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

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slide1

NEW TRENDS IN HIGH-ENERGY PHYSICS(experiment, phenomenology, theory)

Alushta, Crimea, Ukraine, September 23-29, 2013

Volodymyr Magas

Effects of the next-to-leading order terms

in the chiral SU(3) Lagrangianon the

S=-1 s-wave meson-baryon interactions

In collaboration with A. Ramos, A. Feijoo Aliau

University of Barcelona, Spain

slide2

Perturbative QCD, with quark and gluond.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

slide3

Perturbative QCD, with quark and gluond.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

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.

slide6

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

slide7

Perturbative QCD, with quark and gluond.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

slide8

Lippmann-Schwinger equation

On shell factorization

System of the

algebraic equations

Máster Interuniversitario de Física Nuclear (UB)

slide10

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

1995-2003: Kaiser, Oset, Ramos, Oller, Meissner, Jido,

Hosaka, Garcia-Recio, Vicente Vacas

slide11

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

1995-2003: Kaiser, Oset, Ramos, Oller, Meissner, Jido,

Hosaka, Garcia-Recio, Vicente Vacas

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 MeVWidth ~ 30 MeV

slide12

The observed shapes are in good agreement with

corresponding chiral unitarity model calculations:

 Magas, Oset, Ramos,

Phys. Rev. Lett. 95 (05) 052301

 Thomas et al.,

Nucl. Phys. B56 (1973) 15

This combined study gives the first experimental

evidence of the two-pole nature of the Λ(1405)

slide13

Crystall Ball Collaboration data from

(Width ~ 38 MeV)

versus

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

(Width ~ 60 MeV)

Magas, Oset, Ramos,

PRL 95 (2005) 052301;also presented at Crimea’2005

slide14

Chiral meson-baryon effective Lagrangian at NLO

  • 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, MasterThesis, U. of Barcelona (Nov 2012)
  • Z.-H. Guo, J.A. Oller, Phys. Rev. C87 (2013) 035202
slide16

Chiral meson-baryon effective Lagrangian at NLO

- is the symmetry breaking term

7 new parameters to be fixed:

slide17

Chiral meson-baryon effective Lagrangian at NLO

  • WT, lowest order term
  • Next – to – Leading Order term

Máster Interuniversitario de Física Nuclear (UB)

slide18

Chiral meson-baryon effective Lagrangian at NLO

  • WT, lowest order term

At low energies

  • Next – to – Leading Order term

Máster Interuniversitario de Física Nuclear (UB)

slide19

Experimental data

- Cross sections for different channels

- Branching ratios

Máster Interuniversitario de Física Nuclear (UB)

slide20

Fitting parameters

  • Decay constant f
  • 7 parameters of the NLO Lagrangian:
  • - 10 subtracting constants 6 constants:

isospin symmetry

Máster Interuniversitario de Física Nuclear (UB)

slide21

Fitting parameters

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

slide22

Results

  • Branching ratios

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

Máster Interuniversitario de Física Nuclear (UB)

slide25

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) 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

slide27

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

Máster Interuniversitario de Física Nuclear (UB)

slide28

Work in progress

The propagators of the spin-5/2 and -7/2 fermion fields

K. Nakayama, Youngseok Oh, H. Habertzettl, Phys. Rev. C74, 035205 (2006)

K. Shing Man, Youngseok Oh, K. Nakayama,, Phys. Rev. C83, 055201 (2011)

slide29

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

NLO terms in the Lagrangian do improve agreement with data

are very interesting and important for fitting NLO parameters

Work in progress…

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