We are motivated by the recently reported dynamical evidence of stars with short orbital periods moving around the center of the Milky Way and the corresponding hypothesis about the existence of a supermassive black hole hosted at its center. In this paper we show how the mass and rotation parameters of a Kerr black hole (assuming that the putative supermassive black hole is of this type), as well as the distance that separates the black hole from the Earth, can be estimated in a relativistic way in terms of (i) the redshift and blueshift of photons that are emitted by geodesic massive particles (stars) and travel along null geodesics towards a distant observer (located at a finite distance), and (ii) the radius of these star orbits. As a concrete example and as a first step towards a full relativistic analysis of the above-mentioned star orbits around the center of our Galaxy, we consider stable equatorial circular orbits of stars and express their corresponding redshift/blueshift in terms of the metric parameters (mass and angular momentum per unit mass) and the orbital radii of both the emitter star and the distant observer. These radii are linked through the constants of motion along the null geodesics followed by photons since their emission until their detection, allowing us to get a closed expression for the orbital radius of the observer in terms of the emitter orbital radius, which is known from observations, and the black hole parameters $M$ and $a$. In principle, these expressions allow one to statistically estimate the mass and rotation parameters of the Kerr black hole, and the radius of our orbit, through a Bayesian fitting, i.e., with the aid of observational data: the redshift/blueshift measured at certain points of stars’ orbits and their radii, with their respective errors, a task that we hope to perform in the near future. We also point to several astrophysical phenomena, like accretion disks of rotating black holes, binary systems and active galactic nuclei, among others, to which this formalism can be applied.

The inspiral and merger of supermassive black hole binary systems with high orbital eccentricity are among the promising sources of the advanced gravitational wave observatories. In this paper we compute gravitational waveforms in the frequency domain to the first post-Newtonian order, emitted by compact binary systems with arbitrary eccentricity. Our results are fully analytic, ready-to-use expressions of the waveforms in terms of a suitable generalization of Hansen coefficients known from celestial mechanics. Secular terms induced by the eccentricity are eliminated by introducing a suitable phase shift. The obtained waveforms have a rather simple structure, greatly facilitating their use in applications.

Space-borne gravitational wave detectors, such as (e)LISA, are designed to operate in the low-frequency band (mHz to Hz), where there is a variety of gravitational wave sources of great scientific value [arXiv:1305.5720 and S. Babak et al., Classical Quantum Gravity 28, 114001 (2011)]. To achieve the extraordinary sensitivity of these detectors, the precise synchronization of the clocks on the separate spacecraft and the accurate determination of the interspacecraft distances are important ingredients. In our previous paper [Y. Wang et al., Phys. Rev. D 90, 064016 (2014)], we have described a hybrid-extend Kalman filter with a full state vector to do this job. In this paper, we explore several different state vectors and their corresponding (phenomenological) dynamic models to reduce the redundancy in the full state vector, to accelerate the algorithm, and to make the algorithm easily extendable to more complicated scenarios.

Disformally coupled, light scalar fields arise in many of the theories of dark energy and modified gravity that attempt to explain the accelerated expansion of the Universe. They have proved difficult to constrain with precision tests of gravity because they do not give rise to fifth forces around static nonrelativistic sources. However, because the scalar field couples derivatively to standard model matter, measurements at high-energy particle colliders offer an effective way to constrain and potentially detect a disformally coupled scalar field. Here we derive new constraints on the strength of the disformal coupling from LHC run 1 data and provide a forecast for the improvement of these constraints from run 2. We additionally comment on the running of disformal and standard model couplings in this scenario under the renormalization group flow.

