Chiral Algebra, Configuration Mixing, and Magnetic Moments

Gerstein, I. S.; Lee, B.W.

doi:10.1103/physrevlett.16.1060

Cited by 53 publications

(25 citation statements)

References 12 publications

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“…This finding is in line with the old current algebra results of Gerstein and Lee [7] and of Harari [8,9], updated to include recently measured values of F and D couplings, Ref. [1], and extended to include the flavor-singlet coupling g ð0Þ A of the nucleon, which was not considered in the mid-1960s at all, presumably due to the lack of data.…”

Section: Introductionsupporting

confidence: 83%

Baryon fields withUL(3)×UR(3)chiral symmetry. III. Interactions with chiral
Chen
¹
,
Dmitrašinović
²

2011
Phys. Rev. D

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Three-quark nucleon interpolating fields in QCD have well-defined SU L ð3Þ Â SU R ð3Þ and U A ð1Þ chiral transformation properties, viz. ½ð6; 3Þ È ð3; 6Þ, ½ð3; " 3Þ È ð " 3; 3Þ, ½ð8; 1Þ È ð1; 8Þ, and their mirror images; see [H. X. Chen, V. Dmitrašinović, A. Hosaka, K. Nagata, and S. L. Zhu, Phys. Rev. D 78, 054021 (2008)]. It has been shown (phenomenologically) in [H. X. Chen, V. Dmitrašinović, and A. Hosaka, Phys. Rev. D 81, 054002 (2010)] that mixing of the ½ð6; 3Þ È ð3; 6Þ chiral multiplet with one ordinary (naive) and one mirror field belonging to the ½ð3; " 3Þ È ð " 3; 3Þ, ½ð8; 1Þ È ð1; 8Þ multiplets can be used to fit the values of the isovector (g ð3Þ A ) and the flavor-singlet (isoscalar) axial coupling (g ð0Þ A ) of the nucleon and then predict the axial F and D coefficients, or vice versa, in reasonable agreement with experiment. In an attempt to derive such mixing from an effective Lagrangian, we construct all SU L ð3Þ Â SU R ð3Þ chirally invariant nonderivative one-meson-baryon interactions and then calculate the mixing angles in terms of baryons' masses. It turns out that there are (strong) selection rules: for example, there is only one nonderivative chirally symmetric interaction between J ¼ 1 2 fields belonging to the ½ð6; 3Þ È ð3; 6Þ and the ½ð3; " 3Þ È ð " 3; 3Þ chiral multiplets, that is also U A ð1Þ symmetric. We also study the chiral interactions of the ½ð3; " 3Þ È ð " 3; 3Þ and ½ð8; 1Þ È ð1; 8Þ nucleon fields. Again, there are selection rules that allow only one off-diagonal nonderivative chiral SU L ð3Þ Â SU R ð3Þ interaction of this type, that also explicitly breaks the U A ð1Þ symmetry. We use this interaction to calculate the corresponding mixing angles in terms of baryon masses and fit two lowest-lying observed nucleon (resonance) masses, thus predicting the third (J ¼ 1 2 , I ¼ 3 2 ) Á resonance, as well as one or two flavor-singlet Ã hyperon(s), depending on the type of mixing. The effective chiral Lagrangians derived here may be applied to high density matter calculations.

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Section: Introductionsupporting

confidence: 83%

Baryon fields withUL(3)×UR(3)chiral symmetry. III. Interactions with chiral
Chen
¹
,
Dmitrašinović
²

2011
Phys. Rev. D

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“…In one of the earliest physical applications of the chiral configuration mixing idea, Harari [22], Bincer [56], Gerstein and Lee [23], and Gatto et al [57] used the mixing of three of the aforementioned six chiral multiplets to fit the nucleon's isovector axial coupling constant g (1) A value at 1.267, [58] and thus explain its being different from unity, as was seemingly demanded by the Gell-Mann-Lévy model [17]. It turned out, however, that this application was not selective at all: all mixing scenarios could reproduce this value, so long as the [(6…”

Section: B Chiral Mixingmentioning

confidence: 99%

“…Chiral symmetry is spontaneously broken through the "condensation" of the sigma field σ → σ 0 = σ 0 = f π , which leads to the dynamical generation of baryon masses, as can be seen from the linearized chiral invariant interaction Lagrangians Eqs. (20), (21), (22) and (23).…”

Section: B Baryon Masses In the Chiral Limitmentioning

confidence: 99%

Baryon fields withUL(3)×UR(3)chiral symmetry. V. Pion-nucleon and kaon-nucleon
Dmitrašinović¹,
Chen²
2016
Phys. Rev. C

