Chiral perturbation theory to one loop

Gasser, J.; Leutwyler, H.

doi:10.1016/0003-4916(84)90242-2

Cited by 4,314 publications

(7,240 citation statements)

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“…iii) The third source of error is the T -matrix used to build the spectral function Eq. (65) for s < s 1 . Three different models of T -matrix have been used [32,33,31].…”

Section: Estimate Of X(3) and Of Lec'smentioning

confidence: 97%

“…However, their determination remains a particularly awkward problem. In most cases [1,[3][4][5][6], their values have been inferred from observables for the pseudoscalar mesons, with the help of two assumptions: (1) the quark condensate is the dominant order parameter to describe the Spontaneous Breakdown of Chiral Symmetry (SBχS) [1], and (2) the pattern of SBχS agrees correctly with a large-N c description of QCD [7], in which quantum fluctuations are treated as small perturbations.…”

Section: Introductionmentioning

confidence: 99%

“…This determination starts with quark mass expansion of measured observables such as F 2 π M 2 π or F 2 K M 2 K , using Chiral Perturbation Theory (χPT) [1]:…”

Section: Introductionmentioning

confidence: 99%

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Zweig rule violation in the scalar sector and values of low-energy constants

Descotes

2001

J. High Energy Phys.

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We discuss the role of the Zweig rule (ZR) violation in the scalar channel for the determination of low-energy constants and condensates arising in the effective chiral Lagrangian of QCD. The analysis of the Goldstone boson masses and decay constants shows that the three-flavor condensate and some low-energy constants are very sensitive to the value of the ZR violating constant L 6 . A similar study is performed in the case of the decay constants. A chiral sum rule based on experimental data in the 0 ++ channel is used to constrain L 6 , indicating a significant decrease between the two-and the three-flavor condensates. The analysis of the scalar form factors of the pion at zero momentum suggests that the pseudoscalar decay constant could also be suppressed from N f = 2 to 3.

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“…iii) The third source of error is the T -matrix used to build the spectral function Eq. (65) for s < s 1 . Three different models of T -matrix have been used [32,33,31].…”

Section: Estimate Of X(3) and Of Lec'smentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Zweig rule violation in the scalar sector and values of low-energy constants

Descotes

2001

J. High Energy Phys.

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“…2 In this form, and once the topological charge is known, the calculation of the quark condensate requires the computation of the propagator in the sector without zero modes only [7].…”

Section: Numerical Estimatormentioning

confidence: 99%

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

Giusti¹,

Necco²

2007

J. High Energy Phys.

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Spontaneous chiral symmetry breaking in QCD with massless quarks at infinite volume can be seen in a finite box by studying, for instance, the dependence of the chiral condensate from the volume and the quark mass. We perform a feasibility study of this program by computing the quark condensate on the lattice in the quenched approximation of QCD at small quark masses. We carry out simulations in various topological sectors of the theory at several volumes, quark masses and lattice spacings by employing fermions with an exact chiral symmetry, and we focus on observables which are infrared stable and free from mass-dependent ultraviolet divergences. The numerical calculation is carried out with an exact variance-reduction technique, which is designed to be particularly efficient when spontaneous symmetry breaking is at work in generating a few very small low-lying eigenvalues of the Dirac operator. The finite-size scaling behaviour of the condensate in the topological sectors considered agrees, within our statistical accuracy, with the expectations of the chiral effective theory. Close to the chiral limit we observe a detailed agreement with the first Leutwyler-Smilga sum rule. By comparing the mass, the volume and the topology dependence of our results with the predictions of the chiral effective theory, we extract the corresponding low-energy constant.

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“…It has long been realized that ChPT may be employed to study SU (3) breaking effects on the MMs of the baryon octet. The first effort was undertaken by Caldi and Pagels in 1974 [11] , even before ChPT as we know today was formulated.…”

Section: Introductionmentioning

confidence: 99%

Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

Geng¹,

Camalich²,

Alvarez‐Ruso³

et al. 2010

Chinese Phys. C

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We review some recent progress in our understanding of the lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments (MMs) in terms of Chiral Perturbation Theory (ChPT). In particular, we show that at next-to-leading-order ChPT can describe the MMs of the octet baryons quite well. We also make predictions for the decuplet MMs at the same chiral order. Among them, the MMs of the ∆ ++ and ∆ + are found to agree well with data within the experimental uncertainties.

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Chiral perturbation theory to one loop

Cited by 4,314 publications

References 103 publications

Zweig rule violation in the scalar sector and values of low-energy constants

Zweig rule violation in the scalar sector and values of low-energy constants

Spontaneous chiral symmetry breaking in QCD: a finite-size scaling study on the lattice

Lowest-lying spin-1/2 and spin-3/2 baryon magnetic moments in chiral perturbation theory

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