Trends in particle physics

  • C. H. Llewellyn Smith
Session XI
Part of the Lecture Notes in Physics book series (LNP, volume 134)


Higgs Boson Chiral Symmetry Neutrino Oscillation Goldstone Boson Neutral Current 
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Footnotes and References

  1. 1).
    I am referring to work by M. Creutz and K. Wilson which is apparently not yet published. Some of the results are quoted by C. Callan et al. Phys. Rev. Lett. 44, 435, 1980.CrossRefGoogle Scholar
  2. 2).
    For a lucid review see E. Witten Harvard preprint 79/A0 07;to be published in Nucl. Phys. B and Harvard preprint HUTP 79/A078, lectures at 1979 Cargèse institute.Google Scholar
  3. 3).
    For a review see R.J.Crewther Riv. Nuovo Cimento 2, 63, 1979 and CERN TH 2791, 1979. Because of the anomaly the gauge invariant isoscalar axial current is not conserved but there is another (gauge dependent) isoscalar axial current which is conserved, which must therefore be coupled to zero mass particles. However, since the current is not observable, being gauge dependent, there might be two massless particles with opposite metric, allowing them to cancel exactly in observable amplitudes.This happens in the two dimensional Schwinger model (J. Kogut and L. Susskind Phys. Rev. D 11, 3594, 1974). 't Hooft Whys. Rev. Lett. 37, 8, 1976 and Phys. Rev. D 14, 3432, 1976, (E) D 18, 2199, 1978) claims that it happens in QCD also. Crewther (loc. cit.) argues that in the approximation considered, in which gauge fields become pure gauges at ∞, isovector chiral symmetry would not be spontaneously broken and claims that this invalidates 't Hooft's conclusion. Furthermore, he stresses the difficulty of satisfying all the Ward identities if the U(1) boson decouples. However, it seems that they are satisfied in the 1/N c expansion (see P. Di Vecchia Phys. Lett. 85B, 357, 1979 and references therein).Google Scholar
  4. 4).
    For a review see R.D. Peccei, Munich preprint MPI-PAE/ P Th 59/78. For a recent brief summary of attempts to explain the small value of 0 see M. Gaillard, Fermilab-Conf. 79/87-Thy.It might seem that this term has no effect because it can be written as a total divergence, whose contribution to the action can be expressed as a surface integral (of a gauge dependent current). However this is not true because of the rich vacuum structure in QCD. Even if the Fμνi vanish at infinity, which is presumably not the case in a confining theory,there are configurations of non-zero winding number, in which the Aμ i} become pure gauges at infinity but cannot be simultaneously transformed away in all directions. These configurations contribute to the surface term. There are two contributions to 0: 1) It enters as a coupling constant (even if it is zero initially this term will be needed to cancel divergences induced by the weak interactions)2) It enters the effective Lagrangian as a reflection of the phase of the relative contributions of configurations of different winding number to Green functions (expressed as path integrals), which is an (arbitrary ?) parameter. These two contributions must combine to give a net θ which is small.Google Scholar
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    R.M. Barnett, M. Dine and L. Mclerran. SLAC-PUB-2475, 1980.Google Scholar
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    R.Q. Hung and J.J. Sakurai Phys. Lett. 88B, 91, 1979.Google Scholar
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    P. Langacker et al. BNL-26498, 1979. See also I. Liede and M. Roos. Helsinki preprint HU-TFT-79-27.Google Scholar
  8. 8).
    See e.g. G.G. Ross and T. Weiler. Journal of Physics G5, 733, 1979. H. Georgi and S. Weinberg Phys. Rev. D. 17, 275, 1978. E.H. de Groot, G.J. Gounaris and D. Schildkneckt Phys. Lett. 85B, 399, 1979, and Bielefeld preprints B1-TP 79137, and B1-TP 79-39.Google Scholar
  9. 9).
    There is simple way to see this. For light fermions we only need the WO-B propagator matrix in which the new neutrals change MB 2 — q2 to MB 2 (q2 ). Expanding MB 2 (q2) = (MB 0)2 + λq2 + λ′(q2)2 ... we car, rescale the B field to obtain λ = 1. Dropping terms of 0(q2)2) and higher we obtain exactly the same propagator matrix as originallyin SU2 L x U(1).However, although elsewhere we can neglect it, we must include the effects of the λ′(q2)2 term in calculating the photon eigenvalue of the inverse propagator matrix which becomes q2 (1-λ′ cos20wq2) + 0(q2)3). This changes \(\frac{1}{{_q 2}}\)(Jλ em)2 to \(\frac{1}{{_q 2}}\)(Jλ em)2 + λ'cos2θw(Jλ em)2 + 0(q2) in the effective Lagrangian at low q2.Google Scholar
  10. 10).
    de Groot et al., loc. cit.Google Scholar
  11. 11).
