In this paper, we give a direct method for calculating the partition function, and hence the equation of state (EOS) of quantum chromodynamics (QCD) at finite chemical potential and zero temperature. In the EOS derived in this paper the pressure density is the sum of two terms: the first term $\mathcal{P}(\mu ){|}_{\mu =0}$ (the pressure density at $\mu =0$) is a $\mu$-independent constant; the second term, which is totally determined by $G_R[\mu ](p)$ (the renormalized dressed quark propagator at finite $\mu$), contains all the nontrivial $\mu$-dependence. By applying a general result in the rainbow-ladder approximation of the Dyson-Schwinger approach obtained in our previous study [Phys. Rev. C 71, 015205 (2005)], $G_R[\mu ](p)$ is calculated from the meromorphic quark propagator proposed in [Phys. Rev. D 70, 014014 (2004)]. From this the full analytic expression of the EOS of QCD at finite $\mu$ and zero $T$ is obtained (apart from the constant term $\mathcal{P}(\mu ){|}_{\mu =0}$ which can in principle be calculated from the Cornwall-Jackiw-Tomboulis effective action). A comparison between our EOS and the cold, perturbative EOS of QCD of Fraga, Pisarski, and Schaffner-Bielich is made. It is expected that our EOS can provide a possible new approach for the study of neutron stars.

The decay $\tau \to \pi \pi \pi \nu$ is analyzed using different methods to account for the resonance structure, which is usually ascribed to the $a_1$. One scenario is based on the recently developed techniques to generate axial-vector resonances dynamically, whereas in a second calculation the $a_1$ is introduced as an explicit resonance. We investigate the influence of different assumptions on the result. In the molecule scenario the spectral function is described surprisingly well by adjusting only one free parameter. This result can be systematically improved by adding higher-order corrections to the iterated Weinberg-Tomozawa interaction. Treating the $a_1$ as an explicit resonance on the other hand leads to peculiar properties.

We propose a new way to hide large extra dimensions without invoking branes, based on Lorentz-violating tensor fields with expectation values along the extra directions. We investigate the case of a single vector aether field on a compact circle. In such a background, interactions of other fields with the aether can lead to modified dispersion relations, increasing the mass of the Kaluza-Klein excitations. The mass scale characterizing each Kaluza-Klein tower can be chosen independently for each species of scalar, fermion, or gauge boson. No small-scale deviations from the inverse square law for gravity are predicted, although light graviton modes may exist.

Discreteness effects are a source of uncontrolled systematic errors of N-body simulations, which are used to compute the evolution of a self-gravitating fluid. We have already developed the so-called “particle linear theory”(PLT), which describes the evolution of the position of self-gravitating particles located on a perturbed simple cubic lattice. It is the discrete analogue of the well-known (Lagrangian) linear theory of a self-gravitating fluid. Comparing both theories permits us to quantify precisely discreteness effects in the linear regime. It is useful to develop the PLT also for other perturbed lattices because they represent different discretizations of the same continuous system. In this paper we detail how to implement the PLT for perturbed cubic Bravais lattices (simple, body, and face-centered) in a cubic simulation box. As an application, we will study the discreteness effects—in the linear regime—of N-body simulations for which initial conditions have been set up using these different lattices.

A neutrino mass matrix model $M_{\nu }$ with $M_{\nu }^T=M_{\nu }$ and a model with its inverse matrix form ${\tilde{M}}_{\nu }=m_0^2(M_{\nu }^{*}{)}^{-1}$ can be diagonalized by the same mixing matrix $U_{\nu }$. It is investigated whether a scenario which provides a matrix model $M_{\nu }$ with normal mass hierarchy can also give a model with an inverted mass hierarchy by considering a model with an inverse form of $M_{\nu }$.

We discuss the minimum requirements for a neutrino beta beam if ${\theta }_{13}$ is discovered by an upcoming reactor experiment, such as Double Chooz or Daya Bay. We require that both neutrino mass hierarchy and leptonic $CP$ violation can be measured to competitive precisions with a single-baseline experiment in the entire remaining ${\theta }_{13}$ range. For example, we find that a $({}^{18}\mathrm{Ne},{}^6\mathrm{He})$ beta beam from Fermilab to a water Cherenkov detector at Homestake with $\gamma \gtrsim 190$ could outperform practically any other beam technology including wide-band beam and neutrino factory.

