Fragmentation functions for eta mesons are extracted at next-to-leading order accuracy of QCD in a global analysis of data taken in electron-positron annihilation and proton-proton scattering experiments. The obtained parametrization is in good agreement with all data sets analyzed and can be utilized, for instance, in future studies of double-spin asymmetries for single-inclusive eta production. The Lagrange multiplier technique is used to estimate the uncertainties of the fragmentation functions and to assess the role of the different data sets in constraining them.

Two-body charmless hadronic $B$ decays involving a tensor meson in the final state are studied within the framework of QCD factorization (QCDF). Because of the $G$-parity of the tensor meson, both the chiral-even and chiral-odd two-parton light-cone distribution amplitudes of the tensor meson are antisymmetric under the interchange of momentum fractions of the quark and antiquark in the SU(3) limit. Our main results are: (i) In the naïve factorization approach, the decays such as $B^{-}\to {\overline{K}}_2^{*0}{\pi }^{-}$ and ${\overline{B}}^0\to K_2^{*-}{\pi }^{+}$ with a tensor meson emitted are prohibited because a tensor meson cannot be created from the local $V-A$ or tensor current. Nevertheless, the decays receive nonfactorizable contributions in QCDF from vertex, penguin and hard spectator corrections. The experimental observation of $B^{-}\to {\overline{K}}_2^{*0}{\pi }^{-}$ indicates the importance of nonfactorizable effects. (ii) For penguin-dominated $B\to TP$ and $TV$ decays, the predicted rates in naïve factorization are usually too small by 1 to 2 orders of magnitude. In QCDF, they are enhanced by power corrections from penguin annihilation and nonfactorizable contributions. (iii) The dominant penguin contributions to $B\to K_2^{*}{\eta }^{{(}^{\prime })}$ arise from the processes: (a) $b\to ss\overline{s}\to s{\eta }_s$ and (b) $b\to sq\overline{q}\to q{\overline{K}}_2^{*}$ with ${\eta }_q=(u\overline{u}+d\overline{d})/\sqrt{2}$ and ${\eta }_s=s\overline{s}$. The interference, constructive for $K_2^{*}{\eta }^{\prime }$ and destructive for $K_2^{*}\eta$, explains why $\Gamma (B\to K_2^{*}{\eta }^{\prime })\gg \Gamma (B\to K_2^{*}\eta )$. (iv) We use the measured rates of $B\to K_2^{*}(\omega ,\varphi )$ to extract the penguin-annihilation parameters ${\rho }_A^{TV}$ and ${\rho }_A^{VT}$ and the observed longitudinal polarization fractions $f_L(K_2^{*}\omega )$ and $f_L(K_2^{*}\varphi )$ to fix the phases ${\varphi }_A^{VT}$ and ${\varphi }_A^{TV}$. (v) The experimental observation that $f_T/f_L\ll 1$ for $B\to K_2^{*}(1430)\varphi$, whereas $f_T/f_L\sim 1$ for $B\to K_2^{*}(1430)\omega$ with $f_T$ being the transverse polarization fraction, can be accommodated in QCDF, but it cannot be dynamically explained at first place. For penguin-dominated $B\to TV$ decays, we find $f_L(K_2^{*}\rho )\sim f_L(K_2^{*}\omega )\sim 0.65$, whereas $f_L(K^{*}{f}_2)\sim 0.93$. It will be of great interest to measure $f_L$ for these modes to test QCDF. Theoretically, transverse polarization is expected to be small in tree-dominated $\overline{B}\to TV$ decays except for the $a_2^{-}{\rho }^0$, $a_2^{-}{\rho }^{+}$, $K_2^{*0}{K}^{*-}$ and $K_2^{*0}{\overline{K}}^{*0}$ modes. (vi) For tree-dominated decays, their rates are usually very small except for the $a_2^0({\pi }^{-},{\rho }^{-})$, $a_2^{+}({\pi }^{-},{\rho }^{-})$ and $f_2({\pi }^{-},{\rho }^{-})$ modes with branching fractions of order ${10}^{-6}$ or even larger.

Hadronic event shapes, that is, event shapes at hadron colliders, could provide a great way to test both standard and nonstandard theoretical models. However, they are significantly more complicated than event shapes at $e^{+}{e}^{-}$ colliders, involving multiple hard directions, multiple channels, and multiple color structures. In this paper, hadronic event shapes are examined with soft-collinear effective theory (SCET) by expanding around the dijet limit. A simple event shape, threshold thrust, is defined. This observable is global and has no free parameters, making it ideal for clarifying how resummation of hadronic event shapes can be done in SCET. Threshold thrust is calculated at next-to-leading fixed order (NLO) in SCET and resummed to next-to-next-to-leading logarithmic (NNLL) accuracy. The scale-dependent parts of the soft function are shown to agree with what is expected from general observations, and the factorization formula is explicitly shown to be renormalization group invariant to 1-loop. Although threshold thrust is not itself expected to be phenomenologically interesting, it can be modified into a related observable which allows the jet $p_T$ distribution to be calculated and resummed to $\mathrm{NNLL}+\mathrm{NLO}$ accuracy. As in other processes, one expects resummation to be important even for moderate jet momenta due to dynamical threshold enhancement. A general discussion of threshold enhancement and nonglobal logs in hadronic event shapes is also included.

