The article delivers the only still unknown coefficient in the 4th post-Newtonian energy expression for binary point masses on circular orbits as a function of orbital angular frequency. Apart from a single coefficient, which is known solely numerically, all the coefficients are given as exact numbers. The shown Hamiltonian is presented in the center-of-mass frame and out of its 57 coefficients, 51 are given fully explicitly. Those coefficients are six coefficients more than previously achieved [P. Jaranowski and G. Schäfer, Phys. Rev. D 86, 061503(R) (2012)]. The local divergences in the point-mass model are uniquely controlled by the method of dimensional regularization. As an application, the last stable circular orbit is determined as a function of the symmetric-mass-ratio parameter.

Searches of lepton-number violation in different processes are very useful to constrain the parameter space of Majorana neutrinos. Here we use available upper bounds on the branching fractions of $B^{-}\to D^0{\pi }^{+}{\mu }^{-}{\mu }^{-}$ and $D^0\to ({\pi }^{-}{\pi }^{-}/K^{-}{\pi }^{-}){\mu }^{-}{\mu }^{-}$ decays to derive constraints on the mass and mixings of Majorana neutrinos by assuming they are produced resonantly in these four-body decays. While the excluded region obtained from $B^{-}$ decays are competitive with existing limits from three-body $D^{-}$ and $B^{-}$ decays, it is shown that experimental improvements on $D^0$ decays offer a good potential to provide similar results.

We analyze QCD and Weinberg-type sum rules in a low-temperature pion gas using vector and axial-vector spectral functions following from the model-independent chiral-mixing scheme. Toward this end we employ recently constructed vacuum spectral functions with ground and first-excited states in both channels and a universal perturbative continuum; they quantitatively describe hadronic $\tau$-decay data and satisfy vacuum sum rules. These features facilitate the implementation of chiral mixing without further assumptions, and lead to in-medium spectral functions which exhibit a mutual tendency of compensating resonance and dip structures, suggestive for an approach toward structureless distributions. In the sum rule analysis, we account for pion mass corrections, which turn out to be significant. While the Weinberg sum rules remain satisfied even at high temperatures, the numerical evaluation of the QCD sum rules for vector and axial-vector channels reveals significant deviations setting in for temperatures beyond $\sim 140\mathrm{MeV}$, suggestive of additional physics beyond low-energy chiral pion dynamics.

We consider an extension of the minimal supersymmetric Standard Model with anomaly mediation as the only source of supersymmetry breaking, and the tachyonic slepton problem solved by a gauged $\mathrm{U}(1)$ symmetry. The extra gauge symmetry is broken at high energies in a manner preserving supersymmetry, while also introducing both the seesaw mechanism for neutrino masses, and the Higgs $\mu$-term. We call the model strictly anomaly mediated supersymmetry breaking. We present typical spectra for the model and compare them with those from so-called minimal anomaly mediated supersymmetry breaking. We find a Standard Model-like Higgs of mass 125 GeV with a gravitino mass of 140 TeV and $\tan \beta =16$. However, the muon anomalous magnetic moment is $3\sigma$ away from the experimental value. The model naturally produces a period of hybrid inflation, which can exit to a false vacuum characterized by large Higgs vacuum expectation values, reaching the true ground state after a period of thermal inflation. The scalar spectral index is reduced to approximately 0.975, and the correct abundance of neutralino dark matter can be produced by decays of thermally produced gravitinos, provided the gravitino mass (and hence the Higgs mass) is high. Naturally light cosmic strings are produced, satisfying bounds from the cosmic microwave background. The complementary pulsar timing and cosmic ray bounds require that strings decay primarily via loops into gravitational waves. Unless the loops are extremely small, the next generation pulsar timing array will rule out or detect the string-derived gravitational radiation background in this model.

In order to raise the Higgs mass to 125 GeV and relieve the fine-tuning associated with the heavy s-top mass in the minimal supersymmetric standard model, we propose a new singlet extension of the minimal supersymmetric standard model. In this scenario, the additional Higgs mass is radiatively generated in a hidden sector, and the effect is transmitted to the Higgs through a messenger field. The Higgs mass can be efficiently increased by the parameters of the superpotential as in the extra matter scenario, but free from the constraints on extra colored matter fields by the LHC experiments. As a result, the tuning problem can be remarkably mitigated by taking low enough messenger mass ($\sim 300\mathrm{GeV}$) and mass parameter scales ($\sim 500\mathrm{GeV}$). We also discuss how to enhance the diphoton decay rate of the Higgs over the SM expectation in this framework.

