No Anomaly and New Renormalization Scheme

Affiliation(s)

Department of Physics, Faculty of Science and Technology, Nihon University, Tokyo, Japan.

Department of Physics, Faculty of Science and Technology, Nihon University, Tokyo, Japan.

ABSTRACT

We review the physics of chiral anomaly and show that the anomaly equation of δ_{μ}J^{μ}_{5} =e^{2}16π^{2}ε_{μνρδ} F^{μν}F^{ρδ}is not connected to any physical observables. This is based on the fact that the reaction process of π^{0}→2γ has no diver- gence at all, and the triangle diagrams with the vertex of γ^{μ}γ_{5} describing the Z^{0}→2γ decay do not have any di- vergences either. The recent calculated branching ratio of the Z^{0}→2γ decay rate is found to be Г_{Z0→2γ}/Г□2.4×10^{-8}. Further, we discuss the anomaly equation in the Schwinger model which is known as δ_{μ}J^{μ}_{5}=e2πε_{μν}F^{μν} , and prove that this anomaly equation disagrees with the exact value of the chiral charge δ_{5}=±1 in the Schwinger vacuum.
Therefore, the chiral anomaly is a spurious effect induced by the regularization. In connection with the anomaly prob- lem, we clarify the physical meaning why the self-energy of photon should not be included in the renormalization scheme. Also, we present the renormalization scheme in weak interactions without Higgs particles, and this is achieved with a new propagator of massive vector bosons, which does not give rise to any logarithmic divergences in the vertex corrections. Therefore, there is no necessity of the renormalization procedure of the vertex corrections arising from the weak vector boson propagation.

We review the physics of chiral anomaly and show that the anomaly equation of δ

Cite this paper

T. Fujita and N. Kanda, "No Anomaly and New Renormalization Scheme,"*Journal of Modern Physics*, Vol. 3 No. 8, 2012, pp. 665-681. doi: 10.4236/jmp.2012.38091.

T. Fujita and N. Kanda, "No Anomaly and New Renormalization Scheme,"

References

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[12] N. Kanda, R. Abe, T. Fujita and H. Tsuda, “Z0 Decay Into Two Photons,” arXiv:1109.0926v1 [hep-ph], 2011.

[13] C. Amsler, et al., “Review of Particle Physics,” Physics Letters B, Vol. 667, No. 1-5, 2008, pp. 1-6. doi:10.1016/j.physletb.2008.07.018

[14] T. Tomachi and T. Fujita, “Fermion Condensate and the Spectrum of Massive Schwinger Model in Bogoliubov Transformed Vacuum,” Annals of Physics, Vol. 223, No. 2, 1993, pp. 197-215. doi:10.1006/aphy.1993.1031

[15] H. A. Bethe, “The Electromagnetic Shift of Energy Lev- els,” Physical Review, Vol. 72, 1947, pp. 339-341. doi:10.1103/PhysRev.72.339

[16] J. D. Bjorken and S. D. Drell, “Relativistic Quantum Mechanics,” McGraw-Hill, New York, 1964.

[17] J. C. Ward, “An Identity in Quantum Electrodynamics,” Physical Review, Vol. 78, No. 2, 1950, p. 182. doi:10.1103/PhysRev.78.182

[18] W. Pauli and F. Villars, “On the Invariant Regularization in Relativistic Quantum Theory,” Reviews of Modern Physics, Vol. 21, No. 3, 1949, pp. 434-444. doi:10.1103/RevModPhys.21.434

[19] G. Hooft and M. Veltman, “Regularization and Renor- malization of Gauge Fields,” Nuclear Physics B, Vol. 44, No. 1, 1972, pp. 189-213. doi:10.1016/0550-3213(72)90279-9

[20] G. Hooft and M. Veltman, “Combinatorics of Gauge Fields,” Nuclear Physics B, Vol. 50, No. 1, 1972, pp. 318-353. doi:10.1016/S0550-3213(72)80021-X

[21] T. Fujita and N. Kanda, “Tomonaga’s Conjecture on Photon Self-Energy,” 2011.

[22] J. J. Sakurai, “Advanced Quantum Mechanics,” Addison- Wesley, Boston, 1967.

[23] W. Heisenberg, “Bemerkungen zur Diracschen Theorie des Positrons,” Zeitschrift für Physik, Vol. 90, No. 3-4, 1934, pp. 209-231. doi:10.1007/BF01333516

[24] W. Heisenberg and H. Euler, “Folgerungen aus der Diracschen Theorie des Positrons,” Zeitschrift für Physik, Vol. 98, No. 11-12, 1936, pp. 714-732. doi:10.1007/BF01343663

[25] N. Kanda, “Light-Light Scattering,” hep-ph/1106.0592, 2011.

