We report the nonperturbative tuning of parameters—${\kappa }_c$, ${\kappa }_b$, and ${\kappa }_{\mathrm{crit}}$—that are related to the bare heavy-quark mass in the Fermilab action. This requires the computation of the masses of $D_s^{(*)}$ and $B_s^{(*)}$ mesons comprised of a Fermilab heavy quark and a staggered light quark. Additionally, we report the hyperfine splittings for $D_s^{(*)}$ and $B_s^{(*)}$ mesons as a cross-check of our simulation and analysis methods. We find a splitting of $145\pm 15\mathrm{MeV}$ for the $D_s$ system and $40\pm 9\mathrm{MeV}$ for the $B_s$ system. These are in good agreement with the Particle Data Group average values of $143.9\pm 0.4\mathrm{MeV}$ and $46.1\pm 1.5\mathrm{MeV}$, respectively. The calculations are carried out with the MILC $2+1$ flavor gauge configurations at three lattice spacings $a\approx 0.15$, 0.12, and 0.09 fm.

In the littlest Higgs model with $T$-parity (LHT), the mirror quarks have flavor structures and will contribute to the top quark flavor changing neutral current. In this work, we perform an extensive investigation of the top quark rare three-body decays $t\to cVV$, ($V=\gamma$, $Z$, $g$) and $t\to cf\overline{f}$, ($f=b$, $\tau$, $\mu$, $e$) at one-loop level. Our results show that the branching ratios of $t\to cgg$ and $t\to cb\overline{b}$ could reach $\mathcal{O}({10}^{-3})$ in the favorite parameter space of the littlest Higgs model with $T$-parity, which implies that these decays may be detectable at the LHC or ILC, while for the other decays, their rates are too small to be observable at the present or future colliders.

The shear viscosity to entropy density ratio, $\eta /s$, characterizes how perfect a fluid is. We calculate the leading order $\eta /s$ of a gluon plasma in perturbation using the kinetic theory. The leading order contribution only involves the elastic $gg\leftrightarrow gg$ (22) process and the inelastic $gg\leftrightarrow ggg$ (23) process. The hard-thermal-loop (HTL) treatment is used for the 22 matrix element, while the exact matrix element in vacuum is supplemented by the gluon Debye mass insertion for the 23 process. Also, the asymptotic mass is used for the external gluons in the kinetic theory. The errors from not implementing HTL and the Landau-Pomeranchuk-Migdal effect in the 23 process, and from the uncalculated higher order corrections, are estimated. Our result smoothly connects the two different approximations used by Arnold, Moore, and Yaffe (AMY) and Xu and Greiner (XG). At small ${\alpha }_s$ (${\alpha }_s\ll 1$), our result is closer to AMY’s collinear result while at larger ${\alpha }_s$ the finite angle noncollinear configurations become more important and our result is closer to XG’s soft bremsstrahlung result. In the region where perturbation is reliable (${\alpha }_s\lesssim 0.1$), we find no indication that the proposed perfect fluid limit $\eta /s\simeq 1/(4\pi )$ can be achieved by perturbative QCD alone. Whether this can be achieve for ${\alpha }_s\gtrsim 0.1$ is still an open question.

Charmed mesons may be produced when a primary cosmic ray or the leading hadron in an air shower collide with an atmospheric nucleon. At energies $\ge {10}^8\mathrm{GeV}$ their decay length becomes larger than 10 km, which implies that they tend to interact in the air instead of decaying. We study the collisions of long-lived charmed hadrons in the atmosphere. We show that $({\Lambda }_c,D)$-proton diffractive processes and partonic collisions of any $q^2$ where the charm quark is a spectator have lower inelasticity than $(p,\pi )$-proton collisions. In particular, we find that a $D$ meson deposits in each interaction just around 55% of the energy deposited by a pion. On the other hand, collisions involving the valence $c$-quark (its annihilation with a sea $\overline{c}$-quark in the target or $c$-quark exchange in the $t$ channel) may deposit most of the $D$ meson energy, but their frequency is low (below 0.1% of inelastic interactions). As a consequence, very energetic charmed hadrons may keep a significant fraction of their initial energy after several hadronic interactions, reaching much deeper in the atmosphere than pions or protons of similar energy.

