γγ Collisions pp 357-375 | Cite as

# Trends in particle physics

Session XI

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## Keywords

Higgs Boson Chiral Symmetry Neutrino Oscillation Goldstone Boson Neutral Current## Preview

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## Footnotes and References

- 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).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).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).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 F
_{μν}^{i}vanish at infinity, which is presumably not the case in a confining theory,there are configurations of non-zero winding number, in which the A_{μ}^{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 - 5).R.M. Barnett, M. Dine and L. Mclerran. SLAC-PUB-2475, 1980.Google Scholar
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- 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).There is simple way to see this. For light fermions we only need the W
^{O}-B propagator matrix in which the new neutrals change M_{B}^{2}— q^{2}to M_{B}^{2}(q^{2}). Expanding M_{B}^{2}(q^{2}) = (M_{B}^{0})^{2}+ λq^{2}+ λ′(q^{2})^{2}... we car, rescale the B field to obtain λ = 1. Dropping terms of 0(q^{2})^{2}) and higher we obtain exactly the same propagator matrix as originallyin SU^{2}_{L}x U(1).However, although elsewhere we can neglect it, we must include the effects of the λ′(q^{2})^{2}term in calculating the photon eigenvalue of the inverse propagator matrix which becomes q^{2}(1-λ′ cos^{2}0_{w}q^{2}) + 0(q^{2})^{3}). This changes \(\frac{1}{{_q 2}}\)(J_{λ}^{em})^{2}to \(\frac{1}{{_q 2}}\)(J_{λ}^{em})^{2}+ λ'cos^{2}θ_{w}(J_{λ}^{em})^{2}+ 0(q^{2}) in the effective Lagrangian at low q^{2}.Google Scholar - 10).de Groot et al., loc. cit.Google Scholar
- 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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- 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
- 16).H. Georgi and S.L. Glashow. Harvard preprint HUTP79/A073.Google Scholar
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- 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 et.al.Phys. 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
- 19).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).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).ECFA 80/42 DESY-HERA 80/01.Google Scholar
- 22).H. GeorgiHarvard preprint HUTP 79/ A036.Google Scholar
- 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).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 Te
_{52}^{130}decays it yields Te_{52}^{129}whereas if a proton decays it yields Sb_{51}^{129}which β decays in 10^{4}secs. to give Te_{52}^{129}also. Te_{54}^{129}then β decays in 10^{4}secs. to I_{53}^{129}which then β decays in 1.7 × 10^{7}years to Xe_{54}^{129}, which is stable. Any primordial I_{53}^{129}will have decayed by now so the detection on of I_{53}^{129}in Te ore could be attributed to the accumulated effect of nucleon decay over 10^{7}years (provided it exceeds the amount produced by cosmic ray induced inverse β decay etc.) A nucleon lifetime of 10^{30}years would give 10^{3}atoms of I^{129}/Kg. I^{129}provides the only negative ion of mass 129 and can be detected using a Van de Graff as a mass spectrometer.Google Scholar - 25).For an introductory account see M.S. Turner and D.N. Sehramm Physics Today, p. 42, Sept. 1979.Google Scholar
- 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).For recent discussions see H. Georgi and D. Nanopoulos Nucl. Phys. B. 155, 52, 1979.Google Scholar
- 28).M. Gell-Mann, P. Ramond and R. Slansky (unpublished) have suggested a mechanism which naturally gives v
_{R}a large Majorana mass leaving v_{L}nearly massless. Witten has shown (Phys. Lett. 91B, 81, 1980) that in the minimal 0(10) model the mass of v_{L}would be 10^{0}±^{2}eV. 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 et.al. (Wisconsin preprint C00-881-135, 1980, to be published in Physics Letters) claim reactor data show evidence for oscillations.Google Scholar - 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).F. Wilczek and A. Zee Princeton preprint “Spinors and Families”, 1979.Google Scholar
- 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 φ
^{2}radiative corrections give rise to the required heirarchy of masses of order e^{1/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 M_{X}itself might be understood in terms of the Planck mass in this case.Google Scholar - 32).This argument is discussed by L. Susskind (ref. 34) who attributes it to K. Wilson.Google Scholar
- 33).G. 't Hooft. Lecture at the 1979 Cargèse institute.Google Scholar
- 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).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 m
_{u}m_{d}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).E. Eichten and K. Lane (loc. cit.) whose discussion of the general implications of these models we follow. See also M. Beg et.al., 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).S. Dimopoulos, S. Raby and L. Susskind Stanford preprint 1TP-662, 1980.Google Scholar
- 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).Possibly we could argue that E
^{B}> 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).For a review see P. van Niewenhuisen Physics Reports(in press).Google Scholar
- 41).C.W. Misner, K.S. Thorne and J.A. Wheeler “Gravitation”, Freeman, 1973.Google Scholar
- 42).A. Linde JETP Lett. 19, 183, 1974. M. Veltman Phys. Rev. Lett. 34, 777, 1975.Google Scholar
- 43).I understand that A. Guth has investigated the consequences.Google Scholar
- 44).V. de Alfaro, S. Fubini and G. Furlan CERN TH 2799, 1979.Google Scholar

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© Springer-Verlag 1980