}$ installed in the detector with an exposure of 5.26 y, ($4968\pm 74$) events corresponding to the $2\nu \beta \beta$ decay of ${}^{116}\mathrm{Cd}$ to the ground state of ${}^{116}\mathrm{Sn}$ have been observed with a signal to background ratio of about 12. The half-life of the $2\nu \beta \beta$ decay has been measured to be $T_{1/2}^{2\nu }=[2.74\pm 0.04(\text{stat})\pm 0.18(\text{syst})]\times 10^{19}\mathrm{y}$. No events have been observed above the expected background while searching for $0\nu \beta \beta$ decay. The corresponding limit on the half-life is determined to be $T_{1/2}^{0\nu }\ge 1.0\times 10^{23}\mathrm{y}$ at the 90% C.L. which corresponds to an upper limit on the effective Majorana neutrino mass of $⟨m_{\nu }⟩\le 1.4–2.5\mathrm{eV}$ depending on the nuclear matrix elements considered. Limits on other mechanisms generating $0\nu \beta \beta$ decay such as the exchange of R-parity violating supersymmetric particles, right-handed currents and majoron emission are also obtained.

Recently Witten introduced a type IIB brane construction with certain boundary conditions to study knot invariants and Khovanov homology. The essential ingredients used in his work are the topologically twisted $\mathcal{N}=4$ Yang-Mills theory, localization equations and surface operators. In this paper we extend his construction in two possible ways. On one hand we show that a slight modification of Witten’s brane construction could lead, using certain well-defined duality transformations, to the model used by Ooguri-Vafa to study knot invariants using gravity duals. On the other hand, we argue that both these constructions, of Witten and of Ooguri-Vafa, lead to two different seven-dimensional manifolds in M-theory from where the topological theories may appear from certain twisting of the G-flux action. The non-Abelian nature of the topological action may also be studied if we take the wrapped M2-brane states in the theory. We discuss explicit constructions of the seven-dimensional manifolds in M-theory, and show that both the localization equations and surface operators appear naturally from the Hamiltonian formalism of the theories. Knots and link invariants are then constructed using M2-brane states in both the models.

We discuss a supersymmetric generalization of the Sachdev-Ye-Kitaev (SYK) model. These are quantum mechanical models involving $N$ Majorana fermions. The supercharge is given by a polynomial expression in terms of the Majorana fermions with random coefficients. The Hamiltonian is the square of the supercharge. The $\mathcal{N}=1$ model with a single supercharge has unbroken supersymmetry at large $N$, but nonperturbatively spontaneously broken supersymmetry in the exact theory. We analyze the model by looking at the large $N$ equation, and also by performing numerical computations for small values of $N$. We also compute the large $N$ spectrum of “singlet” operators, where we find a structure qualitatively similar to the ordinary SYK model. We also discuss an $\mathcal{N}=2$ version. In this case, the model preserves supersymmetry in the exact theory and we can compute a suitably weighted Witten index to count the number of ground states, which agrees with the large $N$ computation of the entropy. In both cases, we discuss the supersymmetric generalizations of the Schwarzian action which give the dominant effects at low energies.

The effects of a nonminimally coupled curvature-matter model of gravity on a perturbed Minkowski metric are presented. The action functional of the model involves two functions $f^1(R)$ and $f^2(R)$ of the Ricci scalar curvature $R$. This work expands upon previous results, extending the framework developed there to compute corrections up to order $O(1/c^4)$ of the 00 component of the metric tensor. It is shown that additional contributions arise due to both the nonlinear form $f^1(R)$ and the nonminimal coupling $f^2(R)$, including exponential contributions that cannot be expressed as an expansion in powers of $1/r$. Some possible experimental implications are assessed with application to perihelion precession.

Any recipe to grow black hole hair has to circumvent no-hair theorems by violating some of their assumptions. Recently discovered hairy black hole solutions exist due to the fact that their scalar fields don’t inherit the symmetries of the spacetime metric. We present here a general analysis of the constraints which limit the possible forms of such a hair, for both the real and the complex scalar fields. These results can be taken as a novel piece of the black hole uniqueness theorems or simply as a symmetry noninheriting Ansätze guide. In addition, we introduce new classification of the gravitational field equations which might prove useful for various generalizations of the theorems about spacetimes with symmetries.

A spherically symmetric collapsing scalar field model is discussed with a dissipative fluid which includes a heat flux. This vastly general matter distribution is analyzed at the expense of a high degree of symmetry in the space-time, that of conformal flatness and self-similarity. Indeed collapsing models terminating into a curvature singularity can be obtained. The formation of black holes or the occurrence of naked singularities depends on the initial collapsing profiles.

We take the JUNO experiment as an example to explore nuclearites in the future large liquid scintillator detector. Comparing to the previous calculations, the visible energy of nuclearites across the liquid scintillator will be reestimated for the liquid scintillator based detector. Then the JUNO sensitivities to the nuclearite flux are presented. It is found that the JUNO projected sensitivities can be better than $7.7\times {10}^{-17}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}{\mathrm{sr}}^{-1}$ for the nuclearite mass $10^{15}\mathrm{GeV}\le M\le 10^{24}\mathrm{GeV}$ and initial velocity ${10}^{-4}\le {\beta }_0\le {10}^{-1}$ with a 20 year running. Note that the JUNO will give the most stringent limits for downgoing nuclearites with $1.6\times 10^{13}\mathrm{GeV}\le M\le 4.0\times 10^{15}\mathrm{GeV}$ and a typical galactic velocity ${\beta }_0={10}^{-3}$.

