ε′K/εK in the chiral limit

Journal of High Energy Physics

Volumn 4, Issue 6, 2000, Pages 1-27

  Bijnens, Johan ^a   Prades, Joaquim ^b  

^a LUND UNIVERSITY   (Sweden)

^b UNIVERSITY OF GRANADA   (Spain)

Author keywords

1 N Expansion; CP violation; Kaon Physics; Weak Decays

Indexed keywords

EID: 7044247867     PISSN: 10298479     EISSN: None     Source Type: Journal    
DOI: 10.1088/1126-6708/2000/06/035     Document Type: Article

References (80)

1. S,L → ππ decays, Phys. Rev. Lett. 83 (1999) 22 [hep-ex/9905060]; E. Blucher, ε′/ε results from KTEV, hep-ex/0001042; NA48 collaboration, A new measurement of direct CP-violation in two pion decays of the neutral kaon, Phys. Lett. B 465 (1999) 335 [hep-ex/9909022]; Results on direct CP-violation from NA48, hep-ex/9912042; A. Ceccucci (NA48 collaboration), CERN Seminar February 29th 2000, http://www.cern.ch/NA48.
2. S,L → ππ decays, Phys. Rev. Lett. 83 (1999) 22 [hep-ex/9905060]; E. Blucher, ε′/ε results from KTEV, hep-ex/0001042; NA48 collaboration, A new measurement of direct CP-violation in two pion decays of the neutral kaon, Phys. Lett. B 465 (1999) 335 [hep-ex/9909022]; Results on direct CP-violation from NA48, hep-ex/9912042; A. Ceccucci (NA48 collaboration), CERN Seminar February 29th 2000, http://www.cern.ch/NA48.
3. S,L → ππ decays, Phys. Rev. Lett. 83 (1999) 22 [hep-ex/9905060]; E. Blucher, ε′/ε results from KTEV, hep-ex/0001042; NA48 collaboration, A new measurement of direct CP-violation in two pion decays of the neutral kaon, Phys. Lett. B 465 (1999) 335 [hep-ex/9909022]; Results on direct CP-violation from NA48, hep-ex/9912042; A. Ceccucci (NA48 collaboration), CERN Seminar February 29th 2000, http://www.cern.ch/NA48.
4. S,L → ππ decays, Phys. Rev. Lett. 83 (1999) 22 [hep-ex/9905060]; E. Blucher, ε′/ε results from KTEV, hep-ex/0001042; NA48 collaboration, A new measurement of direct CP-violation in two pion decays of the neutral kaon, Phys. Lett. B 465 (1999) 335 [hep-ex/9909022]; Results on direct CP-violation from NA48, hep-ex/9912042; A. Ceccucci (NA48 collaboration), CERN Seminar February 29th 2000, http://www.cern.ch/NA48.
5. S,L → ππ decays, Phys. Rev. Lett. 83 (1999) 22 [hep-ex/9905060]; E. Blucher, ε′/ε results from KTEV, hep-ex/0001042; NA48 collaboration, A new measurement of direct CP-violation in two pion decays of the neutral kaon, Phys. Lett. B 465 (1999) 335 [hep-ex/9909022]; Results on direct CP-violation from NA48, hep-ex/9912042; A. Ceccucci (NA48 collaboration), CERN Seminar February 29th 2000, http://www.cern.ch/NA48.
6. A. 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, 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].
7. A. 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, 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].
8. G. Buchalla, A.J. Buras and M.E. Lautenbacher, Weak decays beyond leading logarithms, Rev. Mod. Phys. 68 (1996) 1125 [hep-ph/9512380].
9. S. Bosch, A.J. Buras, M. Gorbahn, S. Jäger, M. Jamin, M.E. Lautenbacher and L. Silvestrini, Standard model confronting new results for ε′/ε, Nucl. Phys. B 565 (2000) 3 [hep-ph/9904408].
10. S. Bertolini, M. Fabbrichesi and J.O. Eeg, Estimating ε′/ε: a review, Rev. Mod. Phys. 72 (2000) 65 [hep-ph/9802405].
11. A.J. Buras, Weak hamiltonian, CP-violation and rare decays, in Probing the standard model of particle interactions, Les Houches Lectures 1997, F. David and R. Gupta 4 eds., Elsevier Science, 1999 [hep-ph/9806471].
