Triplet extensions are attractive alternatives to the standard model (SM) of particle physics. While models with only one triplet are highly constrained by electroweak precision observables, this is not necessarily the case once several triplets are present as in the Georgi-Machacek model. As in all other BSM models, the parameter space of triplet extensions is constrained by the condition that perturbative unitarity is not violated. For this purpose, limits on the eigenvalues of the scalar $2\to 2$ scattering matrix are set. It is very common in the BSM literature that the scattering matrix is calculated under one crucial assumption: the scattering energy $s$ is so large that only point interactions involving quartic couplings provide non-negligible contributions. However, it is not given that this approximation is always valid—in fact, diagrams involving propagators can play an important role. We discuss the examples of (i) the SM model extended by a real triplet, (ii) the $Y=1$ triplet extension of the SM, and (iii) the Georgi-Machacek model, how the tree-level unitarity constraints are affected once the large $s$ approximation is given up. For all models we find that the impact of (effective) cubic couplings can be crucial.

We study natural supersymmetry in the generalized minimal supergravity (GmSUGRA). For the parameter space with low energy, electroweak fine-tuning measures less than 50, we are left with only the $Z$-pole, Higgs-pole, and Higgsino LSP scenarios for dark matter (DM). We perform the focused scans for such parameter space and find that it satisfies various phenomenological constraints and is compatible with the current direct detection bound on neutralino DM reported by the LUX experiment. Such parameter space also has solutions with correct DM relic density besides the solutions with DM relic density smaller or larger than $5\sigma$ WMAP9 bounds. We present five benchmark points as examples. In these benchmark points, the gluino and the first two generations of squarks are heavier than 2 TeV, stop ${\tilde{t}}_{1,2}$ are in the mass range [1, 2] TeV, while sleptons are lighter than 1 TeV. Some part of the parameter space can explain the muon anomalous magnetic moment within $3\sigma$ as well. We also perform the collider study of such solutions by implementing and comparing with relevant studies done by the ATLAS and CMS Collaborations. We find that the points with Higgsino dominant ${\tilde{\chi }}_2^0/{\tilde{\chi }}_1^{\pm }$ mass up to 300 GeV are excluded in $Z$-pole scenario while for Higgs-pole scenario, the points with ${\tilde{\chi }}_2^0$ mass up to 460 GeV are excluded. We also notice that the Higgsino LSP points in our present scans are beyond the reach of present LHC searches. Next, we show that for both the $Z$-pole and Higgs-pole scenarios, the points with electroweak fine-tuning measures around 20 do still survive.

Anomaly-mediated supersymmetry breaking (AMSB) models seem to have become increasingly implausible due to 1) difficulty in generating a Higgs mass $m_h\sim 125\mathrm{GeV}$, 2) typically unnatural superparticle spectra characterized by a large superpotential mu term, and 3) the possibility of a winolike lightest supersymmetry particle as dark matter now seems to be excluded. In the present paper, we propose some modifications to the paradigm model which solve these three issues. Instead of adding a universal bulk scalar mass to avoid tachyonic sleptons, we add distinct Higgs and matter scalar soft masses which then allow for light Higgsinos. To gain accord with the measured Higgs mass, we also include a bulk trilinear soft term. The ensuing natural generalized AMSB model then has a set of light Higgsinos with mass nearby the weak scale $m(W,Z,h)\sim 100\mathrm{GeV}$ as required by naturalness, while the winos populate the several hundred GeV range and gluinos and squarks occupy the multi-TeV range. For LHC searches, the wino pair production followed by decay to the same-sign diboson signature channel offers excellent prospects for discovery at the high luminosity LHC along with Higgsino pair production leading to soft dileptons plus $\mathrm{jet}(\mathrm{s})+\mathrm{MET}$. A linear $e^{+}{e}^{-}$ collider operating above the Higgsino pair production threshold should be able to distinguish the AMSB gaugino spectra from unified or mirage unified scenarios. Dark matter is expected to occur as a Higgsino-like weakly interacting massive particle plus axion admixture.

A nonuniversal Abelian extension ${\mathrm{U}(1)}_X$ free from chiral anomalies is introduced into the standard model (SM), in order to evaluate its suitability in addressing the fermion mass hierarchy (FMH) by using seesaw mechanisms (SSM). In order to break the electroweak symmetry, three Higgs doublets are introduced, which give mass at tree level to the top and bottom quarks, and the muon lepton. With an electroweak singlet scalar field, the $U(1{)}_X$ symmetry is broken and the exotic particles acquire masses. The light particles in the SM obtain their masses via SSM and Yukawa couplings differences. Active neutrino masses are generated through inverse seesaw mechanisms (ISM). Additionally, the algebraic expressions for the mixing angles for quarks and leptons are also shown in the article.