We determine quark mass dependent order $a$ improvement terms of the form $b_{J}am$ for nonsinglet scalar, pseudoscalar, vector and axialvector currents using correlators in coordinate space on a set of Coordinated Lattice Simulations ensembles. These have been generated employing nonperturbatively improved Wilson fermions and the tree-level Lüscher-Weisz gauge action at $\beta =3.4$, 3.46, 3.55 and 3.7, corresponding to lattice spacings ranging from $a\approx 0.085\mathrm{fm}$ down to 0.05 fm. In the $N_f=2+1$ flavor theory two types of improvement coefficients exist: $b_J$, proportional to nonsinglet quark mass combinations, and ${\overline{b}}_J$ (or ${\tilde{b}}_J$), proportional to the trace of the quark mass matrix. Combining our nonperturbative determinations with perturbative results, we quote Padé approximants parametrizing the $b_J$ improvement coefficients within the above window of lattice spacings. We also give preliminary results for ${\tilde{b}}_J$ at $\beta =3.4$.

We derive the medium-induced, fully coherent soft gluon radiation spectrum associated with the hard forward scattering of an energetic parton off a nucleus, in the saturation formalism within the Gaussian approximation for the relevant correlators of Wilson lines and for finite number of colors. The validity range of the result is rigorously specified by keeping track of the order of magnitude of subleading contributions to the spectrum. The connection between the saturation formalism and the opacity expansion used in previous studies of the same observable is made apparent. Our calculation sets the basis for further studies of the interplay between saturation and fully coherent energy loss in hard forward parton scattering.

In this paper we extend our recent nonperturbative functional renormalization group analysis of Reggeon field theory to the interactions of Pomeron and Odderon fields. We establish the existence of a fixed point and its universal properties, which exhibits a novel symmetry structure in the space of Odderon-Pomeron interactions. As in our previous analysis, this part of our program aims at the investigation of the IR limit of Reggeon field theory (the limit of high energies and large transverse distances). It should be seen in the broader context of trying to connect the nonperturbative infrared region (large transverse distances) with the UV region of small transverse distances where the high energy limit of perturbative QCD applies. We briefly discuss the implications of our findings for the existence of an Odderon in high energy scattering.

The classical approach to spacetime singularities leads to a simplified dynamics in which spatial derivatives become unimportant compared to time derivatives, and thus each spatial point essentially becomes uncoupled from its neighbors. This uncoupled dynamics leads to sharp features (called “spikes”) as follows: particular spatial points follow an exceptional dynamical path that differs from that of their neighbors, with the consequence that, in the neighborhood of these exceptional points, the spatial profile becomes ever more sharp. Spikes are consequences of the BKL-type oscillatory evolution towards generic singularities of spacetime. Do spikes persist when the spacetime dynamics is treated using quantum mechanics? To address this question, we treat a Hamiltonian system that describes the dynamics of the approach to the singularity and consider how to quantize that system. We argue that this particular system is best treated using an affine quantization approach (rather than the more familiar methods of canonical quantization), and we set up the formalism needed for this treatment. Our investigation, based on this affine approach, shows the nonexistence of quantum spikes.

We perform a comprehensive study of the dark energy equation of state (EoS) utilizing the model-independent Gaussian processes (GP). Using a combination of the Union 2.1 data set, the 30 newly added H(z) cosmic chronometer data points and Planck’s shift parameter, we modify the usual GaPP code and provide a tighter constraint on the dark energy EoS than the previous literature about GP reconstructions. Subsequently, we take the “controlling variable method ” to investigate directly the effects of the variable matter density parameter ${\mathrm{\Omega }}_{m0}$, variable cosmic curvature ${\mathrm{\Omega }}_{k0}$, and variable Hubble constant $H_0$ on the dark energy EoS. We find that too small or large ${\mathrm{\Omega }}_{m0}$, ${\mathrm{\Omega }}_{k0}$, and $H_0$ are all disfavored by our GP reconstructions based on current cosmological observations. Subsequently, we find that variables ${\mathrm{\Omega }}_{m0}$ and ${\mathrm{\Omega }}_{k0}$ affect the reconstructions of the dark energy EoS but hardly affect the reconstructions of the normalized comoving distance $D(z)$ and its derivatives $D^{\prime }(z)$ and $D^{\prime \prime }(z)$. However, variable $H_0$ affects the reconstructions of the dark energy EoS by affecting obviously those of $D(z)$, $D^{\prime }(z)$, and $D^{\prime \prime }(z)$. Furthermore, we find that the results of our reconstructions support substantially the recent local measurement of $H_0$ reported by Riess et al.

The relaxion mechanism elegantly solves the Higgs hierarchy problem, but it requires that the early Universe experiences a long inflation phase with a small energy scale since the settle down of the relaxion needs to take place during inflation. In this paper, unlike the original one, we consider another scenario in which the Higgs vacuum expectation value is determined after inflation. To accomplish the mechanism, we take into account the effects of the Hubble-induced mass and thermal one in the dynamics of the relaxion. Then, we find that for the relaxion mechanism the coupling of the relaxion with the additional mass terms should be large.

We have carried out a phenomenological analysis of the latest deep virtual Compton scattering experimental data based on the generalized parton distribution formalism. This allows us to extract the dependence of the spatial size of the proton on the quark’s longitudinal momentum. This results in the first continuous two-dimensional momentum-space image and tomography of the proton based on experimental data.