Observable quarks, gluons and the leptons

  • Jogesh C. Pati
Part of the Lecture Notes in Physics book series (LNP, volume 56)


Decay Mode Hadronic Collision Heavy Lepton Physical Color Gauge Particle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References and footnotes

  1. 1.
    J.C. Pati and Abdus Salam; Phys. Rev. D8, 1240 (1973); Phys. Rev. Lett. 31, 661(1973); Phys. Rev. D10, 275(1974) and Physics Letters (1975)Google Scholar
  2. 2.
    H. Georgi and S.L. Glashow, Phys. Rev. Lett. 32, 438 (1974), H. Fritzsch and P. Minkowski, Annals of Physics 93, 222 (1975); F. Gürsey and P. Sikivie (Preprint, 1976) and P. Ramond (Preprint, 1976)Google Scholar
  3. 3.
    By “Good” we mean that the symmetry breaking terms are of order a or few times α. Operationally we require that “color” as a global symmetry be at least as good as SU(3).Google Scholar
  4. 4.
    R.N. Mohapatra, J.C. Pati and Abdus Salam, Univ. of Md. Tech. Rep. No. 1975; Phys. Rev. D (to appear)Google Scholar
  5. 5.
    See for example the comprehensive summary of this point by R. Dashen, SLAC Conference Proceedings (August, 1975)Google Scholar
  6. 6.
    In both cases asymptotic freedom is lost only due to the quartic terms of the Higgs-potential (note at least the weak gauge bosons have to be massive in both cases). Since the renormalized values of these quartic couplings may typically be chosen to be less than e (at low energies), such loss of asymptotic freedom would not manifest itself until much higher energies. In this sence both theories are “temporarily” asymptotically free in the present energy regime (see D. Politzer, Physics Reports, 1974). Alternatively if Higgs-Kibble fields arise dynamically as composite fields, both theories would be truly asymptotically free.Google Scholar
  7. 7.
    See, for example, A. de Rujula's talk at this conference. Other references may be found in here.Google Scholar
  8. 8.
    See, for example, C.H. Llewellyn Smith, Rapporteur's talk at SLAC-Lepton-Photon-Symposium, August, 1975, and A. De Rujula, H. Georgi and S.L. Glashow, Phys. Rev. 12, 147 (1975).Google Scholar
  9. 9.
    J.C. Pati and Abdus Salam, Phys. Rev. Lett. 36, 11 (1976); J.C. Pati, Report of a Talk presented at the Conference on Gauge Theories and Modern Field Theory at North Eastern University (Sept., 1975), Univ. of Md. Tech. Rep. No. 76-071 (to appear in the proceedings).Google Scholar
  10. 10.
    G. Rajasekharan and P. Roy; TIFR Preprints TH75-38 and TH/75-42.Google Scholar
  11. 11.
    J.C. Pati, Abdus Salam and S. Sakakibara, U. of Md. Tech. Rep. (1975); J.C. Pati (North Eastern Talk, Sept. 1975, see ref. 9).Google Scholar
  12. 12.
    M.L. Perl et al., Phys. Rev. Letters 35, 1489 (1975)Google Scholar
  13. 13.
    G. Hanson et al., Phys. Rev. Lett. 35, 16109 (1975)Google Scholar
  14. 14.
    R.N. Mohapatra and J.C. Pati, Phys. Rev. D11, 566 (1975).Google Scholar
  15. 15.
    For example, the contribution to (g-2) of muon due to \(\tilde U\)-exchange is (1/8π2) (2e2/√3f)2 (mμ/mU)2 ≈ 10−8 for mU ≈ 2 GeV and f2/4π≈ 2. The present value of (expt.−(q.e.d.) theory)for (g-2)μ is ≲ 3 · 10−8.Google Scholar
  16. 16.
    J.C. Pati and Abdus Salam, Phys. Rev. D11, 1137 (1975); Physics Letters, R.N. Mohapatra and J.C. Pati, Phys. Rev. D11, 2558; H. Fritzsch and P. Minkowski, Annals of Physics 93, 222(1975).Google Scholar
  17. 17.
