More news about quarks

More News about Quarks Christian Klixbtill Jorgensen

D6partement de Chimie min6rale, analytique et appliqu6e, Universit6 de Gen6ve, CH-1211 Gen6ve

The "constituents" quarks and leptons of matter (with rest-mass) are compared with the historical development of "elements" in chemistry. If unsaturated quarks induce high (and at the moment unpre- dictable) rest-masses above 10GeV, we have a new view of nuclei comprising (2Z+N) u-quarks and (Z +2N) d-quarks in their low-energy states, without any reference to protons and neutrons as permanent building-blocks. Recent studies of quarks and possible rishons (sub-quarks) and technicolour hadrons are reviewed, and the r61e of identity and cardinality in quantum mechanics analyzed.

Analogies with Earlier Chemistry

When Columbus rediscovered America in 1492, it was not immediately evident in Europe that the Middle Age had finished. By the same token, we have since about 1974 1-1] gone through the re- alization that matter with positive rest-mass is con- stituted by leptons and quarks. Entities with vanishing rest-mass (such as photons) move in vacuo with the same speed c relative to all observers, and are not matter in a narrow-minded operational sense. Neutrinos most likely belong to this category too [2] but may represent a border-line case with a rest- mass comparable to the energy of a visible photon. However much we are in the middle of a theoretical turmoil of unprecedented complexity [3, 4], it is worthwhile for a chemist to note similarities and differences from the concept "element" slowly elab- orated in the century between Boyle and Lavoisier. The "principles" (able to occur in all samples) were supposed to lack mass, and very few were accepted, such as heat, light and (one or two) electricities. On the other hand, when radioactivity was discovered a century later, in 1896, 76 distinct elements had been characterized 1-5]. Their (almost unique) parameter,

the atomic weight, was thought of as an infinite decimal fraction, and the hypothesis of Prout (from 1815) of atomic weights as integral multiples of hydrogen was, at the same time, distinctly disagreeing with some of the careful determinations by Marig- nac I-6] but having a vertiginous statistical support. Among the 83 elements possessing non-radioactive isotopes (and including for this purpose thorium and uranium) 39 have atomic weights (on the 12C scale) between (A+0.05) and (A-0.10) (where A is an integer). The statistical probability of this deviation from the expected average 0.15.83--12.45 is 4.2.10 -12. Already 1897, Thomson demonstrated the electrons in a Crookes tube to be the same from differing cathodes, having a definite atomic weight (at low velocities) 0.00055. It is true that a kinetic energy 511000eV doubles this value. This allowed a renewed promiscuity between principles and elements; the electron is the most mobile of the two electricities and the material agent of redox reactions, in other words it is phlogiston. The a-particles available from radioactive isotopes (such as radium and radon) made it possible for Rutherford to show that nuclei with a density close to 1014g/cm3 contain nearly all the mass, whereas the densities 0.5 to 20g/cm 3 typical for condensed matter correspond to a very dilute dispersion of electrons. Since quantum mechanics took shape around 1925, it is clear that the low compressibility of matter is related to the kinetic energy of electrons [7] under equal circumstances being inversely proportional to the square of the linear extension, ef- ficiently counteracting the electrostatic attraction by the nuclei (+Ze). The world looked very simple in 1928; the nuclei presumably contained A protons (A is the integer close to the atomic weight of the isotope) and (A-Z) confined electrons (having enor- mous kinetic energy) and were surrounded, in a neutral atom, by Z electrons distributed on orbitals having highly different ionization energies. This aus-

420 Naturwissenschaften 69, 420-427 (1982) �9 Springer-Verlag 1982

tere simplicity was a great satisfaction for chemists; Bronsted described acid-base reactions as the ex- change of the other massive elementary particle, the proton. It is worthwhile to realize that this picture broke down for a reason (looking very esoteric) before the neutron was discovered. Quantum mechanics insist heavily that entities either are fermions, obeying Fer- mi-Dirac statistics and having quantum numbers (such as S and J for monatomic entities, called I for nuclei, but again J for smaller systems) being half an odd, positive integer, or are bosons, obeying Bose- Einstein statistics and having non-negative integers as quantum numbers. A manifold containing an even number of fermions is a boson, whereas a set of an odd number of fermions is itself a fermion. Molecular spectra of Ni ~ demonstrated beyond doubt that the Z CN nucleus is a boson, though it was supposed to contain 21 fermions. The description changed to N = ( A - Z ) neutrons and Z protons in the nucleus, and it was considered a numerical accident that the free neutron is/Lradioactive (forming a proton, an electron and an anti-neutrino) with the half-life 11 minutes. However, once the door was opened for radioactive "elementary" particles, there was no good reason to exclude entities (frequently with alternative, competing modes of de- cay) with half-lives in the 10 _6 or 10-1~ range. Space is not available here to describe the flourish- ing natural history of "elementary" particles, re- minding one about elements before the Periodic Ta- ble. However, we must add a few words to our vocabulary, Leptons (such as electrons, muons,... and their neutrinos) do not undergo the strong interactions keeping nuclei together. As the name in- dicates, they used to be (much) lighter than a proton, but this is not true for tauons (rest-mass 1784MeV; 1 unit of atomic weight is 931.50 MeV), and they are all fermions. Hadrons undergoing strong interactions are either mesons (always bosons) among which the lightest are the neutral pion (134.96MeV) and the positive and the negative pion (139.57 MeV), or they are baryons (always fermions). The two lightest baryons, the proton (938.28MeV) and the neutron (939.57MeV) have the title nucleons because they constitute nuclei, whereas the third (the neutral A ~ l l l5.6MeV) and subsequent baryons are called hy- perons. The observation that the lightest baryon, the proton, has a half-life (at least) above 1030 years is expressed by the baryon conservation rule that the baryon number B is invariant. B = + 1 for conventional baryons, - 1 for the anti-proton, anti-neutron (decaying to an anti-proton, a positron and a neutrino) etc., and B = A for nuclei. B is zero for mesons, which are all rather short-lived, forming leptons and