We present the first lattice $N_f=2+1+1$ determination of the tensor form factor $f_T^{D\pi (K)}(q^2)$ corresponding to the semileptonic $D\to \pi (K)\ell {\nu }_{\ell }$ and rare $D\to \pi (K)\ell \ell$ decays as a function of the squared four-momentum transfer $q^2$. Together with our recent determination of the vector $f_{+}^{D\pi (K)}(q^2)$ and scalar $f_0^{D\pi (K)}(q^2)$ form factors, we complete the set of hadronic matrix elements regulating the semileptonic $D\to \pi (K)\ell {\nu }_{\ell }$ and rare $D\to \pi (K)\ell \ell$ transitions within and beyond the standard model, when a nonzero tensor coupling is possible. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with $N_f=2+1+1$ flavors of dynamical quarks, which include in the sea, besides two light mass-degenerate quarks, also the strange and charm quarks with masses close to their physical values. We simulated at three different values of the lattice spacing and with pion masses as small as 220 MeV and with the valence heavy quark in the mass range from $\simeq 0.7m_c^{\mathrm{phys}}$ to $\simeq 1.2m_c^{\mathrm{phys}}$. The matrix elements of the tensor current are determined for a plethora of kinematical conditions in which parent and child mesons are either moving or at rest. As in the case of the vector and scalar form factors, Lorentz symmetry breaking due to hypercubic effects is clearly observed also in the data for the tensor form factor and included in the decomposition of the current matrix elements in terms of additional form factors. After the extrapolations to the physical pion mass and to the continuum and infinite volume limits, we determine the tensor form factor in the whole kinematical region from $q^2=0$ up to $q_{\max }^2=(M_D-M_{\pi (K)}{)}^2$ accessible in the experiments. A set of synthetic data points, representing our results for $f_T^{D\pi (K)}(q^2)$ for several selected values of $q^2$, is provided and the corresponding covariance matrix is also available. At zero four-momentum transfer, we get $f_T^{D\pi }(0)=0.506(79)$ and $f_T^{DK}(0)=0.687(54)$, which correspond to $f_T^{D\pi }(0)/f_{+}^{D\pi }(0)=0.827(114)$ and $f_T^{DK}(0)/f_{+}^{DK}(0)=0.898(50)$.

We propose a way to improve the resolution of the spatial momentum and the time interval for hadron propagators utilizing the lattice geometry. We demonstrate the validity of the method presenting results for pseudoscalar meson energies with and without finite momenta in a large-scale quenched QCD simulation. The method should be useful especially for master-field simulations.

We deliver lattice results for the $I=0$ $\pi \pi$ elastic $s$-wave scattering length calculated with the MILC $N_f=3$ flavors of the Asqtad-improved staggered fermions. The scattering phase shifts are determined by Lüscher’s formula from the energy-eigenvalues of $\pi \pi$ systems at one center of mass frame and four moving frames using the moving wall source technique. Our measurements are good enough to resolve the scattering length $a$ and effective range $r$, moreover, it allows us to roughly estimate the shape parameter $P$. Using our lattice results, the scattering length $a$ and effective range $r$ at the physical point are extrapolated by chiral perturbation theory. Our results are reasonably consistent with the Roy equation determinations and the newer experimental data. Numerical computations are carried out with two MILC fine ($a\approx 0.09\mathrm{fm}$, $L^3\times T=40^3\times 96$) and one MILC superfine ($a\approx 0.06\mathrm{fm}$, $L^3\times T=48^3\times 144$) lattice ensembles at three pion masses of $m_{\pi }\sim 247\mathrm{MeV}$, 249 MeV, and 314 MeV, respectively.

We determine the charm and strange quark masses in the $\overline{\mathrm{MS}}$ scheme, using $n_f=2+1+1$ lattice QCD calculations with highly improved staggered quarks and the regularization-independent symmetric momentum-subtraction intermediate scheme to connect the bare lattice quark masses to continuum renormalization schemes. Our study covers the analysis of systematic uncertainties from this method, including nonperturbative artifacts and the impact of the nonzero physical sea quark masses. We find $m_c^{\overline{\mathrm{MS}}}(3\mathrm{GeV})=0.9896(61)\mathrm{GeV}$ and $m_s^{\overline{\mathrm{MS}}}(3\mathrm{GeV})=0.08536(85)\mathrm{GeV}$, where the uncertainties are dominated by the tuning of the bare lattice quark masses. These results are consistent with, and of similar accuracy to, those using the current-current correlator approach coupled to high-order continuum QCD perturbation theory, implemented in the same quark formalism and on the same gauge field configurations. This provides a strong test of the consistency of methods for determining the quark masses to high precision from lattice QCD. We also give updated lattice QCD world averages for $c$ and $s$ quark masses.