12. 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; G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, A possible mechanism for the ΔT = 1/2 rule in nonleptonic decays of strange particles, Sov. Phys. JETP Lett. 22 (1975) 55; 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; M. Lusignoli, Electromagnetic corrections to the effective hamiltonian for strangeness changing decays and ε′/ε, Nucl. Phys. B 325 (1989) 33; J.M. Flynn and L. Randall, The electromagnetic penguin contribution to ε′/ε for large top quark mass, Phys. Lett. B 224 (1989) 221.
13. 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; G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, A possible mechanism for the ΔT = 1/2 rule in nonleptonic decays of strange particles, Sov. Phys. JETP Lett. 22 (1975) 55; 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; M. Lusignoli, Electromagnetic corrections to the effective hamiltonian for strangeness changing decays and ε′/ε, Nucl. Phys. B 325 (1989) 33; J.M. Flynn and L. Randall, The electromagnetic penguin contribution to ε′/ε for large top quark mass, Phys. Lett. B 224 (1989) 221.
14. 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; G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, A possible mechanism for the ΔT = 1/2 rule in nonleptonic decays of strange particles, Sov. Phys. JETP Lett. 22 (1975) 55; 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; M. Lusignoli, Electromagnetic corrections to the effective hamiltonian for strangeness changing decays and ε′/ε, Nucl. Phys. B 325 (1989) 33; J.M. Flynn and L. Randall, The electromagnetic penguin contribution to ε′/ε for large top quark mass, Phys. Lett. B 224 (1989) 221.
15. 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; G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, A possible mechanism for the ΔT = 1/2 rule in nonleptonic decays of strange particles, Sov. Phys. JETP Lett. 22 (1975) 55; 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; M. Lusignoli, Electromagnetic corrections to the effective hamiltonian for strangeness changing decays and ε′/ε, Nucl. Phys. B 325 (1989) 33; J.M. Flynn and L. Randall, The electromagnetic penguin contribution to ε′/ε for large top quark mass, Phys. Lett. B 224 (1989) 221.
16. 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; G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, A possible mechanism for the ΔT = 1/2 rule in nonleptonic decays of strange particles, Sov. Phys. JETP Lett. 22 (1975) 55; 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; M. Lusignoli, Electromagnetic corrections to the effective hamiltonian for strangeness changing decays and ε′/ε, Nucl. Phys. B 325 (1989) 33; J.M. Flynn and L. Randall, The electromagnetic penguin contribution to ε′/ε for large top quark mass, Phys. Lett. B 224 (1989) 221.
17. 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; G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, A possible mechanism for the ΔT = 1/2 rule in nonleptonic decays of strange particles, Sov. Phys. JETP Lett. 22 (1975) 55; 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; M. Lusignoli, Electromagnetic corrections to the effective hamiltonian for strangeness changing decays and ε′/ε, Nucl. Phys. B 325 (1989) 33; J.M. Flynn and L. Randall, The electromagnetic penguin contribution to ε′/ε for large top quark mass, Phys. Lett. B 224 (1989) 221.
