Scheme dependence of weak matrix elements in the 1/Nc expansion

Journal of High Energy Physics

Volumn 4, Issue 1, 2000, Pages 12-21

  Bijnens, Johan ^a   Prades, Joaquim ^b  

^a LUND UNIVERSITY   (Sweden)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

1 N Expansion; CP violation; Kaon Physics

Indexed keywords

EID: 7444259867     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2000/01/002     Document Type: Article

References (68)

1. Proc. of the Workshop on K Physics, Orsay, France, L. Iconomidou-Fayard ed., Editions Frontières, 1997.
2. See http://hep.uchicago.edu/kaon99/.
3. W.A. Bardeen, A.J. Buras and J.M. Gérard, The K → ππ decays in the large-N limit: quark evolution, Nucl. Phys. B 293 (1987) 787; A consistent analysis of the ΔI = 1/2 rule for K decays, Phys. Lett. B 192 (1987) 138; The B parameter beyond the leading order of 1/N expansion, Phys. Lett. B 211 (1988) 343; J.-M. Gérard, Electroweak interactions of hadrons, Acta Phys. Polon. B 21 (1990) 257; A.J. Buras in CP violation, C. Jarlskog ed., World Scientific 1989, p. 575.
4. W.A. Bardeen, A.J. Buras and J.M. Gérard, The K → ππ decays in the large-N limit: quark evolution, Nucl. Phys. B 293 (1987) 787; A consistent analysis of the ΔI = 1/2 rule for K decays, Phys. Lett. B 192 (1987) 138; The B parameter beyond the leading order of 1/N expansion, Phys. Lett. B 211 (1988) 343; J.-M. Gérard, Electroweak interactions of hadrons, Acta Phys. Polon. B 21 (1990) 257; A.J. Buras in CP violation, C. Jarlskog ed., World Scientific 1989, p. 575.
5. W.A. Bardeen, A.J. Buras and J.M. Gérard, The K → ππ decays in the large-N limit: quark evolution, Nucl. Phys. B 293 (1987) 787; A consistent analysis of the ΔI = 1/2 rule for K decays, Phys. Lett. B 192 (1987) 138; The B parameter beyond the leading order of 1/N expansion, Phys. Lett. B 211 (1988) 343; J.-M. Gérard, Electroweak interactions of hadrons, Acta Phys. Polon. B 21 (1990) 257; A.J. Buras in CP violation, C. Jarlskog ed., World Scientific 1989, p. 575.
6. W.A. Bardeen, A.J. Buras and J.M. Gérard, The K → ππ decays in the large-N limit: quark evolution, Nucl. Phys. B 293 (1987) 787; A consistent analysis of the ΔI = 1/2 rule for K decays, Phys. Lett. B 192 (1987) 138; The B parameter beyond the leading order of 1/N expansion, Phys. Lett. B 211 (1988) 343; J.-M. Gérard, Electroweak interactions of hadrons, Acta Phys. Polon. B 21 (1990) 257; A.J. Buras in CP violation, C. Jarlskog ed., World Scientific 1989, p. 575.
7. W.A. Bardeen, A.J. Buras and J.M. Gérard, The K → ππ decays in the large-N limit: quark evolution, Nucl. Phys. B 293 (1987) 787; A consistent analysis of the ΔI = 1/2 rule for K decays, Phys. Lett. B 192 (1987) 138; The B parameter beyond the leading order of 1/N expansion, Phys. Lett. B 211 (1988) 343; J.-M. Gérard, Electroweak interactions of hadrons, Acta Phys. Polon. B 21 (1990) 257; A.J. Buras in CP violation, C. Jarlskog ed., World Scientific 1989, p. 575.
8. C QCD, Nucl. Phys. 7A (Proc. Suppl.) (1989) 149.
9. c limit, preprint FERMILAB-Conf-99/255-T, to be published in Proc. of Kaon '99, Chicago, USA, June 1999.
10. 0 mass difference, Phys. Rev. Lett. 62 (1989) 1343.