    The relevant formulae are given, for example, by C.H. Llewellyn Smith and D.V. Nanopoulos Nucl.Phys. B78, 205, 1974, with important corrections in Nucl Phys. B83, 544, 1974.CrossRefGoogle Scholar
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    F. Antonelli Phys. Lett. 91B, 90, 1980. M. Veltman Phys. Lett. 91B, 95, 1980.Google Scholar
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    D. Horn and G.G. Ross Phys. Lett. 67B, 460, 1977. G. Pltarelli et al. Phys. Lett. 67B, 463, 1977.Google Scholar
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    V. Barger and S. Pakvasa Phys. Lett. 81B, 1955 1979.Google Scholar
  15. 15).
    H. Georgi and A. Pais Phys. Rev. D 19, 2746, 1979. There can of course be λ′ third triplet and hence another quark with Q = 2/3 in this model.Google Scholar
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    H. Georgi and S.L. Glashow. Harvard preprint HUTP79/A073.Google Scholar
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    E. Derman Phys. Rev D19, 317, 1979.Google Scholar
  18. 18).
    This value is obtained if syraetry breaking is due entirely to radiative corrections. For a discussion of the phenomenology of a 10 GeV Higgs boson and references see J. Ellis Lett. 83B, 339, 1979 (see also footnote 31). The mass of the Higgs meson is also predicted if the couplings lie in the domain of attraction of infrared stable fixed points (B.J. Pendleton and G.G. Ross, Oxford preprint in preparation).Google Scholar
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    C.E. Vayonakis Nuovo Cimento Lett 17, 383, 1977. B.W. Lee, C. Quigg and H.B. Thacker Phys. Rev. Lett. 38, 883, 1977 and Phys. Rev. D.16, 1519, 1977.Google Scholar
  20. 20).
    For λ′ recent analysis and references see G. Ecker Vienna preprint UWTh Ph 79-30, to be published in Proc. 1979 Visegrad symposium.Google Scholar
  21. 21).
    ECFA 80/42 DESY-HERA 80/01.Google Scholar
  22. 22).
    H. GeorgiHarvard preprint HUTP 79/ A036.Google Scholar
  23. 23).
    For recent reviews and references see S.L. Glashow, lectures at the 1979 Cargèse institute (Harvard preprint HUTP79/A059) and J. Ellis, CEPN-2723 (to be published in Proc. 1979 EPS conference).Google Scholar
  24. 24).
    Indirect searches for nucleon decay may produce very interesting limits. See J.C. Evans and R.I. Steinberg. Science, 2 Sept. 1977, p.989. K.W. Allen (private communication) has proposed an interesting experiment with tellurium.If a neutron in Te52 130 decays it yields Te52 129 whereas if a proton decays it yields Sb51 129 which β decays in 104 secs. to give Te52 129 also. Te54 129 then β decays in 104 secs. to I53 129 which then β decays in 1.7 × 107 years to Xe54 129, which is stable. Any primordial I53 129 will have decayed by now so the detection on of I53 129 in Te ore could be attributed to the accumulated effect of nucleon decay over 107 years (provided it exceeds the amount produced by cosmic ray induced inverse β decay etc.) A nucleon lifetime of 1030 years would give 103 atoms of I129/Kg. I129 provides the only negative ion of mass 129 and can be detected using a Van de Graff as a mass spectrometer.Google Scholar
  25. 25).
    For an introductory account see M.S. Turner and D.N. Sehramm Physics Today, p. 42, Sept. 1979.Google Scholar
  26. 26).
    For recent discussions and references see R. Barbieri and D.V. Nanopoulos, CERN TH 2810, 1980 and H. Ruegg and T. Shücker Nucl. Phys. B. 161, 388, 1979.Google Scholar
  27. 27).
    For recent discussions see H. Georgi and D. Nanopoulos Nucl. Phys. B. 155, 52, 1979.Google Scholar
  28. 28).
