Nucleon decay in supergravity unified theories

Pran Nath; A. H. Chamseddine; R. Arnowitt

doi:10.1103/PhysRevD.32.2348

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Nucleon decay in supergravity unified theories

Pran Nath and A. H. Chamseddine

R. Arnowitt

Department of Physics, Northeastern University, Boston, Massachusetts 02115

Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts 02138

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Phys. Rev. D 32, 2348 – Published 1 November, 1985

DOI: https://doi.org/10.1103/PhysRevD.32.2348

Abstract

A general analysis of nucleon decay in supergravity unified models is given including the full set of W-gaugino, gluino, and Z-gaugino dressing diagrams (with gauge as well as Yukawa interactions at vertices) of LLLL and RRRR dimension-five operators generated by Higgs-triplet exchange. The analysis is carried out within the framework of a model-independent formalism of SU(2)×U(1) breaking in supergravity models. Full symmetry-breaking effects on the vertices as well as all the allowed mass splittings of the supersymmetric particles that enter the dressing diagrams (i.e., W gauginos, Z gauginos, scalar quarks, and scalar leptons) are included. L-R mixing effects on scalar-quark–scalar-lepton masses, which are quite significant for the third generation for a heavy top quark, are also taken into account. Applications of the general analysis are made and it is shown that modification of supersymmetry predictions of nucleon decay can arise due to the inclusion of the new effects. It is shown specifically that ν¯π modes dominate nucleon decay in certain domains of the parameter space rather than ν¯K modes as is conventionally the case.

References (33)

