Muon capture in a general class of weak models

F. J. Botella

doi:10.1103/PhysRevD.32.1760

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Muon capture in a general class of weak models

F. J. Botella

Department of Physics, Brookhaven National Laboratory, Upton, New York, 11973

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Phys. Rev. D 32, 1760 – Published 1 October, 1985

DOI: https://doi.org/10.1103/PhysRevD.32.1760

Abstract

We study muon capture by ${}^{12}C$ in a general class of weak models. There is always a parameter characteristic of the weak model that can be extracted in a nuclear-model-independent way from the average polarization $P_{av}$ , the longitudinal polarization $P_{L}^{N}$ and the asymmetry α in the angular distribution of recoils. For a less general class of models the asymmetry α is unnecessary. Using the experimental values of $P_{L}^{N}$ and $P_{av}$ we get a lower bound for the mass of the right-handed gauge boson of the left-right-symmetric model, $M_{W_{R} \geq 2.5 M_{W_{L}}}$ , in a nuclear-model-independent way. The dependence of this bound on the experimental values is also discussed.

References (18)

F. J. Botella and J. Bernabeu, Nucl. Phys. A414, 456 (1984).
F. J. Botella and J. Bernabeu, Valencia University report, 1984 (unpublished).
Y. Kuno, J. Imazato, K. Nishiyama, K. Nagamine, T. Yamazaki and T. Minamisono, Phys. Lett. 140B, 270 (1984). See references therein.
J. C. Pati and A. Salam, Phys. Rev. D 10, 275 (1974); M. A. B. Bég, R. V. Budny, R. Mohapatra and A. Sirlin, Phys. Rev. Lett. 38, 1252 (1977).
F. J. Botella and J. Bernabeu, Phys. Lett. 114B, 208 (1982); J. Delorme, thesis, Lyon, 1972.
W. -Y. P. Hwang, Phys. Rev. C 20, 805 (1979); 20, 2457(E) (1979).
We have neglected $E^{(ν)}$ and $m_{mu}$ versus the nuclear mass in getting Eq. (4) and if we do not make this approximation we must only redefine the parameters $G_{A}$ , $G_{V}$ , and $G_{P}$ in Eq. (3). But still they contain all the nuclear information.
Omitted end note.
F. J. Botella, University of Valencia, thesis, 1983; J. Maalampi, K. Mursula and M. Roos, Nucl. Phys. B207, 233 (1982).
J. Carr, G. Gidal, B. Gobbi, A. Jodidio, C. J. Oram, K. A. Shinsky, H. M. Steiner, D. P. Stoker, M. Strovink and R. D. Tripp, Phys. Rev. Lett. 51, 627 (1983), and references therein.
J. Bernabeu, Phys. Lett. 55B, 313 (1975).
Omitted end note.
L. Ph. Roesch, V. L. Telegdi, P. Truttmann, A. Zenuder, L. Grenacs, and L. Palffy, Helv. Phys. Acta 55, (1982) 74; P. A. Truttmann, Diss. ETH No. 6753 Zurich, 1981; A. Possoz et al., Phys. Lett. 70B, 265 (1977); L. P. Roesch et al., Phys. Rev. Lett. 46, 1507 (1981).
Omitted end note.
Of course, the best lower bound for $M_{w_{R}}$ comes from the mass difference $K_{L}$ - $K_{S}$ . This bound is placed in the TeV region. Independent of the gauge problems in the box graph, which appear to be correctable without drastic changes (Ref. 16), we must stress that this bound is not the result of a fit to the experimental values, but it is the result of assuming that the left-right box graph must give, by itself, a contribution smaller than the standard box graph. Although this assumption is extremely reasonable, we must say that this lower bound is in some sense model dependent. On the contrary we must also add that the bounds considered in the present paper are only valid for Dirac neutrinos, although the one obtained from the box graph is independent of the neutrino type.
G. Beall, M. Bander and A. Soni, Phys. Rev. Lett. 48, 848 (1982); D. Chang, J. Basecq, L. -F. Li and P. B. Pal, Phys. Rev. D 30, 1601 (1984); W. -S. Hou and A. Soni, ibid. 32, 163 (1985); J. Basecq, L. -F. Li and P. B. Pal, ibid. 32, 175 (1985).
Equation (12) is valid for all the models defined by (1) and (8) with the obvious change Δ -> beta.
J. F. Donoghue and B. R. Holstein, Phys. Lett. 113B, 382 (1982); L. Wolfenstein, Phys. Rev. D 29, 2130 (1984).