We investigate the hadronic production of the doubly heavy baryon ${\Xi }_{bc}$ at the Large Hadron Collider (LHC), where contributions from the four $(bc)$-diquark states $(bc{)}_{\overline{\mathbf{3}},\mathbf{6}}[{}^{1}S_0]$ and $(bc{)}_{\overline{\mathbf{3}},\mathbf{6}}[{}^{3}S_1]$ have been taken into consideration. Numerical results show that under the condition of $p_T>4\mathrm{GeV}$ and $|y|<1.5$, sizable ${\Xi }_{bc}$ events about $1.7\times {10}^7$ and $3.5\times {10}^9$ per year can be produced for the center-of-mass energy $\sqrt{S}=7\mathrm{TeV}$ and $\sqrt{S}=14\mathrm{TeV}$, respectively. For experimental usage, the total and the interested differential cross sections are estimated under some typical $p_T$ and $y$ cuts for the LHC detectors CMS, ATLAS, and LHCb. The main uncertainties are discussed and a comparative study on the hadronic production of ${\Xi }_{cc}$, ${\Xi }_{bc}$, and ${\Xi }_{bb}$ at the LHC are also presented.

Various theories beyond the standard model predict new particles with masses in the sub-eV range with very weak couplings to ordinary matter. A $P$-odd and $T$-odd interaction between polarized and unpolarized nucleons proportional to $\overrightarrow{s}·\overrightarrow{r}$ involving a scalar coupling $g_s$ at one vertex and a pseudoscalar coupling $g_p$ at the other vertex is one such possibility. We show that measurements of the transverse spin relaxation rate ${\Gamma }_2$ for polarized gas can be used to set limits on $g_s{g}_p$ for boson masses in the $10\mu$eV to $100$ meV range, corresponding to distances from centimeters to micrometers. We present limits from both a reanalysis of previous measurements of ${\Gamma }_2$ in ${}^3\mathrm{He}$ spin exchange cells and from data in a test experiment searching for a change in ${\Gamma }_2$ upon the motion of an unpolarized test mass. The outlook for more sensitive measurements using this technique is discussed.

The $t\overline{t}$ spin correlation at production is a fundamental prediction of QCD and a potentially incisive test of new physics coupled to top quarks. We measure the $t\overline{t}$ spin state in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$ using 1001 candidate events in the lepton plus jets decay channel reconstructed in the CDF II detector. In the helicity basis, for a top-quark mass of $172.5\mathrm{GeV}/c^2$, we find a spin correlation coefficient $\kappa =0.60\pm 0.50(\mathrm{stat})\pm 0.16(\mathrm{syst})$, consistent with the QCD prediction, $\kappa \approx 0.40$.

We perform an analytic continuation of the two-loop remainder function for the six-point planar maximally helicity violating amplitude in $\mathcal{N}=4$ supersymmetry, found by Goncharov, Spradlin, Vergu and Volovich from the lightlike Wilson loop representation. The remainder function is continued into a physical region, where all but two energy invariants are negative. It turns out to be pure imaginary in the multi-Regge kinematics, which is in agreement with the predictions based on the Steinmann relations for the Regge poles and Mandelstam cut contributions. The leading term correctly reproduces the expression calculated by one of the authors in the Balitsky-Fadin-Kuraev-Lipatov approach, while the subleading term presents a result that has not been found before with the use of unitarity techniques. This finding supports the applicability of the Wilson loop approach to the planar maximally helicity violating amplitudes in $\mathcal{N}=4$ supersymmetry.

Separate regions in space are generally entangled, even in the vacuum state. It is known that this entanglement can be swapped to separated Unruh-DeWitt detectors, i.e., that the vacuum can serve as a source of entanglement. Here, we demonstrate that, in the presence of curvature, the amount of entanglement that Unruh-DeWitt detectors can extract from the vacuum can be increased.

The computation of the gravitational radiation emitted by a particle falling into a Schwarzschild black hole is a classic problem that was already studied in the 1970s. Here we present a detailed numerical analysis of the case of radial infall starting at infinity with no initial velocity. We compute the radiated waveforms, spectra, and energies for multipoles up to $l=6$, improving significantly on the numerical accuracy of existing results. This is done by integrating the Zerilli equation in the frequency domain using the Green’s function method. The resulting wave exhibits a “ring-down” phase whose dominant contribution is a superposition of the quasinormal modes of the black hole. The numerical accuracy allows us to recover the frequencies of these modes through a fit of that part of the wave. Comparing with direct computations of the quasinormal modes, we reach a $\sim {10}^{-4}$ to $\sim {10}^{-2}$ accuracy for the first two overtones of each multipole. Our numerical accuracy also allows us to display the power-law tail that the wave develops after the ring-down has been exponentially cut off. The amplitude of this contribution is $\sim {10}^2$ to $\sim {10}^3$ times smaller than the typical scale of the wave.

