Nonrelativistic Constituent Quark Model Research Articles

Pure leptonic decays of theBcmeson and their radiative corrections

The radiative corrections to the pure leptonic decay $B_c \to \ell\nu_{\ell}$ up-to one-loop order is presented. How to cancel the infrared divergences appearing in the loop calculations, and the radiative decay $B_c \to \ell\nu_{\ell}\gamma$ is shown precisely. It is emphasized that the radiative decay may be separated properly and may compare with measurements directly as long as the theoretical `softness' of the photon corresponds to the experimental resolutions. Furthermore with a kind of non-relativistic constituent quark model, a kind of typical long distance contributions to the radiative decays is estimated, and it is shown that the contributions are negligible in comparison with the accuracy of one-loop corrections and the expected experimental measurements.

NNinteraction in a Goldstone boson exchange model

Adiabatic nucleon-nucleon potentials are calculated in a six-quark nonrelativistic chiral constituent quark model where the Hamiltonian contains a linear confinement and a pseudoscalar meson (Goldstone boson) exchange interaction between quarks. Calculations are performed both in a cluster model and a molecular orbital basis, through coupled channels. In both cases the potentials present an important hard core at short distances, explained through the dominance of the [51]_{FS} configuration, but do not exhibit an attractive pocket. We add a scalar meson exchange interaction and show how it can account for some middle-range attraction.

Why the Constituent Quark Model Works for Baryon Magnetic Moments

Starting from quantum chromodynamics, we find that aside from some terms that contribute only via the mixing of different Fock components, the baryon magnetic moment can be expressed as μB = [∑qQq/(2⟨κ0⟩q)] (2Sq-2S+Lq-Lq̄), where ⟨κ0⟩q is the q flavor quark's average relativistic energy inside the baryon, and Sq, Lq, Sq̄, Lq̄ are quark and antiquark's relativistic spin and orbital contributions to baryon spin. We demonstrate that within an error of 1/6, this expression can be parameterized as ∑q[Qq/(2mqeff)] (2sq - 2sq̄), (where s is the nonrelativistic Pauli spin contribution and mqeff is of the order of the constituent quark mass) which is just what the nonrelativistic constituent quark model adopts to give a good account of octet baryon magnetic moments.

Important configurations forNNprocesses in a Goldstone boson exchange model

We study the short-range nucleon-nucleon interaction in a nonrelativistic chiral constituent quark model by diagonalizing a Hamiltonian containing a linear confinement and a Goldstone boson exchange interaction between quarks. A finite six-quark basis obtained from single particle cluster model states was previously used. Here we show that the configurations which appear naturally through the use of molecular orbitals, instead of cluster model states, are more efficient in lowering the six-quark energy.

A consistent explanation of the Roper phenomenology

We study the electromagnetic transitions of the Roper N (1440) resonance. Our results, when combined with the previously obtained for the mass and the pionic strong decay widths of the Roper, show that within a non-relativistic constituent quark model scheme, a comprehensible understanding of the Roper phenomenology can be achieved. They also seem to support the view of the Roper as a radial excitation of the nucleon, though more experimental data are needed to reach a definitive conclusion.

Radiative leptonic decays of Bc meson

To the leading order, the radiative leptonic decays B c→γℓ ν ̄ (ℓ= e, μ ) are studied carefully. In the study, a non-relativistic constituent quark model and the effective Lagrangian for the heavy flavour decays are used. As a result, the branching ratios turn out to be of the orders of 10 −5 for B c→γμ ν ̄ or for B c→γe ν ̄ . Based on the study, we point out the decays being accessible experimentally at the future LHC, and the possibility to determine the decay constant f B c through the radiative decays.

Regarding the enigmas ofP-wave meson spectroscopy

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, ${m(a}_{0})\ensuremath{\cong}{m(a}_{2}),$ ${m(K}_{0}^{*})\ensuremath{\cong}{m(K}_{2}^{*}),$ 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 $\ensuremath{\tau}$-decay data suggest, however, a different scenario leading to the ${a}_{1}$ meson mass $\ensuremath{\simeq}1190$ MeV and the ${K}_{1A}$-${K}_{1B}$ mixing angle $\ensuremath{\simeq}(37\ifmmode\pm\else\textpm\fi{}3)\ifmmode^\circ\else\textdegree\fi{}.$ Possible $s\overline{s}$ states of the four nonets are also discussed.

On D-wave meson spectroscopy and the [formula omitted] (1410)- [formula omitted] (1680) problem

The mass spectrum of D-wave mesons is considered in a non-relativistic constituent quark model. The results show a common mass degeneracy of the isovector and isodoublet states of the 1 3 D 1 and 1 3 D 3 nonets, and suggest therefore that the K ∗ (1680) cannot be the I = 1 2 member of the 1 3 D 1 nonet. They also suggest that the η 2 (1870), presently omitted from the Meson Summary Table, should be interpreted as the I = 0 s s state of the 1 1 D 2 nonet.

