We present a calculating method for the quark and lepton mixing angles. After a general discussion in field theoretic models, we present a working model from a string compactification through ${\mathbf{Z}}_{12-I}$ orbifold compactification. It is beyond presenting just three families of the standard model but is the first example from string compactification successfully fitting to the observed data. Assuming that all Yukawa couplings from string compactification are real, we also comment on a relation between the $CP$ phases in the Jarlskog determinants obtained from the Cabibbo-Kobayashi-Maskawa and Pontecorvo-Maki-Nakagawa-Sakada matrices. The flipped SU(5) model leads to the doublet-triplet splitting and possible proton decay operators. It is shown that the vacuum expectation values can be tuned such that the proton lifetime is long enough.

In the traditional neutrinophilic two-Higgs doublet model ($\nu 2\mathrm{HDM}$), there is no nonstandard neutrino interaction (NSI) as the interactions between the Standard Model fermions with neutrinos are negligibly small due to the tiny mixing of the two scalar doublets. In this work, we propose that if $\nu 2\mathrm{HDM}$ is modified by considering the right-handed electron, $e_R$ is negatively charged under a global $U(1)$ symmetry; then, one can generate a significant amount of NSI along with the tiny Dirac neutrino mass. Depending on different constraints from the LEP experiment, tree-level lepton flavor violating processes, big-bang nucleosynthesis, etc., we observe that this model significantly restricts the range of permissible NSI parameters, putting a strict upper bound on different NSIs. Furthermore, considering these model-dependent NSIs, we study their impact on the next-generation superbeam experiment, DUNE. We present a detailed discussion on the mass hierarchy sensitivity and the $CP$-violation discovery study considering the impact of both diagonal and off-diagonal NSIs.

We address the $B$-physics anomalies within a two scalar leptoquark model. The low-energy flavor structure of our setup originates from two $SU(5)$ operators that relate Yukawa couplings of the two leptoquarks. The proposed scenario has a UV completion, can accommodate all measured lepton flavor universality ratios in $B$-meson decays, is consistent with related flavor observables, and is compatible with direct searches at the LHC. We provide prospects for future discoveries of the two light leptoquarks at the LHC and predict several yet-to-be-measured flavor observables.

We present the first lattice results on isovector unpolarized and longitudinally polarized parton distribution functions (PDFs) at physical pion mass. The PDFs are obtained using the large-momentum effective field theory (LaMET) framework where the full Bjorken-$x$ dependence of finite-momentum PDFs, called “quasi-PDFs,” can be calculated on the lattice. The quasi-PDF nucleon matrix elements are renormalized nonperturbatively in the RI/MOM-scheme. However, the recent renormalized quasi-PDFs suffer from unphysical oscillations that alter the shape of the true distribution as a function of Bjorken-$x$. In this paper, we propose two possible solutions to overcome this problem and demonstrate the efficacy of the methods on the $2+1+1$-flavor lattice data at physical pion mass with lattice spacing 0.09 fm and volume $(5.76\mathrm{fm}{)}^3$.

The two-photon-exchange (TPE) effects in the process $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}$ at large momentum transfer are discussed within the perturbative QCD (pQCD). The contributions from the twist-2 and twist-3 distribution amplitudes (DAs) of the pion are considered in the estimation. Different from the results under the one-photon-exchange (OPE) approximation, the TPE effects result in an asymmetry of the differential cross section on the scattering angle. The precise measurement of this asymmetry by the further experiment is a precise test of pQCD at large momentum transfer. The timelike electromagnetic form factor of the pion at the leading order (LO) of pQCD is rediscussed, and the comparison of our results with those in the references is presented. Our results show that the contributions from the twist-2 and twist-3 DAs in the LO of pQCD are much smaller than the experimental data at $Q^2=14.2$, $17.4{\mathrm{GeV}}^2$, which is very different from the conclusion given in the references.

We investigate three possible pentaquark candidates, one of which contains a single charm quark and the other two contain triple charm quarks in their substructure. To this end we apply the QCD sum rule method and take into account both the positive and negative parity states corresponding to each possible pentaquark channel having spin $3/2$ or $1/2$. Insisting on the importance of identification of the members of the pentaquark family we obtain their spectroscopic parameters such as masses and residues. These parameters are the main inputs in the searches for their electromagnetic, strong, and weak interactions.

The $D_{s0}^{*}(2317)D$ and $D_{s1}^{*}(2460)D^{*}$ heavy meson systems can exchange a kaon that is emitted in the S-wave due to the opposite intrinsic parity of the $D_{s0}^{*}(D_{s1}^{*})$ and $D(D^{*})$ mesons. As a consequence of the mass difference of the $D_{s0}^{*}(D_{s1}^{*})$ and $D(D^{*})$ mesons, the range of the kaon exchange potential will be significantly longer than expected, corresponding to an effective mass of about 200 MeV. The potential will be very strong: the strength of the interaction is proportional to $(m_{D_{s0}}-m_D{)}^2/f_{\pi }^2$ and $(m_{D_{s1}}-m_{D^{*}}{)}^2/f_{\pi }^2$. This combination of range and strength almost guarantees the existence of $D_{s0}^{*}(2317)D$ and $D_{s1}^{*}(2460)D^{*}$ bound states with $J^P=0^{-}$ and $J^P=0^{-}$, $2^{-}$, respectively. Concrete calculations indicate a binding energy of 5–15 MeV independently of $J^P$. The $D_{s0}^{*}(2317)D$ and $D_{s1}^{*}(2460)D^{*}$ molecules have manifestly exotic flavor quantum numbers: $C=2$, $S=1$, and $I=1/2$. We expect the existence of bottom counterparts composed of the $B{B}_{s0}$ and $B^{*}{B}_{s1}^{*}$ mesons, which will be more bound and have a richer spectrum that might include a shallow P-wave state and an excited S-wave state.

