Pion decay constant

In particle physics, the pion decay constant is the square root of the coefficient in front of the kinetic term for the pion in the low-energy effective action. It is dimensionally an energy scale and it determines the strength of the chiral symmetry breaking. The values are:

f_{\pi ^{\pm }}=130.41\pm 0.03\pm 0.20~{\mbox{MeV}}

f_{\pi ^{0}}=130\pm 5~{\mbox{MeV}}

Beware: There are several conventions which differ by factors of $\scriptstyle {\sqrt {2}}$ . The textbook by Weinberg uses the value 184 MeV. The textbook by Peskin and Schroeder uses the value 93 MeV.

According to Brown-Rho scaling, the masses of nucleons and most light mesons decrease at finite density as the ratio of the in-medium pion decay rate to the free-space pion decay constant. The pion mass is an exception to Brown-Rho scaling because the pion's mass is protected by its Goldstone boson nature.[1]

References

Holt, J. W.; Brown, G. E.; Kuo, T. T. S.; Holt, J. D.; Machleidt, R. (2008). "Shell Model Description of the ¹⁴C Dating β Decay with Brown-Rho-Scaled NN Interactions". Physical Review Letters. 100 (6): 062501. arXiv:0710.0310. doi:10.1103/PhysRevLett.100.062501. PMID 18352465.

Al, W-M Yao et; Amsler, C.; Asner, D.; Barnett, R. M.; Beringer, J.; Burchat, P. R.; Carone, C. D.; Caso, C.; Dahl, O.; d'Ambrosio, G.; De Gouvea, A.; Doser, M.; Eidelman, S.; Feng, J. L.; Gherghetta, T.; Goodman, M.; Grab, C.; Groom, D. E.; Gurtu, A.; Hagiwara, K.; Hayes, K. G.; Hernández-Rey, J. J.; Hikasa, K.; Jawahery, H.; Kolda, C.; Kwon, Y.; Mangano, M. L.; Manohar, A. V.; Masoni, A.; et al. (2006). "Review of Particle Physics". Journal of Physics G: Nuclear and Particle Physics. 33 (1): 1–1232. Bibcode:2006JPhG...33....1Y. doi:10.1088/0954-3899/33/1/001.
Griffiths, David J. (1987). Introduction to Elementary Particles. Wiley, John & Sons, Inc. ISBN 978-0-471-60386-3.
Particle Data Group: Decay constants of charged pseudoscalar mesons

External links

Particle Data Group & WWW edition of Review of Particle Physics

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[Holt-1] Holt, J. W.; Brown, G. E.; Kuo, T. T. S.; Holt, J. D.; Machleidt, R. (2008). "Shell Model Description of the ¹⁴C Dating β Decay with Brown-Rho-Scaled NN Interactions". Physical Review Letters. 100 (6): 062501. arXiv:0710.0310. doi:10.1103/PhysRevLett.100.062501. PMID 18352465.