    The effective low-energy coupling constants (g and f), which are operative in the flavor and SU(3)′-color sectors can still differ due to finite renormalization effects which are in general different in different sectors due to mass differences between the gauge particles. A practical realization of this low-energy disparity between coupling constants in different sectors within a unified theory remains to be shown.Google Scholar
  18. 18.
    If the octet of color gluons are massive and we demand that SU(3)-color be preserved as a good global symmetry, then it appears that [SU(4)]4 is essentially the unique unifying symmetry barring proliferation of fermions for example through new colors. (This will be discussed in a forthcoming paper by Mohapatra and myself).Google Scholar
  19. 19.
    This may arise if there exist fermions with new colors, the unifying symmetry in this case might be for example [SU(5)]4 or [SU(6)]4 with the basic fermionic multiplet being a 25-plet or a 36-plet (there would still have to be in addition the mirror set F′ to cancel anomalies). All these cases still preserve the interpretation of lepton number as the fourth color (Ref. 1) and put quarks and leptons in the same multiplet. The fermions with new colors (fifth or sixth) do not douple to the SU(3)′-octet of color gauge mesons; thus they max exhibit a new class of interactions (in addition to weak and electromagnetic interactions), which would be characterized by the masses of gauge mesons belonging to SU(6)′ but outside of SU(4)′-subgroup. There is an alternative possibility: quarks and leptons may belong to distinct but parallel multiplets and yet provide a unified theory, this would again need a proliferation of the basic fermions.Google Scholar
  20. 20.
    J.C. Pati and Abdus Salam, Physics Letters 58B, 333 (1975)Google Scholar
  21. 21.
    G. Branco, T. Hagiwara and R.N. Mohapatra (preprint, 1975); Phys. Rev. (to be published).Google Scholar
  22. 22.
    See for example A. DeRujula, H. Georgi and S.L. Glashow, Phys. Rev. D12, 3589 (1975); H. Fritzsch, M. Gell-Mann and P. Minkowski, Phys. Letters 59B, 256 (1975); F. Wilczek, A. Zee, R.L. Kingsley and S.B. Treiman, Phys. Rev. D (to be published) and S. Pakvasa, W.A. Simmons and S.F. Tuan, Phys. Rev. LettersGoogle Scholar
  23. 22.
    35, 702 (1975)Google Scholar
  24. 23.
    F. Sciulli, Talk at Coral Gables Conference, Jan. 1976, to appear in the proceedings.Google Scholar
  25. 24.
    The most recent experimental value of dneutron is (.4 ± 1.1) · 10−24 ecm. (N.F. Ramsey; Invited Talk at New York APS meeting, Febr., 1976).Google Scholar
  26. 25.
    Ref. 1; R.N. Mohapatra and J.C. Pati, Phys. Rev. D11, 2558 (1975); G. Senjanovic and R.N. Mohapatra, Phys. Rev. D12, (1975)Google Scholar
  27. 26.
    See for example S. Pakvasa and H. Sugawara, Hawaii Preprint (1975); L. Maiani, Rome Preprint (1975).Google Scholar
  28. 27.
    J.C. Pati and S. Oneda, Phys. Rev. 140, 1351 (1965).Google Scholar
  29. 28.
    See for example S. Oneda, J.C. Pati and B. Sakita, Phys. Rev. 119, 482 (1960); S. Coleman and S.L. Glashow, Phys. Rev. 134, B681 (1964) and A. Salam and J.C. Wan, Phys. Letters 8, 217(1964).Google Scholar
  30. 29.
    M.K. Gaillard and B.W. Lee, Phys. Rev. Lett. 33, 108 (1974); G. Altarelli and L. Maiani, Phys. Lett. 52B, 351(1974).Google Scholar
  31. 30.
    F. Wilczek, A. Zee, R.L. Kingsley and S.B. Treiman, Phys. Rev. (to be published).Google Scholar
  32. 31.
    J.C. Pati and C.H. Woo, Phys. Rev. D3, 2920 (1971); S. Nussinov and J. Rosner, Phys. Rev. Letter, 23, 1264(1969); C.A. Nelson and K.J. Sebastian, Phys. Rev. D8, 3144(1973).Google Scholar
  33. 32.
