Phenomenological approach to the critical dynamics of the QCD phase transition revisited

The phenomenological dynamics of the QCD critical phenomena is revisited. Recently, Son and Stephanov claimed that the dynamical universality class of the QCD phase transition belongs to model H. In their discussion, they employed a time-dependent Ginzburg-Landau equation for the net baryon number density, which is a conserved quantity. We derive the Langevin equation for the net baryon number density, i.e., the Cahn-Hilliard equation. Furthermore, they discussed the mode coupling induced through the {\it irreversible} current. Here, we show the {\it reversible} coupling can play a dominant role for describing the QCD critical dynamics and that the dynamical universality class does not necessarily belong to model H.Comment: 13 pages, the Curie principle is discussed in S.2, to appear in J.Phys.

A Unified Description of Quark and Lepton Mass Matrices in a Universal Seesaw Model

In the democratic universal seesaw model, the mass matrices are given by \bar{f}_L m_L F_R + \bar{F}_L m_R f_R + \bar{F}_L M_F F_R (f: quarks and leptons; F: hypothetical heavy fermions), m_L and m_R are universal for up- and down-fermions, and M_F has a structure ({\bf 1}+ b_f X) (b_f is a flavour-dependent parameter, and X is a democratic matrix). The model can successfully explain the quark masses and CKM mixing parameters in terms of the charged lepton masses by adjusting only one parameter, b_f. However, so far, the model has not been able to give the observed bimaximal mixing for the neutrino sector. In the present paper, we consider that M_F in the quark sectors are still "fully" democratic, while M_F in the lepton sectors are partially democratic. Then, the revised model can reasonably give a nearly bimaximal mixing without spoiling the previous success in the quark sectors.Comment: 7 pages, no figur

NNI-Form Quark Mass Matrix Expressed by the Observable Quantities

It is pointed out that the phase convention of the CKM matrix V affects texture analysis of the quark mass matrices (M_u, M_d) when we try to describe (M_u, M_d) by the observable quantities (quark masses and CKM matrix parameters) only. This is demonstrated for a case of the non-Hermitian Fritzsch-type mass matrix (tilde{M}_u, tilde{M}_d), which is a general expression of quark mass matrix (M_u, M_d) and is described by twelve parameters. We find that we can always choose a phase convention of V which yields tilde{M}_{u32} = 0, so that the remaining ten parameters in (tilde{M}_u, tilde{M}_d) can completely be expressed by the ten observable quantities.Comment: 11 pages (LaTeX); Title was change

The structure of black hole magnetospheres. I. Schwarzschild black holes

We introduce a multipolar scheme for describing the structure of stationary, axisymmetric, force-free black-hole magnetospheres in the ``3+1'' formalism. We focus here on Schwarzschild spacetime, giving a complete classification of the separable solutions of the stream equation. We show a transparent term-by-term analogy of our solutions with the familiar multipoles of flat-space electrodynamics. We discuss electrodynamic processes around disk-fed black holes in which our solutions find natural applications: (a) ``interior'' solutions in studies of the Blandford-Znajek process of extracting the hole's rotational energy, and of the formation of relativistic jets in active galactic nuclei and ``microquasars'', and, (b) ``exterior'' solutions in studies of accretion disk dynamos, disk-driven winds and jets. On the strength of existing numerical studies, we argue that the poloidal field structures found here are also expected to hold with good accuracy for rotating black holes, except for maximum possible rotation rates. We show that the closed-loop exterior solutions found here are not in contradiction with the Macdonald-Thorne theorem, since these solutions, which diverge logarithmically on the hole's horizon $\cal H$, apply only to those regions which exclude $\cal H$.Comment: 6 figures. Accepted for publication by MNRA

General Relativistic Simulations of Jet Formation in a Rapidly Rotating Black Hole Magnetosphere

To investigate the formation mechanism of relativistic jets in active galactic nuclei and micro-quasars, we have developed a new general relativistic magnetohydrodynamic code in Kerr geometry. Here we report on the first numerical simulation of jet formation in a rapidly-rotating (a=0.95) Kerr black hole magnetosphere. We study cases in which the Keplerian accretion disk is both co-rotating and counter-rotating with respect to the black hole rotation. In the co-rotating disk case, our results are almost the same as those in Schwarzschild black hole cases: a gas pressure-driven jet is formed by a shock in the disk, and a weaker magnetically-driven jet is also generated outside the gas pressure-driven jet. On the other hand, in the counter-rotating disk case, a new powerful magnetically-driven jet is formed inside the gas pressure-driven jet. The newly found magnetically-driven jet in the latter case is accelerated by a strong magnetic field created by frame dragging in the ergosphere. Through this process, the magnetic field extracts the energy of the black hole rotation.Comment: Co-rotating and counter-rotating disks; 8 pages; submitted to ApJ letter