New Predictions for Charmed and Bottom Baryons

I review the recent proposal that there are new isotriplet heavy baryons with masses approximately 2380 MeV and 5760 MeV. This prediction follows from the application of heavy spin-flavor and light SU(3) symmetries to the observed charmed and bottom baryon states. It also entails assumptions about the spin and parity quantum numbers of the observed states which are different than is commonly supposed. The discovery of such states would imply that the nonrelativistic constituent quark model is a poor predictor of heavy baryon spectroscopy. I update the analysis in light of new data which have become available.

Exclusive and inclusive weak decays of the B-meson

A relativistic quark model is applied to the description of semileptonic and non-leptonic charmed decays of the B-meson. The exclusive semileptonic modes B → D lve and → D ∗ lve are described through the universal Isgur-Wise form factor, which is calculated in terms of a constituent quark model wave function for the B-meson. Different approximations for the latter, either based on a phenomenological ansatz or derived from analyses of the meson spectra, are adopted. In particular, two wave functions, constructed via the Hamiltonian light-front formalism using a relativized and a non-relativistic constituent quark model, are considered, obtaining a link between standard spectroscopic quark models and the B-meson decay physics. The inclusive semileptonic and non-leptonic branching ratios are calculated within a convolution approach, inspired by the partonic model and involving the same B-meson wave function used for the evaluation of the exclusive semileptonic modes. Our results for the major branching ratios are consistent with available experimental data and the sum of all the calculated branching ratios turns out to be close to unity. In particular, we found that (i) a remarkable fraction (∼ 35%) of semileptonic decay modes occur in non- D, non- D ∗ final states; (ii) non-perturbative effects enhance the inclusive b → c ud decay channels, with a sizable contribution provided by internal decays into heavy mesons and baryon-antibaryon pairs; the resulting reduction of the semileptonic branching ratio brings the theoretical prediction in agreement with the experimental value without increasing at the same time the charm counting.

Constraint on axial-vector meson mixing angle from the nonrelativistic constituent quark model

In a nonrelativistic constituent quark model we find a constraint on the mixing angle of the strange axial-vector mesons, 35{degree}{approx_lt}{theta}{sub K}{approx_lt}55{degree}, determined solely by two parameters: the mass difference of the a{sub 1} and b{sub 1} mesons and the ratio of the constituent quark masses. {copyright} {ital 1997} {ital The American Physical Society}

Hara's theorem in the constituent quark model.

We show that the parity-violating electromagnetic matrix elements describing the hyperon decay in the nonrelativistic constituent quark model obey Hara{close_quote}s theorem in first-order perturbation theory, i.e., to {ital O}({ital G}{sub {ital F}}), where {ital G}{sub {ital F}}{approx_equal}10{sup {minus}5}{ital M}{sub {ital N}}{sup {minus}2} is the Fermi weak interaction coupling constant and {ital M}{sub {ital N}} is the nucleon mass. Particular emphasis is put on questions of gauge invariance and of threshold behavior. We discuss our results and compare them with the literature. {copyright} {ital 1996 The American Physical Society.}

A chiral quark model and the spin observables in nucleon-nucleon scattering

Abstract We calculate the polarization observables in nucleon-nucleon scattering using a non-relativistic constituent quark model with chiral symmetry. The coupling of the 1S0(NN) partial wave to the 5D0(NΔ) partial wave is included. The results are compared to the polarization observables obtained from the different phase shift analyses. The sensitivity to the different experimental sets of phase shifts is discussed. We find that some of the polarization observables are extremely sensitive to small modifications of the phase shifts. However, the agreement with the experimental data is generally satisfactory. The largest deviations are seen in those observables which mainly depend on the spin-orbit interaction.

Isospin-violating meson-nucleon vertices as an alternate mechanism of charge-symmetry breaking.

We compute isospin-violating meson-nucleon coupling constants and their consequent charge-symmetry-breaking (CSB) nucleon-nucleon potentials. The couplings result from evaluating matrix elements of quark currents between nucleon states in a nonrelativistic constituent quark model; the isospin violations arise from the difference in the up and down constituent quark masses. We find, in particular, that isospin violation in the omega-meson{endash}nucleon vertex dominates the class IV CSB potential obtained from these considerations. We evaluate the resulting spin-singlet{endash}triplet mixing angles, the quantities germane to the difference of neutron and proton analyzing powers measured in elastic {ital n}{searrow}-{ital p}{searrow} scattering, and find them commensurate to those computed originally using the on-shell value of the {rho}-{omega} mixing amplitude. The use of the on-shell {rho}-{omega} mixing amplitude at {ital q}{sup 2}=0 has been called into question; rather, the amplitude is zero in a wide class of models. Our model possesses no contribution from {rho}-{omega} mixing at {ital q}{sup 2}=0, and we find that omega-meson exchange suffices to explain the measured {ital n}-{ital p} analyzing power difference at 183 MeV. {copyright} {ital 1996 The American Physical Society.}

E1+/M1+ and S1+/M1+ from an analysis of p(e,e'p) pi 0 in the region of the Delta (1232) resonance at Q2=3.2(GeV/c)2.

