Study of scalar mesons in chiral Lagrangian frameworks

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Study of scalar mesons in chiral Lagrangian frameworks Deirdre Black & Jonathan Gaunt University

Study of scalar mesons in chiral Lagrangian frameworks Deirdre Black & Jonathan Gaunt University of Cambridge Supported by the Royal Society Ongoing collaboration with A. Abdel-Rehim, A. H. Fariborz, B. M. Harada & J. Schechter

Outline 1. Non-linear chiral Lagrangian approach 2. Radiative decays involving scalar mesons 3. Comparing

Outline 1. Non-linear chiral Lagrangian approach 2. Radiative decays involving scalar mesons 3. Comparing linear and non-linear approaches. Work in progress and future directions.

Light pseudoscalar & scalar mesons in a non-linear chiral Lagrangian approach (Syracuse Group) Usual

Light pseudoscalar & scalar mesons in a non-linear chiral Lagrangian approach (Syracuse Group) Usual leading order chiral Lagrangian for pseudoscalar mesons: Scalar meson Lagrangian includes most general coupling of scalar meson nonet to two pseudoscalars:

Scalar mesons in non-linear chiral Lagrangian approach Trilinear piece of a chiral invariant Lagrangian

Scalar mesons in non-linear chiral Lagrangian approach Trilinear piece of a chiral invariant Lagrangian - hence derivative coupling: SU(3) scalar meson nonet: with

Pseudoscalar meson scattering in scalar channels non-linear chiral Lagrangian approach § Calculate tree amplitudes

Pseudoscalar meson scattering in scalar channels non-linear chiral Lagrangian approach § Calculate tree amplitudes from Lagrangian and use “generalised” Breit-Wigner propagator Aston et al, NPB 296 (1978) §Fit , K scattering & h’ h decay. § Constraints – e. g. predict h scattering and h 3 § Two solutions for s-f mixing angle when we fix the masses – o o q= -20 or -90. Fit to scattering o gives q = -20 (natural for diquarkantidiquark states) Our fit to Real part of J=0, I=1/2 K scattering amplitude. Two scalar resonances: m = 0. 9 Ge. V & m. K 0*=1. 43 Ge. V

Scalar mesons in radiative decays V V V’ S General trilinear scalar-vector chiral invariant

Scalar mesons in radiative decays V V V’ S General trilinear scalar-vector chiral invariant interaction + VMD DB, M Harada, J Schechter (2002)

Scalar mesons in radiative decays S V V V’ S V’ § Many processes

Scalar mesons in radiative decays S V V V’ S V’ § Many processes related. For example fitting to experimental values for a 0 gg, f 0 branching ratios. gg, f a 0 g we predict nine other § Prediction for G(j f 0 g) too small. Also need to fit spectrum.

Chiral Lagrangian approach to radiative f-decays d. B(f hg)/dq (Me. V-1) [DB, M Harada,

Chiral Lagrangian approach to radiative f-decays d. B(f hg)/dq (Me. V-1) [DB, M Harada, J Schechter PRD 73 (2006)] V’ f Derivative P S P’ Fit not great at high end (we know kaon loops important) Non-derivative Interesting to note effect of derivative vs non-derivative coupling of S to PP’ How to treat “production” of S? SND (2000) KLOE (2002) KLOE (2004)

Scalar mesons in SU(3) linear sigma models § No derivatives in coupling of scalars

Scalar mesons in SU(3) linear sigma models § No derivatives in coupling of scalars to pseudoscalars § Calculating tree amplitudes and with K-matrix unitarization we found a good fit to scattering and K at low energies. § Identify physical poles: ms = 457 Me. V mf = 993 Me. V Our Ls. M fit to Real part of I=J=0 scattering amplitude (DB et al 2001) Alekseeva (1982) Grayer (1974)

Work in progress & future directions § K-matrix analysis of and K scattering in

Work in progress & future directions § K-matrix analysis of and K scattering in our non-linear chiral Lagrangian approach. Idea is that we compare across different Lagrangians and different unitarisation techniques. § More detailed treatment of K-Kbar threshold and inelasticity in all scattering channels. §Combination of tree and kaon loop diagrams with scalar meson production picture in radiative f decays. Also two-photon decays of scalar mesons. Example: New pp scattering fit [with J. Gaunt] Non-linear chiral Lagrangian K-Matrix unitarisation (without ρ) SU(3) Linear Sigma Model K-Matrix unitarisation (without ρ) Non-linear chiral Lagrangian (without/with r) Generalised BW regularisation mphys, σ / Me. V 444 457 378/559 Γphys, σ / Me. V 604 632 836/370 mphys, f / Me. V 986 993 987 Γphys, f / Me. V 52 51 65