S. Weinberg, Phys. Rev. D 26, 287 (1982); N. Sakai and T. Yanagida, Nucl. Phys. B197, 533 (1982).
S. Dimopoulos, S. Raby and F. Wilczek, Phys. Lett. 112B, 133 (1982); J. Ellis, D. V. Nanopoulos and S. Rudaz, Nucl. Phys. B202, 43 (1982); D. V. Nanopoulos and K. Tamvakis, Phys. Lett. 113B, 151 (1982); A. Masiero, D. V. Nanopoulos, K. Tamvakis and T. Yanagida, ibid. 115B, 298 (1982); J. P. Derendinger and C. A. Savoy, ibid. 118B, 347 (1982); P. Salati and J. C. Wallet, Nucl. Phys. B209, 389 (1982).
S. Chadha and M. Daniel, Nucl. Phys. B229, 105 (1983).
N. Sakai, Nucl. Phys. B238, 317 (1984).
B. A. Campbell, J. Ellis and D. V. Nanopoulos, Phys. Lett. 141B, 229 (1984).
J. Milutinovic, P. B. Pal and G. Senjanovic, Phys. Lett. 140B, 215 (1983). See also, Refs. 7, 8, and J. McDonald and C. E. Vayonakis, 144B, 199 (1984).
R. Arnowitt, A. H. Chamseddine, and P. Nath, in Proceedings of the Fifth Workshop on Grand Unification, Brown University, 1984, edited by K. Kang, H. Fried, and P. Frampton (World Scientific, Singapore, 1984).
S. Chadha and M. Daniel, Phys. Lett. 137B, 374 (1984).
A. H. Chamseddine, R. Arnowitt and P. Nath, Phys. Rev. Lett. 49, 970 (1982); R. Barbieri, S. Ferrara and A. Savoy, Phys. Lett. 119B, 342 (1982); L. E. Ibañez, ibid. 118, 73 (1982); J. Ellis, D. V. Nanopoulos and K. Tamvakis, ibid. 121B, 123 (1983); L. Alvarez-Gaume, J. Polchinski and M. B. Wise, Nucl. Phys. B221, 495 (1983); L. E. Ibañez and C. Lopez, Phys. Lett. 126B, 54 (1983); L. Hall, J. Lykken and S. Weinberg, Phys. Rev. D 27, 2359 (1983).
A. H. Chamseddine, P. Nath and R. Arnowitt, Phys. Lett. 129B, 445 (1983); J. M. Frere and G. L. Kane, Nucl. Phys. B223, 460 (1983); J. Ellis, J. S. Hagelin, D. V. Nanopoulos and M. Srednicki, Phys. Lett. 127B, 233 (1983).
P. Nath, R. Arnowitt, and A. H. Chamseddine, Applied N=1 Supergravity (ICTP Lecture Series in Theoretical Physics, Vol. 1) (World Scientific, Singapore, 1984); P. Nath, R. Arnowitt, and A. H. Chamseddine, in Proceedings of the Winter School on Supersymmetry, Supergravity/Non-perturbative QCD, edited by P. Roy and V. Singh (Springer, Berlin, 1984), pp. 113–185; J. Ellis, Proceedings of the 1983 International Symposium on Lepton and Photon Interactions at High Energies, edited by D. G. Cassel and D. L. Kreinick (Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, 1984).
A. brief description of some of these results were given in R. Arnowitt, A. H. Chamseddine and P. Nath, Phys. Lett. 156B, 215 (1985).
The diagonalization is affected by using identical transformations on quarks and scalar quarks. This procedure is valid at the GUT scale with unbroken supersymmetry. At low energy with broken supersymmetry one has corrections to these transformations which are different for quarks and scalar quarks. A recent analysis [S. Chadha, G. D. Coughlan, M. Daniel, and G. G. Ross, Phys. Lett. 149B, 477 (1984)] has considered arbitrary quark and scalar-quark transformations leading to additional contributions to the nucleon decay from the mismatch. However, the corrections to the quark and scalar-quark transformations at low energy determined through the renormalization group appear to be quite small (only a few percent) for the models considered here.
R. Barbieri, S. Ferrara and A. Savoy, Phys. Lett. 119B, 343 (1982); L. Hall, J. Lykken and S. Weinberg, Phys. Rev. D 27, 2359 (1983); P. Nath, R. Arnowitt and A. H. Chamseddine, Nucl. Phys. B227, 121 (1983).
The discussion given below, however, will not depend significantly on λ prime and λ prime prime.
Chamseddine, Arnowitt, and Nath (Ref. 9); S. Ferrara, D. V. Nanopoulos and C. A. Savoy, Phys. Lett. 123B, 214 (1983).
J. Ellis, J. S. Hagelin, D. V. Nanopoulos and K. Tamvakis, Phys. Lett. 125B, 275 (1983); C. Kounnas, A. B. Lahanas, D. V. Nanopoulos and M. Quiros, ibid. 127B, 82 (1983); Nucl. Phys. B236, 438 (1984).
J. Ellis, A. B. Lahanas, D. V. Nanopoulos and K. Tamvakis, Phys. Lett. 134B, 429 (1984).
A detailed discussion of the mass-diagonal Higgs-fermion/gaugino states and their couplings to matter is given in Ref. 10.
R. Arnowitt, A. H. Chamseddine, and P. Nath, in Problems in Unification and Supergravity, proceedings of the La Jolla Institute Workshop, edited by Glennys Farrar and Frank Henyey (AIP, New York, 1984); Alvarez-Gaume, Polchinski, and Wise (Ref. 9).
Our complex chiral-multiplet scalars are normalized according to Z = A + i B where the A and B fields are canonically normalized Hermitian fields.
J. Ellis, J. S. Hagelin, D. V. Nanopoulos and K. Tamvakis, Phys. Lett. B124, 484 (1983); V. M. Belyaev and M. I. Vysotsky, ibid. 127B, 215 (1983).
We have omitted in Eq. (4.1) loop corrections to scalar-quark masses due to gaugino couplings. [See, e.g., Kounnas et al., (Ref. 17); J. Ellis and M. Sher, Phys. Lett. 148B, 309 (1984); L. J. Hall and J. Polchinski, 152B, 335 (1985).] They make only a negligible correction to the $ũ - $\tilde{d}$ mass difference.
Note, however, if $m_{t}$ approx 40 GeV, then $ε_{3}^{d}$ is comparable to $ε_{3}^{u}$ for models with small $α_{H}$ .
See, e.g., W. Lucha, Report No. UWThPh-1984-26 (unpublished).
Proton-decay experiments, of course, cannot distinguish the different neutrinos.
A. J. Buras, W. Slominski and H. Steger, Nucl. Phys. B238, 529 (1984).
We use here a B-meson lifetime of 1.0 ps, R = 0.05 and $B_{K}$ = 1.5, which yields KM parameters $s_{1}$ = 0.231, $s_{2}$ apeq2 0.104, $s_{3}$ apeq2 0.0426, δ apeq2 170 ° for the ``upper'' solution. Lowering R does not significantly change the results.
M. Claudson, M. B. Wise and L. J. Hall, Nucl. Phys. B195, 43 (1982).
We include in our calculations a suppression of $L_{5}^{R}$ relative to $L_{5}^{L}$ of apeq2 0.53 due to short-range renormalization-group corrections from the GUT mass to $M_{W}$ as discussed in Ellis et al., Ref. 2.
For a recent summary of the current experimental bounds on nucleon decay see talks by M. Koshiba (Kamiokande), J. LoSecco (Irvine-Michigan-Brookhaven), E. Fiorini [nucleon-stability experiment (NUSEX)], V. S. Narasimham (Kolar Gold Fields), D. Cline (Harvard-Pennsylvania-Wisconsin), and S. Julien (Frejus), in Proceedings of the XXII International Conference on High Energy Physics, Leipzig, 1984, edited by A. Meyer and E. Wieczorek (Academie der Wissenschaften der DDR, Zeuthen, DDR, 1984).
For a current algebra calculation and discussion of previous work see J. Brodsky, J. Ellis, S. Hagelin and C. T. Sachrajda, Nucl. Phys. B238, 561 (1984).
K. Enqvist, A. Masiero and D. V. Nanopoulos, Phys. Lett. 156B, 209 (1985).