We have analyzed exclusive $p(e, {e}^{\ensuremath{'}}p){\ensuremath{\pi}}^{0}$ data to determine the electromagnetic and scalar transition multipoles in the mass region of the $\ensuremath{\Delta}(1232)$ at the highest ${Q}^{2}$ value where data exist. The ratio of the electric quadrupole and the magnetic dipole transition moments is determined to be $\frac{{E}_{1+}}{{M}_{1+}}=0.06\ifmmode\pm\else\textpm\fi{}0.02\ifmmode\pm\else\textpm\fi{}0.03$, and for the scalar quadrupole transition we find $\frac{{S}_{1+}}{{M}_{1+}}=0.07\ifmmode\pm\else\textpm\fi{}0.02\ifmmode\pm\else\textpm\fi{}0.03$. The results rule out that perturbative QCD governs the dynamics of the ${\ensuremath{\gamma}}_{v}p\ensuremath{\Delta}$ transition at such ${Q}^{2}$. They are more consistent with predictions of relativistic extensions of the nonrelativistic constituent quark model.

Isospin-breaking corrections to nucleon electroweak form factors in the constituent quark model.

We examine isospin breaking in the nucleon wave functions due to the {ital u}{minus}{ital d} quark mass difference and the Coulomb interaction among the quarks, and their consequences on the nucleon electroweak form factors in a nonrelativistic constituent quark model. The mechanically induced isospin breaking in the nucleon wave functions and electroweak form factors are exactly evaluated in this model. We calculate the electromagnetically induced isospin admixtures by using first-order perturbation theory, including the lowest-lying resonance with nucleon quantum numbers but isospin 3/2. We find a small ({le} 1%), but finite correction to the anomalous magnetic moments of the nucleon stemming almost entirely from the quark mass difference, while the static nucleon axial coupling remains uncorrected. Corrections of the same order of magnitude appear in charge, magnetic, and axial radii of the nucleon. The correction to the charge radius in this model is primarily isoscalar, and may be of some significance for the extraction of the strangeness radius from, e.g., elastic forward angle parity violating electron-proton asymmetries, or elastic {sup 4}He({bold e},{ital e}{prime}) experiments.

AN ESTIMATE OF CENTRE-OF-MASS EFFECTS IN QUARK POTENTIAL MODELS

The correction to the mass for the spurious centre-of-mass motion in a three-quark system is calculated exactly in the nonrelativistic constituent quark model for the Cornell potential. The result is somewhat higher than MIT bag model estimates but similar to that of a soliton bag model and a relativistic oscillator model.

Constituent quark model calculation for a possible J P=0 −, T=0 dibaryon

The assumption of a narrow (Γ ∼ 5 MeV) dibaryon-resonance with quantum numbers J P =0 −, T=0 and a mass of 2065 MeV allowed recently to describe all pionic double charge exchange cross-sections for various nuclei [1]. We investigate the mass of a 6-quark state with these quantum numbers in the framework of the nonrelativistic constituent quark model. Our shell-model diagonalisation including a large basis of excited states results in masses in the range of 2500 MeV. Since this result depends strongly on the explicit form of the confining potential, we cannot exclude the existence of the proposed dibaryon. For example the usual assumption of a quark-quark pair-confinement mechanism might not be valid in the 6q-system.

Deep-inelastic spin and flavor asymmetry of the nucleon from a QCD-inspired quark model.

A systematic procedure is described which permits the structure functions of nucleons to be calculated from a nonrelativistic constituent quark model. Transformation from the nucleon rest frame to the light cone or infinite momentum frame is accomplished based on work of Susskind, which does not require the weak binding and nonrelativistic kinematical approximations used in previous work. The light-cone distribution functions so obtained are then subjected to QCD evolution, giving predictions for the quark momentum densities. The model incorporates SU(6) breaking by the QCD-inspired one gluon exchange potential originated by De R\'ujula, Georgi, and Glashow, with the parameters fixed by Isgur and Karl from the N-\ensuremath{\Delta} mass splitting. In contrast with some previous work, the parameter values which fit the baryon mass spectrum are here shown to also give rather good agreement with the deep-inelastic flavor and spin asymmetries in the valence region.

Non-Strange Baryon Resonances in the Isgur-Karl Model Including the N=3 Oscillator Shell

Abstract The nonrelativistic constituent quark model for excited baryon states in the version proposed by Isgur and Karl is extended toward higher energies by including all states containing up to three oscillator excitation quanta. At high energies baryon resonances with spins up to 9/2 become accessible. At all energies and in particular for lower spins strong configuration mixing is obtained. Model predictions are compared to the empirical resonance energies derived in the Karlsruhe-Helsinki pion nucleon phase shift analysis. A search is made for parameter sets that apply simultaneously to the positive parity and the negative parity states. Numerical results are presented and discussed in relation to experimental data and to other theoretical works.