18. 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; G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, A possible mechanism for the ΔT = 1/2 rule in nonleptonic decays of strange particles, Sov. Phys. JETP Lett. 22 (1975) 55; 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; M. Lusignoli, Electromagnetic corrections to the effective hamiltonian for strangeness changing decays and ε′/ε, Nucl. Phys. B 325 (1989) 33; J.M. Flynn and L. Randall, The electromagnetic penguin contribution to ε′/ε for large top quark mass, Phys. Lett. B 224 (1989) 221.
19. 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; G. Altarelli and L. Maiani, Octet enhancement of nonleptonic weak interactions in asymptotically free gauge theories, Phys. Lett. B 52 (1974) 351; A.I. Vainshtein, V.I. Zakharov and M.A. Shifman, A possible mechanism for the ΔT = 1/2 rule in nonleptonic decays of strange particles, Sov. Phys. JETP Lett. 22 (1975) 55; 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; M. Lusignoli, Electromagnetic corrections to the effective hamiltonian for strangeness changing decays and ε′/ε, Nucl. Phys. B 325 (1989) 33; J.M. Flynn and L. Randall, The electromagnetic penguin contribution to ε′/ε for large top quark mass, Phys. Lett. B 224 (1989) 221.
20. 2), Nucl. Phys. B 400 (1993) 37 [hep-ph/9211304]; 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].
21. 2), Nucl. Phys. B 400 (1993) 37 [hep-ph/9211304]; 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].
22. 2), Nucl. Phys. B 400 (1993) 37 [hep-ph/9211304]; 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].
23. 2), Nucl. Phys. B 400 (1993) 37 [hep-ph/9211304]; 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].
24. 2), Nucl. Phys. B 400 (1993) 37 [hep-ph/9211304]; 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].
25. W.A. Bardeen, A.J. Buras and J.M. Gérard, A consistent analysis of the ΔI = 1/2 rule for K decays, Phys. Lett. B 192 (1987) 138; The K → ππ decays in the large-N limit: quark evolution, Nucl. Phys. B 293 (1987) 787.
26. W.A. Bardeen, A.J. Buras and J.M. Gérard, A consistent analysis of the ΔI = 1/2 rule for K decays, Phys. Lett. B 192 (1987) 138; The K → ππ decays in the large-N limit: quark evolution, Nucl. Phys. B 293 (1987) 787.
27. L. Lellouch and M. Lüscher, Weak transition matrix elements from finite-volume correlation functions, hep-lat/0003023.
28. S mass difference, Phys. Lett. B 257 (1991) 191; J.P. Fatelo and J.M. Gérard, Current-current operator evolution in the chiral limit, Phys. Lett. B 347 (1995) 136.
29. S mass difference, Phys. Lett. B 257 (1991) 191; J.P. Fatelo and J.M. Gérard, Current-current operator evolution in the chiral limit, Phys. Lett. B 347 (1995) 136.
30. S mass difference, Phys. Lett. B 257 (1991) 191; J.P. Fatelo and J.M. Gérard, Current-current operator evolution in the chiral limit, Phys. Lett. B 347 (1995) 136.
31. c expansion, Nucl. Phys. B 444 (1995) 523 [hep-ph/9502363].
32. c expansion, Nucl. Phys. B 444 (1995) 523 [hep-ph/9502363].
33. C expansion, Nucl. Phys. B 564 (2000) 391 [hep-ph/9906434].
34. C expansion, Nucl. Phys. B 564 (2000) 391 [hep-ph/9906434].
35. C expansion, Nucl. Phys. B 564 (2000) 391 [hep-ph/9906434].
36. J. Bijnens and J. Prades, The ΔI = 1/2 rule in the chiral limit, J. High Energy Phys. 01 (1999) 023 [hep-ph/9811472].
37. c expansion, J. High Energy Phys. 01 (2000) 002 [hep-ph/9911392].
