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

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

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.

Baryon meson interaction at lowest order

WT: Weim

berg

-Tomozawa term

WT baryon meson interaction

WT baryon meson interaction

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

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 TheoryThe pioneering work -- Kaiser, Siegel, Weise , NP A594 (1995) 325

Máster Interuniversitario de Física Nuclear (UB)

System of thealgebraic equations

Lippmann-Schwinger equation

On shell factorization

Loop function

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

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 MeVWidth ~ 130 MeV

Mass ~ 1425 MeVWidth ~ 30 MeV

0Kp

000 pK

)1405(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)

0Kp

Crystall Ball Collaboration data from 000 pK

versus

Thomas et al., NP B 56 (1973) 15

(Width ~ 60 MeV)

(Width ~ 38 MeV)

Magas, Oset, R

amos,

PRL 95 (2005) 052301;

also presented at Crimea’2005

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

Chiral meson-baryon effective Lagrangian at NLO

- is the symmetry breaking term

Chiral meson-baryon effective Lagrangian at NLO

- is the symmetry breaking term

7 new parameters to be fixed:

Máster Interuniversitario de Física Nuclear (UB)

• WT, lowest order term

• Next – to – Leading Order term

Chiral meson-baryon effective Lagrangian at NLO

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

Máster Interuniversitario de Física Nuclear (UB)

Experimental data

- Cross sections for different channels

- Branching ratios

Máster Interuniversitario de Física Nuclear (UB)

Fitting parameters

- Decay constant f

- 7 parameters of the NLO Lagrangian:

- 10 subtracting constants 6 constants:isospin symmetry

Fitting parameters

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

Máster Interuniversitario de Física Nuclear (UB)

• Branching ratios

Results

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

Results

Results

These are particularly interesting for us, becausefor 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) 79Y. Ikeda, T. Hyodo, W. Wiese, Phys. Lett. B706 (2011) 63; Nucl. Phys. A881 (2012) 98Z.-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

- Missing contribution from the heavy high spin resonances

Máster Interuniversitario de Física Nuclear (UB)

In Ref. [Sharov, Korotkikh, Lanskoy, EPJ A47 (11) 109] , trying different combinations, the author conclude thatΣ(2030) and Σ(2250) give the better fit to the data

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

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…