Measurements of double-helicity asymmetries in inclusive hadron production in polarized $p+p$ collisions are sensitive to helicity-dependent parton distribution functions, in particular, to the gluon helicity distribution, $\Delta g$. This study focuses on the extraction of the double-helicity asymmetry in $\eta$ production ($\overrightarrow{p}+\overrightarrow{p}\to \eta +X$), the $\eta$ cross section, and the $\eta /{\pi }^0$ cross section ratio. The cross section and ratio measurements provide essential input for the extraction of fragmentation functions that are needed to access the helicity-dependent parton distribution functions.

We prove that in the limit $m_b,m_c\to \infty$, with $m_c/m_b$ fixed, factorization holds at order ${\alpha }_s$ for the decay ${\Lambda }_b^0\to {\Lambda }_c^{+}{\pi }^{-}$. This proof is done in the infinite-momentum frame in which the momenta of $\pi$, ${\Lambda }_c$, and ${\Lambda }_b$ go to infinity. Our result is renormalization-scale- and scheme-independent at $\mathcal{O}({\alpha }_s)$. This is the same as the QCD factorization for $B\to D\pi$.

A two-flavor color-superconducting Nambu–Jona-Lasinio model is introduced at finite temperature $T$, chemical potential $\mu$, and in the presence of a constant magnetic field $\tilde{e}B$. The effect of $(T,\mu ,\tilde{e}B)$ on the formation of chiral- and color-symmetry-breaking condensates is studied. The complete phase portrait of the model in $T-\mu$, $\mu -\tilde{e}B$, and $T-\tilde{e}B$ phase spaces for various fixed $\tilde{e}B$, $T$, and $\mu$ is explored. A threshold magnetic field $\tilde{e}{B}_t\simeq 0.5{\mathrm{GeV}}^2$ is found, above which the dynamics of the system are solely dominated by the lowest Landau level, and the effects of $T$ and $\mu$ are partly compensated by $\tilde{e}B$.

We consider metric $f(R)$ theories of gravity without mapping them to their scalar-tensor counterpart, but using the Ricci scalar itself as an “extra” degree of freedom. This approach avoids then the introduction of a scalar-field potential that might be ill defined (not single valued). In order to explicitly show the usefulness of this method, we focus on static and spherically symmetric spacetimes and deal with the recent controversy about the existence of extended relativistic objects in certain class of $f(R)$ models.

We discuss the effect of different choices in partial gauge fixing of bulk local Lorentz invariance, on the description of the horizon degrees of freedom of a Schwarzschild black hole as an $SU(2)$ Chern-Simons theory with specific sources. A classically equivalent description in terms of an $ISO(2)$ Chern-Simons theory is also discussed. Further, we demonstrate that both of these descriptions can be partially gauge fixed to a horizon theory with $U(1)$ local gauge invariance, with the solder form sources being subject to extra constraints in directions orthogonal to an internal vector field left invariant by $U(1)$ transformations. Seemingly disparate approaches on characterization of the horizon theory for the Schwarzschild black hole (as well as spherical isolated horizons in general) are thus shown to be equivalent physically.

We formulate $\mathcal{N}=4$ supersymmetric Yang-Mills theory in terms of soft-collinear effective theory. The effective Lagrangian in soft-collinear effective theory is developed according to the power counting by a small parameter $\eta \sim p_{\perp }/Q$. All the particles in this theory are in the adjoint representation of the $SU(N)$ gauge group, and we derive the collinear gauge-invariant Lagrangian in the adjoint and fundamental representations, respectively. We consider collinear and ultrasoft Wilson lines in this theory, and show the ultrasoft factorization of the collinear Lagrangian by redefining the collinear fields with the use of the ultrasoft Wilson lines. The vertex correction for a vector fermion current at one loop is explicitly presented as an example to illustrate how the computation is performed in the effective theory.