One or more heavy spin-1 fields may replace the Higgs boson in keeping perturbative unitarity up to a few TeV. By means of two prototype chiral models for the heavy spin-1 bosons, a composite model or a gauge model, we discuss if and how the sole exchange of the same fields can also account for the electroweak precision tests. While this proves impossible in the gauge model, the composite model hints to a positive solution, which we exploit to constrain the phenomenological properties of the heavy vectors.

In the framework of the left-right symmetric model, we investigate an interesting scenario, in which the so-called vacuum expectation value (VEV)-seesaw problem can be naturally solved with ${\mathcal{Z}}_2$ symmetry. In such a scenario, we find a pair of stable weakly interacting massive particles (WIMPs), which may be the cold dark matter candidates. However, the WIMP-nucleon cross section is 3–5 orders of magnitude above the present upper bounds from the direct dark matter detection experiments for $m\sim {10}^2–{10}^4\mathrm{GeV}$. As a result, the relic number density of two stable particles has to be strongly suppressed to a very small level. Nevertheless, our analysis shows that this scenario cannot provide very large annihilation cross sections so as to give the desired relic abundance except for the resonance case. Only for the case if the rotation curves of disk galaxies are explained by the modified Newtonian dynamics (MOND), the stable WIMPs could be as the candidates of cold dark matter.

We define a $CP$-asymmetric observable that is sensitive to $CP$-violating interactions in the gauge-boson sector. We illustrate the utility of this observable by studying how well the LHC can measure the coefficient of a particular dimension-six $WWZ$ operator. We find that sensitivity at the ${10}^{-3}$ level is possible at the LHC with $100{\mathrm{fb}}^{-1}$ of integrated luminosity, which would greatly exceed the sensitivity achieved at LEP, and would rival or may even better the indirect sensitivities inferred from related operators constrained by electric dipole moment experiments.

We study the azimuthal angular dependence of back-to-back dijet production in unpolarized hadron scattering $H_A+H_B\to J_1+J_2+X$, arising from the product of two Boer-Mulders functions, which describe the transverse spin distribution of quarks inside an unpolarized hadron. We find that when the dijet is of two identical quarks ($J_q+J_q$) or a quark-antiquark pair ($J_q+J_{\overline{q}}$), there is a $\cos \delta \varphi$ angular dependence of the dijet, with $\delta \varphi ={\varphi }_1-{\varphi }_2$, and ${\varphi }_1$ and ${\varphi }_2$ are the azimuthal angles of the two individual jets. In the case of $J_q+J_q$ production, we find that there is a color factor enhancement in the gluonic cross section, compared with the result from the standard generalized parton model. We estimate the $\cos \delta \varphi$ asymmetry of dijet production at RHIC, showing that the color factor enhancement in the angular dependence of $J_q+J_q$ production will reverse the sign of the asymmetry.

The semiclassical description of Skyrmions at small isospin chemical potential ${\mu }_I$ is carefully analyzed. We show that when the calculation of the energy of a nucleon is performed using the straightforward generalization of the vacuum sector techniques (${\mu }_I=0$), together with the “natural” assumption ${\mu }_I=\mathcal{O}(N_c^0)$, the proton and neutron masses are nonlinear in ${\mu }_I$ in the regime $|{\mu }_I|<m_{\pi }$. Although these nonlinearities turn out to be numerically quite small, such a result fails to strictly agree with the very robust prediction that for those values of ${\mu }_I$ the energy excitations above the vacuum are linear in ${\mu }_I$. The resolution of this paradox is achieved by studying the realization of the large $N_c$ limit of QCD in the Skyrme model at finite ${\mu }_I$. This is done in a simplified context devoid of the technical complications present in the Skyrme model but which fully displays the general scaling behavior with $N_c$. The analysis shows that the paradoxical result appears as a symptom of using the semiclassical approach beyond its regime of validity and that, at a formal level, the standard methods for dealing with the Skyrme model are only strictly justified for states of high isospin, $I\sim N_c$.