38. J. Bijnens, E. Pallante and J. Prades, Obtaining K → ππ from off-shell K → π amplitudes, Nucl. Phys. B 521 (1998) 305 [hep-ph/9801326].
39. c expansion, Phys. Lett. B 457 (1999) 227 [hep-ph/9812471].
40. 4) in the chiral expansion, Nucl. Phys. B 514 (1998) 93 [hep-ph/9706260]; S. Bertolini, J.O. Eeg and M. Fabbrichesi, An updated analysis of ε′/ε in the standard model with hadronic matrix elements from the chiral quark model, hep-ph/0002234.
41. 4) in the chiral expansion, Nucl. Phys. B 514 (1998) 93 [hep-ph/9706260]; S. Bertolini, J.O. Eeg and M. Fabbrichesi, An updated analysis of ε′/ε in the standard model with hadronic matrix elements from the chiral quark model, hep-ph/0002234.
42. 4) in the chiral expansion, Nucl. Phys. B 514 (1998) 93 [hep-ph/9706260]; S. Bertolini, J.O. Eeg and M. Fabbrichesi, An updated analysis of ε′/ε in the standard model with hadronic matrix elements from the chiral quark model, hep-ph/0002234.
43. 4) in the chiral expansion, Nucl. Phys. B 514 (1998) 93 [hep-ph/9706260]; S. Bertolini, J.O. Eeg and M. Fabbrichesi, An updated analysis of ε′/ε in the standard model with hadronic matrix elements from the chiral quark model, hep-ph/0002234.
44. 4) in the chiral expansion, Nucl. Phys. B 514 (1998) 93 [hep-ph/9706260]; S. Bertolini, J.O. Eeg and M. Fabbrichesi, An updated analysis of ε′/ε in the standard model with hadronic matrix elements from the chiral quark model, hep-ph/0002234.
45. M. Jamin and A. Pich, QCD corrections to inclusive ΔS = 1,2 transitions at the next-to-leading order, Nucl. Phys. B 425 (1994) 15 [hep-ph/9402363]; last reference in [41] and references therein.
46. A. Duncan, E. Eichten and H. Thacker, Electromagnetic splittings and light quark masses in lattice QCD, Phys. Rev. Lett. 76 (1996) 3894 [hep-lat/9602005].
47. A. Pich, Effective field theory, in Probing the standard model of particle interactions, Les Houches Lectures 1997, F. David and R. Gupta eds., Elsevier Science, 1999 [hep-ph/9806303].
48. 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, Chiral lagrangians and Nambu-Jona-Lasinio like models, Phys. Rep. 265 (1996) 369 [hep-ph/9502335].
49. 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, Chiral lagrangians and Nambu-Jona-Lasinio like models, Phys. Rep. 265 (1996) 369 [hep-ph/9502335].
50. J. Bijnens, E. de Rafael and H. Qing Zheng, Low-energy behavior of two point functions of quark currents, Z. Physik C 62 (1994) 437 [hep-ph/9306323]; J. Bijnens and J. Prades, 2 and 3 point functions in the ENJL model, Nucl. Phys. 39BC (Proc. Suppl.) (1995) 245 [hep-ph/9409231].
51. J. Bijnens, E. de Rafael and H. Qing Zheng, Low-energy behavior of two point functions of quark currents, Z. Physik C 62 (1994) 437 [hep-ph/9306323]; J. Bijnens and J. Prades, 2 and 3 point functions in the ENJL model, Nucl. Phys. 39BC (Proc. Suppl.) (1995) 245 [hep-ph/9409231].
52. J. Bijnens, E. Gámiz and J. Prades, work in progress.
53. J. Bijnens, J. Prades and E. de Rafael, Light quark masses in QCD, Phys. Lett. B 348 (1995) 226 [hep-ph/9411285].
54. J. Prades, The ΔI = 1/2 rule for kaons, Nucl. Phys. 86 (Proc. Suppl.) (2000) 294 [hep-ph/9909245]; J. Bijnens, 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; Progress in K → ππ decays, Nucl. Phys. A 663 (2000) 927 [hep-ph/9907307].
55. J. Prades, The ΔI = 1/2 rule for kaons, Nucl. Phys. 86 (Proc. Suppl.) (2000) 294 [hep-ph/9909245]; J. Bijnens, 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; Progress in K → ππ decays, Nucl. Phys. A 663 (2000) 927 [hep-ph/9907307].
