Baryon Magnetic Moments Research Articles

Implications of baryon magnetic moments for the quark model

The implications of recent baryon-magnetic-moment measurements for various assumptions in the quark model are considered. The static quark model is seen to give a qualitative understanding of the baryon magnetic moments, but fails in a quantitative test ($\frac{{\ensuremath{\chi}}^{2}}{\mathrm{DF}}=\frac{21.5}{5}$), largely due to inconsistency of the now accurate determinations of the ${\ensuremath{\Lambda}}^{0}$ and ${\ensuremath{\Xi}}^{0}$ moments. Introducing nonstatic effects (orbital, relativistic, or exchange) still permits four independent sum rules to be written (for eight moments) if approximate SU(3) symmetry is assumed for quark-model wave functions. Two sum rules give good agreement with experiment, but those sum rules for any case involving the ${\ensuremath{\Xi}}^{\ensuremath{-}}$ or ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ moments do not, suggesting that their experimental determination is inconsistent with such a quark model.

Current status of the Baryon magnetic moments

We have fitted the latest values of the baryon magnetic moments to several theoretical formulations. We find that the additive quark model cannot explain the new data well, but that additional symmetry-breaking assumptions can improve the fits.

Magnetic moments of baryons in broken SU(4)

Assuming that the anomalous magnetic moment interaction has the formaT 1 1 +bT 2 2 +cT 4 4 +sT α α in SU(4), which may arise due to symmetry breaking or some other dynamical effects, we have obtained the magnetic moments and the transition moments of the ordinary and charmed baryons.

Comment on the magnetic moments of baryons in the broken-SU(6)-symmetry model

It is pointed out that the consideration of the physical mass in the computation of the baryon magnetic moments in broken SU(6) symmetry allows us to choose a value of the quark mass ratio different from that chosen by De R\'ujula, Georgi, and Glashow and leads to a prediction significantly different from their results. Precision measurements by hyperon beams, which are planned at the Fermilab and at CERN in the near future, could differentiate between the two sets of predictions.

SU 3 subalgebras ofSU 4 and generalizedU-spin in a new approach to the magnetic moments of charmed baryons

We discuss, from the group-theoretical point of view, a formalism—recently proposed as an useful approach to calculating the magnetic moments of charmed baryons—based on the four sectors ofSU4 which are obtained by picking out three of the four quarks, u, d, s, c in all possible ways. The sectors can be divided into two classes, according to the charge of the removed quark, and aSU3 algebra can be defined for both classes in a suitable way. This leads, among the others, to introduce «generalized hypercharge» and «generalized isospin» operators. Besides the usual strangeness and charm, two new additive quantum numbers «strangenesslike» and «charmlike» are present. With the view of discussing electromagnetic properties, we extend the concept ofU-spin to the sectors different from the «historical» one (u, d, s). Clearly, the interest of this formalism lies in the fact it allows us to reduce many calculations, to be done in the framework ofSU4, to standardSU3 calculations (or even to a straightforward application of well-known formulae of the eightfold way). This is explicitly shown by working out the calculation of the magnetic moments of baryons. The possibility of applying this approach to other physical problems concerning charmed baryons or to quark models with a flavour number higher than four is briefly considered.

Quark anomalous moments and meson radiative decays

It is shown within the framework of the naive quark model that the measured rates $\ensuremath{\Gamma}(\ensuremath{\rho}\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\gamma})$ and $\ensuremath{\Gamma}({K}^{*0}\ensuremath{\rightarrow}{K}^{0}\ensuremath{\gamma})$ can be explained if the quarks have anomalous magnetic moments. However, one is led to contradictions with the measured baryon magnetic moments and other measured radiative rates.

Magnetic moment of ?? from dispersion relations int

Magnetic moments of baryons are calculated from dispersion relations int, including the π\(\bar \pi \)-continuum. The largest deviation from the naiveSU(3)-expectation is found for∑−, leading to μ2211=−1.80 nuclear magnetons instead of −0.66.

Scattering lengths and baryon magnetic moments in a gauge model of strong and electromagnetic interactions

We present a broken SU(3) gauge model of strong and electromagnetic interactions with the usual vector mesons. All particles (9 vectors, 8 baryons and 9 pseudoscalars) have the right masses by means of the Higgs mechanism. We study the consequences of Sakuraï's idea that strong and electromagnetic interactions are mediated by vector mesons universally coupled to nearly conserved currents: one finds encouraging values for scattering lengths except for P-wave parameters in the meson-baryon sector that are too small. The calculation of the baryon anomalous magnetic moments also gives too-small numbers.

Magnetic moments of baryons in higher symmetry schemes including charm

Relations among the magnetic moments of charmed and uncharmed baryons are derived in the framework of SU(4) and SU(8) symmetries. The SU(3) resultμ (Σ o)=−μ(Λ) is not present in SU(4), but is obtained in SU(8). Higher order effects are further considered to improve the situation.