Scalars and fermions can arise as Goldstone modes of nonlinearly realized extensions of the Poincaré group (with important implications for the soft limits of such theories): the Dirac-Born-Infeld scalar realizes a higher-dimensional Poincaré symmetry, while the Volkov-Akulov fermion corresponds to super-Poincaré. In this paper we classify extensions of the Poincaré group which give rise to a vector Goldstone mode instead. Our main result is that there are no healthy (ghost free) interacting $U(1)$ gauge theories that nonlinearly realize space-time symmetries beyond gauge transformations. This implies that the structure of e.g., Born-Infeld theory is not fixed by symmetry.

In this work we analyze the similarities and differences between the equations of motion for the center of mass and intrinsic angular momentum for isolated sources of gravitational radiation obtained by two different formulations. One approach is based on the asymptotic formulation of the general relativity, whereas the other relies on post-Newtonian methods. Several conclusions are obtained which could be useful for further developments in both approaches.

It is (or should be) well known that specification of a heat bath requires both a temperature and a 4-velocity, the rest frame of the heat bath. In static spacetimes there is a very natural and unique candidate for the 4-velocity of the heat bath, the normalized timelike Killing vector. However in stationary nonstatic spacetimes the situation is considerably more subtle, and several different “natural” 4-velocity fields suitable for characterizing the rest frame of a heat bath can be defined—thus Buchdahl’s 1949 analysis for the Tolman temperature gradient in a stationary spacetime is only part of the story. In particular, the heat bath most suitable for describing the Hawking radiation from a rotating black hole is best described in terms of a gradient flow normal to the spacelike hypersurfaces, not in terms of Killing vectors.

Peculiar velocities are an important tool to study the large-scale distribution of matter in the local universe and test cosmological models. However, present measurements of peculiar velocities are based on empirical distance indicators, which introduce large error bars. Here, we present a new method to measure the peculiar velocities, by directly estimating luminosity distances through waveform signals from inspiralling compact binaries and measuring redshifts from electromagnetic (EM) counterparts. In the future, with the distance uncertainty of GW events reducing to 0.1 per cent by future GW detectors, the uncertainty of the peculiar velocity can be reduced to $10\mathrm{km}/\mathrm{s}$ at 100 mega parsecs. We find that dozens of GW events with EM counterparts can provide a Hubble constant $H_0$ uncertainty of 0.5% and the growth rate of structure with a 0.6% precision in the third-generation ground-based GW detectors, which can reconcile the $H_0$ tension and determine the origins for cosmic accelerated expansion.

The standard model (SM) supplemented by type II seesaw and a SM gauge-singlet scalar dark matter (DM) is a very simple framework to incorporate the observed neutrino oscillations and provide a plausible DM candidate. In this framework, the scalar DM naturally has a leptophilic nature with a pair annihilating mainly into the SM ${\mathrm{SU}(2)}_L$ triplet Higgs scalar of type II Seesaw which, in turn, decay into leptons. In this work, we consider indirect signatures of this leptophilic DM and examine the spectrum of the cosmic ray electron/positron flux from DM pair annihilations in the Galactic halo. Given an astrophysical background spectrum of the cosmic ray electron/positron flux, we find that the contributions from DM annihilations can nicely fit the observed data from the AMS-02, DAMPE and Fermi-LAT collaborations, with a multi-TeV range of DM mass and a boost factor for the DM annihilation cross section of $\mathcal{O}(1000)$. The boost factor has a tension with the Fermi-LAT data for gamma-ray from dwarf spheroidal galaxies and the limit from CMB anisotropies, which can be ameliorated with enhanced local DM density by a factor of about two.