[c1] S. Weinberg, Phys. Rev. D 26, 287 (1982); N. Sakai and T. Yanagida, Nucl. Phys. B197, 533 (1982).

[c2] S. Dimopoulos, S. Raby and F. Wilczek, Phys. Lett. 112B, 133 (1982); J. Ellis, D. V. Nanopoulos and S. Rudaz, Nucl. Phys. B202, 43 (1982); D. V. Nanopoulos and K. Tamvakis, Phys. Lett. 113B, 151 (1982); A. Masiero, D. V. Nanopoulos, K. Tamvakis and T. Yanagida, ibid. 115B, 298 (1982); J. P. Derendinger and C. A. Savoy, ibid. 118B, 347 (1982); P. Salati and J. C. Wallet, Nucl. Phys. B209, 389 (1982).

[c3] S. Chadha and M. Daniel, Nucl. Phys. B229, 105 (1983).

[c4] N. Sakai, Nucl. Phys. B238, 317 (1984).

[c5] B. A. Campbell, J. Ellis and D. V. Nanopoulos, Phys. Lett. 141B, 229 (1984).

[c6] J. Milutinovic, P. B. Pal and G. Senjanovic, Phys. Lett. 140B, 215 (1983). See also, Refs. 7, 8, and J. McDonald and C. E. Vayonakis, 144B, 199 (1984).

[c7] R. Arnowitt, A. H. Chamseddine, and P. Nath, in Proceedings of the Fifth Workshop on Grand Unification, Brown University, 1984, edited by K. Kang, H. Fried, and P. Frampton (World Scientific, Singapore, 1984).

[c8] S. Chadha and M. Daniel, Phys. Lett. 137B, 374 (1984).

[c9] A. H. Chamseddine, R. Arnowitt and P. Nath, Phys. Rev. Lett. 49, 970 (1982); R. Barbieri, S. Ferrara and A. Savoy, Phys. Lett. 119B, 342 (1982); L. E. Ibañez, ibid. 118, 73 (1982); J. Ellis, D. V. Nanopoulos and K. Tamvakis, ibid. 121B, 123 (1983); L. Alvarez-Gaume, J. Polchinski and M. B. Wise, Nucl. Phys. B221, 495 (1983); L. E. Ibañez and C. Lopez, Phys. Lett. 126B, 54 (1983); L. Hall, J. Lykken and S. Weinberg, Phys. Rev. D 27, 2359 (1983).

[c10] A. H. Chamseddine, P. Nath and R. Arnowitt, Phys. Lett. 129B, 445 (1983); J. M. Frere and G. L. Kane, Nucl. Phys. B223, 460 (1983); J. Ellis, J. S. Hagelin, D. V. Nanopoulos and M. Srednicki, Phys. Lett. 127B, 233 (1983).

[c11] P. Nath, R. Arnowitt, and A. H. Chamseddine, Applied N=1 Supergravity (ICTP Lecture Series in Theoretical Physics, Vol. 1) (World Scientific, Singapore, 1984); P. Nath, R. Arnowitt, and A. H. Chamseddine, in Proceedings of the Winter School on Supersymmetry, Supergravity/Non-perturbative QCD, edited by P. Roy and V. Singh (Springer, Berlin, 1984), pp. 113–185; J. Ellis, Proceedings of the 1983 International Symposium on Lepton and Photon Interactions at High Energies, edited by D. G. Cassel and D. L. Kreinick (Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, 1984).

[c12] A. brief description of some of these results were given in R. Arnowitt, A. H. Chamseddine and P. Nath, Phys. Lett. 156B, 215 (1985).

[c13] The diagonalization is affected by using identical transformations on quarks and scalar quarks. This procedure is valid at the GUT scale with unbroken supersymmetry. At low energy with broken supersymmetry one has corrections to these transformations which are different for quarks and scalar quarks. A recent analysis [S. Chadha, G. D. Coughlan, M. Daniel, and G. G. Ross, Phys. Lett. 149B, 477 (1984)] has considered arbitrary quark and scalar-quark transformations leading to additional contributions to the nucleon decay from the mismatch. However, the corrections to the quark and scalar-quark transformations at low energy determined through the renormalization group appear to be quite small (only a few percent) for the models considered here.

