Comparison of 
                $\pi K$
               scattering in SU(3) chiral perturbation theory and dispersion relations

Ananthanarayan, B.; Büttiker, P.

doi:10.1007/s100520100629

Cited by 67 publications

(96 citation statements)

References 24 publications

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“…Based on fixed-t and fixed-u dispersion relations for the form factor, we can derive its decomposition into functions of a single variable. Such a decomposition has first been worked out for the ππ scattering amplitude [4] and later for Kπ scattering [5].…”

Section: Decomposition Of the Form Factormentioning

confidence: 99%

A Dispersive Treatment ofK_ℓ4Decays

Colangelo

Passemar

Stoffer

2012

EPJ Web of Conferences

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K 4 are for several reasons an especially interesting decay channel of K mesons:K 4 decays allow an accurate measurement of a combination of S -wave ππ scattering lengths, one form factor of the decay is connected to the chiral anomaly and the decay is the best source for the determination of some low energy constants of ChPT. We present a dispersive approach to K 4 decays, which takes rescattering effects fully into account. Some fits to NA48/2 and E865 measurements and results of the matching to ChPT are shown. MotivationK 4 , the semileptonic decay of a kaon into two pions and a lepton-neutrino pair, plays a crucial role in the context of low energy hadron physics, because it provides almost unique information about some of the O(p 4 ) low energy constants (LECs) of Chiral Perturbation Theory (ChPT), the effective low energy theory of QCD. The physical region of K 4 starts already at the ππ threshold, thus it happens at lower energies than e.g. elastic Kπ scattering. Since ChPT is an expansion in the masses and momenta, it is expected to converge better at lower energies. Therefore K 4 is a particularly interesting process to study.Besides, as the hadronic final state contains two pions, K 4 is also one of the best sources of information on the ππ scattering lengths a 0 0 and a 2 0 [1]. On the experimental side, we are confronted with impressive precision from high statistics measurements. During the last decade, the process has been measured in the E865 experiment at BNL [2] and in the NA48/2 experiment at CERN [1]. Very recently, the NA48/2 collaboration has published the results on the branching ratio and form factors of K 4 , based on more than a million events [3].Here, we present preliminary results of a new dispersive treatment of K 4 decays. Dispersion relations are an interesting tool to treat low energy hadronic processes. They are based on the very general principles of analyticity and unitarity. The derivation of the dispersion relation applies a chiral power counting and is valid up to and including O(p 6 ). The dispersion relation is parametrised by five subtraction constants. As soon as these constants have been fixed, the energy dependence is fully determined by the dispersion relation. The presented method implements a summation of final state rescattering effects, thus we expect it to incorporate the most important contributions beyond O(p 6 ). a

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Section: Decomposition Of the Form Factormentioning

confidence: 99%

A Dispersive Treatment ofK_ℓ4Decays

Colangelo

Passemar

Stoffer

2012

EPJ Web of Conferences

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“…The decay amplitude is identified, up to a constant, to the Omnès factor Ω I (s) in Eq. (27), i.e. the inelastic singularities are neglected.…”

Section: Discussionmentioning

confidence: 99%

“…In Section 5 we shall discuss how these coefficients can be determined by using lattice results at unphysical values of s. The physical amplitude is obtained from (27) by setting s = m 2 K .…”

Section: Inserting (26) Into (23) We Obtain a Representation Of The Amentioning

confidence: 99%

Dispersion relations and Omnès representations for $K\to \pi \pi$ decay amplitudes

2003

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We derive dispersion relations for K → ππ decay, using the LehmannSymanzik-Zimmermann formalism, which allows the analytic continuation of the amplitudes with respect to the momenta of the external particles. No off-shell extrapolation of the field operators is assumed. We obtain generalized Omnès representations, which incorporate the ππ and πK S-wave phase shifts in the elastic region of the direct and crossed channels, according to Watson theorem. The contribution of the inelastic final-state and initialstate interactions is parametrized by the technique of conformal mappings. We compare our results with previous dispersive treatments and indicate how the formalism can be combined with lattice calculations to yield physical predictions.

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“…[32,33] for the computation of similar integrals in the context of the longitudinal WLWL scattering, and refs. [34][35][36][37][38][39][40][41][42][43][44][45][46] for related studies in QCD. with equal amplitudes obtained substituting π 0 with h, i.e.…”

Section: Jhep06(2014)060mentioning

confidence: 99%

Remarks on analyticity and unitarity in the presence of a strongly interacting light Higgs

Urbano

2014

J. High Energ. Phys.

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Applying the three axiomatic criteria of Lorentz invariance, analyticity and unitarity to scattering amplitudes involving the Goldstone bosons and the Higgs boson, we derive a general sum rule for the Strongly Interacting Light Higgs Lagrangian. This sum rule connects the IR coefficient c H to the UV properties of the theory, and can be used, for instance, to capture the role of resonances in processes like

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Comparison of $\pi K$ scattering in SU(3) chiral perturbation theory and dispersion relations

Cited by 67 publications

References 24 publications

A Dispersive Treatment ofK_ℓ4Decays

A Dispersive Treatment ofK_ℓ4Decays

Dispersion relations and Omnès representations for $K\to \pi \pi$ decay amplitudes

Remarks on analyticity and unitarity in the presence of a strongly interacting light Higgs

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Comparison of $\pi K$ scattering in SU(3) chiral perturbation theory and dispersion relations

Cited by 67 publications

References 24 publications

A Dispersive Treatment ofKℓ4Decays

A Dispersive Treatment ofKℓ4Decays

Dispersion relations and Omnès representations for $K\to \pi \pi$ decay amplitudes

Remarks on analyticity and unitarity in the presence of a strongly interacting light Higgs

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Product

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A Dispersive Treatment ofK_ℓ4Decays

A Dispersive Treatment ofK_ℓ4Decays