We propose that natural TeV-scale new physics (NP) with $\mathcal{O}(1)$ couplings to the standard model (SM) quarks may lead to a universal enhancement of the Yukawa couplings of all the light quarks, perhaps to a size comparable to that of the SM $b$-quark Yukawa coupling, i.e., $y_q\sim \mathcal{O}(y_b^{\mathrm{SM}})$ for $q=u$, $d$, $c$, $s$. This scenario is described within an effective field theory (EFT) extension of the SM, for which a potential contribution of certain dimension six effective operators to the light quark Yukawa couplings is $y_q\sim \mathcal{O}(f\frac{v^2}{{\mathrm{\Lambda }}^2})$, where $v$ is the Higgs vacuum expectation value, $v=246\mathrm{GeV}$, $\mathrm{\Lambda }$ is the typical scale of the underlying heavy NP, and $f$ is the corresponding Wilson coefficient which depends on its properties and details. In particular, we study the case of $y_q\sim 0.025\sim y_b^{\mathrm{SM}}$, which is the typical size of the enhanced light-quark Yukawa couplings if the NP scale is around $\mathrm{\Lambda }\sim 1.5\mathrm{TeV}$ and the NP couplings are natural, i.e., $f\sim \mathcal{O}(1)$. We also explore this enhanced light quark Yukawa paradigm in extensions of the SM which contain TeV-scale vectorlike quarks, and we match them to the specific higher dimensional effective operators in the EFT description. We discuss the constraints on this scenario and the flavor structure of the underlying NP dynamics and suggest some resulting “smoking gun” signals that should be searched for at the LHC, such as multi-Higgs production $pp\to hh,hhh$ and single Higgs production in association with a high $p_T$ jet ($j$) or photon $pp\to hj,h\gamma$ and with a single top-quark $pp\to ht$.

We consider measurement of the leading irrelevant scaling exponent ${\gamma }_g^{*}$, given by the slope of the beta function, at the fixed point of SU(2) gauge theory with six or eight flavors. We use the running coupling measured using the gradient flow method and perform the continuum extrapolation by interpolating the measured beta function. We study also the dependence of the results on different discretization of the flow. For the eight flavor theory we find ${\gamma }_g^{*}=0.19(8{)}_{-0.09}^{+0.21}$. Applying the same analysis also for the six flavor theory, we find ${\gamma }_g^{*}=0.648(97{)}_{-0.1}^{+0.16}$ consistently with the earlier analysis.

We apply the event-chain algorithm proposed by Bernard et al. in 2009 to toy models of lattice QCD. We give a formal proof of stability of the algorithm. We study its performance at the example of the massive Gaussian model on the square and the simple cubic lattice, the $O(3)$-invariant nonlinear $\sigma$-model on the square lattice, and the $SU(3)\times SU(3)$ principal chiral model on the square lattice. In all these cases we find that critical slowing down is essentially eliminated.

In this work we investigate the effect of an external magnetic field $B$ on the shape of flux tubes in QCD by means of lattice simulations, performed with $N_f=2+1$ flavors of stout improved dynamical staggered quarks with physical masses. After having discussed some difficulties in the practical definition of the flux tube at $B=0$, we show that these ambiguities do not affect the determination of the flux tube modifications induced by the magnetic field. Different results are obtained depending on the relative orientations of the flux tube and of the magnetic field: they confirm that the magnetic field acts as a transverse confinement catalyzer and longitudinal confinement inhibitor; moreover, the flux tube itself loses its axial symmetry when it is not directed along the magnetic background.

We revisit the issue of the geometrical separability of the Hilbert space of physical states on lattice Abelian theories in the context of entanglement entropy. We discuss the conditions under which vectors in the Hilbert space, as well as the gauge-invariant algebra, admit a tensor product decomposition with a geometrical interpretation. With the exception of pure gauge lattices with periodic boundary conditions which contain topological degrees of freedom, we show that the Hilbert space is geometrically separable.

We consider a $D$-dimensional cosmological model with a dilaton field and two ($D-d-1$)-form field strengths which have nonvanishing fluxes in extra dimensions. Exact solutions for the model with a certain set of couplings are obtained by separation of three variables. Some of the solutions describe accelerating expansion of the $d$-dimensional space. Quantum cosmological aspects of the model are also briefly mentioned.

Black hole (BH) shadows in dynamical binary BHs (BBHs) have been produced via ray-tracing techniques on top of expensive fully nonlinear numerical relativity simulations. We show that the main features of these shadows are captured by a simple quasistatic resolution of the photon orbits on top of the static double-Schwarzschild family of solutions. While the latter contains a conical singularity between the line separating the two BHs, this produces no major observable effect on the shadows, by virtue of the underlying cylindrical symmetry of the problem. This symmetry is also present in the stationary BBH solution comprising two Kerr BHs separated by a massless strut. We produce images of the shadows of the exact stationary corotating (even) and counterrotating (odd) stationary BBH configurations. This allows us to assess the impact on the binary shadows of the intrinsic spin of the BHs, contrasting it with the effect of the orbital angular momentum.

We consider the first order connection formulation of 4D general relativity in the “orthogonal” gauge. We show how the partial gauge fixing of the phase space canonical coordinates leads to the appearance of second class constraints in the theory. We employ the gauge unfixing procedure in order to successfully complete the Dirac treatment of the system. While equivalent to the inversion of the Dirac matrix, the gauge unfixing allows us to work directly with the reduced phase space and the ordinary Poisson bracket. At the same time, we explicitly derive the new set of residual first class constraints preserving the partial gauge fixing, which are linear combinations of the original constraints, and these turn out to contain nonlinear terms. While providing an explicit example of how to consistently recast general relativity in a given partial gauge, the main motivation of this classical analysis is the application of the Quantum Reduced Loop Gravity program to a Schwarzschild black hole geometry.