    See for example H. Harari, Rapporteur's Talk at SLAC-Lepton-Photon-Symposium, August, 1975 (to appear in the proceedings). Harari's arguments against color-interpretation are confined to the case where the only new quantum number excited is color.Google Scholar
  34. 33.
    See for example F. Gilman, proceedings of the 17th International Conference, London (1974); C.H. Llewellyn Smith, Rapporteur's talk at SLAC-Lepton-Photon-Symposium, August 1975; A. DeRujula, H. Georgi and S.L. Glashow, Phys. Rev. 12, 147(1975); S.L. Glashow, after dinner talk at Northeastern University Conference on Gauge Theories and Modern Field Theory (Sept., 1975).Google Scholar
  35. 34.
    See for example, B.C. Barish, Invited Talk at the American Physical Society (Div. of Particles and Fields), Sept. 1974.Google Scholar
  36. 35.
    See for example, J.D. Bjorken, Proceedings of 1973 Bonn Conference, P.25 (1974).Google Scholar
  37. 36.
    We neglect the logarithmic corrections to the propagators, which are not important at present energies (see Ref. 17).Google Scholar
  38. 37.
    We do not exhibit V0 (see eq. (9)), since it is not couplet to leptons. Even if Ũ and V0 mix, our conclusions in this section are not affected.Google Scholar
  39. 38.
    Ũ-exchange-contribution to color-singlet-production is smaller than the one-photon-contribution by a factor = (2/√3) (e2/f2) ≪ 1.Google Scholar
  40. 39.
    Note that multiple Ũ-exchanges for color-production may be neglected to the same extent as multiple-photon-exchange.Google Scholar
  41. 40.
    The results for the present case may be obtained straightforwardly (by invoking the Δ2-factor) from those of N. Babibbo and R. Gatto, Phys. Rev. 124, 1577 (1961) and M.A. Furman and G.J. Komen, Nucl. Phys. B84, 323(1975).Google Scholar
  42. 41.
    If one of the J/ψ-particles is identified with the Ũ-gluon, it is possible to verify that no undue enhancement takes place even though Δ2 ≫1 as q2 → mU2, provided Ũ is the lowest mass color-octet state with JPC = 1 −−. (See Ref. 9 for details.)Google Scholar
  43. 42.
    This net contribution would exhibit as a sum over several possible color-octet states.Google Scholar
  44. 43.
    See for example, J.D. Bjorken, Proceedings of the second International Conference on Elementary Particles, Aix-en-Provence, 1973. Aposteriori, since color-contributions (with the Δ2-factor) turns out to be small ≲ 10 to 20 % compared to flavor-contribution (see later), the determination of the quark-distributions functions does not alter significantly with the inclusion of color-production.Google Scholar
  45. 44.
    C.H. Llewellyn-Smith, Phys. Rev. D4, 2392 (1971).Google Scholar
  46. 45.
    C. Chang et al., Phys. Rev. Lett. 35, 901 (1975); R. Taylor, Report of MIT and SLAC data at the SLAC-Lepton-Photon-Symposium(August, 1975).Google Scholar
  47. 46.
    Asymptotic freedom applies if spontaneous symmetry breaking is dynamical, or else “temporarily” if quartic scalar couplings are small as mentioned before.Google Scholar
  48. 47.
    For simplicity of writing, we do not exhibit the Cabibbo-angle factors (sinθc and cosθc) in eqs. (37) and (38), which are immaterial for total cross sections.Google Scholar
  49. 48.
    Strictly speaking this is divided between different color-octet final states, not all of which need contain a pair of charged gluons.Google Scholar
  50. 49.
    These selection rules and decay modes in fact apply to the lightes color-octet states with quantum numbers of Vρ± and \(V_{K^ + }^ \pm\) Google Scholar
  51. 50.
    This is because mixing angle is proportional to mV2 (eq. (11)) and phase space αmV. We take sin (θL + θL) ≈ cos(σL + σL) ≈ 1/√2 for simplicity.Google Scholar
  52. 51.