11. J. Bijnens, J.-M. Gérard and G. Klein, The KL-KS mass-difference, Phys. Lett. B 257 (1991) 191.
12. C expansion, Nucl. Phys. B 444 (1995) 523 [hep-ph/9502363].
13. C expansion, Nucl. Phys. B 444 (1995) 523 [hep-ph/9502363].
14. A.J. Buras, Weak hamiltonian, CP-violation and rare decays, hep-ph/9806471; G. Buchalla, A.J. Buras and M. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68 (1996) 1125 [hep-ph/9512380].
15. A.J. Buras, Weak hamiltonian, CP-violation and rare decays, hep-ph/9806471; G. Buchalla, A.J. Buras and M. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68 (1996) 1125 [hep-ph/9512380].
16. S), Nucl. Phys. B 400 (1993) 75 [hep-ph/9211321]; A.J. Buras, M. Jamin and M.E. Lautenbacher, The anatomy of ε′/ε′ beyond leading logarithms with improved hadronic matrix elements, Nucl. Phys. B 408 (1993) 209 [hep-ph/9303284]; M. Ciuchini, E. Franco, G. Martinelli and L. Reina, The ΔS = 1 effective hamiltonian including next-to-leading order QCD and QED corrections, Nucl. Phys. B 415 (1994) 403 [hep-ph/9304257]; M. Ciuchini, E. Franco, G. Martinelli, L. Reina and L. Silvestrini, An upgraded analysis of epsilon-prime epsilon at the next-to-leading order, Z. Physik C 68 (1995) 239 [hep-ph/9501265].
17. S), Nucl. Phys. B 400 (1993) 75 [hep-ph/9211321]; A.J. Buras, M. Jamin and M.E. Lautenbacher, The anatomy of ε′/ε′ beyond leading logarithms with improved hadronic matrix elements, Nucl. Phys. B 408 (1993) 209 [hep-ph/9303284]; M. Ciuchini, E. Franco, G. Martinelli and L. Reina, The ΔS = 1 effective hamiltonian including next-to-leading order QCD and QED corrections, Nucl. Phys. B 415 (1994) 403 [hep-ph/9304257]; M. Ciuchini, E. Franco, G. Martinelli, L. Reina and L. Silvestrini, An upgraded analysis of epsilon-prime epsilon at the next-to-leading order, Z. Physik C 68 (1995) 239 [hep-ph/9501265].
18. S), Nucl. Phys. B 400 (1993) 75 [hep-ph/9211321]; A.J. Buras, M. Jamin and M.E. Lautenbacher, The anatomy of ε′/ε′ beyond leading logarithms with improved hadronic matrix elements, Nucl. Phys. B 408 (1993) 209 [hep-ph/9303284]; M. Ciuchini, E. Franco, G. Martinelli and L. Reina, The ΔS = 1 effective hamiltonian including next-to-leading order QCD and QED corrections, Nucl. Phys. B 415 (1994) 403 [hep-ph/9304257]; M. Ciuchini, E. Franco, G. Martinelli, L. Reina and L. Silvestrini, An upgraded analysis of epsilon-prime epsilon at the next-to-leading order, Z. Physik C 68 (1995) 239 [hep-ph/9501265].
19. S), Nucl. Phys. B 400 (1993) 75 [hep-ph/9211321]; A.J. Buras, M. Jamin and M.E. Lautenbacher, The anatomy of ε′/ε′ beyond leading logarithms with improved hadronic matrix elements, Nucl. Phys. B 408 (1993) 209 [hep-ph/9303284]; M. Ciuchini, E. Franco, G. Martinelli and L. Reina, The ΔS = 1 effective hamiltonian including next-to-leading order QCD and QED corrections, Nucl. Phys. B 415 (1994) 403 [hep-ph/9304257]; M. Ciuchini, E. Franco, G. Martinelli, L. Reina and L. Silvestrini, An upgraded analysis of epsilon-prime epsilon at the next-to-leading order, Z. Physik C 68 (1995) 239 [hep-ph/9501265].
20. S), Nucl. Phys. B 400 (1993) 75 [hep-ph/9211321]; A.J. Buras, M. Jamin and M.E. Lautenbacher, The anatomy of ε′/ε′ beyond leading logarithms with improved hadronic matrix elements, Nucl. Phys. B 408 (1993) 209 [hep-ph/9303284]; M. Ciuchini, E. Franco, G. Martinelli and L. Reina, The ΔS = 1 effective hamiltonian including next-to-leading order QCD and QED corrections, Nucl. Phys. B 415 (1994) 403 [hep-ph/9304257]; M. Ciuchini, E. Franco, G. Martinelli, L. Reina and L. Silvestrini, An upgraded analysis of epsilon-prime epsilon at the next-to-leading order, Z. Physik C 68 (1995) 239 [hep-ph/9501265].