New relation between mesons and baryons

A new SU/sub 12/ classification scheme for mesons and baryons is used in conjunction with a simple quark model and results in a striking correlation between the masses of the diquark subsystems in baryons and the masses of several known mesons. The new classification provides a simple scheme which involves a basic 36 multiplet for the pseudoscalar and vector mesons and a 112 multiplet for the baryons and antibaryons. The 36 multiplet of SU/sub 12/ does not treat the eta' as a singlet as in the conventional SU/sub 6/ scheme. The new scheme also has the advantages of providing a simple algebraic form of Zweig's rule for the decay of strange-quark-antiquark pairs. Absolute values of the magnetic moments of baryons are accurately reproduced and are found to be consistent with a model in which the effective quark masses are 338 MeV (nonstrange) and 465 MeV (strange). (AIP)

The magnetic moments of the ground-state baryons in the nonrelativistic free-quark model

We show that the assumption of the identity between the current and the constituent quark in the nonrelativistic free-quark model does not lead to the vanishing of the anomalous magnetic moments of the nucleon but, on the contrary, it reproduces the correct ratio (−3/2) between the magnetic moments of the proton and the neutron. By pointing out the mechanism by which the above model produces this desirable result, we then show that identity of the current and the constituent quark in this context does not imply the identity of theSU6w, currents charges with the generators of theSU6w, constituent symmetry. We also resolve an apparent contradiction between our result and one of Melosh’s assertions regarding the magnetic moments of the baryons. In particular we show that within the framework of the nonrelativistic free-quark model our result is consistent with the Melosh transformation between the current and the constituent quark. In the same framework we also point out an easy way to implement the Melosh transformation in the calculation of the hadronic-current matrix elements.

Angular constraints and the Melosh transformation

The Melosh transformation between current and constituent quarks is discussed when formulated on a light-like plane, as is natural for the description of collinear symmetries like SU(6) W. There is no unique definition of the transformation in this context, but further angular constraints are introduced to ensure that the states coupled by SU(6) W transformations have the correct spin properties. It is then shown that there is no transformation generated by single quark operators which satisfies these requirements, save if only terms to first order in the transverse momentum are kept. Some of the resultant inconsistencies are illustrated by a discussion of baryon magnetic moments. It is concluded that there is no satisfactory explanation of μ p /μ n = − 3 2 from this approach to the Melosh transformation. A non-field theoretic version of the free quark model which solves these angular constraints is exhibited.

A new semiclassical elementary particle model

A semiclassical model in which elementary particles are represented as systems of charged shells with associated quark-like quantum numbers is presented. Specifically the baryons are considered. Formulas are obtained which express baryon masses and magnetic moments in terms of model parameters which relate baryon and quark properties. Basically, the mass and moment formulas are expressions for mass ratios and magnetic moment ratios. Simple identifications for the model parameters lead to a prediction for the proton-electron mass ratio and to fairly accurate predictions for the baryon magnetic moments in units of the proton moment.

Relations among the baryon magnetic moments as a consequence ofSL 3,C

Relations among the baryon magnetic moments as a consequence ofSL 3,C

Magnetic Quarks and Electric Quarks in Hadrons

Dirac's magnetic monopoles are generalized to have aspects which are similar to the conventional quarks (electric quarks). Such magnetic monopoles are called magnetic quarks. This work assumes that a baryon consists of three solid bodies called electromagnetic quarks, and that an electromagnetic quark and an electromagnetic antiquark form a meson. Each of these electromagnetic quarks is considered to be composed of one electric quark and one magnetic antiquark. Such a speculation solves the difficulty in statistics faced by the paraquark model and allows the existence of anomalous charge conjugation parity $C$ of mesonic states. New baryon mass relations and magnetic moments have been derived. Finally, a strong electric dipole moment is predicted to exist in a baryon state with nonzero electromagnetic-quark orbital angular momentum, $L\ensuremath{\ne}0$.

Nonstatic Relations between Magnetic Moments in the Quark Model

Relations between baryon magnetic moments are derived which are independent of orbital corrections, relativistic corrections, and two-body exchange corrections (and generally any two-body correction) in the quark model, provided that the wave-function contributions leading to these corrections are $\mathrm{SU}(3)$-symmetric. Among the relations derived are $\ensuremath{\mu}({\ensuremath{\Xi}}^{\ensuremath{-}})+3\ensuremath{\mu}({\ensuremath{\Xi}}^{0})=6\ensuremath{\mu}(\ensuremath{\Lambda})+2\ensuremath{\mu}({\ensuremath{\Sigma}}^{+})\ensuremath{-}3\ensuremath{\mu}(p)\ensuremath{-}\ensuremath{\mu}(n)$ (independent of quark moments) and $\ensuremath{\mu}({\ensuremath{\Xi}}^{0})\ensuremath{-}\ensuremath{\mu}({\ensuremath{\Xi}}^{\ensuremath{-}})=\ensuremath{\mu}(p)+2\ensuremath{\mu}(n) (\mathrm{if} {\ensuremath{\mu}}_{\mathcal{P}}=\ensuremath{-}2{\ensuremath{\mu}}_{\mathfrak{N}})$.