[1] C. Itzykson and J. B. Zuber, “Quantum Field Theory,” McGraw-Hill, New York, 1980.

[2] L. Ryder, “Quantum Field Theory,” Cambridge University Press, Cambridge, 1996.

[3] S. I. Adler, “Vertex in Spinor Electrodynamics,” Physical Review, Vol. 177, 1969, pp. 2426-2438. doi:10.1103/PhysRev.177.2426

[4] N. S. Manton, “The Schwinger Model and Its Axial Anomaly,” Annals of Physics, Vol. 159, No. 1, 1985, pp. 220-251. doi:10.1016/0003-4916(85)90199-X

[5] J. Schwinger, “Gauge Invariance and Mass,” Physical Review, Vol. 128, No. 5, 1962, pp. 2425-2429. doi:10.1103/PhysRev.128.2425

[6] T. Fujita, “Symmetry and Its Breaking in Quantum Field Theory,” 2nd Edition, Nova Science Publishers, New York, 2011.

[7] K. Nishijima, “Fields and Particles,” W. A. Benjamin, Inc., San Francisco, 1969.

[8] T. P. Cheng and L. F. Li, “Gauge Theory of Elementary Particle Physics,” Oxford University Press, Oxford, 1989.

[9] F. Mandl and G. Shaw, “Quantum Field Theory,” John Wiley & Sons, New York, 1993.

[10] L. D. Landau, “Dokl. Akad. Nawk.,” USSR 60, 1948, pp. 207-209.

[11] C. N. Yang, “Selection Rules for the Dematerialization of a Particle into Two Photons,” Physical Review, Vol. 77, No. 2, 1950, pp. 242-245. doi:10.1103/PhysRev.77.242

[12] N. Kanda, R. Abe, T. Fujita and H. Tsuda, “Z0 Decay Into Two Photons,” arXiv:1109.0926v1 [hep-ph], 2011.

[13] C. Amsler, et al., “Review of Particle Physics,” Physics Letters B, Vol. 667, No. 1-5, 2008, pp. 1-6. doi:10.1016/j.physletb.2008.07.018

[14] T. Tomachi and T. Fujita, “Fermion Condensate and the Spectrum of Massive Schwinger Model in Bogoliubov Transformed Vacuum,” Annals of Physics, Vol. 223, No. 2, 1993, pp. 197-215. doi:10.1006/aphy.1993.1031

[15] H. A. Bethe, “The Electromagnetic Shift of Energy Lev- els,” Physical Review, Vol. 72, 1947, pp. 339-341. doi:10.1103/PhysRev.72.339

[16] J. D. Bjorken and S. D. Drell, “Relativistic Quantum Mechanics,” McGraw-Hill, New York, 1964.

[17] J. C. Ward, “An Identity in Quantum Electrodynamics,” Physical Review, Vol. 78, No. 2, 1950, p. 182. doi:10.1103/PhysRev.78.182

[18] W. Pauli and F. Villars, “On the Invariant Regularization in Relativistic Quantum Theory,” Reviews of Modern Physics, Vol. 21, No. 3, 1949, pp. 434-444. doi:10.1103/RevModPhys.21.434

[19] G. Hooft and M. Veltman, “Regularization and Renor- malization of Gauge Fields,” Nuclear Physics B, Vol. 44, No. 1, 1972, pp. 189-213. doi:10.1016/0550-3213(72)90279-9

[20] G. Hooft and M. Veltman, “Combinatorics of Gauge Fields,” Nuclear Physics B, Vol. 50, No. 1, 1972, pp. 318-353. doi:10.1016/S0550-3213(72)80021-X

[21] T. Fujita and N. Kanda, “Tomonaga’s Conjecture on Photon Self-Energy,” 2011.

[22] J. J. Sakurai, “Advanced Quantum Mechanics,” Addison- Wesley, Boston, 1967.

[23] W. Heisenberg, “Bemerkungen zur Diracschen Theorie des Positrons,” Zeitschrift für Physik, Vol. 90, No. 3-4, 1934, pp. 209-231. doi:10.1007/BF01333516

[24] W. Heisenberg and H. Euler, “Folgerungen aus der Diracschen Theorie des Positrons,” Zeitschrift für Physik, Vol. 98, No. 11-12, 1936, pp. 714-732. doi:10.1007/BF01343663

[25] N. Kanda, “Light-Light Scattering,” hep-ph/1106.0592, 2011.