Properties of the effective Hamiltonian for the system of neutral kaons*
Institute of Physics, University of Zielona Góra, Prof. Z. Szafrana 4a, Zielona Góra, Poland
e-mail: J.Jankiewicz@proton.if.uz.zgora.pl
Received:
Rec. 20 June 2005
DOI: 10.12921/cmst.2005.11.01.31-37
OAI: oai:lib.psnc.pl:579
Abstract:
We study the properties of time evolution of the K0 − K0 system in spectral formulation. Within the one-pole model we find the exact form of the diagonal matrix elements of the effective Hamiltonian for this system. It appears that, contrary to the Lee-Oehme-Yang (LOY) result, these exact diagonal matrix elements are different if the total system is CPT-invariant but CP-noninvariant.
Key words:
neutral K mesons, the CP noninvariance, the CPT invariance, the effective Hamiltonian, the LOY model, the one-pole model
References:
[1] H. Dehmelt, R. Mittleman, R. S. Van Dyck, Jr., P. Schwinberg, Phys. Rev. Lett. 83, 4694 (1999).
[2] K. Urbanowski, Phys. Lett., B 540, 89 (2002).
[3] T. D. Lee, R. Oehme, C. N. Yang, Phys. Rev., 106, 340 (1957).
[4] T. D. Lee, C. S. Wu, Annu. Rev. Nucl. Sci., 16, 471 (1966); M. K. Gaillard, M. Nicolic (Eds.), Weak Interaction, INPN et de Physique des Particules, Paris, 1977, Ch. 5, Appendix A; S. M. Bilenkij, in: Particles and Nucleus, Vol. 1. (1), 1970, p. 227, [in Russian].
[5] L. P. Horwitz, J. P. Marchand, Helv. Phys. Acta, 42, 801 (1969).
[6] J. W. Cronin, Acta Phys. Polon., B 15, 419 (1984); V. V. Barmin et al., Nucl. Phys., B 247, 428 (1984); L. Lavoura, Ann. Phys. (N.Y.), 207, 428 (1991); C. Buchanan et al., Phys. Rev., D 45, 4088 (1992); C. O. Dib, R. D. Peccei, Phys. Rev., D 46, 2265 (1992); M. Zrałek, Acta Phys. Polon., B 29, 3925 (1998); M. Nowakowski, Mod. Phys. Lett. A 17, 2039 (2002).
[7] K. Urbanowski, J. Piskorski, Found. Phys., 30, 839 (2000), physics/9803030.
[8] L. A. Khalfin, Preprints of the University of Texas at Austin: New Results on the CP-violation problem (Report DOE-ER40200-211, February 1990); L. A. Khalfin, A new CP-violation effect and new possibility for investigation of S0 , L0 ( 0, 0 ) K K K K decay modes (Report DOE-ER40200-247, Frebruary 1991).
[9] P. K. Kabir, A. Pilaftsis, Phys. Rev., A 53, 66 (1996).
[10] L. A. Khalfin, Found. Phys., 27, 1549 (1997), and references one can find therein.
[11] O. Nachtmann, Elementary Particle Physics, Springer Verlag, Berlin 1990.
[12] K. Hagiwara et al., Review of Particle Physics, Physical Review D 66, Part 1, No 1–I, 010001 (2002).
[13] M. Nowakowski, Time Evolution of K0 −K0 System in Spectral Formulation, SIS-Pubblicazioni, LNF-96/004(P); M. Nowakowski, Int. J. Mod. Phys., A 14, 589 (1999) .
[14] P. K. Kabir, The CP Puzzle, Academic Press, London 1968.
[15] A. Bohm, Quantum Mechanics: Foundations and Applications, Springer Verlag, Berlin 1986.
[16] I. S. Gradshteyn, I. M. Ryzhik, Tables of Integrals, Series and Products, 4th edition, Academic Press, London 1965.
[17] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series 55, Issued June 1964 Tenth Printing, December 1972, with corrections.
We study the properties of time evolution of the K0 − K0 system in spectral formulation. Within the one-pole model we find the exact form of the diagonal matrix elements of the effective Hamiltonian for this system. It appears that, contrary to the Lee-Oehme-Yang (LOY) result, these exact diagonal matrix elements are different if the total system is CPT-invariant but CP-noninvariant.
Key words:
neutral K mesons, the CP noninvariance, the CPT invariance, the effective Hamiltonian, the LOY model, the one-pole model
References:
[1] H. Dehmelt, R. Mittleman, R. S. Van Dyck, Jr., P. Schwinberg, Phys. Rev. Lett. 83, 4694 (1999).
[2] K. Urbanowski, Phys. Lett., B 540, 89 (2002).
[3] T. D. Lee, R. Oehme, C. N. Yang, Phys. Rev., 106, 340 (1957).
[4] T. D. Lee, C. S. Wu, Annu. Rev. Nucl. Sci., 16, 471 (1966); M. K. Gaillard, M. Nicolic (Eds.), Weak Interaction, INPN et de Physique des Particules, Paris, 1977, Ch. 5, Appendix A; S. M. Bilenkij, in: Particles and Nucleus, Vol. 1. (1), 1970, p. 227, [in Russian].
[5] L. P. Horwitz, J. P. Marchand, Helv. Phys. Acta, 42, 801 (1969).
[6] J. W. Cronin, Acta Phys. Polon., B 15, 419 (1984); V. V. Barmin et al., Nucl. Phys., B 247, 428 (1984); L. Lavoura, Ann. Phys. (N.Y.), 207, 428 (1991); C. Buchanan et al., Phys. Rev., D 45, 4088 (1992); C. O. Dib, R. D. Peccei, Phys. Rev., D 46, 2265 (1992); M. Zrałek, Acta Phys. Polon., B 29, 3925 (1998); M. Nowakowski, Mod. Phys. Lett. A 17, 2039 (2002).
[7] K. Urbanowski, J. Piskorski, Found. Phys., 30, 839 (2000), physics/9803030.
[8] L. A. Khalfin, Preprints of the University of Texas at Austin: New Results on the CP-violation problem (Report DOE-ER40200-211, February 1990); L. A. Khalfin, A new CP-violation effect and new possibility for investigation of S0 , L0 ( 0, 0 ) K K K K decay modes (Report DOE-ER40200-247, Frebruary 1991).
[9] P. K. Kabir, A. Pilaftsis, Phys. Rev., A 53, 66 (1996).
[10] L. A. Khalfin, Found. Phys., 27, 1549 (1997), and references one can find therein.
[11] O. Nachtmann, Elementary Particle Physics, Springer Verlag, Berlin 1990.
[12] K. Hagiwara et al., Review of Particle Physics, Physical Review D 66, Part 1, No 1–I, 010001 (2002).
[13] M. Nowakowski, Time Evolution of K0 −K0 System in Spectral Formulation, SIS-Pubblicazioni, LNF-96/004(P); M. Nowakowski, Int. J. Mod. Phys., A 14, 589 (1999) .
[14] P. K. Kabir, The CP Puzzle, Academic Press, London 1968.
[15] A. Bohm, Quantum Mechanics: Foundations and Applications, Springer Verlag, Berlin 1986.
[16] I. S. Gradshteyn, I. M. Ryzhik, Tables of Integrals, Series and Products, 4th edition, Academic Press, London 1965.
[17] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, National Bureau of Standards Applied Mathematics Series 55, Issued June 1964 Tenth Printing, December 1972, with corrections.
