arXiv subjects
Publications and source records attributed to B. Stech.
For readers interested in the history of chiral symmetry we present the translation of two papaers from 1955 and 1959 from German to English, in which chiral symmetry properties for weak and strong interactions have been postulated and discussed.
We analyse the width of the $θ(\frac12^+)$ pentaquark assuming that it is a bound state of two extended spin-zero $ud$-diquarks and the $\bar s$ antiquark (the Jaffe-Wilczek scenario). The width obtained when the size parameters of the pentaquark wave function are taken to be close to the parameters of the nucleon is found to be $\simeq 150$ MeV, i.e. it has a normal value for a $P$-wave hadron decay with the corresponding energy release.However, we found a strong dynamical suppression of the decay width if the pentaquark has an asymmetric "peanut" structure with the strange antiquark in the center and the two diquarks rotating around. In this case a decay width of $\simeq$ 1 MeV is a natural possibility.
The present volume is the collection of contributions by friends of Holger Bech Nielsen for his 60th birthday. Contents: 1.Unified internal space of spins and charges (N. Mankoc Borstnik) 2.Semitopological Q-Rings (M. Axenides) 3.Non-local axial anomalies in the Standard model (D. Melikhov, B. Stech) 4.Could there be a fourth generation? (C.D. Froggatt) 5.Another complex Bateman equation (D.B. Fairlie) 6.Non-associative loops for Holger Bech Nielsen (P.H. Frampton) 7.Particles, fluids and vortices (J.W. van Holten) 8.Results on 2D current algebras (J.L. Petersen) 9.Phase transition in gauge theories and the Planck scale physics (L.V. Laperashvili and D.A. Ryzhikh) 10.Some remarks on the 'classical' large N limit (P. Olesen) 11.String theory and the size of hadrons (L. Susskind) 12.Relativity and $c/sqrt3$ (S.I. Blinnikov, L.B. Okun and M.I. Vysotsky) 13.Vortices (Jeff Greensite)
We demonstrate that the amplitude $<ργ|\partial_ν(\bar qγ_νγ_5 q)|0>$ does not vanish in the limit of zero quark masses. This represents a new kind of violation of the classical equation of motion for the axial current and should be interpreted as the axial anomaly for bound states. The anomaly emerges in spite of the fact that the one loop integrals are ultraviolet-finite as guaranteed by the presence of the bound-state wave function. As a result, the amplitude behaves like $\sim 1/p^2$ in the limit of a large momentum $p$ of the current. This is to be compared with the amplitude $<γγ|\partial_ν\bar qγ_νγ_5 q|0>$ which remains finite in the limit $p^2\to\infty$. The observed effect leads to the modification of the classical equation of motion of the axial-vector current in terms of the non-local operator and can be formulated as a non-local axial anomaly for bound states.
The ampitude of the $B\toργ$ decay induced by the flavour-changing neutral currents contains the penguin contribution and the weak-annihilation contribution generated by the 4-quark operators in the effective Hamiltonian. The penguin contribution is known quite well. We analyse the weak-annihilation which is suppressed by the heavy-quark mass compared to the penguin contribution. In the factorization approximation, the weak annihilation amplitude is represented in terms of the leptonic decay constants and the meson-photon matrix elements of the weak currents. The latter contain the $Bγ$, $ργ$ transition form factors and contact terms determined by the equations of motion. We calculate the $Bγ$ and $ργ$ form factors within the relativistic dispersion approach and obtain numerical estimates for the weak annihilation amplitude.
We calculate the form factors for weak decays of $B_{(s)}$ and $D_{(s)}$ mesons to light pseudoscalar and vector mesons. To reveal the intimate connection between different decay modes and to be able to perform the calculations in the full physical $q^2$-region we use a relativistic dispersion approach based on the constituent quark picture. This approach gives the form factors as relativistic double spectral representations in terms of the wave functions of the initial and final mesons. The form factors have the correct analytic properties and satisfy general requirements of nonperturbative QCD in the heavy quark limit. The disadvantages of quark models related to ill-defined effective quark masses and not precisely known meson wave functions are reduced by fitting the quark model parameters to lattice QCD results for the $B\to ρ$ transition form factors at large momentum transfers and to the measured total $D\to (K,K^*)lν$ decay rates. This allows us to predict numerous form factors for all kinematically accessible $q^2$ values.
The mass matrices of charged fermions have a simple structure if expressed in powers of the small parameter sigma=(m_c/m_t)^{1/2}. It is suggested that the mass matrix of the three heavy neutrinos occuring in grand unified theories can be expressed in terms of the same parameter. The requirement that these heavy neutrinos carry different U(1) generation quantum numbers gives rise to an almost unique form for this matrix. By applying the see-saw mechanism, the mass splitting of the two lightest neutrinos comes out to be tiny, favoring the vacuum oscillation solution for solar neutrinos. The mixing matrix is of the bimaximal type but contains also CP violating phases.
The mass matrices of quarks have a simple structure if expressed in powers of the small parameter σ=(m_c/m_t)^{1/2}. If there is a close relation between quarks and leptons, one would expect similar structures for the lepton matrices which involve the same parameter. To have a specific proposal, the see-saw mechanism is employed together with the stringent requirement that the singlet neutrinos carry non-zero generation charges. These charges then determine the powers of σin the corresponding heavy neutrino mass matrix. As a result, the neutrino mixing matrix turns out to be of the bimaximal type. In addition, the mass splitting of the two lightest neutrinos is found to be tiny, and just of the correct magnitude necessary for the vacuum solution for solar neutrinos.
We present further tests and applications of the new eta-eta' mixing scheme recently proposed by us. The particle states are decomposed into orthonormal basis vectors in a light-cone Fock representation. Because of flavor symmetry breaking the mixing of the decay constants can be identical to the mixing of particle states at most for a specific choice of this basis. Theoretical and phenomenological considerations show that the quark flavor basis has this property and allows, therefore, for a reduction of the number of mixing parameters. A detailed comparison with other mixing schemes is also presented.
We propose a new eta-eta' mixing scheme where we start from the quark flavor basis and assume that the decay constants in that basis follow the pattern of particle state mixing. On exploiting the divergences of the axial vector currents - which embody the axial vector anomaly - all basic parameters are fixed to first order of flavor symmetry breaking. That approach naturally leads to a mass matrix, quadratic in the masses, with specified elements. We also test our mixing scheme against experiment and determine corrections to the first order values of the basic parameters from phenomenology. Finally, we generalize the mixing scheme to include the eta(c). Again the divergences of the axial vector currents fix the mass matrix and, hence, mixing angles and the charm content of the eta and eta'.
To know and understand form factors of hadronic currents is of decisive importance for analysing exclusive weak decays. The ratios of different form factors of a given process depend on the relativistic spin structure of initial and final particles. It is shown --- assuming simple properties of the spectator particle --- that these ratios can entirely be expresssed in terms of particle and quark mass parameters. For quark masses large compared to the spectator mass the Isgur-Wise relations follow. The corresponding amplitudes for heavy-to-light transitions show a very similar structure. In particular, the $F_0$ and $A_1$ form factors behave again differently from the $F_1, A_2, V$ and $T_1$ form factors.