The search for supersymmetry at run 1 of the LHC has resulted in gluino mass limits $m_{\tilde{g}}\gtrsim 1.3\mathrm{TeV}$ for the case where $m_{\tilde{q}}\gg m_{\tilde{g}}$ and in models with gaugino mass unification. The increased energy and, ultimately, luminosity of LHC13 will explore the range $m_{\tilde{g}}\sim 1.3–2\mathrm{TeV}$. We examine how the discovery of SUSY via gluino pair production would unfold via a comparative analysis of three LSP archetype scenarios: (1) mSUGRA/CMSSM model with a binolike LSP, (2) charged SUSY breaking (CSB) with a winolike LSP, and (3) SUSY with radiatively driven naturalness (RNS) and a Higgsino-like LSP. In all three cases we expect heavy-to-very-heavy squarks as suggested by a decoupling solution to the SUSY flavor and $CP$ problems and by the gravitino problem. For all cases, initial SUSY discovery would likely occur in the multi-$b\text{-jet}+{\cancel{E}}_T$ channel. The CSB scenario would be revealed by the presence of highly ionizing, terminating tracks from quasistable charginos. As further data accrue, the RNS scenario with 100–200 GeV Higgsino-like LSPs would be revealed by the buildup of a mass edge/bump in the opposite sign/same flavor dilepton invariant mass which is bounded by the neutralino mass difference. The mSUGRA/CMSSM archetype would contain neither of these features but would be revealed by a buildup of the usual multilepton cascade decay signatures.

The kinetic mixing of the vector boson of hypercharge with the vector boson(s) associated with particle sectors beyond the standard model is one of the best motivated windows to new physics. The resulting phenomenology depends on whether the new vector boson is massive or massless. The phenomenology associated with the massive phase has received considerable attention in recent years with many theoretical explorations and new experimental efforts, while the massless phase is linked to the phenomenology of millicharged particles. In this paper we introduce the more general case where the kinetic mixing is with a vector boson that is a linear combination of both a massive and a massless state (as the hypercharge is in the standard model). We demonstrate that the general phase is only weakly constrained when the mass scale associated with it is above about 100 MeV. Finally, we show that a new dedicated experiment at the LHC, proposed recently in Haas et al. [Phys. Lett. B 746, 117 (2015)], can explore large parts of the parameter space in the mass range between 100 MeV and 100 GeV. In particular, it is uniquely sensitive to a new signature that only arises in the general phase.

We report the standard model evaluation of the indirect $CP$ violation parameter ${ϵ}_K$ using inputs determined from lattice QCD: the kaon bag parameter ${\widehat{B}}_K$, ${\xi }_0$, $|V_{us}|$ from the $K_{\ell 3}$ and $K_{\mu 2}$ decays, and $|V_{cb}|$ from the axial current form factor for the exclusive decay $\overline{B}\to D^{*}\ell \overline{\nu }$ at zero-recoil. The theoretical expression for ${ϵ}_K$ is thoroughly reviewed to give an estimate of the size of the neglected corrections, including long distance effects. The Wolfenstein parametrization $(|V_{cb}|,\lambda ,\overline{\rho },\overline{\eta })$ is adopted for Cabibbo-Kobayashi-Maskawa matrix elements which enter through the short distance contribution of the box diagrams. For the central value, we take the unitarity triangle apex $(\overline{\rho },\overline{\eta })$ from the angle-only fit of the UTfit collaboration and use $V_{us}$ as an independent input to fix $\lambda$. We find that the standard model prediction of ${ϵ}_K$ with exclusive $V_{cb}$ (lattice QCD results) is lower than the experimental value by $3.4\sigma$. However, with inclusive $V_{cb}$ (results of the heavy quark expansion), there is no gap between the standard model prediction of ${ϵ}_K$ and its experimental value. For the calculation of ${ϵ}_K$, we perform the renormalization group running to obtain ${\eta }_{cc}$ at next-to-next-to-leading-order; we find ${\eta }_{cc}^{\mathrm{NNLO}}=1.72(27)$.

We use lattice formulation of ${\varphi }^4$ theory in order to investigate nonperturbative features of its continuum limit in two dimensions. In particular, by means of Monte Carlo calculations, we obtain the critical coupling constant $g/{\mu }^2$ in the continuum, where $g$ is the unrenormalized coupling. Our final result is $g/{\mu }^2=11.15\pm 0.06_{\text{stat}}\pm 0.03_{\text{syst}}$.