21. S), Nucl. Phys. B 400 (1993) 75 [hep-ph/9211321]; A.J. Buras, M. Jamin and M.E. Lautenbacher, The anatomy of ε′/ε′ beyond leading logarithms with improved hadronic matrix elements, Nucl. Phys. B 408 (1993) 209 [hep-ph/9303284]; M. Ciuchini, E. Franco, G. Martinelli and L. Reina, The ΔS = 1 effective hamiltonian including next-to-leading order QCD and QED corrections, Nucl. Phys. B 415 (1994) 403 [hep-ph/9304257]; M. Ciuchini, E. Franco, G. Martinelli, L. Reina and L. Silvestrini, An upgraded analysis of epsilon-prime epsilon at the next-to-leading order, Z. Physik C 68 (1995) 239 [hep-ph/9501265].
22. S), Nucl. Phys. B 400 (1993) 75 [hep-ph/9211321]; A.J. Buras, M. Jamin and M.E. Lautenbacher, The anatomy of ε′/ε′ beyond leading logarithms with improved hadronic matrix elements, Nucl. Phys. B 408 (1993) 209 [hep-ph/9303284]; M. Ciuchini, E. Franco, G. Martinelli and L. Reina, The ΔS = 1 effective hamiltonian including next-to-leading order QCD and QED corrections, Nucl. Phys. B 415 (1994) 403 [hep-ph/9304257]; M. Ciuchini, E. Franco, G. Martinelli, L. Reina and L. Silvestrini, An upgraded analysis of epsilon-prime epsilon at the next-to-leading order, Z. Physik C 68 (1995) 239 [hep-ph/9501265].
23. S mass difference by short distance QCD corrections beyond leading logarithms, Nucl. Phys. B 419 (1994) 292 [hep-ph/9310311]; Indirect CP violation in the neutral kaon system beyond leading logarithms, Phys. Rev. D 52 (1995) 6505 [hep-ph/9507262]; The complete |ΔS| = 2 - hamiltonian in the next-to-leading order, Nucl. Phys. B 476 (1996) 27 [hep-ph/9604330]; M. Ciuchini E. Franco, V. Lubicz, G. Martinelli, I. Scimemi and L. Silvestrini, Next-to-leading order QCD corrections to ΔF = 2 effective hamiltonians, Nucl. Phys. B 523 (1998) 501 [hep-ph/9711402].
24. S mass difference by short distance QCD corrections beyond leading logarithms, Nucl. Phys. B 419 (1994) 292 [hep-ph/9310311]; Indirect CP violation in the neutral kaon system beyond leading logarithms, Phys. Rev. D 52 (1995) 6505 [hep-ph/9507262]; The complete |ΔS| = 2 - hamiltonian in the next-to-leading order, Nucl. Phys. B 476 (1996) 27 [hep-ph/9604330]; M. Ciuchini E. Franco, V. Lubicz, G. Martinelli, I. Scimemi and L. Silvestrini, Next-to-leading order QCD corrections to ΔF = 2 effective hamiltonians, Nucl. Phys. B 523 (1998) 501 [hep-ph/9711402].
25. S mass difference by short distance QCD corrections beyond leading logarithms, Nucl. Phys. B 419 (1994) 292 [hep-ph/9310311]; Indirect CP violation in the neutral kaon system beyond leading logarithms, Phys. Rev. D 52 (1995) 6505 [hep-ph/9507262]; The complete |ΔS| = 2 - hamiltonian in the next-to-leading order, Nucl. Phys. B 476 (1996) 27 [hep-ph/9604330]; M. Ciuchini E. Franco, V. Lubicz, G. Martinelli, I. Scimemi and L. Silvestrini, Next-to-leading order QCD corrections to ΔF = 2 effective hamiltonians, Nucl. Phys. B 523 (1998) 501 [hep-ph/9711402].
