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References and footnotes
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)
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)
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).
R.N. Mohapatra, J.C. Pati and Abdus Salam, Univ. of Md. Tech. Rep. No. 1975; Phys. Rev. D (to appear)
See for example the comprehensive summary of this point by R. Dashen, SLAC Conference Proceedings (August, 1975)
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.
See, for example, A. de Rujula's talk at this conference. Other references may be found in here.
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).
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).
G. Rajasekharan and P. Roy; TIFR Preprints TH75-38 and TH/75-42.
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).
M.L. Perl et al., Phys. Rev. Letters 35, 1489 (1975)
G. Hanson et al., Phys. Rev. Lett. 35, 16109 (1975)
R.N. Mohapatra and J.C. Pati, Phys. Rev. D11, 566 (1975).
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.
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).
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.
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).
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.
J.C. Pati and Abdus Salam, Physics Letters 58B, 333 (1975)
G. Branco, T. Hagiwara and R.N. Mohapatra (preprint, 1975); Phys. Rev. (to be published).
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. Letters
— 35, 702 (1975)
F. Sciulli, Talk at Coral Gables Conference, Jan. 1976, to appear in the proceedings.
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).
Ref. 1; R.N. Mohapatra and J.C. Pati, Phys. Rev. D11, 2558 (1975); G. Senjanovic and R.N. Mohapatra, Phys. Rev. D12, (1975)
See for example S. Pakvasa and H. Sugawara, Hawaii Preprint (1975); L. Maiani, Rome Preprint (1975).
J.C. Pati and S. Oneda, Phys. Rev. 140, 1351 (1965).
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).
M.K. Gaillard and B.W. Lee, Phys. Rev. Lett. 33, 108 (1974); G. Altarelli and L. Maiani, Phys. Lett. 52B, 351(1974).
F. Wilczek, A. Zee, R.L. Kingsley and S.B. Treiman, Phys. Rev. (to be published).
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).
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.
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).
See for example, B.C. Barish, Invited Talk at the American Physical Society (Div. of Particles and Fields), Sept. 1974.
See for example, J.D. Bjorken, Proceedings of 1973 Bonn Conference, P.25 (1974).
We neglect the logarithmic corrections to the propagators, which are not important at present energies (see Ref. 17).
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.
Ũ-exchange-contribution to color-singlet-production is smaller than the one-photon-contribution by a factor = (2/√3) (e2/f2) ≪ 1.
Note that multiple Ũ-exchanges for color-production may be neglected to the same extent as multiple-photon-exchange.
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).
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 → m 2U , provided Ũ is the lowest mass color-octet state with JPC = 1 −−. (See Ref. 9 for details.)
This net contribution would exhibit as a sum over several possible color-octet states.
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.
C.H. Llewellyn-Smith, Phys. Rev. D4, 2392 (1971).
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).
Asymptotic freedom applies if spontaneous symmetry breaking is dynamical, or else “temporarily” if quartic scalar couplings are small as mentioned before.
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.
Strictly speaking this is divided between different color-octet final states, not all of which need contain a pair of charged gluons.
These selection rules and decay modes in fact apply to the lightes color-octet states with quantum numbers of V ±ρ and \(V_{K^ + }^ \pm\)
This is because mixing angle is proportional to m 2V (eq. (11)) and phase space αmV. We take sin (θL + θL) ≈ cos(σL + σL) ≈ 1/√2 for simplicity.
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).
For decays of (Ũ, V0, \(\tilde V_{K^ + }^ \circ\)) see Refs. 1 and 9; W.R. Franklin, Nucl. Phys. B91, 160 (1975).
A. Benvenuti et al., Phys. Rev. Lett. 34, 419, 597 (1975).
See Ref. 9 and W.R. Franklin, Ref, 52.
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 2X and m 2W ), 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 → 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 p +y,b → μ− + π+ + π+, n 0y,b → μ− + π+, λ 0y,b → e− + π+ etc. are forbidden (neglecting corrections of order GFermi).
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.).
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 4W /m 4q ) > 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.
Although with sufficient data, the sequential decay (Ref. 57) might be distringuishable from the genuine three-body leptonic decays of the parent particles.
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).
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).
See L. Lederman, Rapporteur's talk at SLAC Conference, August, 1975.
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).
The Ũ-color-gluon may be searched for both in e−e+-annihilation and in photo-production experiments allowing for good resolution.
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Pati, J.C. (1976). Observable quarks, gluons and the leptons. In: Körner, J.G., Kramer, G., Schildknecht, D. (eds) Current Induced Reactions. Lecture Notes in Physics, vol 56. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-07866-5_24
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