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arXiv:hep-ph/9802339v1 17 Feb 1998 etn are theoreti- [2]. internal problems by many cal mainly its motivated “”, with and mechanism no Higgs is so-called there by-products, Consequently, the for electri- . need and gauge unstable charged no massive, cally is by theoretical there caused no so, complications and If unification, of electroweak being states. “leakage” fundamental force -antiquark nuclear a by the rather to mediated analogy force but in weak fundamental, states, the multi-preon be Hence, not composite. would being as understood ihetfml ftoqak ( two of family lightest are so- not. leptons the or and stable in quarks fundamental, included all considered been where yet model, not standard ob- has called fundamental wisdom more This even among jects. interpreted processes been of later terms or in “ele- sooner of have decays all mentary” Historically, particles. fundamental as atta h ekguebosons, gauge weak the that fact of pattern a form seemingly “families”. they three that quarks The many and [1]). so leptons, exist in there and given that is are ones review been compelling have (a most decades preons two fundamental for more discussed of terms in leptons h rsos 34,o iia ubro to preons , (two) or of number quark minimal a a inside or [3,4], “rishons” the ( ihramnmlnme f(w)dffrn preons, different (two) of number minimal a either urs u o flpos sdsrbdb h Cabibbo- the by of described conser- mixing as leptons, the the of numbers, explain not lepton but to different quarks, able three (or of been models vation and model) preon consistent have standard simple, Neither the no exists. but model one, predictive light the of tations” e nte ita usrcuei htms ursand quarks most that is substructure a at hint Another ro oeshv ofrfcsdo xliigthe explaining on focused far so have models Preon uhwr ntefil a enisie lob the by also inspired been has field the in work Much and quarks of substructure a of favor in arguments The h w eve aiisaeuulycniee “exci- considered usually are families heavier two The and ν e iha e rosa osbe hsmeans This possible. as preons few as with ) unstable ASnmes 26.c 33.r 46.z 14.65.-q 14.60.-z, 13.35.-r, 12.60.Rc, numbers: quantum-mechan PACS small functions. wave a lepton to and due quark about the come in can violation CP and oos ae nol he udmna n tbespin-1 stable and fundamental three only on based bosons, he e urs he e etn,adsxnwvco vector new six and leptons, new − three quarks, new three aldCbbomxn fthe of Cabibbo-mixing called ewe h etio ¯ the between epeetanwmnmlmdlfrtesbtutr falkno all of substructure the for model minimal new a present We e.g. 4 e/ enJcusDugne, Jean-Jacques mlil ig” cmoieHiggs”, “composite Higgs”, “multiple , .Temdlepan h paetcnevto ftrelep three of conservation apparent the explains model The 3. hc norve iqaie them disqualifies view our in which , 2 3 eateto hsc,Ll˚ nvriyo ehooy SE Technology, Lule˚a of Physics, University of Department eateto hoeia hsc,Uiestad Torino, Universit´a di Physics, Theoretical of Department nvri´ liePsa,Cemn-ern I FR-63177 II, Clermont-Ferrand Pascal, Universit´e Blaise e.g. h hpos [5]. “haplons” the , u and ν µ Z ( ν 0 d 1 µ n w leptons two and ) and ) and vre Fredriksson, Sverker 1 aoaor ePyiu Corpusculaire, Physique de Laboratoire d and W ν e ± (¯ s ν a be can , e urs n rdcseetoantcdcy roscillatio or decays electromagnetic predicts and quarks, ro Trinity Preon .Ohrnurn siltos swl srrrqakmixin quark rarer as well as oscillations, Other ). e.g. , 1 2 elSS ateso ursadlposwudthem- would leptons! leptons and and quarks quarks be the selves of and partners exist, SUSY not need real “sleptons” and “squarks” Hence, evs en pn0budsae “ipen” ftwo of (“di-preons”) states them- bound composite spin-1 spin-0 indeed being are selves, (“spreons”) preons scalar and udmna,adSS ateso ros h symme- the preons, would of try partners SUSY and fundamental, [7]. “supersymme- quoted the of sometimes to models as similar quark- diquarks, in is and It quarks between sym- model. try” phenomenological our purely a in about metry remind to (SUSY), only is of theory “slepton” established and the “squark” within like names to refers which spreon, pnt ul l nw etn n urs ecl the call We quarks. and leptons known spin-1 all build to spin and charges their concerned. as are far states as be- composite spin relation different of (“supersymmetric”) preons pairwise tween a is there that ytehpo oe fFizc n adlam[5], Mandelbaum inspired and 1 Fritzsch been spin of have have preons We model where haplon symme- possible. the much as by as simplicity maintaining and while try preons, of number perma- a all of a defining together, of object. leptons