26. S mass difference by short distance QCD corrections beyond leading logarithms, Nucl. Phys. B 419 (1994) 292 [hep-ph/9310311]; Indirect CP violation in the neutral kaon system beyond leading logarithms, Phys. Rev. D 52 (1995) 6505 [hep-ph/9507262]; The complete |ΔS| = 2 - hamiltonian in the next-to-leading order, Nucl. Phys. B 476 (1996) 27 [hep-ph/9604330]; M. Ciuchini E. Franco, V. Lubicz, G. Martinelli, I. Scimemi and L. Silvestrini, Next-to-leading order QCD corrections to ΔF = 2 effective hamiltonians, Nucl. Phys. B 523 (1998) 501 [hep-ph/9711402].
27. S mass difference by short distance QCD corrections beyond leading logarithms, Nucl. Phys. B 419 (1994) 292 [hep-ph/9310311]; Indirect CP violation in the neutral kaon system beyond leading logarithms, Phys. Rev. D 52 (1995) 6505 [hep-ph/9507262]; The complete |ΔS| = 2 - hamiltonian in the next-to-leading order, Nucl. Phys. B 476 (1996) 27 [hep-ph/9604330]; M. Ciuchini E. Franco, V. Lubicz, G. Martinelli, I. Scimemi and L. Silvestrini, Next-to-leading order QCD corrections to ΔF = 2 effective hamiltonians, Nucl. Phys. B 523 (1998) 501 [hep-ph/9711402].
28. J. Bijnens and J. Prades, The ΔI = 1/2 rule in the chiral limit, J. High Energy Phys. 01 (1999) 023 [hep-ph/9811472].
29. J. Bijnens, Progress in K → ππ decays, hep-ph/9907307; I: Chiral perturbation for kaons. II: The ΔI = 1/2 rule in the chiral limit, hep-ph/9907514; The ΔI = 1/2 rule and other matrix elements, hep-ph/9910263; Models of low energy effective theory applied to kaon non-leptonic decays and other matrix elements, hep-ph/9910415; J. Prades, The ΔI = 1/2 rule for kaons, hep-ph/9909245.
30. J. Bijnens, Progress in K → ππ decays, hep-ph/9907307; I: Chiral perturbation for kaons. II: The ΔI = 1/2 rule in the chiral limit, hep-ph/9907514; The ΔI = 1/2 rule and other matrix elements, hep-ph/9910263; Models of low energy effective theory applied to kaon non-leptonic decays and other matrix elements, hep-ph/9910415; J. Prades, The ΔI = 1/2 rule for kaons, hep-ph/9909245.
31. J. Bijnens, Progress in K → ππ decays, hep-ph/9907307; I: Chiral perturbation for kaons. II: The ΔI = 1/2 rule in the chiral limit, hep-ph/9907514; The ΔI = 1/2 rule and other matrix elements, hep-ph/9910263; Models of low energy effective theory applied to kaon non-leptonic decays and other matrix elements, hep-ph/9910415; J. Prades, The ΔI = 1/2 rule for kaons, hep-ph/9909245.
32. J. Bijnens, Progress in K → ππ decays, hep-ph/9907307; I: Chiral perturbation for kaons. II: The ΔI = 1/2 rule in the chiral limit, hep-ph/9907514; The ΔI = 1/2 rule and other matrix elements, hep-ph/9910263; Models of low energy effective theory applied to kaon non-leptonic decays and other matrix elements, hep-ph/9910415; J. Prades, The ΔI = 1/2 rule for kaons, hep-ph/9909245.
33. J. Bijnens, Progress in K → ππ decays, hep-ph/9907307; I: Chiral perturbation for kaons. II: The ΔI = 1/2 rule in the chiral limit, hep-ph/9907514; The ΔI = 1/2 rule and other matrix elements, hep-ph/9910263; Models of low energy effective theory applied to kaon non-leptonic decays and other matrix elements, hep-ph/9910415; J. Prades, The ΔI = 1/2 rule for kaons, hep-ph/9909245.