We compute the next-to-leading order (NLO) perturbative QCD corrections to the correlators of nucleon interpolating currents in relativistic nuclear matter. The main new result is the calculation of the $\mathcal{O}({\alpha }_s)$ perturbative corrections to the coefficient functions of the vector quark condensate in matter. This condensate appears in matter due to the violation of Lorentz invariance. The NLO perturbative QCD corrections turn out to be large which implies that the NLO corrections must be included in a sum rule analysis of the properties of both bound nucleons and relativistic nuclear matter.

We summarize the most important arguments for why a perturbative description of finite-temperature QCD is unlikely to be possible and review various well-established approaches to deal with this problem. Then, using a recently proposed method, we investigate nonperturbative contributions to the QCD pressure and other observables (such as energy, anomaly, and bulk viscosity) obtained by imposing a functional cutoff at the Gribov horizon. Finally, we discuss how such contributions fit into the picture of consecutive effective theories, as proposed by Braaten and Nieto, and give an outline of the next steps necessary to improve this type of calculation.

We point out that a strong phase from the penguin annihilation channel in $B$ meson decays is sensitive to the treatment of subleading terms with physical $b$ quark mass $m_b$. In the limit of infinite heavy-quark mass, both the soft-collinear effective theory and the perturbative QCD approach based on the $k_T$ factorization theorem agree that the strong phase is suppressed. For finite heavy-quark mass, the two approaches predict different results, which are related to the treatment of subleading terms. This is illustrated by taking a toy model for soft-collinear effective theory, in which a small quantity, suppressed by $O(\Lambda /m_b)$, with $\Lambda$ being a hadronic scale, is kept in the denominators of internal particle propagators. This model can generate a sizable strong phase to accommodate the data of the $B^0\to K^{\mp }{\pi }^{\pm }$ direct $CP$ asymmetry.

We study the finite-temperature behavior of the $A^2$ condensate in the Landau gauge of $SU(2)$ Yang-Mills theory on the lattice in a wide range of temperatures. The asymmetry between the electric (temporal) and magnetic (spatial) components of this unconventional dimension-2 condensate is a convenient ultraviolet-finite quantity which possesses, as we demonstrate, unexpected properties. The low-temperature behavior of the condensate asymmetry suggests that the mass of the lowest thermal excitation in the condensate is unexpectedly low, about 200 MeV, which is much smaller than the glueball mass. The asymmetry is peaking at the phase transition, becoming a monotonically decreasing function in the deconfinement phase. A symmetric point is reached in the deconfinement phase at a temperature approximately equal to twice the critical temperature. The behavior of the electric-magnetic asymmetry of the condensate separates the phase diagram of Yang-Mills theory into three regions. We suggest that these regions are associated with the condensed, liquid, and gaseous states of the confining gluonic objects, the Abelian monopoles.

We use the Boer-Mulders functions parameterized from unpolarized $p+D$ Drell-Yan data by the FNAL E866/NuSea Collaboration combined with recently extracted Collins functions to calculate the $\cos 2\varphi$ asymmetries in unpolarized semi-inclusive deeply inelastic scattering (SIDIS) processes both for ZEUS at the Hadron Electron Ring Accelerator (HERA) and Jefferson Lab (JLab) experiments and to compare our results with their data. We also give predictions for the $\cos 2\varphi$ asymmetries of SIDIS in the kinematical regime of HERMES Collaboration, and the forthcoming JLab experiments. We predict that the $\cos 2\varphi$ asymmetries of semi-inclusive ${\pi }^{-}$ production are somewhat larger than that of ${\pi }^{+}$ production. We suggest the measurement of these two processes separately, which will provide more detailed information on the Boer-Mulders functions as well as on the Collins functions.

We study the interplay between the chiral and the deconfinement transitions, both at high temperature and high quark chemical potential, by a nonlocal Nambu–Jona-Lasinio model with the Polyakov loop in the mean field approximation and requiring neutrality of the ground state. We consider three forms of the effective potential of the Polyakov loop: two of them with a fixed deconfinement scale, cases I and II, and the third one with a $\mu$ dependent scale, case III. In cases I and II, at high chemical potential $\mu$ and low temperature $T$, the main contribution to the free energy is due to the $Z(3)$-neutral three-quark states, mimicking the quarkyonic phase of the large $N_c$ phase diagram. On the other hand, in case III the quarkyonic window is shrunk to a small region. Finally we comment on the relations of these results to lattice studies and on possible common prospects. We also briefly comment on the coexistence of quarkyonic and color superconductive phases.