problem bound and nently the quarks to keep understand- also of that the lack and forces a than to the related of lighter is ing This have much to range. TeV expected so the are in are preons as neutrinos especially quarks, that is ours) neutral in violation CP decays. the and matrix), so- CKM the called by (quantified [6] formalism Kobayashi-Maskawa oa Hansson, Johan u ulpenshm,cnann he fundamental three containing scheme, preon full Our ti ot oigta vni h pen eetruly were spreons the if even that noting worth is It ttrsotta n ed nytrepen feach of preons three only needs one that out turns It h sec fornwpenmdli htw explain we that is model preon new our of essence The (including models preon all with problem classical A nw ursadlposwt h epo minimal a of help the with leptons and quarks known z / / hr r eea esn obleeta the that believe to reasons several are There . / rosi ymti a.Tento fa of notion The way. symmetric a in preons 2 preons 2 ros sacneune epredict we consequence, a As preons. 2 not .Oeo h e urshscharge has quarks new the of One s. nqak,lposadwa gauge weak and leptons quarks, wn eipeetdaogqak n leptons. and quarks among implemented be clmxn ftoo h preons the of two of mixing ical o ubr,a ela h so- the as well as numbers, ton T115Trn,Italy Torino, IT-10125 917Lule˚a,-97187 Sweden 2 α Aubi`ere, France , n nioPredazzi Enrico and β and / n .I diin eguess we addition, In 0. and 2 δ n h pn0ones spin-0 the and , 3 ns gs x , K y spin-1/2 particles, reads: accelerator energies in the TeV range. Among both lep- tons and quarks there are two clear mass-trends. Firstly, charge +e/3 2e/3 +e/3 − the bottom row contains objects that are much heavier spin-1/2 preons α β δ than the others, which must be caused by a “naked” su- ¯¯ ¯ ¯ spin-0 “spreons” x = (βδ) y = (¯αδ) z = (¯αβ) perheavy δ preon. The presence of a δ does not, however, We assume that α, β and δ carry a quantum chromo- make a spreon superheavy, since (αβ) seems to be heav- dynamic (QCD) (anticolor), i.e., the preon ier than (βδ) and (αδ). Secondly, there is an increasing ∗ mass along the diagonals from upper left to lower right. colors are the 3 representation of SU(3)color, when the quark colors are 3. By construction, also the x, y and z The t quark is “predicted” to be superheavy, which are then color-3∗ (3 3 = 3∗ 6). With quarks and lep- explains why it is so much heavier than its conventionally tons as, respectively,⊗ preon-spreon⊕ and preon-antispreon assigned partners, the b quark and the τ lepton. These ad hoc states, the colour representations correctly become 3 for enormous mass differences are hard to accept as quarks and 1 for leptons, as they should. We assume that consequences of the Higgs mechanism in the standard the other mathematically allowed color configurations do model. not exist in . One of the predicted new quarks is the X of charge 4e/3, which seemingly does not belong to the super- The preon assignments we propose are summarised in − the table below, where the result of combining a preon heavy group. This naturally poses a problem to the with a spreon or an antispreon can be found in the re- model, and the apparent lack of experimental indications spective cells. must be analysed. First, we note that quarks belonging to different flavor- x¯ y¯ z¯ x y z SU(3) representations need not have related masses. Nei- (βδ) (αδ) (αβ) (β¯δ¯) (¯αδ¯) (¯αβ¯) ther would quark masses need to be simply related to + α νe µ ντ u s c lepton masses. Therefore, it might well happen that the − − 3∗ β e ν¯µ τ d X b flavor- quarks have rapidly increasing masses, from u + δ ν¯κ1 κ ν¯κ2 t g h to X and h. Then the quark masses would depend not only on the underlying preon masses, but also strongly on There are alternative schemes for building the known the exact composition of the internal wave functions. Ul- quarks and leptons, but these turn out to be less consis- timately, all SU(3) representations need not be realised tent in details, and will not be discussed here. in nature. The rule of the game is, however, that if one In the remainder of this work, we discuss several as- object exists, so should the full representation, which pects of this model, starting with the trivial observation makes it difficult to claim that the X “need not exist”. that all known quarks and leptons are reproduced with A second alternative is that the X quark might indeed their correct charges, color-charges and spins. be the one that is commonly believed to be the , Our scheme does not have the three-family structure, and that the conventional charge assignment (+2e/3) of so much quoted, but not understood, within the stan- the “top” is incorrect. This heretic idea cannot easily dard model. There