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

Abstract

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.

Extracting|Vub|fromB→πlνdecays using a multiply-subtracted Omnès dispersion relation

“…As the subtraction points coalesce to some common s 0 , our result reduces to an expression involving the form factor and its derivatives at s 0 (such a representation was used successfully to account for final state interactions in kaon decays [33]). The asymptotic behaviour of f + imposes a constraint on the subtractions (when more are used than needed for convergence) [34], but we keep in mind that we will apply the representation above only in the physical region of q 2 for B → π decay.…”

Particle production mechanisms from RHIC to LHC

“…c.) contributions of non-valence quark fragmentation to, in particular, baryon production at RHIC. This effect is best documented by several new parametrizations of the baryon fragmentation functions by Albino et al [ 7], Bourelly and Soffer [ 9], and DeFlorian et al [ 10].…”

Hadronization and Chirality in Strongly Interacting Partonic Matter — The Future of the RHIC Program

“…the contribution of each quark flavor to the final hadron is computed separately and then integrated to the final FF [ 19]. Interestingly the study by AKK on the strange mesons, and independently by Bourrely and Soffer on the strange baryons [ 20], shows that there are considerable contributions from fragmentation of non-valence quarks in the production cross section, in particular at low fractional momentum GeV in e + e − collisions according to the statistical approach by Bourrely and Soffer [ 20]. z.…”

“…2. Contributions of individual quark fragmentation functions to octet baryon production at √ s=91.2GeV in e + e − collisions according to the statistical approach by Bourrely and Soffer[ 20].…”