photons (high-energy photons are called v-rays, when originating in nuclear reactions, and X-rays tu inner electronic shells, but there is no intrinsic difference). The most important regularity for our purpose is that all fermions and most bosons (though not photons and neutral pions) have anti- particles able to annihilate mutually under emission of photons. The annihilation of a neutrino and an anti-neutrino has not been detected (and there was at one time a suspicion that a photon is such an adduct).

The Arguments for Quarks

In 1964, Gell-Mann [8, 9] invented three fractionally charged quarks u(up, +}e), d(down, -}e ) and s(strange, also -�89 to classify the behaviour of the eight lightest baryons (with J = �89 stretching from 938.28 to 1321.3MeV. Similar ideas were expressed at the same time by Zweig in a preprint. The (at least highly predominant) quark configuration is u2d for the proton, ud 2 for the neutron, uds for A ~ and so on. Furthermore, ten baryons with J = ~ occur between 1232(A + + u 3) and 1672(g2- s 3) MeV, and the latter particle was found, following Gell-Mann's predictions. Quite generally, baryons "consist" of three quarks, and mesons of one quark and one anti- quark. Thus, the positive pion is ud, the negative pion d~ and the neutral pion may represent mix- tures of u~, dd etc. Glashow, Itiopoulos and Maiani [10] gave convincing theoretical arguments for a fourth quark c(charm, +%) which was found No- vember 1974 [11-13] as charmed mesons c~ around 3.1 to 3.7GeV. A fifth quark b(beauty, -�89 pro- vides the Y(upsilon) mesons [14, 15] around 9.8 to 10.3GeV. For reasons to become apparent below, many people expect a sixth quark t with charge +2e, but the t{mesons have not been found as yet, and must occur above 31 GeV, if they exist. No high-energy physics experiment has yet detected a liberated quark from collisions between electrons, positrons, protons, nuclei .... Nevertheless, quarks have become almost as indispensable as neutrinos and anti-neutrinos, which were postulated by Pauli in 1930 in order to conserve energy (the electrons emitted show a broad distribution of energy, rationalized by Fermi 1934) and fermion or boson character (since A = Z + N remains odd or even) by fl-radioactivity. As discussed by Feynman [1, 16] the magnetic moments of baryons can be explained (within some 10%) as additive quark magnetic moments, and there has always been a suspect side of the neutron magnetic moment, if it does not orig- inate in a charge distribution with zero sum. How- ever, a much more direct evidence is high-energy

421

collisions with protons, where the "hard" partons [17] are quite similar to the nuclei in Rutherford scattering. Actually, both electrons and quarks [14, 18] are point-like at least down to 2.10-16cm, providing a "volume" 10 9 times that occupied by a nucleon in nuclei. Many theorists [4, 14, 19] believe in dogmatic confinement of quarks and have proposed that the (ex- perimentally verified)"asymptotic freedom" by very weak interactions between two quarks at very short distance can be extrapolated to their potential energy being proportional to their distance (the re- ciprocal behaviour is found by electrostatic and gravitational attraction having this singularity at vanishing distance). The argument runs that stretching o f the inter-quark distance induces a kind of dielectric break-down of the vacuo, producing in- tervening qc 7 mesons (in the following, q is the general symbol for a quark). Quantum chromodynamics (QCD) is a theory con- structed by (somewhat remote) analogy to quantum electrodynamics, making special emphasis on the quantum number colour. If quarks are fermions, it is only possible to satisfy Pauli's exclusion principle in baryons with J=-~ (such as u 3 or s 3) if the flavour (u, d, s, c, b,...) is combined with one of three values of colour. The (somewhat debatable [20]) concepts of Ostwald's theory of subtractive colours inspire the allegoric names red, yellow and blue for the quark colours, whereas all observed hadrons (and leptons) are grey. Though the writer [21-25] is in a minority at this point, he suspects that anti-quarks have the same colours (constituting the multiplication table of Klein's Vierergruppe, the product of two different non-grey colours being the third colour, as is the case [7] for several point-groups of order 4) whereas the analogy to charges makes most chromodyna- micists believe that anti-quarks have anti-colours, say green, violet and orange. In spite of extensive theoretical efforts, the necessity of quark confinement in baryons has not yet been proved. DeRfijula, Giles and Jaffe [26] pointed out that if gluons (the QCD analog of photons in electrodynamics) are not entirely massless, unsaturated quarks have a finite rest-mass and form extremely strong adducts quarklei with grey nuclei. It is beyond dispute that systems containing unsaturated quarks are exceedingly scarce (though they may occur in certain minerals to an extent around 10 -zl per nucleon or 600 per g, as discussed below) and it may be that a dynamic relativistic effect [27] ex- plains a very strong propensity toward confinement. Already Lipkin [28] pointed out in his review "Quarks for Pedestrians" that if the free quark has a rest-mass M atomic weight units (ainu), it makes