    With the new results on color-brightening (sec. III), there is the intriguing possibility that color-gluons may in fact be relatively light (mV ≈ 1 to 2 GeV) (J.C. Pati, J. Sucher and C.H. Woo (forthcoming preprint).Google Scholar
  53. 52.
    For decays of (Ũ, V0, \(\tilde V_{K^ + }^ \circ\)) see Refs. 1 and 9; W.R. Franklin, Nucl. Phys. B91, 160 (1975).Google Scholar
  54. 53.
    A. Benvenuti et al., Phys. Rev. Lett. 34, 419, 597 (1975).Google Scholar
  55. 54.
    See Ref. 9 and W.R. Franklin, Ref, 52.Google Scholar
  56. 55.
    In particular, see. J.C. Pati, S. Sakakibara and A. Salam (Trieste Preprint IC/75/93, to appear). The semi-leptonic decay modes such as py,b+ → e + π+ π+ involving emission of a charged lepton require that one of the pions be emitted from a quark-line inside the loop, which would be suppressed by two large masses (mX2 and mW2), if pion-emission is associated with a form factor. (Note pions are composites in the theory.) In this case neutral lepton-emission (i.e. py,b+ → νe + pions, etc.) would be the dominant modes. A second point worth noting is the intricate selection rules, which arise for quark-decays, For example, transitions such as py,b+ → μ + π+ + π+, ny,b0 → μ + π+, λy,b0 → e + π+ etc. are forbidden (neglecting corrections of order GFermi).Google Scholar
  57. 56.
    Otherwise, at least the red-neutron quark (\(\bar n_r\)) would be longer lived (τ(\(\bar n_r\))≈ 10−6 to 10−7 sec. for m(\(\bar n_r\)) ≈ 2 GeV); even though the yellow and blue-quarks would still be shortlived (τ < 10−11 sec.).Google Scholar
  58. 57.
    The rates of semileptonic-decay modes (q → l + Mesons), when allowed (see Ref. 55), exceed those of leptonic decay modes (q→l + l+l) by a factor − 0(mW4/mq4) > 10 within the basic model. This is because the former receive contribution from (convergent) loop-diagrams, while the latter receive contributions from tree-diagrams only.Google Scholar
  59. 58.
    Although with sufficient data, the sequential decay (Ref. 57) might be distringuishable from the genuine three-body leptonic decays of the parent particles.Google Scholar
  60. 59.
    In addition to the production of q\(\bar q\)-pairs, by ee+-annihilation, production of charged color-gluon pairs (Vρ+Vρ and VK++ VK+), which is limited by the net contribution from color-gluons to R = 1/8 (see Sec. III), followed by their two-body leptonic decays would also contribute to the leptonic (\(\bar \mu\)e)-events. The available SPEAR data is not inconsistent with three and two body-decays of parent particles (see M.L. Perl, SLAC-PUB-1644, Nov. 1975).Google Scholar
  61. 60.
    It is important to note that due to selection rules involved in quark-decays (see Ref. 55), yellow and blue-quark-pair production does not give rise to semi leptonic signals with either (\(\bar \mu\)e) or (μ+μ)in the final state. The red-quark pair production (ee+ → na + na+) can give rise to such signals depending upon the semi-leptonic decay-branching ratios of the charged color-gluons (see (43) and (57).Google Scholar
  62. 61.
    See L. Lederman, Rapporteur's talk at SLAC Conference, August, 1975.Google Scholar
  63. 62.
    The heavy-quark-(mirror)-interpretation with Im = 1 for the lowest lying states has the advantage (R.M. Barnett, Phys. Rev. Lett. 34, 41(1975) that their decays into hadrons would be suppressed by mirror-isospin selection rule as well as by the Zweig-rule-factor. This provides a natrual explanation of their extreme narrowness without invoking an unusual Zweig-suppression-factor (as is needed for the charm-anticharm interpretation of 3.1).Google Scholar
  64. 63.
    The Ũ-color-gluon may be searched for both in ee+-annihilation and in photo-production experiments allowing for good resolution.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Jogesh C. Pati
    • 1
  1. 1.Center for Theoretical Physics Department of Physics and AstronomyUniversity of MarylandCollege Park

Personalised recommendations