We discussed quantum deformations of D=4 Lorentz and Poincare algebras. In the case of Poincare algebra it is shown that almost all classical r-matrices of S. Zakrzewski classification correspond to twisted deformations of Abelian and Jordanian types
. A part of twists corresponding to the r-matrices of Zakrzewski classification are given in explicit form.
The spectrum of the SU(2) flavor baryons is studied in the frame of a relativistic chiral quark potential model based on the one-pion and one-gluon exchange mechanisms. It is argued that the N* and Delta* resonances strongly coupled to the pi-N cha
nnel are identified with the orbital configurations $(1S_{1/2})^2(nlj)$ with a single valence quark in the excited state (nlj). With the obtained selection rules based on the chiral constraint, we show that it is possible to construct a schematic periodic table of baryon resonances, consistent with the experimental data and yielding no missing resonances. A new original method for the treatment of the center of mass problem is suggested, which is based on the separation of the three-quark Dirac Hamiltonian into the parts, corresponding to the Jacobi coordinates. The numerical estimations for the energy positions of the Nucleon and Delta baryons (up to and including F-wave resonances), obtained within the field-theoretical framework by using time ordered perturbation theory, yield an overall good description of the experimental data at the level of the relativized CQM of S. Capstick and W. Roberts without any fitting parameters. The Delta(1232) is well reproduced. However, N g. s. and most of the radially excited baryon resonances (including Roper) are overestimated. Contrary, the first band of the orbitally excited baryon resonances with a negative parity are underestimated. At the same time, the second band of the orbitally excited Delta* states with the negative parity are mostly overestimated, while the N* states are close to the experimental boxes. The positive parity baryon resonances with J=5/2, 7/2 are close to the experimental data. At higher energies, where the experimental data are poor, we can extend our model schematically and predict an existence of seven N* and four Delta* new states with larger spin values.
We show that the double diffractive electroweak vector boson production in the $pp$ collisions at the LHC is an ideal probe of QCD based mechanisms of diffraction. Assuming the resolved Pomeron model with flavor symmetric parton distributions, the $W
$ production asymmetry in rapidity equals exactly zero. In other approaches, like the soft color interaction model, in which soft gluon exchanges are responsible for diffraction, the asymmetry is non-zero and equal to that in the inclusive $W$ production. In the same way, the ratio of the $W$ to $Z$ boson production is independent of rapidity in the models with resolved Pomeron in contrast to the predictions of the soft color interaction model.
Some one-neutron halo nuclei can emit a proton in a beta decay of the halo neutron. The branching ratio towards this rare decay mode is calculated within a two-body potential model of the initial core+neutron bound state and final core+proton scatter
ing states. The decay probability per second is evaluated for the $^{11}$Be, $^{19}$C and $^{31}$Ne one-neutron halo nuclei. It is very sensitive to the neutron separation energy.
A convergence of the valence quark self-energies in the 1S, 2S, $1P_{1/2}$, $1P_{3/2}$ orbits induced by pion and gluon field configurations, is shown in the frame of a relativistic chiral quark model. It is shown that in order to reach a convergence
, one needs to include contribution of the intermediate quark and anti-quark states with the total momentum up to $j=25/2$. It is argued that a restriction to the lowest mode when estimating the self-energy is not good approximation.
The lower excitation spectrum of the nucleon and $Delta$ is calculated in a relativistic chiral quark model. Corrections to the baryon mass spectrum from the second order self-energy and exchange diagrams induced by pion and gluon fields are estimate
d in the field -theoretical framework. Convergent results for the self-energy terms are obtained when including the intermediate quark and antiquark states with a total momentum up to $j=25/2$. Relativistic one-meson and color-magnetic one-gluon exchange forces are shown to generate spin 0, 1, 2, etc. operators, which couple the lower and the upper components of the two interacting valence quarks and yield reasonable matrix elements for the lower excitation spectrum of the Nucleon and Delta. The only contribution to the ground state nucleon and $Delta$ comes from the spin 1 operators, which correspond to the exchanged pion or gluon in the l=1 orbit, thus indicating, that the both pion exchange and color-magnetic gluon exchange forces can contribute to the spin of baryons. Is is shown also that the contribution of the color-electric component of the gluon fields to the baryon spectrum is enormously large (more than 500 MeV with a value $alpha_s=0.65$) and one needs to restrict to very small values of the strong coupling constant or to exclude completely the gluon-loop corrections to the baryon spectrum. With this restriction, the calculated spectrum reproduces the main properties of the data, however needs further contribution from the two-pion exchange and instanton induced exchange (for the nucleon sector) forces in consistence with the realistic NN-interaction models.