[c1] F. J. Botella and J. Bernabeu, Nucl. Phys. A414, 456 (1984).

[c2] F. J. Botella and J. Bernabeu, Valencia University report, 1984 (unpublished).

[c3] Y. Kuno, J. Imazato, K. Nishiyama, K. Nagamine, T. Yamazaki and T. Minamisono, Phys. Lett. 140B, 270 (1984). See references therein.

[c4] J. C. Pati and A. Salam, Phys. Rev. D 10, 275 (1974); M. A. B. Bég, R. V. Budny, R. Mohapatra and A. Sirlin, Phys. Rev. Lett. 38, 1252 (1977).

[c5] F. J. Botella and J. Bernabeu, Phys. Lett. 114B, 208 (1982); J. Delorme, thesis, Lyon, 1972.

[c6] W. -Y. P. Hwang, Phys. Rev. C 20, 805 (1979); 20, 2457(E) (1979).

[c7] We have neglected $E^{(ν)}$ and $m_{mu}$ versus the nuclear mass in getting Eq. (4) and if we do not make this approximation we must only redefine the parameters $G_{A}$ , $G_{V}$ , and $G_{P}$ in Eq. (3). But still they contain all the nuclear information.

[c8] Omitted end note.

[c9] F. J. Botella, University of Valencia, thesis, 1983; J. Maalampi, K. Mursula and M. Roos, Nucl. Phys. B207, 233 (1982).

[c10] J. Carr, G. Gidal, B. Gobbi, A. Jodidio, C. J. Oram, K. A. Shinsky, H. M. Steiner, D. P. Stoker, M. Strovink and R. D. Tripp, Phys. Rev. Lett. 51, 627 (1983), and references therein.

[c11] J. Bernabeu, Phys. Lett. 55B, 313 (1975).

[c12] Omitted end note.

[c13] L. Ph. Roesch, V. L. Telegdi, P. Truttmann, A. Zenuder, L. Grenacs, and L. Palffy, Helv. Phys. Acta 55, (1982) 74; P. A. Truttmann, Diss. ETH No. 6753 Zurich, 1981; A. Possoz et al., Phys. Lett. 70B, 265 (1977); L. P. Roesch et al., Phys. Rev. Lett. 46, 1507 (1981).

[c14] Omitted end note.

[c15] Of course, the best lower bound for $M_{w_{R}}$ comes from the mass difference $K_{L}$ - $K_{S}$ . This bound is placed in the TeV region. Independent of the gauge problems in the box graph, which appear to be correctable without drastic changes (Ref. 16), we must stress that this bound is not the result of a fit to the experimental values, but it is the result of assuming that the left-right box graph must give, by itself, a contribution smaller than the standard box graph. Although this assumption is extremely reasonable, we must say that this lower bound is in some sense model dependent. On the contrary we must also add that the bounds considered in the present paper are only valid for Dirac neutrinos, although the one obtained from the box graph is independent of the neutrino type.

[c16] G. Beall, M. Bander and A. Soni, Phys. Rev. Lett. 48, 848 (1982); D. Chang, J. Basecq, L. -F. Li and P. B. Pal, Phys. Rev. D 30, 1601 (1984); W. -S. Hou and A. Soni, ibid. 32, 163 (1985); J. Basecq, L. -F. Li and P. B. Pal, ibid. 32, 175 (1985).

[c17] Equation (12) is valid for all the models defined by (1) and (8) with the obvious change Δ -> beta.

[c18] J. F. Donoghue and B. R. Holstein, Phys. Lett. 113B, 382 (1982); L. Wolfenstein, Phys. Rev. D 29, 2130 (1984).

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