is virtually a pairwise relation be- be dismissed, since there is no absolute experimental ev- tween quarks and leptons, but not with the same pairs idence that the top charge is really +2e/3 [8]. The top as conventionally defined. The true mathematical struc- quark was found through its presumed main decay chan- ture should instead be “SU(3)preon”, i.e., a preon version nels, namely semi-leptonic ones like t b + ℓ+ + ν, or of the flavor-SU(3) adopted for the three lightest quarks non-leptonic ones like t b+u+d¯, where→ a few b quarks (u, d and s), although the symmetry must be severely have been “tagged” by→ a charged in semi-leptonic broken, as far as quark and lepton masses are concerned. decays. However, the situation is rather complex because 3 3 As the preons are flavor- , the three spreons are too. a total event contains the decay of the full tt¯ pair into 3 3∗ 1 8 Hence, the leptons are = , and the quarks several leptons and hadronic jets, and the identification 3 3 3∗ 6 ⊗ ⊕ are = . From the table above it is obvi- and matching of those are non-trivial. In addition, there ⊗ ⊕ 1 ous that the lepton flavor-singlet is to be found among are individual events that seemingly contradict the as- the three neutrinos (νe, ν¯µ, ν¯κ2), along the diagonal. It is sumption of top-quark production. It can therefore not not possible to pinpoint any particular one, or a linear be excluded that a produced “b” is, in fact, an ¯b (and combination, as the singlet, or make an exact analogy vice versa), or that a tagged b has been matched with the to the octet in the , because of the wrong lepton, i.e., from a W decay of the other quark. symmetry breaking. It is less ambiguous that the three These are crucial questions, since the corresponding de- 3∗ + diagonal quarks (u,X,h) are flavor- , while the remain- cay channels for the antiquark X¯ would be X¯ ¯b+ℓ +ν 6 ing ones are flavor- . and X¯ ¯b+u+d¯, so that the full XX¯ decay→ would give The scheme contains three new leptons and three new the same→ leptons and jets as in a tt¯ decay, although with quarks, which could all be too heavy to be created in a different b W matching. This puzzle would require a current experiments, but naturally of interest for future full new analysis− of the “top” data, where all matchings

2 are remade with the assumption of XX¯ decay. has both left-handed and right-handed components, and A third, and even more speculative idea, is that a since the carries away helicity. It should also be “light” X quark has escaped discovery. All searches for observed that charged leptons cannot decay electromag- a new quark seem to focus on a “fourth-family” b′ with netically in this model. charge e/3 [9]. They also rely on model-dependent as- Neutrino oscillations can occur also if there is a sumptions− on b′ decay, e.g., through a flavor-changing quantum-mechanical mixing of the α and δ preons in- neutral current in b′ b + γ [10] (searched for with side spreons, mixing the (αβ) with the (βδ) in the quark gamma detectors). Such→ experiments cannot see a decay and lepton wave functions. This is not forbidden by any of the X as given above. Neither has there been sys- known principles, and would lead to an oscillation be- + − tematic searches for new resonances in e e collisions at tween the νe and the ντ . As will be argued below for high energies in the traditional way of fine-tuning the to- quark decays, there are reasons to believe that such a tal energy in small steps. It is, on the other hand, hard mixing occurs on the per mille level. This would also to believe that a light X would not have been detected mix the e with the τ by as much, but that would hardly in the search for the top quark [8], unless there is some be observable, since the is stable. (The best way (narrow) kinematic region that has not been properly to observe that two particles are mixtures of the same covered. Also, an X quark lighter than the W − should wave-function components is to measure branching ra- have been seen through decays like W − X + d¯ in the tios when they decay to one and the same ground state.) W branching ratios [9]. The case for an→X with a mass In a future work we will analyse if any of these oscilla- below, say, the W mass is therefore weak. tions or electromagnetic decays are in line with the (not Turning now to lepton decays, we note that all the fully consistent) experimental data on neutrino “tran- known ones can be described as regroupings of preons sitions”, e.g., empirical limitations on decays [11], the into less massive states. A decaying charged lepton trans- suppression of atmospheric muon neutrinos [12], and the fers its spreon to a neutrino, while its preon hides inside recent evidence [13] of a νµ νe “oscillation”. 