arXiv subjects
Publications and source records attributed to T. Goldman.
We show that only additivity of inverse Regge slopes is consistent with both the formal chiral limit m(n)\to 0 and the heavy quark limit M(Q)>>M(n), where n=u,d, and m,M are current and constituent quark masses, respectively.
Leading-order electromagnetic loop corrections to the one-pion-exchange potential are computed within the framework of chiral perturbation theory. These corrections generate an effective nucleon-nucleon potential, $V_{πγ}$, which supplements the sum of OPEP and the nucleon-nucleon Coulomb potential. This potential is charge dependent and its construction is demonstrated to be gauge invariant. The potential $V_{πγ}$ has been included in the Nijmegen partial-wave analysis of np data. A particular renormalization scheme is chosen that leads to a negligible change in the charged-piNN coupling constant and in the np 1S0 scattering length and effective range.
We prove the validity of Schwinger's quartic nonet mass formula for a general nonet structure with the isoscalar singlet mass being shifted from its ``ideal'' value. We apply this formula to the problem of the correct q\bar{q} assignment for the scalar meson nonet. The results favor scalar isoscalar singlet and isoscalar octet masses in the vicinity of 1 GeV and 1.45 GeV, respectively. We explain the failure of Schwinger's formula for the pseudoscalar meson nonet, and suggest a new version of this formula, modified by the inclusion of the pseudoscalar decay constants, which holds with improved accuracy for this nonet. We also rederive the new Gell-Mann-Okubo mass formula 3M^2(n\bar{n},I=1)+2M^2(s\bar{s})=4M^2(s\bar{n})+M^2(n\bar{n},I=0) (n=u,d), suggested in our previous publications.
We rederive the new SU(3) multiplet mass formula 2M^2(s\bar{s})+3M^2(n\bar{n}, I=1)=4M^2(s\bar{n})+M^2(n\bar{n},I=0) (n=u,d}, obtained in our previous paper by using Regge phenomenology, for the pseudoscalar and scalar mesons in the Nambu-Jona-Lasinio model with instanton-induced interaction. We apply this formula to the problem of the correct q\bar{q} assignment for the scalar meson nonet. Our results strongly favor the masses of the scalar isoscalar mostly octet and mostly singlet states in the vicinity of 1.45 GeV and 1.1 GeV, respectively
We show that the application of Regge phenomenology to SU(4) meson multiplets leads to a new Gell-Mann-Okubo mass-mixing formula in the SU(3) sector, 3m_1^2 + (cos theta)^2 m_0^2 + (sin theta)^2 m_{0'}^2 + sqrt{2} sin(2theta) (m_0^2 - m_{0'}^2) = 4m_{1/2}^2, where m_1,m_{1/2},m_0,m_{0'} are the masses of the isovector, isodoublet, isoscalar mostly octet and isoscalar mostly singlet states, respectively, and theta is the nonet mixing angle. For an ideally mixed nonet, theta = arctan(1/sqrt{2}), this formula reduces to 2m_0^2 + 3m_1^2 = 4m_{1/2}^2 + m_{0'}^2 which holds with an accuracy of ~1% for vector and tensor mesons. For pseudoscalar mesons, with the eta-eta' mixing angle -arctan[1/(2sqrt{2})] ~ -19.5^o, in agreement with experiment, it leads to the relation 4m_K^2 = 3m_pi^2 + m_{eta'}^2 which holds to an accuracy of better than 1% for the measured pseudoscalar meson masses.
By assuming the existence of (quasi)-linear Regge trajectories for heavy mesons, we derive new quadratic mass relations of non-Gell-Mann-Okubo type, 6M^2(q-qbar)+3M^2(c-cbar)=8M^2(c-qbar), 20M^2(q-qbar)+5M^2(b-bbar)= 16M^2(b-qbar), q=n(=u,d),s, which show excellent agreement with experiment. We also establish the sum rule M^2(i-ibar)+M^2(j-jbar)-2M^2(j-ibar)\approx const for any pair of flavors, (i,j).
By assuming the existence of (quasi)-linear baryon Regge trajectories, we derive new quadratic Gell-Mann-Okubo type baryon mass relations. These relations are used to predict the masses of the charmed baryons absent from the Baryon Summary Table so far, in good agreement with the predictions of many other approaches.
The mass spectrum of P-wave mesons is considered in a nonrelativistic constituent quark model. The results show the common mass degeneracy of the isovector and isodoublet states of the scalar and tensor meson nonets, and do not exclude the possibility of a similar degeneracy of the same states of the axial-vector and pseudovector nonets. Current experimental hadronic and τ-decay data suggest, however, a different scenario leading to the a_1 meson mass \simeq 1190 MeV and the K_{1A}-K_{1B} mixing angle \simeq (37\pm 3)^o. Possible s\bar{s} states of the four nonets are also discussed.