Belinski, Khalatnikov, and Lifshitz pioneered the study of the statistical properties of the never-ending oscillatory behavior (among successive Kasner epochs) of the geometry near a spacelike singularity. We show how the use of a “cosmological billiard” description allows one to refine and deepen the understanding of these statistical properties. Contrary to previous treatments, we do not quotient the dynamics by its discrete symmetry group (of order 6), thereby uncovering new phenomena, such as correlations between the successive billiard corners in which the oscillations take place. Starting from the general integral invariants of Hamiltonian systems, we show how to construct invariant measures for various projections of the cosmological-billiard dynamics. In particular, we exhibit, for the first time, a (non-normalizable) invariant measure on the “Kasner circle” which parametrizes the exponents of successive Kasner epochs. Finally, we discuss the relation between: (i) the unquotiented dynamics of the Bianchi-IX ($a$, $b$, $c$ or mixmaster) model; (ii) its quotienting by the group of permutations of ($a$, $b$, $c$); and (iii) the billiard dynamics that arose in recent studies suggesting the hidden presence of Kac-Moody symmetries in cosmological billiards.

We present two methods for integrating forced geodesic equations in the Kerr spacetime. The methods can accommodate arbitrary forces. As a test case, we compute inspirals caused by a simple drag force, mimicking motion in the presence of gas. We verify that both methods give the same results for this simple force. We find that drag generally causes eccentricity to increase throughout the inspiral. This is a relativistic effect qualitatively opposite to what is seen in gravitational-radiation-driven inspirals, and similar to what others have observed in hydrodynamic simulations of gaseous binaries. We provide an analytic explanation by deriving the leading order relativistic correction to the Newtonian dynamics. If observed, an increasing eccentricity would thus provide clear evidence that the inspiral was occurring in a nonvacuum environment. Our two methods are especially useful for evolving orbits in the adiabatic regime. Both use the method of osculating orbits, in which each point on the orbit is characterized by the parameters of the geodesic with the same instantaneous position and velocity. Both methods describe the orbit in terms of the geodesic energy, axial angular momentum, Carter constant, azimuthal phase, and two angular variables that increase monotonically and are relativistic generalizations of the eccentric anomaly. The two methods differ in their treatment of the orbital phases and the representation of the force. In the first method, the geodesic phase and phase constant are evolved together as a single orbital phase parameter, and the force is expressed in terms of its components on the Kinnersley orthonormal tetrad. In the second method, the phase constants of the geodesic motion are evolved separately and the force is expressed in terms of its Boyer-Lindquist components. This second approach is a direct generalization of earlier work by Pound and Poisson [A. Pound and E. Poisson, Phys. Rev. D 77, 044013 (2008).] for planar forces in a Schwarzschild background.

The massive black holes we observe in galaxies today are the natural end-product of a complex evolutionary path, in which black holes seeded in proto-galaxies at high redshift grow through cosmic history via a sequence of mergers and accretion episodes. Electromagnetic observations probe a small subset of the population of massive black holes (namely, those that are active or those that are very close to us), but planned space-based gravitational wave observatories such as the Laser Interferometer Space Antenna (LISA) can measure the parameters of “electromagnetically invisible” massive black holes out to high redshift. In this paper we introduce a Bayesian framework to analyze the information that can be gathered from a set of such measurements. Our goal is to connect a set of massive black hole binary merger observations to the underlying model of massive black hole formation. In other words, given a set of observed massive black hole coalescences, we assess what information can be extracted about the underlying massive black hole population model. For concreteness we consider ten specific models of massive black hole formation, chosen to probe four important (and largely unconstrained) aspects of the input physics used in structure formation simulations: seed formation, metallicity “feedback”, accretion efficiency and accretion geometry. For the first time we allow for the possibility of “model mixing”, by drawing the observed population from some combination of the “pure” models that have been simulated. A Bayesian analysis allows us to recover a posterior probability distribution for the “mixing parameters” that characterize the fractions of each model represented in the observed distribution. Our work shows that LISA has enormous potential to probe the underlying physics of structure formation.

Intertwiners are the building blocks of spin-network states. The space of intertwiners is the quantization of a classical symplectic manifold introduced by Kapovich and Millson. Here we show that a theorem by Minkowski allows us to interpret generic configurations in this space as bounded convex polyhedra in ${\mathbb{R}}^3$: A polyhedron is uniquely described by the areas and normals to its faces. We provide a reconstruction of the geometry of the polyhedron: We give formulas for the edge lengths, the volume, and the adjacency of its faces. At the quantum level, this correspondence allows us to identify an intertwiner with the state of a quantum polyhedron, thus generalizing the notion of the quantum tetrahedron familiar in the loop quantum gravity literature. Moreover, coherent intertwiners result to be peaked on the classical geometry of polyhedra. We discuss the relevance of this result for loop quantum gravity. In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra. Furthermore, we introduce an operator that measures the volume of a quantum polyhedron and examine its relation with the standard volume operator of loop quantum gravity. We also comment on the semiclassical limit of spin foams with nonsimplicial graphs.

