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

  • Jogesh C. Pati
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 77)


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

  1. 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. 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. 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 QW for Bi lying between-50 ≲ QW ≤ +75, while the simple SU(2)L x U(1)-theory predicts QW = −145 (for sin2Ø6W = 0.30). Quite clearly, improvements in theoretical accuracy, or alternatively measurements in hydrogen are crucial to determine QW accurately.Google Scholar
  4. 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. 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. 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 WL-WR mixing mass may be neglected compared to mW L+. This is discussed later.Google Scholar
  7. 7.
    Barring possible small corrections due to Higgs-boson exchanges. Note if WL and WR have equal mass with no mixing between them, (WL±WR)/ \((W_L \pm W_R )/\sqrt 2\)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. 8.
    We expect neutrinos to be in general four-component objects within the theory, unless vL and vR 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. 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. 10.
    J. C. Pati and Abdus Salam, Phys. Rev. D10, 275 (1974)(Ch. IV, VI & Footnote 21).Google Scholar
  11. 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. 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. 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. 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 vL + βR under parity. Such a distinction between vL 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. 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(−vRp → 0−vRp) versus o(vLp → VLP). 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. 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. 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 WA. Such a theory is vector-like in a broader sense; but within this theory there exist a parallel and distinct set of gauge particles WE with their (V-A) and (V+A) coupling reversed compared to WA; which have no counterparts within the restricted SU(2)L+R x U(1)L+R vector-like theories.Google Scholar
  18. 18.
    It is possible to construct SU(2) x U(1)-models satisfying atomic parity-data as well as neutrino-data. In particular, the E7 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. 19.
    R. N. Mohapatra and J. C. Pati, Phys. Rev. Dll, 566 (1975).Google Scholar
  20. 20.
    uL. Wolfenstein, Phys. Rev. Lett. 13, 562 (1964); Nucl. Phys. B77, 375 (1974). For a gauge theory version see R. N. Mohapatra, J. C. Pati and L. Wolfenstein, Phys. Rev. D 11, 3319 (1975).Google Scholar
  21. 21.
    The lower limit (= 30 GeV) on the mass (mo) of the relevant left over Higgsboson corresponds to the experimental constraint that the relation n+−= noo is known to hold to better 5% (see Ref. 19). In reference 19,m0 a was allowed to be as high as 104 GeV or higher.This led to a prediction for dn varying between 10−24 to 10−29 e cm. The constraint imposed here that mo should not exceed about 1000 GeV (or else Higgs-fields would begin to interact strongly, see e.g. M. Veltman, Utrecht preprint, and B. W. Lee, C. Quigg and H. B. Thacker, Phys. Rev. Lett. 38, 883 (1977)) is important: it makes the dipole moment do to necessarily exceed about 10−27 ecm for the isoconjugate model, bringing the same to an experimentally accessible range. The recent experimental value (.4 ± 1.1) x 10−24 ecm, obtained by W. B. Dress et al., Phys. Rev. D5, 9 (1977), is expected to be improved to the level of = 10−26 ecm in the near future.Google Scholar
  22. 22.
    Extension to mirror-model (J. C. Pati and A. Salam, Physics Letters 58B, 333 (1975)) would need in addition a 16-fold mirror set of heavy quarks and heavy leptons. This is needed for the sake of complete unification. Such extensions do not however alter any of our discussions on neutral current-phenomena.Google Scholar
  23. 23.
    J. C. Pati and Abdus Salam, Phys. Rev. D8, 1240 (1973). C. Itoh, T. Minamikawa, K. Miura and T. Watanabee, Preprint (1973), unpublished.Google Scholar
  24. 24.
    In general, if the basic group G or its subgroup −G descend from a higher unifying group G unifying group (e.g. [SU(4)]4), the coupling constants associated with SU(2)L and SU(2)R may differ from each other through finite renormalization effects, which may in principle introduce large left-right asymmetry at the low energy level, even though the group structure G is left-right symmetric.Google Scholar
  25. 25.
