Topics in Quantum Field Theory and Gauge Theories pp 292-334 | Cite as

# Part B: Basic left-right symmetry in nature: Its implications for atomic parity, neutrino and high-energy e^{−} e^{+}-experiments

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Asymmetry Parameter Spontaneous Symmetry Breaking Atomic Parity Atomic Parity Violation Neutral Current Interaction
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## References and footnotes

- 1.Refer for example to the talks of C. Baltay and J. Steinberger at the European Physical Society meeting, Budapest, Hungary (1977), to appear in the Proceedings.Google Scholar
- 2.S. Weinberg, Phys. Rev. Letters 19, 1264 (1967); Abdus Salam in Elementary Particle Physics, ed. N. Svartholm (Almkvist and Wicksell, Stockholm, 1968), p. 367; S. L. Glasvhow, J. Iliopoulos and L. Maiani, Phys. Rev. D2, 1285 (1970).The SU(2)
_{L}x U(1)-gauge structure without the Higgs-mechanism for generation of gauge masses was proposed by S. L. Glashow, Nucl. Phys. 22, 579 (1961) and Abdus Salam and J. C. Ward, Phys. Letters 13, 168 (1964).Google Scholar - 3.The recent results of L. L. Lewis et al., Phys. Rev. Lett. 39, 795 (1977)) and P. E. G. Baird et al. (Phys. Rev. Lett. 39, 798 (1977)) for the optical rotation parameters in atomic Bismuth are: R(876 nm) = (-.7 ± 3.2) x 10 (−8) (Washington), R(648 run)-(+2.7 ± 4.7) x 10
^{−8}(Oxford). Given the previous atomic theoretical calculations based on relativistic central field approximation (see Ref. 4) together with the shielding effect (discussed by P. G. Sandars at the International Symposium on Lepton and Photon-interactions at high energies, held at Hamburg, W. Germany, August, 1977), the above numbers correspond to a basic atomic parity violation parameter Q_{W}for Bi lying between-50 ≲ Q_{W}≤ +75, while the simple SU(2)_{L}x U(1)-theory predicts Q_{W}= −145 (for sin^{2}Ø6W = 0.30). Quite clearly, improvements in theoretical accuracy, or alternatively measurements in hydrogen are crucial to determine Q_{W}accurately.Google Scholar - 4.I. B. Kriplovich, Soviet Physics-JETP Lett. 20, 315 (1974); E. M. Henley and L. Wilets, Phys. Rev. A19, 1911 (1976); M. Brimicombe, C. E. Loving and P. G. H. Sandars, J. Phys. B9, L237 (1976). Recently shielding effects have been considered (see Ref. 3).Google Scholar
- 5.The first suggestion of the left ↔ right symmetric theory SU(2)
_{I}x SU(2)_{R}x UM_{L+R}comprising all matter (quarks as well as leptons) was made by J. C. Pati and Abdus Salam, Phys. Rev. Letters 31, 661 (1973); ibid. Phys. Rev. D10, 275 (1974).The motivations in these work were the realizations of basic left-right symmetry and quantization of electric charge. Motivation based on considerations of CP violation was provided by R. N. Mohapatra and J. C. Pati, Phys. Rev. Dll, 566 (1975). The second paper (Phys. Rev. D10, 275 (1974), Ch. IV and VI and Footnote 21) proposes two alternative patterns of spontaneous symmetry breaking; both patterns are consistent with the hypothesis of “natural” left-right symmetry. One of the patterns permits only one, while the other permits two relatively light neutral weak gauge particles. It is this second alternative, which is relevant is present atomic parity experiments (Ref. 3), and is pursued recently by several authors (Ref. 11).Google Scholar - 6.J. C. Pati, S. Rajpoot and Abdus Salam, Imperial College Preprint ICTP/76/11, Phys. Rev. D (to be published). The left-right symmetric theory SU(2)
_{L}x SU(2)_{R}x U(l)_{+R}is equivalent to the SU(2)_{L}x U(1)-theory for lefthanded neutrino-processes only to the extent that W_{L}-W_{R}mixing mass may be neglected compared to m_{W}_{L}+. This is discussed later.Google Scholar - 7.Barring possible small corrections due to Higgs-boson exchanges. Note if W
_{L}and W_{R}have equal mass with no mixing between them, (W_{L}±W_{R})/ \((W_L \pm W_R )/\sqrt 2\)are mass eigenstates. The gauge interaction gWV)n by Eq. (1))may be written in terms of these eigenstates as \((g/\sqrt 2 )\frac{{(W_L + W_R )}}{{\sqrt 2 }}(V) + \frac{{(W_L - W_R )}}{{\sqrt 2 }}( - A)\). This generates in second order parity conserving interaction σ (VV+AA).Google Scholar - 8.We expect neutrinos to be in general four-component objects within the theory, unless v
_{L}and v_{R}remain disjoint and therefore massless despite spontaneous symmetry breaking. Such four-component neutrinos may still have arbitrarily small mass. A natural understanding of the smallness of neutrino-mass or its masslessness is yet a challenge to the theory.Google Scholar - 9.In a different context such a postulate was made by M. A. Bég and A. A. Zee, Phys. Rev. Lett. Vol. 30, 675 (1973).Google Scholar