We compare two existing approaches to calculating the decay of molecular quarkonium states to conventional quarkonia in effective field theory, using $X(3872)\to {\chi }_{cJ}{\pi }^0$ as an example. In one approach the decay of the molecular quarkonium proceeds through a triangle diagram with charmed mesons in the loop. We argue this approach predicts excessively large rates for $\mathrm{\Gamma }[X(3872)\to {\chi }_{cJ}{\pi }^0]$ unless both charged and neutral mesons are included and a cancellation between these contributions is arranged to suppress the decay rates. This cancellation occurs naturally if the $X(3872)$ is primarily in the $I=0$ $D{\overline{D}}^{*}+\mathrm{c}.\mathrm{c}$ scattering channel. The factorization approach to molecular decays calculates the rates in terms of tree-level transitions for the $D$ mesons in the $X(3872)$ to the final state, multiplied by unknown matrix elements. We show that this approach is equivalent to the hadronic loops approach if the cutoff on the loop integrations is taken to be a few hundred MeV or smaller, as is appropriate when the charged $D$ mesons have been integrated out of the effective theory.

We examine the sources of parton distribution errors in the $W$ mass measurement, and point out shortcomings in the existing literature. Optimistic assumptions about strategies to reduce the error by normalizing to $Z$ observables are examined and found to rely too heavily on assumptions about the parametrization and degrees of freedom of the parton distribution functions (PDFs). We devise a strategy to combine measurements as efficiently as possible using error correlations to reduce the overall uncertainty of the measurement, including $Z$ data, and estimate a PDF error of ${}_{-12}^{+10}\mathrm{MeV}$ is achievable in a $W$ mass measurement at the LHC. Further reductions of the $W$ mass uncertainty will require improved fits to the parton distribution functions.

We calculate the bosonic boundary state corresponding to a moving fractional $\mathrm{D}p$-brane in a partially orbifoldized spacetime ${\mathbb{R}}^{1,d-5}\times {\mathbb{C}}^2/{\mathbb{Z}}_2$ in the presence of the Kalb-Ramond field, the $U(1)$ gauge potential and the tachyon field. Using this boundary state, we obtain the interaction amplitude of two parallel moving $\mathrm{D}p$-branes with the above background fields. Various properties of the interaction will be investigated. In addition, we study effects of the tachyon condensation on a moving fractional $\mathrm{D}p$-brane with the above background fields through the boundary state formalism.

Determining the structure of spectral densities is important for understanding the behavior of any quantum field theory (QFT). However, the exact calculation of these quantities often requires a full nonperturbative description of the theory, which for physically realistic theories such as quantum chromodynamics (QCD) is currently unknown. Nevertheless, it is possible to infer indirect information about these quantities. In this paper we demonstrate an approach for constraining the form of spectral densities associated with QFT propagators, which involves matching the short distance expansion of the spectral representation with the operator product expansion (OPE) of the propagators. As an application of this procedure we analyze the scalar propagator in ${\varphi }^4$-theory and the quark propagator in QCD, and show that constraints are obtained on the spectral densities and the OPE condensates. In particular, it is demonstrated that the perturbative and nonperturbative contributions to the quark condensate in QCD can be decomposed, and that the nonperturbative contributions are related to the structure of the continuum component of the scalar spectral density.

The recent observations of the massive pulsars PSR J1614-2230 and of PSR J0348+0432 with about two solar masses imply strong constraints on the properties of dense matter in the core of compact stars. Effective models of QCD aiming to describe neutron star matter can thereby be considerably constrained. In this context, a chiral quark-meson model based on a SU(3) linear $\sigma$-model with a vacuum pressure and vector meson exchange is discussed in this work. The impact of its various terms and parameters on the equation of state and the maximum mass of compact stars are delineated to check whether pure quark stars with two solar masses are feasible within this approach. Large vector meson coupling constant and a small vacuum pressure allow for maximum masses of two or more solar masses. However, pure quark stars made of absolutely stable strange quark matter, so-called strange stars, turn out to be restricted to a quite small parameter range.

We apply select ideas from the modern theory of stochastic processes in order to study the continuity/roughness of scalar quantum fields. A scalar field with logarithmic correlations (such as a massless field in $1+1$ spacetime dimensions) has the mildest of singularities, making it a logical starting point. Instead of the usual inner product of the field with a smooth function, we introduce a moving average on an interval which allows us to obtain explicit results and has a simple physical interpretation. Using the mathematical work of Dudley, we prove that the averaged random process is in fact continuous, and give a precise modulus of continuity bounding the short-distance variation.