    Extended models with more than four flavors (e.g. the mirror model, Ref. 22) may in general permit large skewness angles (see Ref. 22) leading to cos0R ≪ cos0L. In such models one could obtain mW t R − mW + 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. 26.
    K. Symanzik, in Fundamental Interactions at High Energies, Ed. A. Perlmutter et al. (Gordon and Breach, 1970).Google Scholar
  27. 27.
    This has been demonstrated for the case of a pair of left-right symmetric Higgs doublets B and C by G. Senjanovic and R. N. Mohapatra, Phys. Rev. D 12, 502 (1975). The result holds more generally in the presence of additional left-right symmetric Higgs-pairs with mutual couplings between them (see e.g. Ref. 31 and 32).Google Scholar
  28. 28.
    G. Rajasekharan and P. Roy, Pramana 6, 303 (1975), J. C. Pati and A. Salam, Phys. Rev. Lett. 36, 11 (1976), V. Elias, J. C. Pati, A. Salam and J. Strathdee, Pramana 4, 303 (1977).Google Scholar
  29. 29.
    R. N. Mohapatra, J. C. Pati and A. Salam, Phys. Rev. D13, 1733 (1976).Google Scholar
  30. 30.
    For a discussion of the consistency and the experimental consequences of the unconfined unstable integer-charge quark-hypothesis, see J. C. Pati and A. Salam, Comments on Nuclear and Particle Physics (1976) and in particular the recent Trieste Preprint, “Design of Experiments to Test...” IC/77/65.Google Scholar
  31. 31.
    H. S. Mani, J. C. Pati and A. Salam, “Naturalness of Atomic Parity Conservation Within Left-Right Symmetric Unified Theories”-Trieste Preprint IC/77/80, Phys. Rev. D (to be published).Google Scholar
  32. 32.
    R. N. Mohapatra, F. E..Paige and D. P. Sidhu, BNL-preprint (1977).Google Scholar
  33. 33.
    S. Coleman and E. Weinberg, Phys. Rev. D7, 1888 (1973).Google Scholar
  34. 34.
    In this case, one needs〈A〉 〈〈 〈C〉in order that the W+ L-W+ R mixing be small, as seems to be required by the neutrino-data together with the present atomic parity data.Google Scholar
  35. 35.
    Here the subscripts L and R refer to the gauge pattern of the basic fermions F. For the mirror fermions (Ref. 22) L and R are interchanged.Google Scholar
  36. 36.
    J. C. Pati, Proc. Second Orbis Scientae, Coral Gables, Florida, Jan, 1975 (P253–256), ed. by A. Perlmutter and S. Widmayer; J. C. Pati, S. Rajpoot and A. Salam (Ref. 6, Footnote 15). The experimental consequences of this group structure have recently been emphasized by Q. Shafi and Ch. Wetterich, Univ. of Freiburg Preprint (1977) and by V. Elias, J. C. Pati and Abdus Salam, Univ. of Md. Tech. Rep. No. 78-043 (1977), Physics Letters to be published.Google Scholar
  37. 37.
    CDHS result, M. Holder et al., CERN Preprint (1977).Google Scholar
  38. 38.
    V. Elias, Phys. Rev. D 14, 1896 (1976); Md. Tech. Rep. No. 77–253, Phys. Rev. D (To be published), Md. Tech. Rep. No. 78-040 (1977), V. Elias, J. Pati and A. Salam, U. of Md. Tech. Rep. 78-041 (1977).Google Scholar
  39. 39.
    H. Georgi, H. R. Quinn and uS. Weinberg, Phys. Rev. Letters 33, 451 (1974).Google Scholar
  40. 40.
    H. Georgi and S. L. Glashow, Phys. Rev. Letters, 32, 438 (1974).Google Scholar
  41. 41.
    Barring finite order a-differences between (gL-gR)/gL.Google Scholar
  42. 42.
    See for example, R. Budny, Physics Letters, 55B, 227 (1975); A. McDonald, Nuclear Physics B75, 343 (1974) and E. Lendavi and G. Pocsik, Physics Letters, 56B, 462 (1975). We follow McDonald's notations.Google Scholar
  43. 43.
    J. C. Pati, S. Rajpoot and Abdus Salam, Physics Lett. 71B, 387 (1977), ICTP/76/15, Physics Letters (To be published).Google Scholar
  44. 44.
    J. Leveille-Imperial College Preprint (1978).Google Scholar
  45. 45.
    Unpublished results of such a preliminary measurement carried out at SPEAR exist, which indicate that the asymmetry is less than 3% in magnitude at a mean center of mass energy = 6.8 GeV (Private communications: B. Richter).Google Scholar
  46. 46.
    R. Cahn and F. Gilman (SLAC-Pub., 1977).Google Scholar
  47. 47.
    A. Janah, U. of Md. Preprint (In preparation).Google Scholar
  48. 48.
    H. S. Mani, J. C. Pati, S. Rajpoot and A. Salam, Trieste Preprint IC/77/88, Physics Letters (1977).Google Scholar
  49. 49.
    S. Weinberg, Phys. Rev. Letters 29, 1698 (1972). In this work, the symmetric gauge-structure is introduced only for quarks for the sake of natural isospin conservation; but leptons are assumed to be singlets of SU(2)R.Google Scholar
  50. 50.
    F. Wilczek and A. Zee, Preprint (1977, Princeton Univ.), S. Weinberg, Preprint (1977); H. Fritzsch, CERN Preprint No. 2358 (1977).Google Scholar

Copyright information

© Springer-Verlag 1978

Authors and Affiliations

  • Jogesh C. Pati
    • 1
  1. 1.Department of Physics and AstronomyUniversity of MarylandCollege ParkMaryland

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