By assuming the existence of (quasi)-linear Regge trajectories for 25-plet mesons in the low energy region, we derive a new, 14th power, meson mass relation. This relation may be reduced to a quadratic Gell-Mann-Okubo type formula by fitting the values of the Regge slopes of these (quasi)-linear trajectories. Such a formula holds with an accuracy of ~2% for vector mesons, and also suggests that the quantum number I(J^P)=1/2(2^{+}) should be assigned to the both B_J(5732) and B_{sJ}(5850) mesons discovered recently. We also discuss reasons for the failure of group theory to produce correct mass relations for heavy quarkonia.
By assuming the existence of (quasi)-linear Regge trajectories for heavy quarkonia in the low energy region, we derive a new, sixth power, meson mass relation which shows good agreement with experiment for both charmed and beauty mesons. This relation may be reduced to a quadratic Gell-Mann-Okubo type formula by fitting the values of the Regge slopes of these (quasi)-linear trajectories. For charmed mesons, such a formula holds with an accuracy of $\sim 1$%, and is in qualitative agreement with the relation obtained previously by the application of the linear spectrum to a meson hexadecuplet.
In a nonrelativistic constituent quark model we find a constraint on the mixing angle of the strange axial-vector mesons, $35^o\stackrel{<}{\sim } θ_K\stackrel{<}{\sim }55^o,$ determined solely by two parameters: the mass difference of the $a_1$ and $b_1$ mesons and the ratio of the constituent quark masses.
The mass spectrum of D-wave mesons is considered in a nonrelativistic constituent quark model. The results show a common mass degeneracy of the isovector and isodoublet states of the 1 $^3D_1$ and 1 $^3D_3$ nonets, and suggest therefore that the $K^\ast (1680)$ cannot be the I=1/2 member of the 1 $^3D_1$ nonet. They also suggest that the $η_2(1870),$ presently omitted form the Meson Summary Table, should be interpreted as the I=0 $s\bar{s}$ state of the 1 $^1D_2$ nonet.
In infrared-stable fixed-point field theories, the interaction energy of a test particle is proportional to the non-relativistic (heavy source) coordinate-space potential derived from the field strength produced by that source. This is no longer true in ultraviolet-stable fixed-point field theories (UVSFPFT) as they may not have a finite infrared fixed point. This leads to the possibility that UVSFPFTs may have quite conventional field strength distributions despite the unusual spatial dependence expected for the interaction energy.
A theoretical structure that involves neutrino mass eigenstates at non relativistic as well as relativistic energies is presented. Using this framework, we find that if the particle X, with mass 33.9 MeV, of the KARMEN collaboration anomaly is identified with the third neutrino mass eigenstate, then the present limit of 23 MeV upper bound on the tau neutrino mass implies |U_{τ3}| < 0.82.
Recent experiments show that the isospin-violating mass splitting of the B mesons is very small, but the best fits with a QCD sum rule analysis give a splitting of at least 1.0 MeV. The isospin-violating mass splittings of the charmed mesons, on the other hand, are in agreement with experiment. In this letter we show that the inclusion of 2$^{nd}$ kind QED penguin diagrams can account for this discrepancy within the errors in the QCD sum rule method.
It is shown that the representation transformations of multiquark wave functions between different coupling schemes are just the Racah coefficients of the permutation group. The transformation coefficients between the flavor-spin (FS) and the color-spin (CS) schemes are obtained. As an example, the expansion of the physical bases in terms of symmetry bases in the CS scheme are given for the interesting cases $YIJ = 201, 210, 000$.
We study the effects of a scalar field, coupled only to neutrinos, on oscillations among weak interaction current eigenstates. The effect of a real scalar field appears as effective masses for the neutrino mass eigenstates, the same for $\nbar$ as for $\n$. Under some conditions, this can lead to a vanishing of $δm^2$, giving rise to MSW-like effects. We discuss some examples and show that it is possible to resolve the apparent discrepancy in spectra required by r-process nucleosynthesis in the mantles of supernovae and by Solar neutrino solutions.
Using a quark model, we study the effect of charge symmetry breaking on the valence quark distributions of the nucleon. The effect due to quark mass differences and the Coulomb interaction of the electrically charged quarks is calculated and, in contrast to recent claims, found to be small. In addition, we investigate the effect of charge symmetry breaking in the confining interaction, and in the perturbative evolution equations used to relate the quark model distributions to experiment. We find that both these effects are small, and that the strong charge symmetry breaking effect included in the scalar confining interactions may be distinguishable from that generated by quark mass differences.