Decuplet Contributions Research Articles

Octet-baryon axial-vector charges andSU(3)-breaking effects in the semileptonic hyperon decays

The octet-baryon axial-vector charges and the g1/f1 ratios measured in the semileptonic hyperon decays are studied up to O(p^3) using the covariant baryon chiral perturbation theory with explicit decuplet contributions. We clarify the role of different low-energy constants and find a good convergence for the chiral expansion of the axial-vector charges of the baryon octet, g1(0), with O(p^3) corrections typically around 20% of the leading ones. This is a consequence of strong cancellations between different next-to-leading order terms. We show that considering only non-analytic terms is not enough and that analytic terms appearing at the same chiral order play an important role in this description. The same effects still hold for the chiral extrapolation of the axial-vector charges and result in a rather mild quark-mass dependence. As a result, we report a determination of the leading order chiral couplings, D=0.623(61)(17) and F=0.441(47)(2), as obtained from a completely consistent chiral analysis up to O(p^3). Furthermore, we note that the appearance of an unknown low-energy constant precludes the extraction of the proton octet-charge from semileptonic decay data alone, which is relevant for an analysis of the composition of the proton spin.

SU(3)-breaking corrections to the hyperon vector couplingf1(0)in covariant baryon chiral perturbation theory

We report on a recent study of the SU(3)-breaking corrections to the hyperon vector coupling $f_1(0)$ up to $\mathcal{O}(p^4)$ in covariant baryon chiral perturbation theory with dynamical octet and decuplet contributions. The decuplet contributions are taken into account for the first time in a covariant ChPT study and are found of similar or even larger size than the octet ones. We predict positive SU(3)-breaking corrections to all the four independent $f_1(0)$'s (assuming isospin symmetry), which are consistent, within uncertainties, with the latest results from large $N_c$ fits, chiral quark models, and quenched lattice QCD calculations. We also discuss briefly the implications of our results for the extraction of $V_{us}$ from hyperon decay data.

Leading-order decuplet contributions to the baryon magnetic moments in chiral perturbation theory

We extend an earlier study of the baryon magnetic moments in chiral perturbation theory by the explicit inclusion of the spin-3/2 decuplet resonances. We find that the corrections induced by these heavier degrees of freedom are relatively small in a covariant framework where unphysical spin-1/2 modes are removed. Consequently, implementing the leading SU(3)-breaking corrections given by both the baryon and decuplet contributions, we obtain a description of the baryon-octet magnetic moments that is better than the Coleman–Glashow relations. Finally, we discuss the uncertainties and compare between heavy baryon and covariant approaches.

Δ contribution to the parity-violating nucleon-nucleon force**Supported by National Natural Science Foundation of China (10625521, 10721063, 10775146), China Postdoctoral Science Foundation (20070420526) and Ministry of Education of China

Because the nucleon may be excited and transformed into a virtual Δ resonance easily, we consider the decuplet contribution to the parity-violating (PV) nucleon-nucleon interaction in the chiral effective field theory. The effective PV nucleon-nucleon potential is derived without introducing any unknown coupling constants.

Decuplet contribution to the meson–baryon scattering lengths

We calculate decuplet contributions to the s-wave pseudoscalar meson octet–baryon scattering lengths to the third order in heavy baryon chiral perturbation theory (HBχPT). Using experimental pion–nucleon and kaon–nucleon scattering lengths as inputs, we determine low-energy constants and predict other meson–baryon scattering lengths. Numerically we consider three cases: (1) the case with only baryon octet contributions; (2) with decuplet contributions and (3) in the large Nc limit. Hopefully, the analytical expressions and the predictions are helpful to future investigations of the meson–baryon scattering lengths.

First lattice QCD study of the [formula omitted] axial and vector form factors with [formula omitted] breaking corrections

We present the first quenched lattice QCD study of the form factors relevant for the hyperon semileptonic decay Σ − → n ℓ ν . The momentum dependence of both axial and vector form factors is investigated and the values of all the form factors at zero-momentum transfer are presented. Following the same strategy already applied to the decay K 0 → π − ℓ ν , the SU ( 3 ) -breaking corrections to the vector form factor at zero-momentum transfer, f 1 ( 0 ) , are determined with great statistical accuracy in the regime of the simulated quark masses, which correspond to pion masses above ≈ 0.7 GeV . Besides f 1 ( 0 ) also the axial to vector ratio g 1 ( 0 ) / f 1 ( 0 ) , which is relevant for the extraction of the CKM matrix element V u s , is determined with significant accuracy. Due to the heavy masses involved, a polynomial extrapolation, which does not include the effects of meson loops, is performed down to the physical quark masses, obtaining f 1 ( 0 ) = − 0.948 ± 0.029 and g 1 ( 0 ) / f 1 ( 0 ) = − 0.287 ± 0.052 , where the uncertainties do not include the quenching effect. Adding a recent next-to-leading order determination of chiral loops, calculated within the Heavy Baryon Chiral Perturbation Theory in the approximation of neglecting the decuplet contribution, we obtain f 1 ( 0 ) = − 0.988 ± 0.029 lattice ± 0.040 HBChPT . Our findings indicate that SU ( 3 ) -breaking corrections are moderate on both f 1 ( 0 ) and g 1 ( 0 ) . They also favor the experimental scenario in which the weak electricity form factor, g 2 ( 0 ) , is large and positive, and correspondingly the value of | g 1 ( 0 ) / f 1 ( 0 ) | is reduced with respect to the one obtained with the conventional assumption g 2 ( q 2 ) = 0 based on exact SU ( 3 ) symmetry.

