Erratum: New Measurement of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>K</mml:mi><mml:mrow><mml:mi>e</mml:mi><mml:mn>4</mml:mn></mml:mrow><mml:mo>+</mml:mo></mml:msubsup></mml:math>Decay and the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>s</mml:mi></mml:math>-Wave<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>π</mml:mi><mml:mi>π</mml:mi></mml:math>Scattering Length<mml:math xmlns:mml=

Pislak, S.; Appel, R.; Atoyan, G. S.; Bassalleck, B.; Bergman, D. R.; Cheung, N.W.; Dhawan, S. K.; Do, Hyo-Sang; Egger, J.; Eilerts, S.; Fischer, H.; Herold, W.; Issakov, Vadim; Kaspar, H.; Kraus, D.; Lazarus, D. M.; Lichard, P.; Lowe, J.; Lozano, J.; Ma, H.L.; Majid, Walid A.; Poblaguev, A.; Řehák, P.; Sher, A.; Thompson, J.; Truöl, P.; Zeller, M.

doi:10.1103/physrevlett.105.019901

Cited by 83 publications

(157 citation statements)

References 5 publications

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“…We will use our computation of the isospin-breaking correction ∆ IB (s, s ℓ ) as a function of the two scattering lengths a 0 0 and a 2 0 to perform an analysis of the available phase shifts from K ± e4 decays, as provided by the old Geneva-Saclay experiment [23], the BNL-E865 experiment [24], and finally the quite recent NA48/2 experiment [27,28] at the CERN SPS. Actually, the high accuracy of the latter analysis dominates completely the discussion, and we will only consider the data coming from NA48/2 in the following.…”

Section: Re-analysis Of Na48/2 Resultsmentioning

confidence: 99%

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 Resultsmentioning

confidence: 99%

Isospin breaking in the phases of the K e4 form factors

2013

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“…We see that one and the same production amplitude T (x 1 , x 2 ; α) or τ P (x; α), corresponding to the space-time representation, enters into relations (5) and (6). The effect of FSI manifests itself in the fact that the role of the functional basis, which the asymptotic two-particle state is projected on, is transferred from the plane waves to Bethe-Salpeter amplitudes Ψ…”

Section: Formalismmentioning

confidence: 99%

“…The second equality in (6), similar to the one in (5), merely arises after the integration over the pair c.m. coordinate X as a consequence of the factorization of the free c.m.…”

Section: Formalismmentioning

confidence: 99%

Finite-size effect on two-particle production in continuous and discrete spectrum

Lednický

2009

Phys. Part. Nuclei

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Abstract. The formalism allowing one to account for the effect of a finite spacetime extent of particle production region is given. Its applications to the lifetime measurement of hadronic atoms produced by a high-energy beam in a thin target, as well as to the femtoscopy techniques widely used to measure space-time characteristics of the production processes, are discussed. Particularly, it is found that the neglect of the finite-size effect on the pionium lifetime measurement in the experiment DIRAC at CERN could lead to the lifetime overestimation comparable with the 10% statistical error. The theoretical systematic errors arising in the calculation of the finite-size effect due to the neglect of non-equal emission times in the pair center-of-mass system, the space-time coherence and the residual charge are shown to be negligible.

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“…In the meantime, the chiral perturbation series of the scattering amplitude has been worked out to NNLO [17] and, matching the chiral and dispersive representations, a very sharp prediction for the scattering lengths was obtained: a 0 0 = 0.220(5), a 2 0 = −0.0444(10) [13]. While the K e4 data of E865 [18], the DIRAC experiment [19] and the NA48 data on the cusp in K → 3π [20] all confirmed the theoretical expectations, the most precise source of information, the beautiful K e4 data of NA48 [21], gave rise to a puzzle. This experiment exploits the fact that -if the electromagnetic interaction and the difference between m u and m d are neglected -the relative phase of the form factors describing the decay K → eνππ coincides with the difference δ 0 0 − δ 1 1 of scattering phase shifts (Watson theorem).…”

Section: Precision Experiments At Low Energymentioning

confidence: 99%

On the low energy end of the QCD spectrum

Leutwyler

2009

Nuclear Physics B - Proceedings Supplements

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The experimental results on the Ke4 and K3π decays, those on pionic atoms and recent work on the lattice confirm the predictions obtained on the basis of χPT. As a result, the energy gap of QCD is now understood very well and there is no doubt that the expansion in powers of the two lightest quark masses does represent a very useful tool for the analysis of the low energy structure. Concerning the expansion in powers of ms, however, the current situation leaves much to be desired. While some of the lattice results indicate, for instance, that the violations of the OkuboIizuka-Zweig rule in the quark condensate and in the decay constants are rather modest, others point in the opposite direction. In view of the remarkable progress being made with the numerical simulation of light quarks, I am confident that the dust will settle soon, so that the effective coupling constants that govern the dependence of the various quantities of physical interest on ms can reliably be determined, to next-to-next-toleading order of the chiral expansion.The range of validity of χPT can be extended by means of dispersive methods. The properties of the physical states occurring in the spectrum of QCD below KK threshold can reliably be investigated on this basis. In particular, as shown only rather recently, general principles of quantum field theory lead to an exact formula that expresses the mass and width of resonances in terms of observable quantities. The formula removes the ambiguities inherent in the analytic continuation from the real axis into the complex plane, which plagued previous determinations of the pole positions of broad resonances. The application to the ππ partial wave amplitude with I = ℓ = 0 shows that there is a resonance in this channel, at Mσ − i 2 Γσ ≃ 441 − i 272 MeV: the lowest resonance of QCD carries the quantum numbers of the vacuum.Talks given at QCD08,

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Erratum: New Measurement ofKe4+Decay and thes-WaveππScattering Length

Cited by 83 publications

References 5 publications

Isospin breaking in the phases of the K e4 form factors

Isospin breaking in the phases of the K e4 form factors

Finite-size effect on two-particle production in continuous and discrete spectrum

On the low energy end of the QCD spectrum

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