Though not completely a surprise according to the standard model and existing indirect constraints, the Higgs-like particle, $h$, of mass around 125 GeV recently observed at the LHC may offer an additional window to physics beyond the standard model. In particular, its decay pattern can be modified by the existence of new particles. One of the popular scenarios involves a $Z^{\prime }$ boson associated with an extra Abelian gauge group. In this study, we explore the potential effects of such a boson with family-nonuniversal couplings on the leptonic decays of $h$, both flavor-conserving and flavor-changing. For current constraints, we take into account leptonic decays at the $Z$ pole, LEP II scattering data, limits on various flavor-changing lepton transitions, and lepton magnetic dipole moments. Adopting a model-independent approach and assuming that the $Z^{\prime }$ has negligible mixing with the $Z$ boson, we find that present data allow the $Z^{\prime }$ effects to reach a few percent or higher on $h$ decays into a pair of leptons. Future measurements on $h$ at the LHC or a linear collider can therefore detect the $Z^{\prime }$ contributions or impose further constraints on its couplings. We also consider $Z^{\prime }$-mediated four-lepton decays of the $Z$ and $W$ bosons.

We calculate the Higgs decay rate of $h\to Z\gamma$ by including the contributions from new scalars with arbitrary quantum numbers of the weak isospin ($T$) and hypercharge ($Y$) in the Standard Model. We find that our general formula for the decay rate of $h\to Z\gamma$ matches with that for $h\to \gamma \gamma$ in the limit of $m_Z=0$, but it is different from those in the literature. To illustrate our result, by taking the current $2\sigma$ excess of the $h\to \gamma \gamma$ rate measured by the LHC, we examine the corresponding shift for the $Z\gamma$ decay channel due to the new scalar. We show that the enhancement or reduction of the $h\to Z\gamma$ rate only depends on the relative size of $T$ and the absolute value of $Y$. Explicitly, we predict $0.76<R_{Z\gamma }\equiv \Gamma (h\to Z\gamma )/{\Gamma }_{\mathrm{SM}}(h\to Z\gamma )<2.05$ by imposing the observed range of $1.5<R_{\gamma \gamma }\equiv \Gamma (h\to Z\gamma \gamma )/{\Gamma }_{\mathrm{SM}}(h\to \gamma \gamma )<2$, which is independent of the number of multiplets and the couplings to the Higgs particle as long as the scalars are heavier than 200 GeV. This result provides a clear signature for the future LHC measurements to test physics beyond the Standard Model.

In SU(3) lattice QCD, we study diagonal and off-diagonal gluon propagators in the maximally Abelian gauge with $\mathrm{U}(1{)}_3\times \mathrm{U}(1{)}_8$ Landau gauge fixing. These propagators are studied both in the coordinate space and in the momentum space. The Monte Carlo simulation is performed on ${16}^4$ at $\beta =6.0$ and ${32}^4$ at $\beta =5.8$ and 6.0 at the quenched level. In the four-dimensional Euclidean space-time, the effective mass of diagonal gluons is estimated as $M_{\mathrm{diag}}\simeq 0.3\mathrm{GeV}$ and that of off-diagonal gluons as $M_{\mathrm{off}}\simeq 1\mathrm{GeV}$ in the region of $r=0.4–1.0\mathrm{fm}$. In the momentum space, the effective mass of diagonal gluons is estimated as $M_{\mathrm{diag}}\simeq 0.3\mathrm{GeV}$ and that of off-diagonal gluons as $M_{\mathrm{off}}\simeq 1\mathrm{GeV}$ in the region of $p<1.1\mathrm{GeV}$. The off-diagonal gluon propagator is relatively suppressed in the infrared region and seems to be finite at zero momentum, while the diagonal gluon propagator is enhanced. Furthermore, we also study the functional form of these propagators in momentum space. These propagators are well fitted by $Z/(p^2+m^2{)}^{\nu }$ with fit parameters, $Z$, $m$, and $\nu$ in the region of $p<3.0\mathrm{GeV}$. From the fit results and lattice calculations, all of the spectral functions of diagonal and off-diagonal gluons would have negative regions.