A new analysis of the precise experimental astrophysical $S$-factors for the direct capture $^3He(alpha,gamma)^7{rm {Be}}$ reaction [B.S. Nara Singh et al., Phys.Rev.Lett. {bf 93} (2004) 262503; D. Bemmerer et al., Phys.Rev.Lett. {bf 97} (2006) 12250
2; F.Confortola et al., Phys.Rev. {bf C 75} (2007) 065803 and T.A.D.Brown et al., Phys.Rev. {bf C 76} (2007) 055801] populating to the ground and first excited states of $^7{rm Be}$ is carried out based on the modified two - body potential approach in which the direct astrophysical $S$-factor, $S_{34}(E)$, is expressed in terms of the asymptotic normalization constants for $^3{rm {He}}+alphato ^7{rm {Be}}$ and two additional conditions are involved to verify the peripheral character of the reaction under consideration. The Woods--Saxon potential form is used for the bound ($alpha+^3{rm {He}}$)- state and the $^3{rm {He}}alpha$- scattering wave functions. New estimates are obtained for the indirectly measured, values of the asymptotic normalization constants (the nuclear vertex constants) for $^3{rm {He}}+alphato^7{rm {Be}}(g.s.)$ and $^3{rm {He}}+alphato^7{rm {Be}}(0.429 MeV)$ as well as the astrophysical $S$-factors $S_{34}(E)$ at E$le$ 90 keV, including $E$=0. The values of asymptotic normalization constants have been used for getting information about the $alpha$-particle spectroscopic factors for the mirror ($^7Li^7{rm {Be}}$)-pair.
We discussed twisted quantum deformations of D=4 Lorentz and Poincare algebras. In the case of Poincare algebra it is shown that almost all classical r-matrices of S.Zakrzewski classification can be presented as a sum of subordinated r-matrices of Ab
elian and Jordanian types. Corresponding twists describing quantum deformations are obtained in explicit form. This work is an extended version of the paper url{arXiv:0704.0081v1 [math.QA]}.
M1 transitions from the $^6$Li($0^+;T=1$) state at 3.563 MeV to the $^6$Li($1^+$) ground state and to the $alpha+d$ continuum are studied in a three-body model. The bound states are described as an $alpha+n+p$ system in hyperspherical coordinates on
a Lagrange mesh. The ground-state magnetic moment and the gamma width of the $^6$Li(0$^+$) resonance are well reproduced. The halo-like structure of the $^6$Li$(0^+)$ resonance is confirmed and is probed by the M1 transition probability to the $alpha+d$ continuum. The spectrum is sensitive to the description of the $alpha+d$ phase shifts. The corresponding gamma width is around 1.0 meV, with optimal potentials. Charge symmetry is analyzed through a comparison with the $beta$-delayed deuteron spectrum of $^6$He. In $^6$He, a nearly perfect cancellation effect between short-range and halo contributions was found. A similar analysis for the $^6$Li($0^+;T=1$) $gamma$ decay is performed; it shows that charge-symmetry breaking at large distances, due to the different binding energies and to different charges, reduces this effect. The present branching ratio $Gamma_{gamma}(0^+to alpha+d)/Gamma_{gamma}(0^+to1^+)approx 1.3times 10^{-4}$ should be observable with current experimental facilities.