0 − − → a W or Z . As an example, the decay µ νµ + e +¯νe Quark decays are known to differ substantially from is the preon processα ¯(¯αδ¯) β¯(¯αδ¯)+ β→(βδ)+¯α(β¯δ¯), those of leptons, in the sense that some quarks clearly mix where the latter two leptons→ are the decay products of quantum-mechanically with each other when decaying. W − = βα¯ (more on vector bosons below). This behavior can be accounted for, but not explained, The observation of three conserved lepton numbers by the , in terms of the CKM matrix [6]. (Le,Lµ,Lτ ) in all known weak decays is a straightforward In particular, it is not understood why there is only one consequence of preon stability. Therefore, this model is to substantial (“Cabibbo”) mixing, i.e., of d and s, while the best of our knowledge the only one that explains the the others are much smaller. empirical lepton-number conservation from a first princi- All this can be qualitatively understood in our model, ple. This feature is, however, more or less accidental for but probably not in any other model where quarks and those preon regroupings that correspond to the known leptons are related. The crucial property of quarks is that decays, and there is no general conservation of lepton they are composed of both preons and antipreons, giving number in the model. A simple example is the decay access to preon-antipreon annihilation channels between + + of the superheavy κ, e.g., through κ µ + νe +¯ντ , certain quarks, or equivalently, giving some quarks iden- violating all three lepton numbers! Such→ violations are tical net preon flavors. In particular, d = β(β¯δ¯) and related to processes that require a break-up of a spreon, s = α(¯αδ¯) have the net flavors of the δ¯ and will mix via and a regrouping of its two preons into other spreons. αα¯ ββ¯ (mediated by a composite Z0, or by any gauge Other possible lepton-number violating processes are boson).↔ The effect is weak, due to either the high Z0 neutrino oscillations and decays, if at least one neutrino mass or a strong di-preon binding, which suppresses the is massive. Indeed, the two superheavy neutrinos must αα¯ (and ββ¯) wave-function overlaps. There are similar − + decay, an example beingν ¯κ2 τ +ν ¯τ + µ . Such mixing channels between c and t, and between b and g. decays relieve us from problems→ with cosmic, superheavy The smaller CKM matrix elements cannot be under- and stable neutrinos surviving from the Big Bang, which stood in the same way. Instead, a weak α δ mixing would have given too much cosmic dark . might be required. It suffices to assume a mixing− of only An interesting observation is that the three neutrinos the deeply bound preons inside a di-preon. This will mix νe,ν ¯µ andν ¯κ2 have identical preon content, differing only u with c, d with b, and t with h. in the grouping into spreons: νe = α(βδ),ν ¯µ = β(αδ) It is possible that also CP violation can be explained by 0 andν ¯κ2 = δ(αβ). This opens up for νe ν¯µ oscillations such a mixing. An interesting observation is that the K ↔ 0 or electromagnetic decays likeν ¯µ νe + γ, which would and K¯ have identical preon content, although in be the equivalent of the decay Σ0 → Λ0 + γ in the quark different preon/spreon configurations. This is no longer model. It should be noted that the→ unorthodox transition true if we introduce a small α δ mixing. If this involves between an antineutrino and another neutrino is not for- also a quantum-mechanical phase,− it should result in a bidden by helicity conservation, since a massive neutrino CP violation in the K0 system. The D0 and B0 mesons

3 do not have preon contents that are identical to those of with a di-preon into quarks is harder to understand. It is their , whatever that means for their possible not possible to introduce a new hyper-color, and require CP violation. that quarks be “hyper-confined” in hyper-color singlets. The vector bosons come about as bound preon- Rather it seems as if this binding is due to a weaker antipreon states. The most likely configurations are (hyper)color-electric force, which could be attractive in W − = βα¯, Z0 = (αα¯ ββ¯)/√2 and W + = αβ¯, in anal- both color-singlet (lepton) and color-triplet (quark) con- ogy with the spin-1 ρ −mesons in the quark model. There figurations. Then the quarks would be bound but uncon- also exist two heavier and orthogonal combinations (Z′ fined, and, in this sense, less “fundamental” than leptons. and Z′′) of αα¯, ββ¯ and δδ¯ (like the ω and φ in the quark Finally, it would be interesting to speculate why nature model). In addition, there are two neutral states with αδ¯ has provided two preons (α and δ) that differ only in and δα¯, as well