Inspiraling compact binaries have been identified as one of the most promising sources for gravitational-wave detection. These binaries are always expected to have been circularized by the gravitational radiation when they enter the detector’s frequency band. However, recent studies indicate that some binaries may still possess a significant eccentricity. In light of the enhanced post-circular waveform model for eccentric binaries in the frequency domain, we do a systematic study of the possible signal-to-noise ratio loss if one uses quasicircular waveform templates to analyze the eccentric signal, and revisit the problem of parameter estimation of gravitational-wave chirp signals from eccentric compact binaries. We confirm previous results from other researchers that the resulting signal-to-noise ratio loss becomes larger than 5% for eccentricity bigger than 0.1 and the resulting parameter estimation bias is more than 0.1%. We study the parameter estimation accuracy for such a waveform with different initial eccentricities from 0.1 to 0.4 by using the Fisher matrix method. As expected, the eccentricity improves the parameter estimation accuracy significantly by breaking degeneracies between different parameters. Particularly, we find that the eccentricity errors improve by 2 orders of magnitude from ${10}^{-2}$ to ${10}^{-4}$ when eccentricity grows from 0.1 to 0.4, and the estimated errors of the chirp mass are about ${10}^{-3}$ for a binary black hole using the Advanced LIGO detector. For the Einstein Telescope detector, the estimated accuracy of parameters will be 2 orders of magnitude higher.

Bekenstein bounds for the entropy of a body imply a universal inequality between size, energy, angular momentum, and charge. We prove this inequality in electromagnetism. We also prove it, for the particular case of zero angular momentum, in general relativity. We further discuss the relation of these inequalities with inequalities between size, angular momentum, and charge recently studied in the literature.

We present a space-time model of the collision of two homogeneous, plane impulsive gravitational waves (each having a delta function profile) propagating in a vacuum before collision and for which the postcollision space-time has constant curvature. The profiles of the incoming waves are $k\delta (u)$ and $l\delta (v)$ where $k,l$ are real constants and $u=0,v=0$ are intersecting null hypersurfaces. The cosmological constant $\mathrm{\Lambda }$ in the postcollision region of the space-time is given by $\mathrm{\Lambda }=-6kl$.

We initiate a study of cosmological implications of sphaleron-mediated $CP$-violation arising from the electroweak vacuum angle under the reasonable assumption that the semiclassical suppression is lifted at finite temperature. In this article, we explore the implications for existing scenarios of baryogenesis. Many compelling models of baryogenesis rely on electroweak sphalerons to relax a $(B+L)$ charge asymmetry. Depending on the sign of the $CP$-violating parameter, it is shown that the erasure of positive $(B+L)$ will proceed more or less quickly than the relaxation of negative $(B+L)$. This is a higher order effect in the kinetic equation for baryon number, which we derive here through order $n_{B+L}^2$. Its impact on known baryogenesis models therefore seems minor, since phenomenologically $n_{B+L}$ is much smaller than the entropy density. However, there remains an intriguing unexplored possibility that baryogenesis could be achieved with the vacuum angle alone providing the required $CP$-violation.

An analysis is given of the chromoelectric dipole moment of quarks and of the neutron in an MSSM extension where the matter sector contains an extra vectorlike generation of quarks and mirror quarks. The analysis includes contributions to the chromoelectric dipole moment from the exchange of the $W$ and the $Z$ bosons, from the exchange of charginos and neutralinos and the gluino. Their contribution to the electric dipole moment (EDM) of quarks is investigated. The interference between the minimal supersymmetric standard model sector and the new sector with vectorlike quarks is investigated. It is shown that inclusion of the vectorlike quarks can modify the quark EDMs in a significant way. Further, this interference also provides a probe of the vectorlike quark sector. These results are of interest as in the future measurements on the neutron EDM could see an improvement up to 2 orders of magnitude over the current experimental limits and provide an instrument for a further probe of new physics beyond the standard model.

Some evidence for sterile neutrinos has been found in short baseline observations where the measured neutrino flux did not agree with expectations. Systematic uncertainties from the expected values have limited the sensitivity of this approach. Observation at multiple distances can remove the normalization uncertainty by isolating the distance dependence. This does not work for high-$\mathrm{\Delta }{m}^2$ sterile neutrinos since they are fully mixed at most observation distances and only shift the normalization of the flux. A compact intense source of neutrinos based on a subcritical fission reactor would permit observation of oscillations on submeter distance scales and clearly distinguish between a systematic normalization and the $L/E$ dependence expected from oscillations.