Current Induced Reactions pp 384-421 | Cite as

# Observable quarks, gluons and the leptons

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Decay Mode Hadronic Collision Heavy Lepton Physical Color Gauge Particle
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## References and footnotes

- 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.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.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.R.N. Mohapatra, J.C. Pati and Abdus Salam, Univ. of Md. Tech. Rep. No. 1975; Phys. Rev. D (to appear)Google Scholar
- 5.See for example the comprehensive summary of this point by R. Dashen, SLAC Conference Proceedings (August, 1975)Google Scholar
- 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.See, for example, A. de Rujula's talk at this conference. Other references may be found in here.Google Scholar
- 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
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- 10.G. Rajasekharan and P. Roy; TIFR Preprints TH75-38 and TH/75-42.Google Scholar
- 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.M.L. Perl et al., Phys. Rev. Letters 35, 1489 (1975)Google Scholar
- 13.G. Hanson et al., Phys. Rev. Lett. 35, 16109 (1975)Google Scholar
- 14.R.N. Mohapatra and J.C. Pati, Phys. Rev. D11, 566 (1975).Google Scholar
- 15.For example, the contribution to (g-2) of muon due to \(\tilde U\)-exchange is (1/8π
^{2}) (2e^{2}/√3f)^{2}(m_{μ}/m_{U})^{2}≈ 10^{−8}for m_{U}≈ 2 GeV and f^{2}/4π≈ 2. The present value of (expt.−(q.e.d.) theory)for (g-2)_{μ}is ≲ 3 · 10^{−8}.Google Scholar - 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.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.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.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.J.C. Pati and Abdus Salam, Physics Letters 58B, 333 (1975)Google Scholar
- 21.G. Branco, T. Hagiwara and R.N. Mohapatra (preprint, 1975); Phys. Rev. (to be published).Google Scholar
- 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
- 22.— 35, 702 (1975)Google Scholar
- 23.F. Sciulli, Talk at Coral Gables Conference, Jan. 1976, to appear in the proceedings.Google Scholar
- 24.The most recent experimental value of d
_{neutron}is (.4 ± 1.1) · 10^{−24}ecm. (N.F. Ramsey; Invited Talk at New York APS meeting, Febr., 1976).Google Scholar - 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
- 26.See for example S. Pakvasa and H. Sugawara, Hawaii Preprint (1975); L. Maiani, Rome Preprint (1975).Google Scholar
- 27.J.C. Pati and S. Oneda, Phys. Rev. 140, 1351 (1965).Google Scholar
- 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
- 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
- 30.F. Wilczek, A. Zee, R.L. Kingsley and S.B. Treiman, Phys. Rev. (to be published).Google Scholar
- 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
- 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
- 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
- 34.See for example, B.C. Barish, Invited Talk at the American Physical Society (Div. of Particles and Fields), Sept. 1974.Google Scholar
- 35.See for example, J.D. Bjorken, Proceedings of 1973 Bonn Conference, P.25 (1974).Google Scholar
- 36.We neglect the logarithmic corrections to the propagators, which are not important at present energies (see Ref. 17).Google Scholar
- 37.We do not exhibit V
^{0}(see eq. (9)), since it is not couplet to leptons. Even if Ũ and V^{0}mix, our conclusions in this section are not affected.Google Scholar - 38.Ũ-exchange-contribution to color-singlet-production is smaller than the one-photon-contribution by a factor = (2/√3) (e
^{2}/f^{2}) ≪ 1.Google Scholar - 39.Note that multiple Ũ-exchanges for color-production may be neglected to the same extent as multiple-photon-exchange.Google Scholar
- 40.The results for the present case may be obtained straightforwardly (by invoking the Δ
^{2}-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 - 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 Δ
^{2}≫1 as q^{2}→ m_{U}^{2}, provided Ũ is the lowest mass color-octet state with J^{PC}= 1^{−−}. (See Ref. 9 for details.)Google Scholar - 42.This net contribution would exhibit as a sum over several possible color-octet states.Google Scholar
- 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 Δ
^{2}-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 - 44.C.H. Llewellyn-Smith, Phys. Rev. D4, 2392 (1971).Google Scholar
- 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
- 46.Asymptotic freedom applies if spontaneous symmetry breaking is dynamical, or else “temporarily” if quartic scalar couplings are small as mentioned before.Google Scholar
- 47.For simplicity of writing, we do not exhibit the Cabibbo-angle factors (sinθ
_{c}and cosθ_{c}) in eqs. (37) and (38), which are immaterial for total cross sections.Google Scholar - 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
- 49.These selection rules and decay modes in fact apply to the lightes color-octet states with quantum numbers of V
_{ρ}^{±}and \(V_{K^ + }^ \pm\) Google Scholar - 50.This is because mixing angle is proportional to m
_{V}^{2}(eq. (11)) and phase space αm_{V}. We take sin (θ_{L}+ θ_{L}) ≈ cos(σ_{L}+ σ_{L}) ≈ 1/√2 for simplicity.Google Scholar - 51.With the new results on color-brightening (sec. III), there is the intriguing possibility that color-gluons may in fact be relatively light (m
_{V}≈ 1 to 2 GeV) (J.C. Pati, J. Sucher and C.H. Woo (forthcoming preprint).Google Scholar - 52.For decays of (Ũ, V
^{0}, \(\tilde V_{K^ + }^ \circ\)) see Refs. 1 and 9; W.R. Franklin, Nucl. Phys. B91, 160 (1975).Google Scholar - 53.A. Benvenuti et al., Phys. Rev. Lett. 34, 419, 597 (1975).Google Scholar
- 54.See Ref. 9 and W.R. Franklin, Ref, 52.Google Scholar
- 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 p
_{y,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 (m_{X}^{2}and m_{W}^{2}), if pion-emission is associated with a form factor. (Note pions are composites in the theory.) In this case neutral lepton-emission (i.e. p_{y,b}^{+}→ ν_{e}+ 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 p_{y,b}^{+}→ μ^{−}+ π^{+}+ π^{+}, n_{y,b}^{0}→ μ^{−}+ π^{+}, λ_{y,b}^{0}→ e^{−}+ π^{+}etc. are forbidden (neglecting corrections of order G_{Fermi}).Google Scholar - 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 - 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(m
_{W}^{4}/m_{q}^{4}) > 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 - 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
- 59.In addition to the production of q\(\bar q\)-pairs, by e
^{−}e^{+}-annihilation, production of charged color-gluon pairs (V_{ρ}^{+}V_{ρ}^{−}and V_{K+}^{+}V_{K+}^{−}), 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 - 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 (e^{−}e^{+}→ n_{a}^{−}+ n_{a}^{+}) 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 - 61.See L. Lederman, Rapporteur's talk at SLAC Conference, August, 1975.Google Scholar
- 62.The heavy-quark-(mirror)-interpretation with I
_{m}= 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 - 63.The Ũ-color-gluon may be searched for both in e
^{−}e^{+}-annihilation and in photo-production experiments allowing for good resolution.Google Scholar

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