34. G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; M.K. Gaillard and B.W. Lee, ΔI = 1/2 rule for nonleptonic decays in asymptotically free field theories, Phys. Rev. Lett. 33 (1974) 108; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, On the general structure of the effective hamiltonian of weak nonleptonic decays, Sov. Phys. JETP 45 (1977) 670; F.J. Gilman and M.B. Wise, Effective hamiltonian for ΔS = 1 weak nonleptonic decays in the six quark model, Phys. Rev. D 20 (1979) 2392; B. Guberina and R.D. Peccei, Quantum chromodynamic effects and CP-violation in the Kobayashi-Maskawa model, Nucl. Phys. B 163 (1980) 289; J. Bijnens and M.B. Wise, Electromagnetic contribution to ε′/ε, Phys. Lett. B 137 (1984) 245.
35. G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; M.K. Gaillard and B.W. Lee, ΔI = 1/2 rule for nonleptonic decays in asymptotically free field theories, Phys. Rev. Lett. 33 (1974) 108; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, On the general structure of the effective hamiltonian of weak nonleptonic decays, Sov. Phys. JETP 45 (1977) 670; F.J. Gilman and M.B. Wise, Effective hamiltonian for ΔS = 1 weak nonleptonic decays in the six quark model, Phys. Rev. D 20 (1979) 2392; B. Guberina and R.D. Peccei, Quantum chromodynamic effects and CP-violation in the Kobayashi-Maskawa model, Nucl. Phys. B 163 (1980) 289; J. Bijnens and M.B. Wise, Electromagnetic contribution to ε′/ε, Phys. Lett. B 137 (1984) 245.
36. G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; M.K. Gaillard and B.W. Lee, ΔI = 1/2 rule for nonleptonic decays in asymptotically free field theories, Phys. Rev. Lett. 33 (1974) 108; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, On the general structure of the effective hamiltonian of weak nonleptonic decays, Sov. Phys. JETP 45 (1977) 670; F.J. Gilman and M.B. Wise, Effective hamiltonian for ΔS = 1 weak nonleptonic decays in the six quark model, Phys. Rev. D 20 (1979) 2392; B. Guberina and R.D. Peccei, Quantum chromodynamic effects and CP-violation in the Kobayashi-Maskawa model, Nucl. Phys. B 163 (1980) 289; J. Bijnens and M.B. Wise, Electromagnetic contribution to ε′/ε, Phys. Lett. B 137 (1984) 245.
37. G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; M.K. Gaillard and B.W. Lee, ΔI = 1/2 rule for nonleptonic decays in asymptotically free field theories, Phys. Rev. Lett. 33 (1974) 108; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, On the general structure of the effective hamiltonian of weak nonleptonic decays, Sov. Phys. JETP 45 (1977) 670; F.J. Gilman and M.B. Wise, Effective hamiltonian for ΔS = 1 weak nonleptonic decays in the six quark model, Phys. Rev. D 20 (1979) 2392; B. Guberina and R.D. Peccei, Quantum chromodynamic effects and CP-violation in the Kobayashi-Maskawa model, Nucl. Phys. B 163 (1980) 289; J. Bijnens and M.B. Wise, Electromagnetic contribution to ε′/ε, Phys. Lett. B 137 (1984) 245.
38. G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; M.K. Gaillard and B.W. Lee, ΔI = 1/2 rule for nonleptonic decays in asymptotically free field theories, Phys. Rev. Lett. 33 (1974) 108; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, On the general structure of the effective hamiltonian of weak nonleptonic decays, Sov. Phys. JETP 45 (1977) 670; F.J. Gilman and M.B. Wise, Effective hamiltonian for ΔS = 1 weak nonleptonic decays in the six quark model, Phys. Rev. D 20 (1979) 2392; B. Guberina and R.D. Peccei, Quantum chromodynamic effects and CP-violation in the Kobayashi-Maskawa model, Nucl. Phys. B 163 (1980) 289; J. Bijnens and M.B. Wise, Electromagnetic contribution to ε′/ε, Phys. Lett. B 137 (1984) 245.
