N K and Delta K states in the chiral SU(3) quark model

The isospin I=0 and I=1 kaon-nucleon $S$, $P$, $D$, $F$ wave phase shifts are studied in the chiral SU(3) quark model by solving the resonating group method (RGM) equation. The calculated phase shifts for different partial waves are in agreement with the experimental data. Furthermore, the structures of the $\Delta K$ states with L=0, I=1 and I=2 are investigated. We find that the interaction between $\Delta$ and $K$ in the case of L=0, I=1 is attractive, which is not like the situation of the $NK$ system, where the $S$-wave interactions between $N$ and $K$ for both I=0 and I=1 are repulsive. Our numerical results also show that when the model parameters are taken to be the same as in our previous $NN$ and $YN$ scattering calculations, the $\Delta K$ state with L=0 and I=1 is a weakly bound state with about 2 MeV binding energy, while the one with I=2 is unbound in the present one-channel calculation.Comment: 14 pages, 6 figures. PRC70,064004(2004

Massive and Massless Neutrinos on Unbalanced Seesaws

The observation of neutrino oscillations requires new physics beyond the standard model (SM). A SM-like gauge theory with p lepton families can be extended by introducing q heavy right-handed Majorana neutrinos but preserving its SU(2)_L x U(1)_Y gauge symmetry. The overall neutrino mass matrix M turns out to be a symmetric (p+q) x (p+q) matrix. Given p>q, the rank of M is in general equal to 2q, corresponding to 2q non-zero mass eigenvalues. The existence of (p-q) massless left-handed Majorana neutrinos is an exact consequence of the model, independent of the usual approximation made in deriving the Type-I seesaw relation between the effective p x p light Majorana neutrino mass matrix M_\nu and the q x q heavy Majorana neutrino mass matrix M_R. In other words, the numbers of massive left- and right-handed neutrinos are fairly matched. A good example to illustrate this seesaw fair play rule is the minimal seesaw model with p=3 and q=2, in which one massless neutrino sits on the unbalanced seesaw.Comment: RevTex 8 pages, 1 PS figure. Two crucial references adde

Lepton masses and mixing without Yukawa hierarchies

We investigate the neutrino masses and mixing patten in a version of the $SU(3)_c\otimes SU(3)_L\otimes U(1)_X$ model with one extra exotic charged lepton per family as introduced by Ozer. It is shown that an extended scalar sector, together with a discrete $Z_2$ symmetry, is able to reproduce a consistent lepton mass spectrum without a hierarchy in the Yukawa coupling constants, the former as a carefull balance between one universal see-saw and two radiative mechanisms.Comment: 7 pages, 2 figures, accepted for publication in Phys. Rev. D

Updated Values of Running Quark and Lepton Masses

Reliable values of quark and lepton masses are important for model building at a fundamental energy scale, such as the Fermi scale M_Z \approx 91.2 GeV and the would-be GUT scale \Lambda_GUT \sim 2 \times 10^16 GeV. Using the latest data given by the Particle Data Group, we update the running quark and charged-lepton masses at a number of interesting energy scales below and above M_Z. In particular, we take into account the possible new physics scale (\mu \sim 1 TeV) to be explored by the LHC and the typical seesaw scales (\mu \sim 10^9 GeV and \mu \sim 10^12 GeV) which might be relevant to the generation of neutrino masses. For illustration, the running masses of three light Majorana neutrinos are also calculated. Our up-to-date table of running fermion masses are expected to be very useful for the study of flavor dynamics at various energy scales.Comment: 23 pages, 6 tables, 2 figures; version published in PR