In the continuum the definitions of the covariant Dirac operator and of the gauge covariant derivative operator are tightly intertwined. We point out that the naive discretization of the gauge covariant derivative operator is related to the existence of local unitary covariant ladder operators which allow the definition of a natural lattice gauge covariant derivative. The associated lattice Dirac operator has all the properties of the classical continuum Dirac operator, in particular anti-Hermiticity and chiral invariance in the massless limit, but is of course nonlocal in accordance to the Nielsen-Ninomiya theorem. We show that this lattice Dirac operator coincides in the limit of an infinite lattice volume with the naive gauge covariant generalization of the SLAC derivative, but contains nontrivial boundary terms for finite-size lattices. Its numerical complexity compares pretty well on finite lattices with smeared lattice Dirac operators.

In this work, we present the extension of an alternative subtraction scheme for next-to-leading order QCD calculations to the case of an arbitrary number of massless final state partons. The scheme is based on the splitting kernels of an improved parton shower and comes with a reduced number of final state momentum mappings. While a previous publication including the setup of the scheme has been restricted to cases with maximally two massless partons in the final state, we here provide the final state real emission and integrated subtraction terms for processes with any number of massless partons. We apply our scheme to three jet production at lepton colliders at next-to-leading order and present results for the differential $C$ parameter distribution.

Using the covariant constituent quark model previously developed by us, we calculate the differential rate and the forward-backward asymmetries on the lepton and hadron side for the rare baryon decays ${\Lambda }_b\to \Lambda {\ell }^{+}{\ell }^{-}$ ($\ell =e$, $\mu$, $\tau$) and ${\Lambda }_b\to \Lambda \gamma$. We use helicity methods to write down a threefold joint angular decay distribution for the cascade decay ${\Lambda }_b\to \Lambda (\to p{\pi }^{-})+J_{\mathrm{eff}}(\to {\ell }^{+}{\ell }^{-})$. Through appropriate angular integrations, we obtain expressions for the rates, the lepton-side forward-backward asymmetry, and the polarization of the daughter baryon $\Lambda$ leading to a hadron-side forward-backward asymmetry. We present numerical results on these observables using the covariant quark model and compare our results to the results of other calculations that have appeared in the literature.

Within the framework of the perturbative QCD approach, we study the branching ratios of the two-body charmed decays $B_{(s)}\to a_1(b_1)D_{(s)}$, $a_1(b_1)D_{(s)}^{*}$, which, including Cabibbo-Kobayashi-Maskawa, allowed and suppressed decays. Our calculations are consistent with the currently available data and the experimental upper limits. Certainly, many of these predicted channels have not been measured by experiments and can be confronted with the future experimental data. We also discuss the polarization factions of the decays $B_{(s)}\to a_1(b_1)D_{(s)}^{*}$, some of which are sensitive to the distinct Gegenbauer moments of the wave functions and the decay constants of mesons $a_1$ and $b_1$.

Multiplicities in semi-inclusive deep-inelastic scattering are presented for each charge state of ${\pi }^{\pm }$ and ${\mathrm{K}}^{\pm }$ mesons. The data were collected by the HERMES experiment at the HERA storage ring using 27.6 GeV electron and positron beams incident on a hydrogen or deuterium gas target. The results are presented as a function of the kinematic quantities $x_{\mathrm{B}}$, $Q^2$, $z$, and $P_{h\perp }$. They represent a unique data set for identified hadrons that will significantly enhance our understanding of the fragmentation of quarks into final-state hadrons in deep-inelastic scattering.

Recent evidence from observation of the flavor-changing neutral current decay $B_s^0\to {\mu }^{+}{\mu }^{-}$ by the LHCb Collaboration $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-})=({3.2}_{-1.2}^{+1.5})\times {10}^{-9}$ is consistent with the latest standard model prediction ${\mathcal{B}}_{\mathcal{S}\mathcal{M}}(B_s^0\to {\mu }^{+}{\mu }^{-})=(3.23\pm 0.27)\times {10}^{-9}$. While new physics can still affect this decay amplitude, its contribution is certainly not the dominant one. We analyze branching ratios of the decays $B_s^0\to {\mu }^{+}{\mu }^{-}X$, with $X=\gamma$ or $\nu \overline{\nu }$, which can mimic $B_s^0\to {\mu }^{+}{\mu }^{-}$ on portions of the parameter space where $X$ is soft. Since detection efficiency of $\gamma$ or $\nu \overline{\nu }$ in modern charm-physics experiments is quite low in that region, those processes could be misidentified as $B_s^0\to {\mu }^{+}{\mu }^{-}$. We perform a model-independent standard model calculation of those processes incorporating heavy quark and chiral symmetries of QCD concentrating on the soft-$X$ region. We show that misidentification of the considered processes can only boost the $B_s^0\to {\mu }^{+}{\mu }^{-}$ rate by less than a percent.

