Analysis and interpretation of new low-energy 
                $\pi\pi$
               scattering data

Descotes, Sebastien; Fuchs, Norman H.; Girlanda, L.; Stern, J.

doi:10.1007/s10052-002-0965-3

Cited by 117 publications

(167 citation statements)

References 33 publications

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“…We see that in absence of isospin breaking, larger values of a 0 0 are preferred, which brings in better agreement the extended fit (including data in I = 2 channel) with the scalar fit. Once isospin-breaking corrections are included, one recovers the mild discrepancy previously observed between these two kinds of fits [26], whereas the larger uncertainty of the S-P fit covers both solutions.…”

Section: Re-analysis Of Na48/2 Resultssupporting

confidence: 70%

“…A first analysis using the Roy equations together with a theoretical estimate of the scalar radius of the pion led to a determination of the scattering lengths in close agreement with the predictions from two-loop χPT [25]. Another analysis of the data available at that time (including I = 2 low-energy phase shifts) favoured a slightly larger value for a 2 0 , 1 σ away from the two-loop χPT prediction [26]. Recently, the NA48/2 collaboration has performed a remarkable work in collecting high-statistics K ± e4 data at the CERN SPS [27,28].…”

Section: Introductionmentioning

confidence: 65%

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Isospin breaking in the phases of the K e4 form factors

2013

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Isospin breaking in the K ℓ4 form factors induced by the difference between charged and neutral pion masses is studied. Starting from suitably subtracted dispersion representations, the form factors are constructed in an iterative way up to two loops in the low-energy expansion by implementing analyticity, crossing, and unitarity due to two-meson intermediate states. Analytical expressions for the phases of the two-loop form factors of the K ± → π + π − e ± νe channel are given, allowing one to connect the difference of form-factor phase shifts measured experimentally (out of the isospin limit) and the difference of S-and P -wave ππ phase shifts studied theoretically (in the isospin limit). The isospin-breaking correction consists of the sum of a universal part, involving only ππ rescattering, and a process-dependent contribution, involving the form factors in the coupled channels. The dependence on the two S-wave scattering lengths a 0 0 and a 2 0 in the isospin limit is worked out in a general way, in contrast to previous analyses based on one-loop chiral perturbation theory. The latter is used only to assess the subtraction constants involved in the dispersive approach. The two-loop universal and process-dependent contributions are estimated and cancel partially to yield an isospin-breaking correction close to the one-loop case. The recent results on the phases of K ± → π + π − e ± νe form factors obtained by the NA48/2 collaboration at the CERN SPS are reanalysed including this isospin-breaking correction to extract values for the scattering lengths a 0 0 and a 2 0 , as well as for low-energy constants and order parameters of two-flavour χPT.

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Section: Re-analysis Of Na48/2 Resultssupporting

confidence: 70%

Section: Introductionmentioning

confidence: 65%

Isospin breaking in the phases of the K e4 form factors

2013

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“…As in our previous work, L 4 and L 6 do not show any sign of Zweig suppression and the competition between LO and NLO in three-flavour chiral expansions is clearly seen. We obtain values for the N f = 2 chiral order parameters in agreement with expectations from two-flavour chiral perturbation theory [13] as well as experimental information on ππ scattering, such as that from K l4 decays [1][2][3][4][5][6][7]. The values ofl 3 andl 4 given there can be compared to the one obtained from the RBC/UKQCD collaboration, ref.…”

Section: Jhep06(2012)051supporting

confidence: 81%

“…[48]. 2 As indicated by eqs. (1.3) and (1.5), the propagation and coupling of the π 0 and η mesons will play a particular role for the analysis of the topological susceptibility.…”

Section: Resummed Chiral Perturbation Theory and η Observablesmentioning

confidence: 98%

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Topological susceptibility on the lattice and the three-flavour quark condensate

Bernard

Descotes-Genon

Toucas

2012

J. High Energ. Phys.

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We reanalyse the topological susceptibility assuming the possibility of a significant paramagnetic suppression of the three-flavour quark condensate and a correlated enhancement of vacuum fluctuations of ss pairs. Using the framework of resummed χPT, we point out that simulations performed near the physical point, with a significant mass hierarchy between u, d and s dynamical quarks, are not able to disentangle the contributions from the quark condensate and sea ss-pair fluctuations, and that simulations with three light quark masses of the same order are better suited for this purpose. We perform a combined fit of recent RBC/UKQCD data on pseudoscalar masses and decay constants as well as the topological susceptibility, and we reconsider the determination of lattice spacings in our framework, working out the consequences on the parameters of the chiral Lagrangian. We obtain (Σ(3; 2 GeV)) 1/3 = 243 ± 12 MeV for the three-flavour quark condensate in the chiral limit. We notice a significant suppression compared to the twoflavour quark condensate Σ(2; 2 GeV)/Σ(3; 2 GeV) = 1.51 ± 0.11 and we confirm previous findings of a competition between leading order and next-to-leading order contributions in three-flavour chiral series.

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Chiral dynamics with strange quarks in the light of recent lattice simulations

Bernard

Descotes-Genon

Toucas

2011

J. High Energ. Phys.

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Several lattice collaborations performing simulations with 2+1 light dynamical quarks have experienced difficulties in fitting their data with standard N f = 3 chiral expansions at next-to-leading order, yielding low values of the quark condensate and/or the decay constant in the N f = 3 chiral limit. A reordering of these expansions seems required to analyse these data in a consistent way. We discuss such a reordering, known as Resummed Chiral Perturbation Theory, in the case of pseudoscalar masses and decay constants, pion and kaon electromagnetic form factors and K ℓ3 form factors. We show that it provides a good fit of the recent results of two lattice collaborations (PACS-CS and RBC/UKQCD). We describe the emerging picture for the pattern of chiral symmetry breaking, marked by a strong dependence of the observables on the strange quark mass and thus a significant difference between chiral symmetry breaking in the N f = 2 and N f = 3 chiral limits. We discuss the consequences for the ratio of decay constants F K /F π and the K ℓ3 form factor at vanishing momentum transfer.

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Analysis and interpretation of new low-energy $\pi\pi$ scattering data

Cited by 117 publications

References 33 publications

Isospin breaking in the phases of the K e4 form factors

Isospin breaking in the phases of the K e4 form factors

Topological susceptibility on the lattice and the three-flavour quark condensate

Chiral dynamics with strange quarks in the light of recent lattice simulations

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