We derive and apply the finite energy sum rules to pion photoproduction. We evaluate the low-energy part of the sum rules using several state-of-the-art models. We show how the differences in the low-energy side of the sum rules might originate from different quantum number assignments of baryon resonances. We interpret the observed features in the low-energy side of the sum rules with the expectation from Regge theory. Finally, we present a model, in terms of a Regge-pole expansion, that matches the sum rules and the high-energy observables.

Inspired by the recent discovery of the ${\mathrm{\Xi }}_{cc}^{++}$ by the LHCb Collaboration, we study the magnetic moments of the spin-$1/2$ doubly charmed baryons up to the next-to-leading order in covariant baryon chiral perturbation theory with the extended-on-mass-shell renormalization scheme. There are three low energy constants at this order: $a_1$, $a_2$, and $g_a$. The latest lattice QCD simulations allow us to fix a combination of $a_1$ and $a_2$, while the axial-vector coupling $g_a$ can be determined in three different ways: by fitting to the lattice QCD data, by the quark model, or by the heavy antiquark diquark symmetry. The magnetic moments of the spin-$1/2$ doubly charmed baryons, ${\mathrm{\Xi }}_{cc}^d$ and ${\mathrm{\Xi }}_{cc}^s$, can then be predicted. We compare our results with those obtained in the heavy baryon chiral perturbation theory and other approaches, and point out some inconsistencies between the lattice QCD simulations and the quark model.

Using $e^{+}{e}^{-}$ annihilation data taken with the CLEO-c detector, measurements of two major ${\mathrm{\Omega }}^{-}$ branching fractions have been made using the reaction $\psi (2S)\to {\mathrm{\Omega }}^{-}{\overline{\mathrm{\Omega }}}^{+}$. The ${\mathrm{\Omega }}^{-}$ decay channels are identified through momentum distributions of charged particles, and systematics of the ${\mathrm{\Omega }}^{-}$ branching fractions have been studied. The results are $\mathcal{B}({\mathrm{\Omega }}^{-}\to {\mathrm{\Lambda }}^0{K}^{-})=(68.9\pm 9.5\pm 4.3)\%$ and $\mathcal{B}({\mathrm{\Omega }}^{-}\to {\mathrm{\Xi }}^0{\pi }^{-})=(19.0\pm 4.0\pm 1.2)\%$.

In the Hamiltonian formulation of general relativity, Einstein’s equation is replaced by a set of four constraints. Classically, the constraints can be identified with the generators of the hypersurface-deformation Lie algebroid (HDA) that belongs to the groupoid of finite evolutions in space-time. Taken over to deformed general relativity, this connection allows one to study possible Drinfeld twists of space-time diffeomorphisms with Hopf-algebra techniques. After a review of noncommutative differential structures, two cases—twisted diffeomorphisms with standard action and deformed (or $\star$-) diffeomorphisms with deformed action—are considered in this paper. The HDA of twisted diffeomorphisms agrees with the classical one, while the HDA obtained from deformed diffeomorphisms is modified due to the explicit presence of $\star$-products in the brackets. The results allow one to distinguish between twisted and deformed symmetries, and they indicate that the latter should be regarded as the relevant symmetry transformations for noncommutative manifolds. The algebroid brackets maintain the same general structure regardless of space-time noncommutativity, but they still show important consequences of nonlocality.

We study the Becchi-Rouet-Stora-Tyutin (BRST) renormalization of an alternative formulation of the Yang-Mills theory, where the matrix-propagator of the gluon and the complementary fields is diagonal. This procedure involves scalings as well as nonlinear mixings of the fields and sources. We show, in the Landau gauge, that the BRST identities implement a recursive proof of renormalizability to all orders.

We introduce an efficient and straightforward technique for rapidly detecting gravitational waves from compact binary mergers. We show that this method achieves the low latencies required to alert electromagnetic partners of candidate binary mergers, aids in data monitoring, and makes use of multidetector networks for sky localization. This approach was instrumental to the analysis of gravitational-wave candidates during the second observing run of Advanced LIGO, including the period of coincident operation with Advanced Virgo, and in particular the analysis of the first observed binary neutron star merger GW170817, where it led to the first tightly localized sky map ($31{\mathrm{deg}}^2$) used to identify AT 2017gfo. Operation of this analysis also enabled the initial discovery of GW170104 and GW170608 despite non-nominal observing of the instrument.

We investigate the hyperbolic scattering of test particles, spinning test particles, and particles with spin-induced quadrupolar structure by a Kerr black hole in the ultrarelativistic regime. We also study how the features of the scattering process modify if the source of the background gravitational field is endowed with a nonzero mass quadrupole moment as described by the (approximate) Hartle-Thorne solution. We compute the scattering angle either in closed analytical form, when possible, or as a power series of the (dimensionless) inverse impact parameter. It is a function of the parameters characterizing the source (intrinsic angular momentum and mass quadrupole moment) as well as the scattered body (spin and polarizability constant). Measuring the scattering angle thus provides useful information to determine the nature of the two components of the binary system undergoing high-energy scattering processes.