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We have previously calculated the pion-nucleon ΣπN term in the chiral mixing approach with u, d flavors only, and found the lower bound ΣπN ≥ 1 + 16 3 sin 2 θ 3 2 m 0 u + m 0 d where m 0 u , m 0 d are the current quark masses, and θ is the mixing angle of the [( 1 2 , 0) ⊕ (0, 1 2 )] and the [(1, 1 2 ) ⊕ ( 1 2 , 1)] chiral multiplets. This mixing angle can be calculated as sin 2 θ = 3 8 g (0)A + g(3) A, where gA , gA , are the flavor-singlet and the isovector axial couplings. With presently accepted values of current quark masses, this leads to ΣπN ≥ 58.0 ± 4.5 +11.4 −6.5 MeV, which is in agreement with the values extracted from experiments, and substantially higher than most previous two-flavour calculations. The causes of this enhancement are: 1) the large, ( 16 3 ≃ 5.3), purely SUL(2) × SUR(2) algebraic factor; 2) the admixture of the [(1, 12 ) ⊕ ( 1 2 , 1)] chiral multiplet component in the nucleon, whose presence has been known for some time, but that had not been properly taken into account, yet. We have now extended these calculations of ΣπN to three light flavours, i.e., to SUL(3) × SUR(3) multiplet mixing. Phenomenology of chiral SUL(3) × SUR(3) multiplet mixing demands the presence of three chiral SUL(3) × SUR(3) multiplets, viz. [(6, 3) ⊕ (3, 6)], [(3, 3) ⊕ ( 3, 3)] and [( 3, 3) ⊕ (3, 3)], in order to successfully reproduce the baryons' flavor-octet and flavor-singlet axial currents, as well as the baryon anomalous magnetic moments. Here we use these previously obtained results, together with known constraints on the explicit chiral symmetry breaking in baryons to calculate the ΣπN term, but find little, or no change of ΣπN from the above successful two-flavor result. The physical significance of these results lies in the fact that they show no need for q 4 q components, and in particular, no need for an ss component in the nucleon, in order to explain the large "observed" ΣπN value. We also predict the experimentally unknown kaon-nucleon sigma term ΣKN .

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“…That led to two permissible scenarios: a) the Gerstein-Lee [3] and b) the Harari scenario [5,6], neither of which could be eliminated on the basis of axial currents and baryon masses alone.…”

Section: Discussionmentioning

confidence: 99%

Baryon fields with UL(3)×UR(3)chiral s

Chen

Dmitrašinović

2012

Phys. Rev. C

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We construct all SU L (3) × SU R (3) chirally invariant anomalous magnetic, i.e., involving a Pauli tensor and one-derivative, interactions of one chiral [(8, 1) ⊕ (1, 8)] meson field with chiral [(6, 3) ⊕ (3, 6)], [(3, 3) ⊕ (3, 3)], and [(8, 1) ⊕ (1, 8)] baryon fields and their "mirror" images. We find strong chiral selection rules; e.g., there is only one off-diagonal chirally symmetric anomalous magnetic interaction between J = 1 2 fields belonging to the [(6, 3) ⊕ (3, 6)] and the [(3, 3) ⊕ (3, 3)] chiral multiplets. We also study the chiral selection rules for the anomalous magnetic interactions of the [(3, 3) ⊕ (3, 3)] and the [(8, 1) ⊕ ( 1, 8)] baryon fields. Again, no diagonal and only one off-diagonal chiral SU L (3) × SU R (3) interaction of this type is allowed, that turns out also to conserve the U A (1) symmetry. We calculate the F /D ratios for the baryons' anomalous magnetic moments predicted by these interactions in the SU (3) symmetry limit and find that only the [(6, 3) ⊕ (3, 6)]-[(3, 3) ⊕ (3, 3)] one reproduces F /D = 1/3, in close proximity to the value extracted from experiment.

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Chiral Algebra, Configuration Mixing, and Magnetic Moments

Cited by 53 publications

References 12 publications

Baryon fields withUL(3)×UR(3)chiral symmetry. III. Interactions with chiral
Chen
¹
,
Dmitrašinović
²

2011
Phys. Rev. D

Baryon fields withUL(3)×UR(3)chiral symmetry. III. Interactions with chiral
Chen
¹
,
Dmitrašinović
²

2011
Phys. Rev. D

Baryon fields withUL(3)×UR(3)chiral symmetry. V. Pion-nucleon and kaon-nucleon
Dmitrašinović¹,
Chen²
2016
Phys. Rev. C

Baryon fields with UL(3)×UR(3)chiral s

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Chiral Algebra, Configuration Mixing, and Magnetic Moments

Cited by 53 publications

References 12 publications

Baryon fields withUL(3)×UR(3)chiral symmetry. III. Interactions with chiralChen1, Dmitrašinović2 2011Phys. Rev. D

Baryon fields withUL(3)×UR(3)chiral symmetry. III. Interactions with chiralChen1, Dmitrašinović2 2011Phys. Rev. D

Baryon fields withUL(3)×UR(3)chiral symmetry. V. Pion-nucleon and kaon-nucleonDmitrašinović1, Chen2 2016Phys. Rev. C

Baryon fields with UL(3)×UR(3)chiral s

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Product

Resources

About

Baryon fields withUL(3)×UR(3)chiral symmetry. III. Interactions with chiral
Chen
¹
,
Dmitrašinović
²

2011
Phys. Rev. D

Baryon fields withUL(3)×UR(3)chiral symmetry. III. Interactions with chiral
Chen
¹
,
Dmitrašinović
²

2011
Phys. Rev. D

Baryon fields withUL(3)×UR(3)chiral symmetry. V. Pion-nucleon and kaon-nucleon
Dmitrašinović¹,
Chen²
2016
Phys. Rev. C