Strong Λπ phase shifts for CP violation in weak Ξ → Λπ decay

Lu, M.; Wise, Mark B.; Savage, Martin J.

doi:10.1016/0370-2693(94)91456-7

Cited by 30 publications

(38 citation statements)

References 12 publications

(17 reference statements)

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“…(8). This number is consistent with earlier findings in CHPT (or extensions thereof) [4][5][6][7][8]. We have also shown why the K-matrix approach of ref.…”

supporting

confidence: 92%

“…consistent with earlier CHPT findings [4][5][6][7][8]. We should stress that set I gives the better fit in theKN sector and should be preferred.…”

supporting

confidence: 89%

“…To extract the CP violating phase, one has to know the strong Λπ S-and P-wave phase shifts at the mass of the cascade, denoted δ 0 and δ 1 , respectively. While earlier calculations [2,3] were inconclusive on the value of δ 0 , a leading order heavy baryon chiral perturbation theory (HBCHPT) analysis led to a vanishing S-wave phase shift [4] and corrections including excited Σ intermediate states were shown to give a bound of δ 0 ∼ 0.5 • [4,5]. Relativistic tree level calculations have also been performed, leading to a somewhat larger band of values for δ 0 , but still |δ 0 | ≤ 2 • [6,7].…”

mentioning

confidence: 98%

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S-waveΛπphase shift is not large

Meißner¹,

Oller²

2001

Phys. Rev. D

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We study the strong interaction S-wave Λπ phase shift in the region of the Ξ mass in the framework of a relativistic chiral unitary approach based on coupled channels. All parameters have been previously determined in a fit to strangeness S = −1 S-wave kaon-nucleon data. We find 0 • ≤ δ0 ≤ 1.1 • in agreement with previous chiral perturbation theory calculations (or extensions thereof). We also discuss why a recent coupled channel K-matrix calculation gives a result for δ0 that is negative and much bigger in magnitude. We argue why that value should not be trusted.PACS numbers: 13.75. Gx, 13.30.Eg, 12.39.Fe 1. Direct CP violation can be measured in the decay Ξ → Λπ → pππ (for a recent experiment, see [1]). To extract the CP violating phase, one has to know the strong Λπ S-and P-wave phase shifts at the mass of the cascade, denoted δ 0 and δ 1 , respectively. While earlier calculations [2,3] were inconclusive on the value of δ 0 , a leading order heavy baryon chiral perturbation theory (HBCHPT) analysis led to a vanishing S-wave phase shift [4] and corrections including excited Σ intermediate states were shown to give a bound of δ 0 ∼ 0.5 • [4,5]. Relativistic tree level calculations have also been performed, leading to a somewhat larger band of values for δ 0 , but still |δ 0 | ≤ 2 • [6,7]. A more recent calculation using also dimension two operators [8] with the corresponding lowenergy constants fixed from kaon-nucleon scattering [9] gave the range −3.0 • ≤ δ 0 ≤ +0.4 • . * In that paper, the effect of channel coupling was also investigated, based on the observation that in SU(3), the Λπ state is coupled to the Σπ, NK, Ση and ΞK states with strangeness S = −1 and isospin I = 1. A K-matrix approach was used to calculate the channel coupling effects and a surprisingly large δ 0 ≃ −7 • was found. The authors of ref. [8] have been careful to point out that more refined coupled channel calculations based on chiral perturbation theory (CHPT) are necessary to further clarify this surprising result. We have recently presented a novel relativistic chiral unitary approach based on coupled channels [11]. Dispersion relations are used to perform the necessary resummation of the lowest order relativistic chiral Lagrangian. Within this framework, the S-wave kaon-nucleon interactions for strangeness S = −1 were studied and a good description of the data in the K − p, πΣ and πΛ channels (cross sections, threshold ratios, mass distribution in the region of the Λ(1405)) was obtained. This method can be systematically extended to higher orders, emphasizing its applicability to any scenario of strong self-interactions where the perturbative series diverges even at low energies. It is straightforward * Note that the parameters obtained in [9] need to be taken with some care since the important η channels were not considered, as stressed in [10].to project out the Λπ → Λπ amplitude from our coupled channel solutions and extract in a parameter-free manner the corresponding S-wave phase shift. This is done here. To close the introducti...

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“…(8). This number is consistent with earlier findings in CHPT (or extensions thereof) [4][5][6][7][8]. We have also shown why the K-matrix approach of ref.…”

supporting

confidence: 92%

“…consistent with earlier CHPT findings [4][5][6][7][8]. We should stress that set I gives the better fit in theKN sector and should be preferred.…”

supporting

confidence: 89%

mentioning

confidence: 98%

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S-waveΛπphase shift is not large

Meißner¹,

Oller²

2001

Phys. Rev. D

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“…In contrast, the strong Λπ scattering phases have not been measured. Modern calculations based on chiral perturbation theory indicate that these phases are small, with δ Ξ S being at most 7 • [12][13][14][15][16][17]. For our numerical estimates, we will allow the Λπ phases to vary within the range obtained at next-to-leading order in heavy-baryon chiral perturbation theory [15],…”

Section: Introductionmentioning

confidence: 99%

CPviolation in hyperon nonleptonic decays within the standard model

Tandean

Valencia

2003

Phys. Rev. D

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We calculate the CP -violating asymmetries A(Λ 0 − ) and A(Ξ − − ) in nonleptonic hyperon decay within the Standard Model using the framework of heavy-baryon chiral perturbation theory (χPT). We identify those terms that correspond to previous calculations and discover several errors in the existing literature. We present a new result for the lowest-order (in χPT) contribution of the penguin operator to these asymmetries, as well as an estimate for the uncertainty of our result that is based on the calculation of the leading nonanalytic corrections. ‡ Present address.

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“…The K − n interaction is important for the description of kaon condensation in the interior of neutron stars [17], and meson-baryon interactions are essential input in determining the final-state interactions of various decays that are interesting for standardmodel phenomenology (See Ref. [18] for an example). In determining baryon excited states on the lattice, it is clear that the energy levels that represent meson-baryon scattering on the finite-volume lattice must be resolved before progress can be made regarding the extraction of single-particle excitations.…”

Section: Meson-baryon Interactionsmentioning

confidence: 99%