CMB Signals of Neutrino Mass Generation

We propose signals in the cosmic microwave background to probe the type and spectrum of neutrino masses. In theories that have spontaneous breaking of approximate lepton flavor symmetries at or below the weak scale, light pseudo-Goldstone bosons recouple to the cosmic neutrinos after nucleosynthesis and affect the acoustic oscillations of the electron-photon fluid during the eV era. Deviations from the Standard Model are predicted for both the total energy density in radiation during this epoch, \Delta N_nu, and for the multipole of the n'th CMB peak at large n, \Delta l_n. The latter signal is difficult to reproduce other than by scattering of the known neutrinos, and is therefore an ideal test of our class of theories. In many models, the large shift, \Delta l_n \approx 8 n_S, depends on the number of neutrino species that scatter via the pseudo-Goldstone boson interaction. This interaction is proportional to the neutrino masses, so that the signal reflects the neutrino spectrum. The prediction for \Delta N_nu is highly model dependent, but can be accurately computed within any given model. It is very sensitive to the number of pseudo-Goldstone bosons, and therefore to the underlying symmetries of the leptons, and is typically in the region of 0.03 < \Delta N_nu < 1. This signal is significantly larger for Majorana neutrinos than for Dirac neutrinos, and, like the scattering signal, varies as the spectrum of neutrinos is changed from hierarchical to inverse hierarchical to degenerate.Comment: 40 pages, 4 figure

The Null Decomposition of Conformal Algebras

We analyze the decomposition of the enveloping algebra of the conformal algebra in arbitrary dimension with respect to the mass-squared operator. It emerges that the subalgebra that commutes with the mass-squared is generated by its Poincare subalgebra together with a vector operator. The special cases of the conformal algebras of two and three dimensions are described in detail, including the construction of their Casimir operators.Comment: 31 page

Relation between the neutrino and quark mixing angles and grand unification

We argue that there exists simple relation between the quark and lepton mixings which supports the idea of grand unification and probes the underlying robust bi-maximal fermion mixing structure of still unknown flavor physics. In this framework the quark mixing matrix is a parameter matrix describing the deviation of neutrino mixing from exactly bi-maximal, predicting theta_{sol}+theta_C=pi/4, where theta_C is the Cabibbo angle, theta_{atm}+theta_{23}^{CKM}=pi/4 and theta_{13}^{MNS} ~ theta_{13}^{CKM} ~ O(lambda^3), in a perfect agreement with experimental data. Both non-Abelian and Abelian flavor symmetries are needed for such a prediction to be realistic. An example flavor model capable to explain this flavor mixing pattern, and to induce the measured quark and lepton masses, is outlined.Comment: references added, title changed in journa

SU(4) Skyrmions and Activation Energy Anomaly in Bilayer Quantum Hall Systems

The bilayer QH system has four energy levels in the lowest Landau level, corresponding to the layer and spin degrees of freedom. We investigate the system in the regime where all four levels are nearly degenerate and equally active. The underlying group structure is SU(4). At $\nu =1$ the QH state is a charge-transferable state between the two layers and the SU(4) isospin coherence develops spontaneously. Quasiparticles are isospin textures to be identified with SU(4) skyrmions. The skyrmion energy consists of the Coulomb energy, the Zeeman energy and the pseudo-Zeeman energy. The Coulomb energy consists of the self-energy, the capacitance energy and the exchange energy. At the balanced point only pseudospins are excited unless the tunneling gap is too large. Then, the SU(4) skyrmion evolves continuously from the pseudospin-skyrmion limit into the spin-skyrmion limit as the system is transformed from the balanced point to the monolayer point by controlling the bias voltage. Our theoretical result explains quite well the experimental data due to Murphy et al. and Sawada et al. on the activation energy anomaly induced by applying parallel magnetic field.Comment: 22 pagets, 6 figures, the final version to be published in PR

Renormalization group evolution of neutrino masses and mixing in seesaw models: A review

We consider different extensions of the standard model which can give rise to the small active neutrino masses through seesaw mechanisms, and their mixing. These tiny neutrino masses are generated at some high energy scale by the heavy seesaw fields which then get sequentially decoupled to give an effective dimension-5 operator. The renormalization group evolution of the masses and the mixing parameters of the three active neutrinos in the high energy as well as the low energy effective theory is reviewed in this article.Comment: 54 pages. Invited review submitted to IJMP