39. G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; M.K. Gaillard and B.W. Lee, ΔI = 1/2 rule for nonleptonic decays in asymptotically free field theories, Phys. Rev. Lett. 33 (1974) 108; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, On the general structure of the effective hamiltonian of weak nonleptonic decays, Sov. Phys. JETP 45 (1977) 670; F.J. Gilman and M.B. Wise, Effective hamiltonian for ΔS = 1 weak nonleptonic decays in the six quark model, Phys. Rev. D 20 (1979) 2392; B. Guberina and R.D. Peccei, Quantum chromodynamic effects and CP-violation in the Kobayashi-Maskawa model, Nucl. Phys. B 163 (1980) 289; J. Bijnens and M.B. Wise, Electromagnetic contribution to ε′/ε, Phys. Lett. B 137 (1984) 245.
40. M. Ciuchini, E. Franco, L. Giusti, V. Lubicz and G. Martinelli, ε′/ε from lattice QCD, hep-ph/9910237.
41. J. Bijnens, E. Pallante and J. Prades, work in progress.
42. 8 in K → ππ decays, Phys. Rev. D 58 (1998) 014017 [hep-ph/9802300].
43. 8 in K → ππ decays, Phys. Rev. D 58 (1998) 014017 [hep-ph/9802300].
44. 8 in K → ππ decays, Phys. Rev. D 58 (1998) 014017 [hep-ph/9802300].
45. 8 in K → ππ decays, Phys. Rev. D 58 (1998) 014017 [hep-ph/9802300].
46. A.J. Buras and P.H. Weisz, QCD nonleading corrections to weak decays in dimensional regularization and 't Hooft-Veltman schemes, Nucl. Phys. B 333 (1990) 66.
47. J. Bijnens and J. Prades, Electromagnetic corrections for pions and kaons: masses and polarizabilities, Nucl. Phys. B 490 (1997) 239 [hep-ph/9610360].
48. J. Bijnens, Violations of Dashen's theorem, Phys. Lett. B 306 (1993) 343 [hep-ph/9302217].
49. c expansion, Phys. Lett. B 443 (1998) 255 [hep-ph/9809594].
50. 2), Eur. Phys. J. C 4 (1998) 409.
51. J. Bijnens, C. Bruno and E. de Rafael, Nambu-Jona-Lasinio like models and the low-energy effective action of QCD, Nucl. Phys. B 390 (1993) 501 [hep-ph/9206236]; J. Bijnens, E. de Rafael and H. Zheng, Low-energy behavior of two point functions of quark currents, Z. Physik C 62 (1994) 437 [hep-ph/9306323]; J. Prades, Massive spin 1 field chiral lagrangian from an extended Nambu-Jona-Lasinio model of QCD, Z. Physik C 63 (1994) 491 [hep-ph/9302246], erratum Eur. Phys. J. C 11 (1999) 571; J. Bijnens and J. Prades, Anomalies, VMD and the NJL model, Phys. Lett. B 320 (1994) 130 [hep-ph/9310355]; Two and three point functions in the extended NJL model, Z. Physik C 64 (1994) 475 [hep-ph/9403233]; J. Bijnens, Chiral lagrangians and Nambu-Jona-Lasinio-like models, Phys. Rep. 265 (1996) 369 [hep-ph/9502335].
52. J. Bijnens, C. Bruno and E. de Rafael, Nambu-Jona-Lasinio like models and the low-energy effective action of QCD, Nucl. Phys. B 390 (1993) 501 [hep-ph/9206236]; J. Bijnens, E. de Rafael and H. Zheng, Low-energy behavior of two point functions of quark currents, Z. Physik C 62 (1994) 437 [hep-ph/9306323]; J. Prades, Massive spin 1 field chiral lagrangian from an extended Nambu-Jona-Lasinio model of QCD, Z. Physik C 63 (1994) 491 [hep-ph/9302246], erratum Eur. Phys. J. C 11 (1999) 571; J. Bijnens and J. Prades, Anomalies, VMD and the NJL model, Phys. Lett. B 320 (1994) 130 [hep-ph/9310355]; Two and three point functions in the extended NJL model, Z. Physik C 64 (1994) 475 [hep-ph/9403233]; J. Bijnens, Chiral lagrangians and Nambu-Jona-Lasinio-like models, Phys. Rep. 265 (1996) 369 [hep-ph/9502335].