56. J. Prades, The ΔI = 1/2 rule for kaons, Nucl. Phys. 86 (Proc. Suppl.) (2000) 294 [hep-ph/9909245]; J. Bijnens, 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; Progress in K → ππ decays, Nucl. Phys. A 663 (2000) 927 [hep-ph/9907307].
57. J. Prades, The ΔI = 1/2 rule for kaons, Nucl. Phys. 86 (Proc. Suppl.) (2000) 294 [hep-ph/9909245]; J. Bijnens, 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; Progress in K → ππ decays, Nucl. Phys. A 663 (2000) 927 [hep-ph/9907307].
58. A. Sirlin, Ten years of precision electroweak physics, hep-ph/9912227.
59. A.F. Falk, B decays, the unitarity triangle and the universe, hep-ph/9908520.
60. A. Pich, Tau physics, hep-ph/9912294.
61. S. Herrlich and U. Nierste, The complete |ΔS| = 2 hamiltonian in the next-to-leading order, Nucl. Phys. B 476 (1996) 27 [hep-ph/9604330].
62. A.J. Buras and J.M. Gérard, Isospin breaking contributions to epsilon-prime/epsilon, Phys. Lett. B 192 (1987) 156; E. de Rafael, Introduction to weak decays and QCD: short distance corrections, Nucl. Phys. 7A (Proc. Suppl) (1989) 1.
63. A.J. Buras and J.M. Gérard, Isospin breaking contributions to epsilon-prime/epsilon, Phys. Lett. B 192 (1987) 156; E. de Rafael, Introduction to weak decays and QCD: short distance corrections, Nucl. Phys. 7A (Proc. Suppl) (1989) 1.
64. L. Lellouch, D.-J. Lin and UKQCD collaboration, ΔS = 1 and ΔI = 3/2 matrix elements in quenched QCD, Nucl. Phys. 73 (Proc. Suppl.) (1999) 312 [hep-lat/9809142]; C.R. Allton, L. Conti, A. Donini, V. Giménez, L. Giusti, G. Martinelli, M. Talevi and A. Vladikas, B-parameters for ΔS = 2 supersymmetric operators, Phys. Lett. B 453 (1999) 30 [hep-lat/9806016]; L. Conti, A. Donini, V. Giménez, G. Martinelli, M. Talevi and A. Vladikas, Lattice B-parameters for ΔS = 2 and ΔI = 3/2 operators, Phys. Lett. B 421 (1998) 273 [hep-lat/9711053].
65. L. Lellouch, D.-J. Lin and UKQCD collaboration, ΔS = 1 and ΔI = 3/2 matrix elements in quenched QCD, Nucl. Phys. 73 (Proc. Suppl.) (1999) 312 [hep-lat/9809142]; C.R. Allton, L. Conti, A. Donini, V. Giménez, L. Giusti, G. Martinelli, M. Talevi and A. Vladikas, B-parameters for ΔS = 2 supersymmetric operators, Phys. Lett. B 453 (1999) 30 [hep-lat/9806016]; L. Conti, A. Donini, V. Giménez, G. Martinelli, M. Talevi and A. Vladikas, Lattice B-parameters for ΔS = 2 and ΔI = 3/2 operators, Phys. Lett. B 421 (1998) 273 [hep-lat/9711053].
66. L. Lellouch, D.-J. Lin and UKQCD collaboration, ΔS = 1 and ΔI = 3/2 matrix elements in quenched QCD, Nucl. Phys. 73 (Proc. Suppl.) (1999) 312 [hep-lat/9809142]; C.R. Allton, L. Conti, A. Donini, V. Giménez, L. Giusti, G. Martinelli, M. Talevi and A. Vladikas, B-parameters for ΔS = 2 supersymmetric operators, Phys. Lett. B 453 (1999) 30 [hep-lat/9806016]; L. Conti, A. Donini, V. Giménez, G. Martinelli, M. Talevi and A. Vladikas, Lattice B-parameters for ΔS = 2 and ΔI = 3/2 operators, Phys. Lett. B 421 (1998) 273 [hep-lat/9711053].
67. 3/2 in the chiral limit, Phys. Lett. B 478 (2000) 172 [hep-ph/9911309].
68. S. Narison, New QCD-estimate of the kaon penguin matrix elements and ε′/ε, hep-ph/0004247.
69. B. Ananthanarayan, G. Colangelo, J. Gasser and H. Leutwyler, Roy equations analysis of ππ scattering, hep-ph/0005297.
70. E. Pallante and A. Pich, Strong enhancement of ε′/ε through final state interactions, Phys. Rev. Lett. 84 (2000) 2568 [hep-ph/9911233].