Spin Path Integrals and Generations

The spin of a free electron is stable but its position is not. Recent quantum information research by G. Svetlichny, J. Tolar, and G. Chadzitaskos have shown that the Feynman \emph{position} path integral can be mathematically defined as a product of incompatible states; that is, as a product of mutually unbiased bases (MUBs). Since the more common use of MUBs is in finite dimensional Hilbert spaces, this raises the question "what happens when \emph{spin} path integrals are computed over products of MUBs?" Such an assumption makes spin no longer stable. We show that the usual spin-1/2 is obtained in the long-time limit in three orthogonal solutions that we associate with the three elementary particle generations. We give applications to the masses of the elementary leptons.Comment: 20 pages, 2 figures, accepted at Foundations of Physic

Lepton Flavor Violating Z Decays in the Zee Model

We calculate lepton flavor violating (LFV) Z decays Z \to {{e_i^\pm}}e_j^\mp (i, j = e, \mu, \tau ; i\neq j) in the Zee model keeping in view the radiative leptonic decays e_i\to e_j\gamma (i = \mu, \tau ; j = e, \mu ; i\neq j), \mu decay and anomalous muon magnetic moment (\mu AMM). We investigate three different cases of Zee f_{ij} coupling (A) f_{e\mu}^2 = f_{\mu\tau}^2= f_{\tau e}^2, (B) f_{e\mu}^2 \gg f_{\tau e}^2 \gg f_{\mu\tau}^2, and (C) f_{\mu\tau}^2 \gg f_{e\mu}^2 \gg f_{\tau e}^2 subject to the neutrino phenomenology. Interestingly, we find that, although the case (C) satisfies the large excess value of \mu AMM, however, it is unable to explain the solar neutrino experimental result, whereas the case (B) satisfies the bi-maximal neutrino mixing scenario, but confronts with the result of \mu AMM experiment. We also find that among all the three cases, only the case (C) gives rise to largest contribution to the ratio B(Z\to e^\pm\tau^\mp)/B(Z\to \mu^\pm \mu^\mp) \simeq {10}^{-8} which is still two order less than the accessible value to be probed by the future linear colliders, whereas for the other two cases, this ratio is too low to be observed even in the near future for all possible LFV Z decay modes.Comment: 12 pages, RevTex, 2 figures, 3 Tables, typos corrected, reference added, version to appear in Phys. Rev.

Leading Order Textures for Lepton Mass Matrices

In theories with three light neutrinos, certain simplicity assumptions allow the construction of a complete list of leading order lepton mass matrices. These matrices are consistent with m_{tau} \neq 0, Delta m^2_{12} \ll Delta m^2_{23}, theta_{23} approx 1, and theta_{13} = 0, as suggested by measurements of atmospheric and solar neutrino fluxes. The list contains twelve generic cases: two have three degenerate neutrinos, eight have two neutrinos forming a Dirac state, and in only two cases is one neutrino much heavier than the other two. For each of these twelve generic cases the possible forms for the perturbations which yield m_{mu} are given. Ten special textures are also found.Comment: 17 pages, added reference

Bendings of radio jets in BL Lacertae objects I: EVN and MERLIN observations

Several blazars, and BL Lac objects in particular, show a misalignment between the jet orientation on parsec and kiloparsec scales. Some authors (i.e. Conway & Murphy, 1993) have attempted to explain this behaviour invoking helical jets for misalignment angles around 90\degr, showing how in this case there are interesting implications for the understanding of the medium into which the jet is expanding. By comparing sensitive VLA observations (Cassaro et al., 1999) with images available in the literature for the BL Lac objects from the 1-Jy Sample (Stickel et al., 1991), it is clear that there is a wide range of misalignments between the initial jet direction and the kpc-scale jet, when detected. We have carried out VLBI observations of these BL Lac objects, in order to investigate the spatial evolution of the radio jets from few tens to hundreds of mas, and to search for helical jets in this class of sources. We present here the first dataset obtained from EVN+MERLIN observations at 5 GHz for seven objects. From these observations we never have a clear detection of helical jets, we only have a possible signature of their presence in 2 objects. In only one of the sources with a misalignment angle around 90\degr the presence of helical jets can be ruled out. This implies that it is not possible to invoke helical jets to explain the morphology of all the sources showing a misalignment of about 90\degr between the parsec and the kiloparsec scale jets.Comment: 12 pages, 9 figures, latex, accepted by Astronomy & Astrophysic