as two charged states of βδ¯ and δβ¯ (like mass. Is there some other property that separates them, the four K∗ mesons). There should be mixings among and are there more superheavy preons to be “discovered”, these states, especially as they are all heavy and unstable. e.g., a heavier version also of the β? One can restrain these mixings by fits to the known W Still, as long as preon models have not yet developed and Z decay modes, but that would be beyond the scope into something as complicated as the standard model of this first qualitative analysis. It should be added that (with the Higgs mechanism), we consider them worthy the lightest Z′ could be lighter than the lower (model- of continued theoretical and experimental efforts. Many dependent) mass limit quoted in [9]. issues, such as the existence of heavy quarks, leptons and In models with composite W and Z one also expects vector bosons, will hopefully be clarified by the next gen- scalar partners. The fact that they have not been ob- eration of high-energy accelerators. served can be blamed either on high masses or on very We acknowledge an illuminating correspondence with weak couplings to quarks and leptons [1]. The latter H. Fritzsch, as well as valuable experimental informa- seems more realistic since spin-0 systems are normally tion from R. Partridge and G. VanDalen. This project is lighter than those with spin 1. The similarity with the supported by the European Commission under contract mesons in the quark model, and the considerable mass CHRX-CT94-0450, within the network “The Fundamen- difference between the π and ρ mesons, make us suspect tal Structure of Matter”. that the missing scalars are rather light, and hence inter- esting to search for in existing experimental data. One possibility is that some of the heavier scalar mesons are indeed hybrids of quark-antiquark and preon-antipreon states. In conclusion, our model provides qualitative explana- [1] I.A. D’Souza, C.S. Kalman, Preons (Singapore, World tions of several phenomena that are not even addressed Scientific 1992). in the standard model, or in other composite models. [2] For a review of the Higgs mechanism, see B.A. Kniehl, Most of them have to do with the (electro)weak interac- Phys. Rep. 240, 211 (1994). tion, which is the most troublesome part of the standard [3] H. Harari, Phys. Lett. 86B, 83 (1979); H. Harari, model, with its many ad hoc parameters and hypothetical N. Seiberg, Phys. Lett. 98B, 269 (1981); Nucl. Phys. particles and processes. B 204, 141 (1982). However, many problems remain to be solved before it [4] M.A. Shupe, Phys. Lett. 86B, 87 (1979). 102B can be considered also a quantitative alternative. One is [5] H. Fritzsch, G. Mandelbaum, Phys. Lett. , 319 the mass-ordering of quarks and leptons, which does not (1981). [6] N. Cabibbo, Phys. Rev. Lett. 10, 531 (1963); follow the flavor-SU(3) quark-model recipe of the light M. Kobayashi, T. Maskawa, Prog. Theor. Phys. 49, 652 baryons. Obviously, the masses are determined not only (1973). by those of the deeply bound preons, but also of the ex- [7] For a review of diquarks, see M. Anselmino, E. Predazzi, act structure of the composed objects. It seems as if the S. Ekelin, S. Fredriksson, D.B. Lichtenberg, Rev. Mod. “net” quantum numbers are important, so that the col- Phys. 65, 1199 (1993). ored quarks are heavier than the color-neutral leptons, [8] F. Abe et al., Phys. Rev. Lett. 74, 2626 (1995); S. Abachi and the normal neutrinos are light because they carry et al., Phys. Rev. Lett. 74, 2632 (1995). almost no quantum properties. Theν ¯κ1 andν ¯κ2 are dif- [9] R.M. Barnett et al., Review of Physics, Phys. ferent due to the very heavy, “naked” δ. Rev. D 54, 1 (1996). 78 There is also a long way to go before we understand [10] S. Abachi et al., Phys. Rev. Lett. , 3818 (1997); and how preons bind into quarks and leptons, which is re- references therein for other searches of new quarks. [11] For a review of empirical information on neutrino decay, lated to the mass problem. Clearly, the strong binding see S. Sarkar, to be published in Proc. XVI Int. Workshop e.g. into di-preons must be due to attractive spin forces, , on Weak Interactions and Neutrinos, Capri (1997); hep- color-magnetism in terms of normal QCD or some even ph/9710273. more . The binding of a preon

4 [12] Y. Fukuda et al., Phys. Lett. 335B, 237 (1994); 280B, 146 (1992); 205B, 416 (1988); D. Casper et al., Phys. Rev. Lett. 66, 2561 (1991); Phys. Rev. D 46, 3720 (1992); W. Allison et al., Phys. Lett. 391B, 491 (1997). [13] C. Athanassopoulos et al., Phys. Rev. C 54, 2685 (1996); Phys. Rev. Lett. 77, 3082 (1996); nucl-ex/9709006.

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