53. J. Bijnens, C. Bruno and E. de Rafael, Nambu-Jona-Lasinio like models and the low-energy effective action of QCD, Nucl. Phys. B 390 (1993) 501 [hep-ph/9206236]; J. Bijnens, E. de Rafael and H. Zheng, Low-energy behavior of two point functions of quark currents, Z. Physik C 62 (1994) 437 [hep-ph/9306323]; J. Prades, Massive spin 1 field chiral lagrangian from an extended Nambu-Jona-Lasinio model of QCD, Z. Physik C 63 (1994) 491 [hep-ph/9302246], erratum Eur. Phys. J. C 11 (1999) 571; J. Bijnens and J. Prades, Anomalies, VMD and the NJL model, Phys. Lett. B 320 (1994) 130 [hep-ph/9310355]; Two and three point functions in the extended NJL model, Z. Physik C 64 (1994) 475 [hep-ph/9403233]; J. Bijnens, Chiral lagrangians and Nambu-Jona-Lasinio-like models, Phys. Rep. 265 (1996) 369 [hep-ph/9502335].
54. J. Bijnens, C. Bruno and E. de Rafael, Nambu-Jona-Lasinio like models and the low-energy effective action of QCD, Nucl. Phys. B 390 (1993) 501 [hep-ph/9206236]; J. Bijnens, E. de Rafael and H. Zheng, Low-energy behavior of two point functions of quark currents, Z. Physik C 62 (1994) 437 [hep-ph/9306323]; J. Prades, Massive spin 1 field chiral lagrangian from an extended Nambu-Jona-Lasinio model of QCD, Z. Physik C 63 (1994) 491 [hep-ph/9302246], erratum Eur. Phys. J. C 11 (1999) 571; J. Bijnens and J. Prades, Anomalies, VMD and the NJL model, Phys. Lett. B 320 (1994) 130 [hep-ph/9310355]; Two and three point functions in the extended NJL model, Z. Physik C 64 (1994) 475 [hep-ph/9403233]; J. Bijnens, Chiral lagrangians and Nambu-Jona-Lasinio-like models, Phys. Rep. 265 (1996) 369 [hep-ph/9502335].
55. J. Bijnens, C. Bruno and E. de Rafael, Nambu-Jona-Lasinio like models and the low-energy effective action of QCD, Nucl. Phys. B 390 (1993) 501 [hep-ph/9206236]; J. Bijnens, E. de Rafael and H. Zheng, Low-energy behavior of two point functions of quark currents, Z. Physik C 62 (1994) 437 [hep-ph/9306323]; J. Prades, Massive spin 1 field chiral lagrangian from an extended Nambu-Jona-Lasinio model of QCD, Z. Physik C 63 (1994) 491 [hep-ph/9302246], erratum Eur. Phys. J. C 11 (1999) 571; J. Bijnens and J. Prades, Anomalies, VMD and the NJL model, Phys. Lett. B 320 (1994) 130 [hep-ph/9310355]; Two and three point functions in the extended NJL model, Z. Physik C 64 (1994) 475 [hep-ph/9403233]; J. Bijnens, Chiral lagrangians and Nambu-Jona-Lasinio-like models, Phys. Rep. 265 (1996) 369 [hep-ph/9502335].
56. J. Bijnens, C. Bruno and E. de Rafael, Nambu-Jona-Lasinio like models and the low-energy effective action of QCD, Nucl. Phys. B 390 (1993) 501 [hep-ph/9206236]; J. Bijnens, E. de Rafael and H. Zheng, Low-energy behavior of two point functions of quark currents, Z. Physik C 62 (1994) 437 [hep-ph/9306323]; J. Prades, Massive spin 1 field chiral lagrangian from an extended Nambu-Jona-Lasinio model of QCD, Z. Physik C 63 (1994) 491 [hep-ph/9302246], erratum Eur. Phys. J. C 11 (1999) 571; J. Bijnens and J. Prades, Anomalies, VMD and the NJL model, Phys. Lett. B 320 (1994) 130 [hep-ph/9310355]; Two and three point functions in the extended NJL model, Z. Physik C 64 (1994) 475 [hep-ph/9403233]; J. Bijnens, Chiral lagrangians and Nambu-Jona-Lasinio-like models, Phys. Rep. 265 (1996) 369 [hep-ph/9502335].
57. A. Pich, Tau physics, in Heavy flavours II, A.J. Buras and M. Lindner eds., World Scientific 1998, p. 453, hep-ph/9704453.