Dark matter in the cosmological concordance model is parametrized by a single number, describing the covariantly conserved energy density of a nonrelativistic fluid. Here we test this assumption in a model-independent and conservative way by considering the possibility that, at any point during the cosmological evolution, dark matter may be converted into a noninteracting form of radiation. This scenario encompasses, but is more general than, the cases where dark matter decays or annihilates into these states. We show that observations of the cosmic microwave background allow us to strongly constrain this scenario for any conversion time after big bang nucleosynthesis. We discuss in detail, both from a Bayesian and frequentist point of view, in which sense adding large-scale structure observations may even provide a certain preference for a conversion of dark matter to radiation at late times. Finally we apply our general results to a specific particle physics realization of such a scenario, featuring late kinetic decoupling and Sommerfeld-enhanced dark matter annihilation. We identify a small part of parameter space that both mitigates the tension between cosmic microwave and large-scale structure data and allows for velocity-dependent dark matter self-interactions strong enough to address the small-scale problems of structure formation.

The scotogenic model proposed by Ernest Ma represents an attractive and minimal example for the generation of small Standard Model neutrino masses via radiative corrections in the dark matter sector. In this paper, we demonstrate that, in addition to neutrino masses and dark matter, the scotogenic model also allows to explain the baryon asymmetry of the Universe via low-scale leptogenesis. First, we consider the case of two right-handed neutrinos (RHNs) $N_{1,2}$, for which we provide an analytical argument why it is impossible to push the RHN mass scale below $M_1^{\min }\sim {10}^{10}\mathrm{GeV}$, which is identical to the value in standard thermal leptogenesis in the type-I seesaw scenario with the same washout strength. Then, we present a detailed study of the three-RHN case based on both an analytical and a numerical analysis. In the case of three RHNs, we obtain a lower bound on the $N_1$ mass of around 10 TeV. Remarkably enough, successful low-scale leptogenesis can be achieved without any degeneracy in the RHN mass spectrum. The only necessary condition is a suppression in the $N_1$ Yukawa couplings, which results in suppressed washout and a small active neutrino mass of around ${10}^{-12}\mathrm{eV}$. This leads to the fascinating realization that low-scale leptogenesis in the scotogenic model can be tested in experiments that aim at measuring the absolute neutrino mass scale.

We discuss a methodology of machine learning to deduce the neutron star equation of state from a set of mass-radius observational data. We propose an efficient procedure to deal with a mapping from finite data points with observational errors onto an equation of state. We generate training data and optimize the neural network. Using independent validation data (mock observational data) we confirm that the equation of state is correctly reconstructed with precision surpassing observational errors. We finally discuss the relation between our method and Bayesian analysis with an emphasis put on generality of our method for underdetermined problems.

In theories of gravity that include a scalar field, a compact object’s scalar charge is a crucial quantity since it controls dipole radiation, which can be strongly constrained by pulsar timing and gravitational wave observations. However, in most such theories, computing the scalar charge requires simultaneously solving the coupled, nonlinear metric and scalar field equations of motion. In this article, we prove that in linearly coupled Einstein-dilaton-Gauss-Bonnet gravity, a black hole’s scalar charge is completely determined by the horizon surface gravity times the Euler characteristic of the bifurcation surface, without solving any equations of motion. Within this theory, black holes announce their horizon topology and surface gravity to the rest of the Universe through the dilaton field. In our proof, a four-dimensional topological density descends to a two-dimensional topological density on the bifurcation surface of a Killing horizon. We also comment on how our proof can be generalized to other topological densities on general $G$-bundles, and to theories where the dilaton is nonlinearly coupled to the Euler density.

We calculate the next-to-leading order (NLO) radiative correction to the color-octet $h_c$ inclusive production in $e^{+}{e}^{-}$ annihilation at a super $B$ factory, within the nonrelativistic QCD factorization framework. The analytic expression for the NLO short-distance coefficient (SDC) accompanying the color-octet production operator ${\mathcal{O}}_8^{h_c}{(}^1{S}_0)$ is obtained after summing both virtual and real corrections. The size of NLO correction for the color-octet production channel is found to be positive and substantial. The NLO prediction to the $h_c$ energy spectrum is plagued with unphysical end-point singularity. With the aid of the soft-collinear effective theory, those large end-point logarithms are resummed to the next-to-leading logarithmic (NLL) accuracy. Consequently, further supplemented with the nonperturbative shape function, we obtain the well-behaved predictions for the $h_c$ energy spectrum in the entire kinematic range, which awaits examination by the forthcoming Belle II experiment.