BrokenSU(3)Symmetry, Sum Rules, and the Magnetic Moments of the Baryons

Motivated by the increasing accuracy with which the magnetic moments of strange baryons are being measured, we present a calculation of these moments in broken $\mathrm{SU}(3)$ symmetry without appeal to a highly detailed theory of symmetry breaking. As primary ingredients in the calculation, we assume only the $\mathrm{SU}(2)$ transformation properties of the electromagnetic current, the octet transformation property of the symmetry-breaking medium-strong interaction, and the validity of the Drell-Hearn-Gerasimov sum rule for the anomalous moments. Saturating this sum rule with the dominant states, the decuplet and a singlet, but making no $\mathrm{SU}(3)$ assumptions on the couplings of these states or their masses, we find that all eight baryon anomalous magnetic moments and the ${\ensuremath{\Sigma}}^{0}\ensuremath{\Lambda}$ transition moment can be expressed in terms of ${\ensuremath{\kappa}}_{n}$, ${\ensuremath{\kappa}}_{\ensuremath{\Lambda}}$, and ${{\ensuremath{\kappa}}_{\ensuremath{\Sigma}}}^{+}$ through relations that are valid in broken symmetry with an expected accuracy of about 10%. Further assuming the absence of the 27, in the current, we have, in addition, ${{\ensuremath{\kappa}}_{\ensuremath{\Sigma}}}^{+}={\ensuremath{\kappa}}_{n}\ensuremath{-}4{\ensuremath{\kappa}}_{\ensuremath{\Lambda}}$. We also find that our saturation assumption implies the absence of a unitary singlet piece in the electromagnetic current in the symmetry limit, so that the existing particle spectrum supports the hypothesis of a pure octet transformation property for the electromagnetic current. We also examine the Drell-Hearn-Gerasimov sum rule for high-spin systems, and this forward-direction sum rule would appear to require towers of states require towers of states for its saturation. Forward-direction sum rules for the nonflip Compton amplitude, based on the absence of fixed or moving poles in the $J$ plane with $I=2$, are also considered and found to be consistent with the results obtained from the magnetic-moment sum rules.

A Model of Baryons Made of Quarks with Hidden Spin

The quark model of baryons is investigated in an attempt to combine its excellent agreement with experiment with a consistent foundation. It is found that effective Bose statistics for the spin states of identical quarks (quark statistics) is sufficient to explain the properties of baryons as if the three-quark wave functions were in the 56 representation of $\mathrm{SU}(6)$. A new internal degree of freedom is suggested as a mechanism for achieving quark statistics with fermion quarks. This mechanism also can produce quark saturation (at 3) and allows for the possibility of light quarks ($\ensuremath{\sim}\frac{1}{3}{M}_{p}$) that have a large effective mass if removed from baryons. Baryon magnetic moments and mass differences are analyzed in the quark model with the primary purpose of determining the required properties of quarks. Sum rules that are independent of quark moments in a static $s$-wave model are derived for baryon magnetic moments. Relativistic effects on magnetic moments are considered and are shown to be a likely mechanism for the deviation of the proton-neutron magnetic-moment ratio from the static prediction of $\ensuremath{-}\frac{3}{2}$. Higher-orbital states are also considered and a general formula is derived for orbital contributions to baryon magnetic moments.

Magnetic moments of baryons in a quark model

Magnetic moments of octet baryons are calculated in a non-relativistic quark model with scalar binding, using a model for SU(3) breaking developed earlier. Violation of ordinary spin symmetry is also considered, leading to a mixture of spin-orbital states. Consistency relations are derivable. In a special case, restricted to the 56, the results are given explicitly.

Nucleon Magnetic Moments in a Bootstrap Model

The bootstrap calculations of baryon magnetic moments by Dashen and Frautschi and by Barton and Dare are examined in an ${\mathrm{SU}}_{2}$ model. The pion contribution to the nucleon magnetic moment, which Dashen and Frautschi neglected, is calculated using their method, and is shown to reduce to Barton and Dare's estimate in a nonrelativistic limit. In the ${\mathrm{SU}}_{2}$ model, Dashen and Frautschi's method gives for the nucleon isoscalar and vector magnetic moments: ${\ensuremath{\mu}}_{S}=0$ and $0<{\ensuremath{\mu}}_{V}<5.7(\frac{e}{2M})$, where $M$ is the nucleon mass.