We discuss the thermodynamic aspects of a simple model of cosmic string loops, whose energy is nonlinearly related to their lengths. We obtain in a direct way an equation of state having the form $p=-(1+\alpha )\rho /3$, with $\rho$ the energy density and $1+\alpha$ the exponent which relates the energy $u_l$ of a loop with its length $l$ as $u_l\sim l^{1+\alpha }$. In the linear situation ($\alpha =0$) one has $p=-\rho /3$, in the quadratic one ($\alpha =1$) $p=-2\rho /3$, and in the cubic case ($\alpha =2$) $p=-\rho$. For all values of $\alpha$ the entropy goes as $S\sim (2-\alpha )L^{3/2}$ ($L$ being the string length density). The expression of $S$ is useful to explore the behavior of such string loops under adiabatic expansion of the Universe. Thermodynamic stability suggests that the gas of string loops must coexist with several long strings, longer than the horizon radius.

Postulating that the nonminimal supersymmetric standard model singlet is a meson of a microscopic confining theory opens up new model-building possibilities. Based on this, we construct calculable models of direct mediation that solve the $\mu /B_{\mu }$ problem and simultaneously lead to realistic phenomenology. The singlet that couples to the Higgs fields develops a runaway produced by soft interactions and then stabilized by a small superpotential perturbation. The mechanism is first realized in an O’Raifeartaigh model of direct gauge mediation with metastable supersymmetry breaking. Focusing then on the microscopic theory, we argue that super QCD with massless and massive flavors in the free magnetic phase gives rise to this dynamics in the infrared. A deformation of the super QCD superpotential leads to large spontaneous $R$-symmetry breaking, gaugino masses naturally at the scale of the Higgs mass parameters, and the absence of $CP$ violating phases.

We use gauge/string duality to investigate the free energy of two static color sources (a heavy-quark–antiquark pair) in a Yang-Mills theory in strongly interacting matter, varying temperature and chemical potential. The dual space geometry is anti–de Sitter with a charged black hole to describe finite temperature and density in the boundary theory, and we also include a background warp factor to generate confinement. The resulting deconfinement line in the $\mu -T$ plane is similar to the one obtained by lattice and effective models of QCD.

The rare $K\to \pi \nu \overline{\nu }$ decays play a central role in testing the standard model and its extensions. Upcoming experiments plan to measure the decay rates with high accuracy. Yet, unknown higher-order electroweak corrections result in a sizeable theory error. We remove this uncertainty by computing the full two-loop electroweak corrections to the top-quark contribution $X_t$ to the rare decays $K_L\to {\pi }^0\nu \overline{\nu }$, $K^{+}\to {\pi }^{+}\nu \overline{\nu }$, and $B\to X_{d,s}\nu \overline{\nu }$ in the standard model. The remaining theoretical uncertainty related to electroweak effects is now far below 1%. Finally we update the branching ratios to find $\mathrm{Br}(K_L\to {\pi }^0\nu \overline{\nu })=2.43(39)(6)\times {10}^{-11}$ and $\mathrm{Br}(K^{+}\to {\pi }^{+}\nu \overline{\nu })=7.81(75)(29)\times {10}^{-11}$. The first error summarizes the parametric, the second the remaining theoretical uncertainties.

Ratios of charmed meson and baryon semileptonic decay rates appear to be satisfactorily described by considering only the lowest-lying (S-wave) hadronic final states and assuming the kinematic factor describing phase space suppression is the same as that for free quarks. For example, the rate for $D_s$ semileptonic decay is known to be $(17.0\pm 5.3)\%$ lower than those for $D^0$ or $D^{+}$, and the model accounts for this difference. When applied to hadrons containing $b$ quarks, this method implies that the $B_s$ semileptonic decay rate is about 1% higher than that of the nonstrange $B$ mesons. This small difference thus suggests surprisingly good local quark-hadron duality for $B$ semileptonic decays, complementing the expectation based on inclusive quark-hadron duality that these differences in rates should not exceed a few tenths of a percent. For ${\Lambda }_b$ semileptonic decay, however, the inclusive rate is predicted to be about 13% greater than that of the nonstrange $B$ mesons. This value, representing a considerable departure from a calculation using a heavy-quark expansion, is close to the corresponding experimental ratio $\Gamma ({\Lambda }_b)/\overline{\Gamma }(B)=1.13\pm 0.03$ of total decay rates.

Extensions of the standard model often predict new chiral interactions for top quarks, which will contribute to top quark spin correlation and polarization in $t\overline{t}$ production at the LHC. In this work, under the constraints from the current Tevatron measurements, a comparative study of the spin correlation and polarization is performed in three new physics models: the minimal supersymmetric model without R-parity, the third-generation enhanced left-right model, and the axigluon model. We find that the polarization asymmetry may be enhanced to the accessible level in all these models, while the correction to the spin correlation may be detectable in the axigluon model and the minimal supersymmetric model without R-parity with ${\lambda }^{\prime \prime }$ couplings.