[c14] R. Barbieri, S. Ferrara and A. Savoy, Phys. Lett. 119B, 343 (1982); L. Hall, J. Lykken and S. Weinberg, Phys. Rev. D 27, 2359 (1983); P. Nath, R. Arnowitt and A. H. Chamseddine, Nucl. Phys. B227, 121 (1983).

[c15] The discussion given below, however, will not depend significantly on λ prime and λ prime prime.

[c16] Chamseddine, Arnowitt, and Nath (Ref. 9); S. Ferrara, D. V. Nanopoulos and C. A. Savoy, Phys. Lett. 123B, 214 (1983).

[c17] J. Ellis, J. S. Hagelin, D. V. Nanopoulos and K. Tamvakis, Phys. Lett. 125B, 275 (1983); C. Kounnas, A. B. Lahanas, D. V. Nanopoulos and M. Quiros, ibid. 127B, 82 (1983); Nucl. Phys. B236, 438 (1984).

[c18] J. Ellis, A. B. Lahanas, D. V. Nanopoulos and K. Tamvakis, Phys. Lett. 134B, 429 (1984).

[c19] A detailed discussion of the mass-diagonal Higgs-fermion/gaugino states and their couplings to matter is given in Ref. 10.

[c20] R. Arnowitt, A. H. Chamseddine, and P. Nath, in Problems in Unification and Supergravity, proceedings of the La Jolla Institute Workshop, edited by Glennys Farrar and Frank Henyey (AIP, New York, 1984); Alvarez-Gaume, Polchinski, and Wise (Ref. 9).

[c21] Our complex chiral-multiplet scalars are normalized according to Z = A + i B where the A and B fields are canonically normalized Hermitian fields.

[c22] J. Ellis, J. S. Hagelin, D. V. Nanopoulos and K. Tamvakis, Phys. Lett. B124, 484 (1983); V. M. Belyaev and M. I. Vysotsky, ibid. 127B, 215 (1983).

[c23] We have omitted in Eq. (4.1) loop corrections to scalar-quark masses due to gaugino couplings. [See, e.g., Kounnas et al., (Ref. 17); J. Ellis and M. Sher, Phys. Lett. 148B, 309 (1984); L. J. Hall and J. Polchinski, 152B, 335 (1985).] They make only a negligible correction to the $ũ - $\tilde{d}$ mass difference.

[c24] Note, however, if $m_{t}$ approx 40 GeV, then $ε_{3}^{d}$ is comparable to $ε_{3}^{u}$ for models with small $α_{H}$ .

[c25] See, e.g., W. Lucha, Report No. UWThPh-1984-26 (unpublished).

[c26] Proton-decay experiments, of course, cannot distinguish the different neutrinos.

[c27] A. J. Buras, W. Slominski and H. Steger, Nucl. Phys. B238, 529 (1984).

[c28] We use here a B-meson lifetime of 1.0 ps, R = 0.05 and $B_{K}$ = 1.5, which yields KM parameters $s_{1}$ = 0.231, $s_{2}$ apeq2 0.104, $s_{3}$ apeq2 0.0426, δ apeq2 170 ° for the ``upper'' solution. Lowering R does not significantly change the results.

[c29] M. Claudson, M. B. Wise and L. J. Hall, Nucl. Phys. B195, 43 (1982).

[c30] We include in our calculations a suppression of $L_{5}^{R}$ relative to $L_{5}^{L}$ of apeq2 0.53 due to short-range renormalization-group corrections from the GUT mass to $M_{W}$ as discussed in Ellis et al., Ref. 2.

[c31] For a recent summary of the current experimental bounds on nucleon decay see talks by M. Koshiba (Kamiokande), J. LoSecco (Irvine-Michigan-Brookhaven), E. Fiorini [nucleon-stability experiment (NUSEX)], V. S. Narasimham (Kolar Gold Fields), D. Cline (Harvard-Pennsylvania-Wisconsin), and S. Julien (Frejus), in Proceedings of the XXII International Conference on High Energy Physics, Leipzig, 1984, edited by A. Meyer and E. Wieczorek (Academie der Wissenschaften der DDR, Zeuthen, DDR, 1984).

[c32] For a current algebra calculation and discussion of previous work see J. Brodsky, J. Ellis, S. Hagelin and C. T. Sachrajda, Nucl. Phys. B238, 561 (1984).

[c33] K. Enqvist, A. Masiero and D. V. Nanopoulos, Phys. Lett. 156B, 209 (1985).

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Nucleon decay in supergravity unified theories

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