In this work, we investigate $B_c\to D^{(*)}T$ decays in the perturbative QCD approach, based on $k_T$ factorization, where $T$ denotes a light tensor meson. For all decays considered in this work, there are no contributions from factorizable emission diagrams because the emitted tensor meson cannot be generated from (axial-)vector current or (pseudo)scalar density. We find that the annihilation amplitudes are dominant in these decays due to the large Cabibbo-Kobayashi-Maskawa elements, which can be perturbatively calculated without parametrization in the pQCD approach. The branching ratios of the $B_c\to D^{(*)}{K}_2^{*}$ decays can reach ${10}^{-5}$ to ${10}^{-4}$, which is one order of magnitude larger than that of the corresponding $B_c\to D^{(*)}{K}^{*}$ decays, where heavy cancellation occurred between the penguin emission and tree annihilation diagrams. With such large branching ratios, they can very likely be observed in the ongoing LHCb experiments. We also predict a large percentage of transverse polarizations in those $W$-annihilation-diagram dominant $B_c\to D^{*}T$ decay channels.

After a rediscussion of the vanishing theorems for helicity amplitudes in unbroken gauge theories, we study the case of spontaneously broken gauge theories at high energy. The vanishing theorems generalize to a definite pattern of $m/E$ suppression of the amplitudes that vanish in the massless case, where $E$ is the energy scale of the process and $m$ is the mass of the gauge vectors. We use only elementary arguments, and as an application we show how these methods can be employed to understand some aspects of the effective $W$ approximation in the polarized case.

We construct an evolution equation for the invariant-mass distribution of light-quark and gluon jets in the framework of QCD resummation. The solution of the evolution equation exhibits a behavior consistent with Tevatron CDF data: the jet distribution vanishes in the small invariant-mass limit, and its peak moves toward the high invariant-mass region with the jet energy. We also construct an evolution equation for the energy profile of the light-quark and gluon jets in the similar framework. The solution shows that the energy accumulates faster within a light-quark jet cone than within a gluon jet cone. The jet energy profile convoluted with hard scattering and parton distribution functions matches well with the Tevatron CDF and the LHC CMS data. Moreover, comparison with the CDF and CMS data implies that jets with large (small) transverse momentum are mainly composed of the light-quark (gluon) jets. At last, we discuss the application of the above solutions for the light-particle jets to the identification of highly boosted heavy particles produced at the LHC.

Using a momentum space model for the dipole scattering amplitude we present an analysis of the saturation effects at LHC energies, describing the data on proton-proton and proton-lead collisions. The model is based on the asymptotic solutions of the Balitsky-Kovchegov equation, being ideal in the saturation domain where the target wave function has a high occupation number. We also make predictions for the nuclear modification ratios on charged hadron and prompt photon production in the forward region, where the high parton density effects are important.

Double parton fragmentation is a process in which a pair of partons produced in the short-distance process hadronize into the final state hadron. This process is important for quarkonium production when the transverse momentum is much greater than the quark mass. Resummation of logarithms of the ratio of these two scales requires the evolution equations for double parton fragmentation functions (DPFF). In this paper we complete the one-loop evaluation of the anomalous dimensions for the DPFF. We also consider possible mixing between the DPFF and single parton power suppressed gluon fragmentation and show that such effects are subleading.

The covariant quark model represents an appropriate theoretical framework to describe the recent results on $B_s\to J/\psi +\eta$ and $B_s\to J/\psi +{\eta }^{\prime }$ decays from the Belle and LHCb collaborations. In this article, we present the main features of the covariant quark model together with details on some of its aspects and methods, which we consider to be important. Further, we apply the model specifically to the studied decay processes and give numerical results on decay widths as they follow from the model. We conclude that the model, with most of its parameters previously fixed from different processes, is able to incorporate the new experimental measurements. In particular, we found that the ratio of the branching fractions of the decays $B_s$ into $J/\psi +{\eta }^{\prime }$ and $J/\psi +\eta$ is equal to $R\approx 0.86$, in agreement with the data reported by the Belle and LHCb collaborations.