Perturbative $\mathcal{O}({\alpha }_s^2)$ corrections to $\mathcal{B}(\overline{B}\to X_s\gamma )$ in the Brodsky-Lepage-Mackenzie approximation receive contributions from two-, three-, and four-body final states. While all the two-body results are well established by now, the other ones have remained incomplete for several years. Here, we calculate the last contribution that has been missing to date, namely, the one originating from interference of the current-current and gluonic dipole operators ($K_{18}^{(2){\beta }_0}$ and $K_{28}^{(2){\beta }_0}$). Moreover, we confirm all the previously known results for Brodsky-Lepage-Mackenzie corrections to the photon energy spectrum that involve the current-current operators (e.g., $K_{22}^{(2){\beta }_0}$ and $K_{27}^{(2){\beta }_0}$). Finally, we also confirm the recent findings of Ferroglia and Haisch on self-interference of the gluonic dipole operator ($K_{88}^{(2){\beta }_0}$).

The essence of the chiral magnetic effect is generation of an electric current along an external magnetic field. Recently it has been studied by Rebhan, Schmitt, and Stricker within the Sakai-Sugimoto model, where it was shown to be zero. As an alternative, we calculate the chiral magnetic effect in soft-wall AdS/QCD and find a nonzero result with the natural boundary conditions. The mechanism of the dynamical neutralization of the chiral chemical potential via the string production is discussed in the dual two-form representation.

In certain scenarios of deformed relativistic symmetries relevant for noncommutative field theories particles exhibit a momentum space described by a non-Abelian group manifold. Starting with a formulation of phase space for such particles which allows for a generalization to include group-valued momenta we discuss quantization of the corresponding field theory. Focusing on the particular case of $\kappa$-deformed phase space we construct the one-particle Hilbert space and show how curvature in momentum space leads to an ambiguity in the quantization procedure reminiscent of the ambiguities one finds when quantizing fields in curved space-times. The tools gathered in the discussion on quantization allow for a clear definition of the basic deformed field mode operators and two-point function for $\kappa$-quantum fields.

Continuing work initiated in an earlier publication [Yamada, Asada, Phys. Rev. D 82, 104019 (2010)], we investigate collinear solutions to the general relativistic three-body problem. We prove the uniqueness of the configuration for given system parameters (the masses and the end-to-end length). First, we show that the equation determining the distance ratio among the three masses, which has been obtained as a seventh-order polynomial in the previous paper, has at most three positive roots, which apparently provide three cases of the distance ratio. It is found, however, that, even for such cases, there exists one physically reasonable root and only one, because the remaining two positive roots do not satisfy the slow-motion assumption in the post-Newtonian approximation and are thus discarded. This means that, especially for the restricted three-body problem, exactly three positions of a third body are true even at the post-Newtonian order. They are relativistic counterparts of the Newtonian Lagrange points $L_1$, $L_2$, and $L_3$. We show also that, for the same masses and full length, the angular velocity of the post-Newtonian collinear configuration is smaller than that for the Newtonian case. Provided that the masses and angular rate are fixed, the relativistic end-to-end length is shorter than the Newtonian one.

We study ultrarelativistic encounters of two spinning, equal-mass black holes through simulations in full numerical relativity. Two initial data sequences are studied in detail: one that leads to scattering and one that leads to a grazing collision and merger. In all cases, the initial black hole spins lie in the orbital plane, a configuration that leads to the so-called superkicks. In astrophysical, quasicircular inspirals, such kicks can be as large as $\sim 3000\mathrm{km}/\mathrm{s}$; here, we find configurations that exceed $\sim 15000\mathrm{km}/\mathrm{s}$. We find that the maximum recoil is to a good approximation proportional to the total amount of energy radiated in gravitational waves, but largely independent of whether a merger occurs or not. This shows that the mechanism predominantly responsible for the superkick is not related to merger dynamics. Rather, a consistent explanation is that the “bobbing” motion of the orbit causes an asymmetric beaming of the radiation produced by the in-plane orbital motion of the binary, and the net asymmetry is balanced by a recoil. We use our results to formulate some conjectures on the ultimate kick achievable in any black hole encounter.

In this (second) part of the work we present the results of numerical and qualitative analysis, based on a new model of the Archimedean-type interaction between dark matter and dark energy. The Archimedean-type force is linear in the four-gradient of the dark energy pressure and plays a role of self-regulator of the energy redistribution in a cosmic dark fluid. Because of the Archimedean-type interaction the cosmological evolution is shown to have a multistage character. Depending on the choice of the values of the model-guiding parameters, the Universe expansion is shown to be perpetually accelerated, periodic or quasiperiodic with a finite number of deceleration/acceleration epochs. We distinguished the models, which can be definitely characterized by the inflation in the early Universe, by the late-time accelerated expansion and nonsingular behavior in intermediate epochs, and classified them with respect to a number of transition points. Transition points appear, when the acceleration parameter changes the sign, providing the natural partition of the Universe’s history into epochs of accelerated and decelerated expansion. The strategy and results of numerical calculations are advocated by the qualitative analysis of the instantaneous phase portraits of the dynamic system associated with the key equation for the dark energy pressure evolution.