    M. Gell-Mann, P. Ramond and R. Slansky (unpublished) have suggested a mechanism which naturally gives vR a large Majorana mass leaving vL nearly massless. Witten has shown (Phys. Lett. 91B, 81, 1980) that in the minimal 0(10) model the mass of vL would be 100 ± 2eV. Note that existing data are compatible with substantial mixing angles and neutrino masses in the eV. range, giving oscillations to which reactor and accelerator experiments would be sensitive (for a recent discussion see A. De Rujula et. al. CERN preprint TH 2788-1979). The low solar neutrino flux may be evidence for oscillations.Barger (Wisconsin preprint C00-881-135, 1980, to be published in Physics Letters) claim reactor data show evidence for oscillations.Google Scholar
  29. 29).
    See F. Wilczek and A. Zee Phys. Rev. Lett. 42, 421, 1979 and P. RaMond Caltech preprint CALT-68-709-1979 for examples.Google Scholar
  30. 30).
    F. Wilczek and A. Zee Princeton preprint “Spinors and Families”, 1979.Google Scholar
  31. 31).
    This can be done (A. Buras, J. Ellis and M. Gaillard Nucl. Phys. B. 135, 66, 1978). Weinberg (Phys. Rev. Lett. 82B, 387, 1979) has shown that if we view the adjustment in terms of the effective potential and tune the ~2 term to be zero (which could possibly be required by some symmtry in a future theory), then φ2 radiative corrections give rise to the required heirarchy of masses of order e1/g2. The mass of the light Higgs is of 0(10 GeV) in this case. J. Ellis et. al. (Nucl. Phys. B. 164, 253, 1980) argue that MX itself might be understood in terms of the Planck mass in this case.Google Scholar
  32. 32).
    This argument is discussed by L. Susskind (ref. 34) who attributes it to K. Wilson.Google Scholar
  33. 33).
    G. 't Hooft. Lecture at the 1979 Cargèse institute.Google Scholar
  34. 34).
    This relatively old idea has been vigorously investigated by S. Weinberg (Phys. Rev. D 13, 974, 1975 and D 19, 1277, 1979). L. Susskind and collaborators (Phys. Rev. D 20, 2619, 1979, Nucl. Phys. B 155, 237, 1979 and Phys. Rev. D 20, 3404, 1979) and E.Eichten and K. Lane (Harvard preprint HUTP-79/A062).Google Scholar
  35. 35).
    M. Weinstein (Phys. Rev. D 8, 2511, 1973) was apparently the first to point out that this“weak ΔI = 1/2 rule” depends on therepresentation content of the unphysical Goldstone bosons and not on whether they are elementary or composite. Care must be taken to ensure that this relation is maintained when isospin breaking sufficient to obtain the correct value of mu md is introduced. See P. Sikivie et. al. Stanford preprint 1TP-661, 1980 and A. Carter and H. Pagels, Rockefeller report 000-2232B-187, 1979.Google Scholar
  36. 36).
    E. Eichten and K. Lane (loc. cit.) whose discussion of the general implications of these models we follow. See also M. Beg, Rockefeller report 000-2732B-189, 1979 and S. Dimopoulos, invited talk at the 1979 EPS conference for a discussion of the properties of the pseudo Goldstone bosons.Google Scholar
  37. 37).
    S. Dimopoulos, S. Raby and L. Susskind Stanford preprint 1TP-662, 1980.Google Scholar
  38. 38).
    H. Lipkin Riv. del Nuovo Cimento 1, 134, 1969 and FermiLab-Conf 79/60-THY. See also M. Gluck Phys. Lett. 87B, 247, 1979.Google Scholar
  39. 39).
    Possibly we could argue that EB > 0 (μ−1), giving enormous binding energies for leptons but leaving open the possibility that quarks will appear composite at 10's of GeV.Google Scholar
  40. 40).
    For a review see P. van Niewenhuisen Physics Reports(in press).Google Scholar
  41. 41).
    C.W. Misner, K.S. Thorne and J.A. Wheeler “Gravitation”, Freeman, 1973.Google Scholar
  42. 42).
    A. Linde JETP Lett. 19, 183, 1974. M. Veltman Phys. Rev. Lett. 34, 777, 1975.Google Scholar
  43. 43).
    I understand that A. Guth has investigated the consequences.Google Scholar
  44. 44).
    V. de Alfaro, S. Fubini and G. Furlan CERN TH 2799, 1979.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • C. H. Llewellyn Smith
    • 1
  1. 1.Department of Theoretical PhysicsOxfordEngland

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