Introduction to Dispersion Techniques in Field Theory

Barton, G.

doi:10.1119/1.1973962

Cited by 85 publications

(140 citation statements)

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“…The full knowledge of the strong interaction meson-meson form factors can be obtained only if the strong meson-meson interaction is known at all energies [44]. Consequently some information on the K 0 ρ(770) 0 strong interaction would be required to estimate the K 0 to ρ(770) 0 transition form factor.…”

Section: Summary Conclusion and Perspectivesmentioning

confidence: 99%

Dalitz plot studies ofD0→KS0π+

et al. 2014

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The presently available high-statistics data of the D 0 → K 0 S π + π − processes measured by the Belle and BABAR Collaborations are analyzed within a quasi two-body factorization framework. Starting from the weak effective Hamiltonian, tree and annihilation amplitudes build up the D 0 → K 0 S π + π − decay amplitude. Two of the three final-state mesons are assumed to form a single scalar, vector or tensor state originating from a quark-antiquark pair so that the factorization hypothesis can be applied. The meson-meson final state interactions are described by Kπ and ππ scalar and vector form factors for the S and P waves and by relativistic Breit-Wigner formulae for the D waves. A combined χ 2 fit to a Belle Dalitz plot density distribution, to the total experimental branching fraction and to the τ − → K 0 S π − ντ decay data is carried out to fix the 33 free parameters. These are mainly related to the strengths of the scalar form factors and to unknown meson to meson transition form factors at a large momentum transfer squared equal to the D 0 mass squared. A good overall agreement to the Belle Dalitz plot density distribution is achieved. Another set of parameters fits equally well the BABAR Collaboration Dalitz plot model. The parameters of both fits are close, following from similar Dalitz density distribution data for both collaborations. The corresponding one-dimensional effective mass distributions display the contributions of the ten quasi two-body channels entering our D 0 → K 0 S π + π − decay amplitude. The branching fractions of the dominant channels compare well with those of the isobar Belle or BABAR models. The lower-limit values of the branching fractions of the annihilation amplitudes are significant. Built upon experimental data from other processes, the unitary Kπ and ππ scalar form factors, entering our decay amplitude and satisfying analyticity and chiral symmetry constraints, are furthermore constrained by the present Dalitz plot analysis. Our D 0 → K 0 S π + π − decay amplitude could be a useful input for determinations of D 0 -D 0 mixing parameters and of the CKM angle γ (or φ3).

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Section: Summary Conclusion and Perspectivesmentioning

confidence: 99%

Dalitz plot studies ofD0→KS0π+

et al. 2014

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“…As discussed at the end of Section 2, this method amounts to insert in the unitarity sum the complete set of states 1/2|in + 1/2|out . We recall that this method was applied to include inelastic effects through complex phases in the dispersive analysis of the electromagnetic form factors [10], [11]. In our case this procedure yields, instead of (31), the modified dispersion relation…”

Section: Dispersion Relations In the External Mass Variablementioning

confidence: 99%

“…Heuristic derivations of such dispersion relations are based on the Lehmann, Symanzik, Zimmermann (LSZ) reduction formalism [8], combined with causality and hadronic unitarity. As emphasized in [11] one must be cautious in using such dispersion relations, since the heuristic conjectures might be violated, in particular through the appearance of anomalous thresholds.…”

Section: Introductionmentioning

confidence: 99%

“…We recall that dispersion relations in the external mass variables were derived in the frame of axiomatic field theory [5]- [8], and were used in phenomenological calculations of form factors [9], [10] (see also [11]). Heuristic derivations of such dispersion relations are based on the Lehmann, Symanzik, Zimmermann (LSZ) reduction formalism [8], combined with causality and hadronic unitarity.…”

Section: Introductionmentioning

confidence: 99%

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Dispersion relations and rescattering effects inBnonleptonic decays

1999

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Recently, the final state strong interactions in nonleptonic B decays were investigated in a formalism based on hadronic unitarity and dispersion relations in terms of the off-shell mass squared of the B meson. We consider an heuristic derivation of the dispersion relations in the mass variables using the reduction LSZ formalism and find a discrepancy between the spectral function and the dispersive variable used in the recent works. The part of the unitarity sum which describes final state interactions is shown to appear as spectral function in a dispersion relation based on the analytic continuation in the mass squared of one final particles. As an application, by combining this formalism with Regge theory and SU (3) flavour symmetry we obtain constraints on the tree and the penguin amplitudes of the decay B 0 → π + π − .

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“…It appears to be widely believed that, because of equation (61), p( ( 2 ) ~ 0 can be violated only if the metric of the Hilbert space is not positive definite (Barton 1963;R, p. 472), but we now see that this is not so. In analytic S-matrix theory, of which there are several versions, it is a basic relation that the residue of the s-channel scattering amplitude Ms be positive at particle poles.…”

Section: Some Other Aspectsmentioning

confidence: 75%

Elimination of Primitive Divergents from Field Theory by Means of Complex Coupling Constants

Nicholson¹

1973

Aust. J. Phys.

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LSZ. iteration theory is extended to accommodate quantum fields coupled by complex constants, while retaining a positive metric and a Hermitian Hamiltonian. Interpolating and particle (~in, out) fields are linked by an operator U(t) which is nonunitary, so that Haag's theorem may be avoided. It is shown that U(t) may be rendered sufficiently well-behaved as t -+ ± 00 to allow development of the iteration series for the T function. For certain combinations of fields the coupling constants and masses can then be chosen so as to eliminate the primitive divergents from the iteration series for any S-matrix element. The theory is illustrated by two models: four spinor plus two scalar fields, and the electromagnetic plus several spinor fields. In the second model not every spinor field corresponds to a stable physical particle, and the LSZ formalism is extended to allow for this.

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Introduction to Dispersion Techniques in Field Theory

Cited by 85 publications

References 0 publications

Dalitz plot studies ofD0→KS0π+

Dalitz plot studies ofD0→KS0π+

Dispersion relations and rescattering effects inBnonleptonic decays

Elimination of Primitive Divergents from Field Theory by Means of Complex Coupling Constants

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