We establish a new self-consistent model in order to explain from a unified viewpoint two key features of the cosmological evolution: the inflation in the early Universe and the late-time accelerated expansion. The key element of this new model is the Archimedean-type coupling of the dark matter with dark energy, which form the so-called cosmic dark fluid. We suppose that dark matter particles immersed into the dark energy reservoir are affected by the force proportional to the four-gradient of the dark energy pressure. The Archimedean-type coupling is shown to play a role of effective energy-momentum redistributor between the dark matter and the dark energy components of the dark fluid, thus providing the Universe evolution to be a quasiperiodic and/or multistage process. In the first part of the work we discuss a theoretical base and new exact solutions of the model master equations. Special attention is focused on the exact solutions, for which the scale factor is presented by the anti-Gaussian function: these solutions describe the late-time acceleration and are characterized by a nonsingular behavior in the early Universe. The second part contains qualitative and numerical analysis of the master equations; we focus there on the solutions describing a multi-inflationary Universe.

This work has attempted to reconcile puzzling neutrino oscillation results from the LSND, KARMEN, and MiniBooNE experiments. We show that the LSND evidence for ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_e$ oscillations, its long-standing disagreement with the results from KARMEN, and the anomalous event excess observed by MiniBooNE in ${\nu }_{\mu }$ and ${\overline{\nu }}_{\mu }$ data could all be explained by the existence of a heavy sterile neutrino (${\nu }_h$). All these results are found to be consistent with each other, assuming that the ${\nu }_h$ is created in ${\nu }_{\mu }$ neutral-current interactions and decays radiatively into a photon and a light neutrino. Assuming the ${\nu }_h$ is produced through mixing with ${\nu }_{\mu }$, the combined analysis of the LSND and MiniBooNe excess events suggests that the ${\nu }_h$ mass is in the range from 40 to 80 MeV, the mixing strength is $|U_{\mu h}{|}^2\simeq {10}^{-3}–{10}^{-2}$, and the lifetime is ${\tau }_{{\nu }_h}\lesssim {10}^{-9}\mathrm{s}$. Surprisingly, this LSND-MiniBooNE parameter window is found to be unconstrained by the results from the most sensitive experiments. We set new limits on $|U_{\mu h}{|}^2$ for the favorable mass region from the precision measurements of the Michel spectrum by the TWIST experiment. The results obtained provide a strong motivation for a sensitive search for the ${\nu }_h$ in a near future $K$ decay or neutrino experiments, which fit well in the existing and planned experimental programs at CERN or FNAL. The question of whether the heavy neutrino is a Dirac or Majorana particle is briefly discussed.

We make a QCD light-cone sum rule assessment of $B_{(s)}$ semileptonic decays to a light scalar meson, $B_{(s)}\to Sl{\overline{\nu }}_l$, $Sl\overline{l}(l=e,\mu ,\tau )$. Chiral current correlators are used and calculations are performed at leading order in ${\alpha }_s$. Having little knowledge of the ingredients of the scalar mesons, we confine ourself to the two-quark picture for them and work with the two possible scenarios. The resulting sum rules for the form factors receive no contributions from the twist-3 distribution amplitudes, in comparison with the calculation of the conventional light-cone sum rule approach where the twist-3 parts usually play an important role. We specify the range of the squared momentum transfer $q^2$, in which the operator product expansion for the correlators remains valid approximately. It is found that the form factors satisfy a relation consistent with the prediction of soft collinear effective theory. In the effective range we investigate behaviors of the form factors and differential decay widths and compare our calculations with the observations from other approaches.

We describe a class of unified theories of electromagnetism and gravity. The Lagrangian is of the BF type, with a potential for the B field, the gauge group is U(2) (complexified). Given a choice of the potential function the theory is a deformation of (complex) general relativity and electromagnetism, and describes just two propagating polarizations of the graviton and two of the photon. When gravity is switched off the theory becomes the usual nonlinear electrodynamics with a general structure function. The Einstein-Maxwell theory can be recovered by sending some of the parameters of the defining potential to zero, but for any generic choice of the potential the theory is indistinguishable from Einstein-Maxwell at low energies. A real theory is obtained by imposing suitable reality conditions. We also study the spherically-symmetric solution and show how the usual Reissner-Nordstrom solution is recovered.

In Einstein-aether theory and Horava gravity, a timelike unit vector is coupled to the spacetime metric. It has previously been shown that in an exponentially expanding homogeneous, isotropic background, small perturbations of the vector relax back to the isotropic frame. Here we investigate large deviations from isotropy, maintaining homogeneity. We find that, for generic values of the coupling constants, the aether and metric relax to the isotropic configuration if the initial aether hyperbolic boost angle and its time derivative in units of the cosmological constant are less than something of order unity. For larger angles or angle derivatives, the behavior is strongly dependent on the values of the coupling constants. Generally, there is runaway behavior, in which the anisotropy increases with time, and/or singularities occur.