Theoretical aspects of Chiral Dynamics

Leutwyler, H.

doi:10.22323/1.253.0022

Cited by 13 publications

(17 citation statements)

References 90 publications

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“…In the one-channel Khuri-Treiman framework, both M 0 and M 2 are usually assumed to behave linearly in w when w → ∞. With this asymptotic behaviour, there is 1 It is convenient to formally factor out L but the amplitude is actually of the form…”

Section: Single-variable Amplitudes For η → 3πmentioning

confidence: 99%

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Extended chiral Khuri–Treiman formalism for $$\eta \rightarrow 3\pi $$ η → 3 π and the role of the $$a_0(980)$$ a 0 ( 980 ) , $$f_0(980)$$ f 0 ( 980 ) resonances

Albaladejo

Moussallam

2017

Eur. Phys. J. C

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Recent experiments on η → 3π decays have provided an extremely precise knowledge of the amplitudes across the Dalitz region which represent stringent constraints on theoretical descriptions. We reconsider an approach in which the low-energy chiral expansion is assumed to be optimally convergent in an unphysical region surrounding the Adler zero, and the amplitude in the physical region is uniquely deduced by an analyticity-based extrapolation using the Khuri-Treiman dispersive formalism. We present an extension of the usual formalism which implements the leading inelastic effects from the KK channel in the finalstate ππ interaction as well as in the initial-state ηπ interaction. The constructed amplitude has an enlarged region of validity and accounts in a realistic way for the influence of the two light scalar resonances f 0 (980) and a 0 (980) in the dispersive integrals. It is shown that the effect of these resonances in the low-energy region of the η → 3π decay is not negligible, in particular for the 3π 0 mode, and improves the description of the energy variation across the Dalitz plot. Some remarks are made on the scale dependence and the value of the double quark mass ratio Q.

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Section: Single-variable Amplitudes For η → 3πmentioning

confidence: 99%

“…The low-energy dynamics can then be described accurately through an expansion built from a chiral effective theory (e.g. [1] for a recent review). This approach, which applies in both the Euclidean and the Minkowski space-times is, to some extent, complementary to the purely numerical lattice simulation method.…”

Section: Introductionmentioning

confidence: 99%

Extended chiral Khuri–Treiman formalism for $$\eta \rightarrow 3\pi $$ η → 3 π and the role of the $$a_0(980)$$ a 0 ( 980 ) , $$f_0(980)$$ f 0 ( 980 ) resonances

Albaladejo

Moussallam

2017

Eur. Phys. J. C

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“…Discussions on the application of ChPT to the determination of σ πN can be found, for example, in Ref. [79]. 10 The lower limit can be obtained by extrapolating from the mπ ∼ 150 MeV point using σ πN = −4c 1 m 2 π − 9g 2 A m 3 π /(64πF 2 π ), and ignoring higher order corrections that are in the opposite direction.…”

Section: Comparison With Other Recent Determinations Of σπN and Ft Smentioning

confidence: 99%

Direct determinations of the nucleon and pionσterms at nearly physical quark masses

et al. 2016

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We present a high statistics study of the pion and nucleon light and strange quark sigma terms using N f = 2 dynamical non-perturbatively improved clover fermions with a range of pion masses down to mπ ∼ 150 MeV and several volumes, Lmπ = 3.4 up to 6.7, and lattice spacings, a = 0.06 − 0.08 fm, enabling a study of finite volume and discretisation effects for mπ 260 MeV. Systematics are found to be reasonably under control. For the nucleon we obtain σπN = 35(6) MeV and σs = 35(12) MeV, or equivalently in terms of the quark fractions, fT u = 0.021(4), fT d = 0.016(4) and fT s = 0.037(13), where the errors include estimates of both the systematic and statistical uncertainties. These values, together with perturbative matching in the heavy quark limit, lead to fT c = 0.075(4), fT b = 0.072(2) and fT t = 0.070(1). In addition, through the use of the (inverse) Feynman-Hellmann theorem our results for σπN are shown to be consistent with the nucleon masses determined in the analysis. For the pion we implement a method which greatly reduces excited state contamination to the scalar matrix elements from states travelling across the temporal boundary. This enables us to demonstrate the Gell-Mann-Oakes-Renner expectation σπ = mπ/2 over our range of pion masses.2 Note that for the nucleon we apply the parity projection operator 1 2 [1 + sign(t f − t i )γ 4 ].

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“…[15,81] (see also ref. [82] for related discussion). The large estimated theoretical error comes from the delta-loop diagram contributions by using eq.…”

Section: Jhep05(2016)038mentioning

confidence: 99%

Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

Yao

Siemens

Bernard

et al. 2016

J. High Energ. Phys.

100

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We present the results of a third order calculation of the pion-nucleon scattering amplitude in a chiral effective field theory with pions, nucleons and delta resonances as explicit degrees of freedom. We work in a manifestly Lorentz invariant formulation of baryon chiral perturbation theory using dimensional regularization and the extended on-mass-shell renormalization scheme. In the delta resonance sector, the on mass-shell renormalization is realized as a complex-mass scheme. By fitting the low-energy constants of the effective Lagrangian to the S-and P -partial waves a satisfactory description of the phase shifts from the analysis of the Roy-Steiner equations is obtained. We predict the phase shifts for the D and F waves and compare them with the results of the analysis of the George Washington University group. The threshold parameters are calculated both in the delta-less and delta-full cases. Based on the determined low-energy constants, we discuss the pion-nucleon sigma term. Additionally, in order to determine the strangeness content of the nucleon, we calculate the octet baryon masses in the presence of decuplet resonances up to next-to-next-to-leading order in SU(3) baryon chiral perturbation theory. The octet baryon sigma terms are predicted as a byproduct of this calculation.

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Theoretical aspects of Chiral Dynamics

Cited by 13 publications

References 90 publications

Extended chiral Khuri–Treiman formalism for $$\eta \rightarrow 3\pi $$ η → 3 π and the role of the $$a_0(980)$$ a 0 ( 980 ) , $$f_0(980)$$ f 0 ( 980 ) resonances

Extended chiral Khuri–Treiman formalism for $$\eta \rightarrow 3\pi $$ η → 3 π and the role of the $$a_0(980)$$ a 0 ( 980 ) , $$f_0(980)$$ f 0 ( 980 ) resonances

Direct determinations of the nucleon and pionσterms at nearly physical quark masses

Pion-nucleon scattering in covariant baryon chiral perturbation theory with explicit Delta resonances

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