1. NEW TRENDS IN HIGH-ENERGY PHYSICS (experiment, phenomenology, theory) Alushta, Crimea, Ukraine, September 23-29, 2013 Effects of the next-to-leading order terms in the chiral SU(3) Lagrangian on the S=-1 s-wave meson-baryon interactions In collaboration with A. Ramos, A. Feijoo Aliau

2. Chiral Perturbation Theory: which is based on effective Lagrangian with hadron d.o.f., which respects the symmetries of QCD, in particular chiral symmetry Perturbative QCD, with quark and gluon d.o.f., works well at high energies and high momentum transfers, but fails to describe dynamics of hadrons at low energies

3. Chiral Perturbation Theory: which is based on effective Lagrangian with hadron d.o.f., which respects the symmetries of QCD, in particular chiral symmetry Perturbative QCD, with quark and gluon d.o.f., works well at high energies and high momentum transfers, but fails to describe dynamics of hadrons at low energies The spontaneous chiral symmetry breaking causes the appearance of the Nambu–Goldstone (NG) bosons as the light pseudoscalar mesons and the dynamical mass generation of hadrons.

4. Baryon meson interaction at lowest order WT: Weimberg -Tomozawa term

5. WT baryon meson interaction

6. The only model parameter is pion decay constant, f En real calculations it is usually taken in order to partly simulate effects of higher order corrections

7. Perturbative QCD, with quark and gluon d.o.f., works well at high energies and high momentum transfers, but fails to describe dynamics of hadrons at low energies Chiral Perturbation Theory: which is based on effective Lagrangian with hadron d.o.f., which respects the symmetries of QCD, in particular chiral symmetry Unitary extension of Chiral Perturbation Theory The pioneering work -- Kaiser, Siegel, Weise, NP A594 (1995) 325

8. Máster Interuniversitario de Física Nuclear (UB) System of the algebraic equations Lippmann-Schwinger equation On shell factorization

9. Loop function

10. Boost in unitary extensions of chiral perturbation theory 1995-2003: Kaiser, Oset, Ramos, Oller, Meissner, Jido, Hosaka, Garcia-Recio, Vicente Vacas Λ (1405) as a dynamically generated resonance Jones, Dalitz and Horgan, Nucl. Phys. B129 (1977) 45 – Λ (1405) is dynamical generated

11. Boost in unitary extensions of chiral perturbation theory Jones, Dalitz and Horgan, Nucl. Phys. B129 (1977) 45 – Λ (1405) is dynamical generated 1995-2003: Kaiser, Oset, Ramos, Oller, Meissner, Jido, Hosaka, Garcia-Recio, Vicente Vacas Λ (1405) as a dynamically generated resonance Surprisingly there are two poles in the neighborhood of the Λ(1405) both contributing to the final experimental invariant mass distribution Mass ~ 1390 MeV Width ~ 130 MeV Mass ~ 1425 MeV Width ~ 30 MeV

12. The observed shapes are in good agreement with corresponding chiral unitarity model calculations: This combined study gives the first experimental evidence of the two-pole nature of the Λ(1405)

13. Crystall Ball Collaboration data from versus Thomas et al., NP B 56 (1973) 15 (Width ~ 60 MeV) (Width ~ 38 MeV) Magas, Oset, Ramos, PRL 95 (2005) 052301; also presented at Crimea’2005

14. Recent Publications: - B. Borasoy, R. Nißler, W. Wiese, Eur. Phys. J. A25 (2005) 79 - Y. Ikeda, T. Hyodo, W. Wiese, Phys. Lett. B706 (2011) 63; Nucl. Phys. A881 (2012) 98 - A. Feijoo Aliau, Master Thesis, U. of Barcelona (Nov 2012) - Z.-H. Guo, J.A. Oller, Phys. Rev. C87 (2013) 035202 Chiral meson-baryon effective Lagrangian at NLO

15. - is the symmetry breaking term

16. Chiral meson-baryon effective Lagrangian at NLO - is the symmetry breaking term 7 new parameters to be fixed:

17. Máster Interuniversitario de Física Nuclear (UB) WT, lowest order term Next – to – Leading Order term Chiral meson-baryon effective Lagrangian at NLO

18. Máster Interuniversitario de Física Nuclear (UB) At low energies Chiral meson-baryon effective Lagrangian at NLO WT, lowest order term Next – to – Leading Order term

19. Máster Interuniversitario de Física Nuclear (UB) Experimental data - Cross sections for different channels - Branching ratios

20. Máster Interuniversitario de Física Nuclear (UB) Fitting parameters - Decay constant f - 7 parameters of the NLO Lagrangian: - 10 subtracting constants 6 constants: isospin symmetry

21. Fitting parameters [1] Borasoy, Nißler, Wiese, Eur. Phys. J. A25 (2005) 79

22. Máster Interuniversitario de Física Nuclear (UB) Branching ratios Results [1] Borasoy, Nißler, Wiese, Eur. Phys. J. A25 (2005) 79

23. Results

25. These are particularly interesting for us, because for WT interaction channels are very sensitive to the NLO terms in the Lagrangian Also these channels are not included in the other fits! B. Borasoy, R. Nißler, W. Wiese, Eur. Phys. J. A25 (2005) 79 Y. Ikeda, T. Hyodo, W. Wiese, Phys. Lett. B706 (2011) 63; Nucl. Phys. A881 (2012) 98 Z.-H. Guo, J.A. Oller, Phys. Rev. C87 (2013) 035202 But studied in the phenomenological model of D. A. Sharov, V. L. Korotkikh, D. E. Lanskoy, Eur. Phys. J. A47 (2011) 109

26. - Missing contribution from the heavy high spin resonances

27. ResonanciaMass (MeV) _ _ _ _ _ _ Máster Interuniversitario de Física Nuclear (UB) In Ref. [Sharov, Korotkikh, Lanskoy, EPJ A47 (11) 109], trying different combinations, the author conclude that Σ(2030) and Σ(2250) give the better fit to the data

28. Work in progress K. Nakayama, Youngseok Oh, H. Habertzettl, Phys. Rev. C74, 035205 (2006) K. Shing Man, Youngseok Oh, K. Nakayama,, Phys. Rev. C83, 055201 (2011) The propagators of the spin-5/2 and -7/2 fermion fields

29. Conclusions Chiral Perturbation Theory with unitarization in coupled channels is a very powerful technique to describe low energy hadron dynamics Next – to – leading order calculations are now possible are very interesting and important for fitting NLO parameters NLO terms in the Lagrangian do improve agreement with data Work in progress…