58. c QCD, hep-ph/9910396.
59. c QCD, hep-ph/9910396.
60. c QCD, hep-ph/9910396.
61. LS in the chiral quark model, Nucl. Phys. B 493 (1997) 281 [hep-ph/9610230]; The ΔI = 1/2 selection rule, Nucl. Phys. B 469 (1996) 181 [hep-ph/9511341]; V. Antonelli, S. Bertolini, J.O. Eeg, M. Fabbrichesi and E.I. Lashin, The ΔS = 1 weak chiral lagrangian as the effective theory of the chiral quark model, Nucl. Phys. B 469 (1996) 143 [hep-ph/9511255].
62. LS in the chiral quark model, Nucl. Phys. B 493 (1997) 281 [hep-ph/9610230]; The ΔI = 1/2 selection rule, Nucl. Phys. B 469 (1996) 181 [hep-ph/9511341]; V. Antonelli, S. Bertolini, J.O. Eeg, M. Fabbrichesi and E.I. Lashin, The ΔS = 1 weak chiral lagrangian as the effective theory of the chiral quark model, Nucl. Phys. B 469 (1996) 143 [hep-ph/9511255].
63. LS in the chiral quark model, Nucl. Phys. B 493 (1997) 281 [hep-ph/9610230]; The ΔI = 1/2 selection rule, Nucl. Phys. B 469 (1996) 181 [hep-ph/9511341]; V. Antonelli, S. Bertolini, J.O. Eeg, M. Fabbrichesi and E.I. Lashin, The ΔS = 1 weak chiral lagrangian as the effective theory of the chiral quark model, Nucl. Phys. B 469 (1996) 143 [hep-ph/9511255].
64. LS in the chiral quark model, Nucl. Phys. B 493 (1997) 281 [hep-ph/9610230]; The ΔI = 1/2 selection rule, Nucl. Phys. B 469 (1996) 181 [hep-ph/9511341]; V. Antonelli, S. Bertolini, J.O. Eeg, M. Fabbrichesi and E.I. Lashin, The ΔS = 1 weak chiral lagrangian as the effective theory of the chiral quark model, Nucl. Phys. B 469 (1996) 143 [hep-ph/9511255].
65. LS in the chiral quark model, Nucl. Phys. B 493 (1997) 281 [hep-ph/9610230]; The ΔI = 1/2 selection rule, Nucl. Phys. B 469 (1996) 181 [hep-ph/9511341]; V. Antonelli, S. Bertolini, J.O. Eeg, M. Fabbrichesi and E.I. Lashin, The ΔS = 1 weak chiral lagrangian as the effective theory of the chiral quark model, Nucl. Phys. B 469 (1996) 143 [hep-ph/9511255].
66. LS in the chiral quark model, Nucl. Phys. B 493 (1997) 281 [hep-ph/9610230]; The ΔI = 1/2 selection rule, Nucl. Phys. B 469 (1996) 181 [hep-ph/9511341]; V. Antonelli, S. Bertolini, J.O. Eeg, M. Fabbrichesi and E.I. Lashin, The ΔS = 1 weak chiral lagrangian as the effective theory of the chiral quark model, Nucl. Phys. B 469 (1996) 143 [hep-ph/9511255].
67. LS in the chiral quark model, Nucl. Phys. B 493 (1997) 281 [hep-ph/9610230]; The ΔI = 1/2 selection rule, Nucl. Phys. B 469 (1996) 181 [hep-ph/9511341]; V. Antonelli, S. Bertolini, J.O. Eeg, M. Fabbrichesi and E.I. Lashin, The ΔS = 1 weak chiral lagrangian as the effective theory of the chiral quark model, Nucl. Phys. B 469 (1996) 143 [hep-ph/9511255].
68. LS in the chiral quark model, Nucl. Phys. B 493 (1997) 281 [hep-ph/9610230]; The ΔI = 1/2 selection rule, Nucl. Phys. B 469 (1996) 181 [hep-ph/9511341]; V. Antonelli, S. Bertolini, J.O. Eeg, M. Fabbrichesi and E.I. Lashin, The ΔS = 1 weak chiral lagrangian as the effective theory of the chiral quark model, Nucl. Phys. B 469 (1996) 143 [hep-ph/9511255].