- 10.J. C. Pati and Abdus Salam, Phys. Rev. D10, 275 (1974)(Ch. IV, VI & Footnote 21).Google Scholar
- 11.The consequences of the zeroth-order solution 〈B〉= 〈C〉0 arising within the model proposed in Ref. 5 was first examined by H. Fritzsch and P. Minkowski, Nucl. Phys. B103, 61 (1976), and more recently by R. N. Mohapatra and D. P. Sidhu, Phys. Rev. Letters 38, 667 (1977).The more general case comprising 〈B〉-〈C〉and 〈B〉= 〈C〉has been examined by J. C. Pati, S. Rajpoot and Abdus Salam, Imperial College, London, preprint ICTP/76/11 (to be published in Phys. Rev. D), and Physics Letters 71B, 387 (1977). For a somewhat different treatment of spontaneous symmetry breaking of the group structure proposed in Ref. 5 see, A. De Rujula, H. Georgi and S. L. Glashow, Harvard preprint, 1977. For an analogous phenomenological discussion containing the basic ingredients of the gauge-framework, see B. Kayser, Phys. Rev. D15, 3407 (1977). The equivalence theorem stating the equivalence of the left-right symmetric theory SU(2)
_{L}x SU(2)_{R}x U(1)_{L+R}with the left-handed theory SU(2)_{L}x U(1) for neutrino processes (see Ref. 6 and Chapter 3) has been further generalized to comprise extended groupstructures by H. Georgi and S. Weinberg (Harvard preprint, HUTP-77/A052).Google Scholar - 12.The choice 〈B〉= 〈C〉J 0 is in general not a “natural” solution of the theory in the technical sense; this is the case for example for Ref. 11. Mechanisms permitting 〈B〉= 〈C〉0 0 naturally despite radiative corrections are briefly mentioned later.Google Scholar
- 13.R. N. Mohapatra and J. C. Pati, Phys. Rev. Dll, 566, 2558 (1975). For a calculation of such 0(
*a*) radiative corrections, see Q. Shafi and Ch. Wetterich, University of Freiburg preprint (THEP 77/3).Google Scholar - 14.It needs to be stressed that contrary to common impression \((\sigma _{v_L p^{ \ne \sigma } \bar v_{R^P } } )\)NC does not imply parity non-conservation since v
_{L}*+*β_{R}under parity. Such a distinction between v_{L}and −v R cross-sections eliminates only the class of parity-conserving theories, which are vector-like with no AA piece (see discussion below).Google Scholar - 15.A. Benvenutti et al., Phys. Rev. Letters 37, 1039 (1976); J. Blietschau et al., Preprint CERN/EP/Phys. 76-55; B. C. Barish, Ca. Tech. preprint CALT-68-544.The clearest distinction is shown by measurements of a(−v
_{R}p → 0−v_{R}p) versus o(v_{L}p → V_{L}P). See D. Cline et a1., Phys. Rev. Letters 37, 252, 648 (1976) and W. Lee et al., Phys. Rev. Letters 37, 186 (1976).Google Scholar - 16.M. A. B. Bég and A. Zee, Phys. Rev. Letters 30, 675 (1973). For a list of references on other vector-like models, see R. M. Barnett, Review talk, Brookhaven, APS Meeting, SLAC-PUB 1850.Google Scholar
- 17.We call them “restricted” vector-like theories to distinguish them from the mirror theory (J. C. Pati and A. Salam, Physics Letters 58B, 333 (1975)), in which (V-A) current of the basic fermions (p,n,X,c)
_{L}and (V+A) current of the mirror fermions (p',n',a',c')_{R}couple to the same gauge particles W_{A}. Such a theory is vector-like in a broader sense; but within this theory there exist a parallel and distinct set of gauge particles W_{E}with their (V-A) and (V+A) coupling reversed compared to W_{A}; which have no counterparts within the restricted SU(2)_{L+R}x U(1)_{L+R}vector-like theories.Google Scholar - 18.It is possible to construct SU(2) x U(1)-models satisfying atomic parity-data as well as neutrino-data. In particular, the E
_{7}model descending through SU(2)x U(1)-component (F. Gursey and P. Sikivie, Phys. Rev. Lett. 36, 775 (1976), ibid, Phys. Rev. D. 16, 816 (1977) and P. Ramond, Nucl. Phys. B 110, 214 (1976)) is interesting in this connection. However there is a possible question regarding “natural” suppression of strangeness changing neutral current-processes in such models (see S. L. Glashow and S. Weinberg, Harvard Preprint HUTP-75/A158).Google Scholar - 19.R. N. Mohapatra and J. C. Pati, Phys. Rev. Dll, 566 (1975).Google Scholar
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_{R}≪ cos0_{L}. In such models one could obtain m_{W}^{t}_{R}− m_{W}^{+}_{L}. However, within unified theories with no abelian factor, such loss of manifest left-right symmetry in physical currents (in the sense defined recently by M. A. B. Bég, R. Budny, R. N. Mohapatra and A. Sirlin, Phys. Rev. Lett. 38, 1252 (1977)) is not permissible (see remark by J. Pati, 1976 Scottish University Lecture Notes, Page 109, Ed. I. M. Barbour and A. T. Davis).Google Scholar - 26.K. Symanzik, in Fundamental Interactions at High Energies, Ed. A. Perlmutter et al. (Gordon and Breach, 1970).Google Scholar
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