Long distance regularization in chiral perturbation theory with decuplet fields

We investigate the use of long distance regularization in $\mathrm{SU}(3)$ baryon chiral perturbation theory with decuplet fields. The one-loop decuplet contributions to the octet baryon masses, axial-vector couplings, S-wave nonleptonic hyperon decays and magnetic moments are evaluated in a chirally consistent fashion by employing a cutoff to implement long distance regularization. The convergence of the chiral expansions of these quantities is improved compared to the dimensionally regularized version which indicates that the propagation of Goldstone bosons over distances smaller than a typical hadronic size, which is beyond the regime of chiral perturbation theory but included by dimensional regularization, is removed by use of a cutoff.

Recoil order chiral corrections to baryon octet axial vector currents and largeNcQCD

We compute the chiral corrections to octet baryon axial vector currents through $\mathcal{O}{(p}^{3})$ in heavy baryon chiral perturbation theory, including both octet and decuplet baryon intermediate states. We include the latter in a consistent way by using the small scale expansion. We find that, in contrast to the situation at $\mathcal{O}{(p}^{2}),$ there exist no cancellations between octet and decuplet contributions at $\mathcal{O}{(p}^{3}).$ Consequently, the $\mathcal{O}{(p}^{3})$ corrections spoil the expected scaling behavior of the chiral expansion. We discuss this result in terms of the ${1/N}_{c}$ expansion. We also consider the implications for the determination of the strange quark contribution to the nucleon spin from polarized deep inelastic scattering data.

Baryon octet magnetic moments in chiral perturbation theory: More on the importance of the decuplet

We address the impact of treating the decuplet of spin-3/2 baryons as an explicit degree of freedom in the chiral expansion of the magnetic moments of the octet of spin-1/2 baryons. We carry out a complete calculation of the octet moments to O(1/\lamchic), including decuplet contributions to the chiral loops. In contrast to results of previous analyses, we find that inclusion of the decuplet preserves the convergence behavior of the chiral expansion implied by power counting arguments.

Chiral perturbation theory analysis of the baryon magnetic moments reexamined

We reexamine critically the chiral expansion for the baryon magnetic moments including the contributions from loops which involve intermediate octet and decuplet baryons. We find that, contrary to some claims, the nonanalytic loop contributions of orders $m_s^{1/2}$ and $m_s ln m_s$ are of the same general size because of large coupling factors for the latter, and that the decuplet contributions are as large as the octet contributions and must be included in a consistent calculation. There is no clear evidence of the convergence of the chiral series. The adequacy of the theory will not be established until dynamical models are able to calculate the contributions from the counterterms that largely hide the loop effects in fits to the data.

Decuplet contributions to hyperon axial vector form factors

We consider the predictions of chiral perturbation theory for SU (3) breaking in the axial vector form factor g 1 measured in semileptonic hyperon decays. Including only octet baryon intermediate states, the non-analytic correlations are ∼ 100%. These corrections are dominated by an SU (3)-symmetric wavefunction renormalization, which explains the fact that the “corrected” predictions still fit the data well. We argue that the large corrections are nonetheless strong evidence that the chiral expansion is breaking down. We theninclude decuplet baryon intermediate states. We find that the effects of a non-zero octet-decuplet mass difference, Δ, significantly changes the pattern of corrections from the Δ = 0 case. The decuplet corrections can cancel the large octet contributions in a non-trivial way, but the corrections no longer favor the SU (6) values of the axial couplings. We also argue the D and F axial couplings cannot be reliably extracted from calculations which keep only the non-analytic corrections.

Nonleptonic and Weak-Electromagnetic Decays of Hyperons in the Pole Model

An estimate is made for the contribution of the decuplet poles to the weak decays of hyperons using the Rarita-Schwinger formalism for spin-$\frac{3}{2}$ fields. $\mathrm{SU}(3)$ symmetry is used in conjunction with the Gourdin-Salin model for the $D\ensuremath{-}B\ensuremath{-}\ensuremath{\pi}$ and $D\ensuremath{-}B\ensuremath{-}\ensuremath{\gamma}$ couplings. It is shown that the decuplet contribution is large for the parity-violating amplitudes. For weak-electromagnetic decays, this predicts asymmetry parameters which are at variance with earlier calculations. The decay rate for ${\ensuremath{\Sigma}}^{+}\ensuremath{\rightarrow}p\ensuremath{\gamma}$ agrees well with the experimental result.

Parity-Violating Hyperon Decays inSU(3)

It is shown that any $\mathrm{SU}(3)$ model with (i) $\mathrm{CP}$ invariance, (ii) the weak current in an octet, and (iii) vanishing decuplet contributions, reproduces the experimental results on the parity-violating hyperon decays in terms of one parameter. Beyond the $\ensuremath{\Delta}I=\frac{1}{2}$ restrictions, such a model gives three relations among the remaining four independent observable amplitudes, which are well satisfied experimentally.

SU(6) predictions from Adler-Weisbarger sum rules and the Johnson-Treiman relations

Adler-Weisberger sum rules obtained from U(3) × U(3) are approximated by the decouplet for the low energy scattering while the high-energy continuum is taken to satisfy the Johnson-Treiman relations. This leads to the SU(6) prediction for the meson-baryon d/f ratio and a sum for the decuplet contribution.