71. A.J. Buras, M. Ciuchini, E. Franco, G. Isidori, G. Martinelli and L. Silvestrini, Final state interactions and ε′/ε: a critical look, Phys. Lett. B 480 (2000) 80 [hep-ph/0002116]; E.A. Paschos, Rescattering effects for (ε′/ε), hep-ph/9912230.
72. A.J. Buras, M. Ciuchini, E. Franco, G. Isidori, G. Martinelli and L. Silvestrini, Final state interactions and ε′/ε: a critical look, Phys. Lett. B 480 (2000) 80 [hep-ph/0002116]; E.A. Paschos, Rescattering effects for (ε′/ε), hep-ph/9912230.
73. 0-η mixing and CP-violation, Phys. Lett. B 477 (2000) 88 [hep-ph/9912264].
74. J. Kambor, J. Missimer and D. Wyler, K → 2π and K → 3π decays in next-to-leading order chiral perturbation theory, Phys. Lett. B 261 (1991) 496.
75. S. Gardner and G. Valencia, Additional isospin-breaking effects in ε′/ε, Phys. Lett. B 466 (1999) 355 [hep-ph/9909202]; V. Cirigliano, J.F. Donoghue and E. Golowich, Electromagnetic corrections to K → ππ, 1. Chiral perturbation theory, Phys. Rev. D 61 (2000) 093001 [hep-ph/9907341]; Electromagnetic corrections to K → ππ, 2. Dispersive matching, Phys. Rev. D 61 (2000) 093002 [hep-ph/9909473]; C.E. Wolfe and K. Maltman, Strong isospin-breaking effects on the ΔI = 3/2 amplitude in K → 2π at next-to-leading order in the chiral expansion, Phys. Lett. B 482 (2000) 77 [hep-ph/9912254].
76. S. Gardner and G. Valencia, Additional isospin-breaking effects in ε′/ε, Phys. Lett. B 466 (1999) 355 [hep-ph/9909202]; V. Cirigliano, J.F. Donoghue and E. Golowich, Electromagnetic corrections to K → ππ, 1. Chiral perturbation theory, Phys. Rev. D 61 (2000) 093001 [hep-ph/9907341]; Electromagnetic corrections to K → ππ, 2. Dispersive matching, Phys. Rev. D 61 (2000) 093002 [hep-ph/9909473]; C.E. Wolfe and K. Maltman, Strong isospin-breaking effects on the ΔI = 3/2 amplitude in K → 2π at next-to-leading order in the chiral expansion, Phys. Lett. B 482 (2000) 77 [hep-ph/9912254].
77. S. Gardner and G. Valencia, Additional isospin-breaking effects in ε′/ε, Phys. Lett. B 466 (1999) 355 [hep-ph/9909202]; V. Cirigliano, J.F. Donoghue and E. Golowich, Electromagnetic corrections to K → ππ, 1. Chiral perturbation theory, Phys. Rev. D 61 (2000) 093001 [hep-ph/9907341]; Electromagnetic corrections to K → ππ, 2. Dispersive matching, Phys. Rev. D 61 (2000) 093002 [hep-ph/9909473]; C.E. Wolfe and K. Maltman, Strong isospin-breaking effects on the ΔI = 3/2 amplitude in K → 2π at next-to-leading order in the chiral expansion, Phys. Lett. B 482 (2000) 77 [hep-ph/9912254].
78. S. Gardner and G. Valencia, Additional isospin-breaking effects in ε′/ε, Phys. Lett. B 466 (1999) 355 [hep-ph/9909202]; V. Cirigliano, J.F. Donoghue and E. Golowich, Electromagnetic corrections to K → ππ, 1. Chiral perturbation theory, Phys. Rev. D 61 (2000) 093001 [hep-ph/9907341]; Electromagnetic corrections to K → ππ, 2. Dispersive matching, Phys. Rev. D 61 (2000) 093002 [hep-ph/9909473]; C.E. Wolfe and K. Maltman, Strong isospin-breaking effects on the ΔI = 3/2 amplitude in K → 2π at next-to-leading order in the chiral expansion, Phys. Lett. B 482 (2000) 77 [hep-ph/9912254].
79. c-expansions, Phys. Lett. B 374 (1996) 186 [hep-ph/9511465]; Four quark operators and nonleptonic weak transitions, Nucl. Phys. B 358 (1991) 311.
80. c-expansions, Phys. Lett. B 374 (1996) 186 [hep-ph/9511465]; Four quark operators and nonleptonic weak transitions, Nucl. Phys. B 358 (1991) 311.