very little difference for the feasible experiments how large M is, if it is above 10. Close [17] argues that a diquark qq would show roughly the same M as one q. We return to this question below, but want to point out that M might conceivably be 1000 for q but only 50 for qq. These huge masses have no direct relation to the effective masses inside hadrons [19]. Relative to a badly defined zero-point of u and d quarks, s, c and b are heavier to the extent 0.2, 1.4 and 4.6 amu [14, 29]. For the chemist, the most striking consequence of a defined atomic weight M of a free quark is that the ratio R between the binding energy of a system and the sum of the rest-masses of the products is the large number ( 3 M - l ) for a nucleon. Lavoisier assumed additive masses of the elements in compounds, and it is sad that analytical balances are not reliable beyond the ninth decimal, because R is below 10 9 for all chemical reactions except the com- bination of two hydrogen atoms. Nearly all nuclei [25] have R close to 0.008, and the chemists have been so clever in choosing the ~2C scale that they forget that the sum of the atomic weights of 90 hydrogen atoms and 142 neutrons (able to form 232Th) is 234. There is something surrealistic about the energy levels of a given number of quarks varying far more than the rest-mass of the most stable level. In a way, this is similar to the non-relativistic description of atomic spectra in cm 1 whereas including mo c2 of the electrons (=1372 times 2 ryd- berg) makes the binding energies negligible. Thus, the total binding energy of 90 electrons to a thorium nucleus represents only 1.2mo c2 and of this quan- tity, 0.2too c2 is provided by each of the two l s electrons, whereas the loosest bound electron only costs 10- ~ mo c2 to remove.

Diquarks and the Vacuum Storehouse

The inertial (and hence gravitational) mass stored in a baryon must be located in extremely intense, local fields, having brought the three quarks almost to the brim of annihilation. Hence, R =(2M-0 .15 ) for the pions is hardly larger percentagewise, than ( 3 M - 1 ) for the nucleons. Quite recently [30, 31] the proof has been given that the gravitational collapse yield- ing a black hole always leaves a positive (and distinctly not a negative) mass. Apparently, there is no, even qualitative, theory available for these exorbitant binding energies in q3 and qc 7 systems, though they represent a certain similarity with gravitational sin- gularities. Many authors argue that only grey systems have accessible masses, and hence, the number of quarks (minus the number of anti-quarks) is divisible by 3,

422

explaining why fractionally charged objects are so scarce. It cannot be argued that diquarks cannot be grey (as can be true in Klein's Vierergruppe) since it is well known from atomic spectra [25, 32, 33] that the totally symmetric state (the neutral element of Hund vector-coupling) is found, not only for isolat- ed groundstates of closed-shell systems, but also for highly excited states (e.g. of an even number of electrons in one partly filled shell). The question of diquarks became important when Fredriksson and J~indel [34] asked whether the deuteron does not have a low-lying tris (diquark) state explaining some reactive modifications of nuclear matter. It is likely to be grey, since each diquark can have the colour of an anti-quark, and the whole system be grey like an anti-baryon. However, Close [35] has discussed some theoretical difficulties for this description. Weinstein and isgur [36] asked whether two re- sonances just below the threshold 987 MeV for forming a kaon (u~) and an anti-kaon (s~) may not represent totally symmetric q2(q-)2 states. It is worthwhile noting that the free quark may have a very large atomic weight (and, in the extreme, be dogmatically confined) and the diquark a moderate value, say 20. If it is below 15, it would probably have been detected [37] at a recent experiment by Litke at the PEP accelerator in Stanford, Cf. A seemingly critical limit is whether q2 is less than half as heavy as q (in what case q + baryon --+ two q2) but a more subtle criterion is whether a baryon and an anti-quark can be formed from a diquark:

ud=uZd~ uu=u2dd

ud=ud2 d dd=udZ ~ (1)

Like in all other cases of anti-particles, the vacuum is an indefinite reservoir of pairs of a particle and its corresponding anti-particle. As soon the atomic weight of an anti-quark is one unit higher (corrected for binding to the nucleon) than of a diquark, the reactions (1) proceed to the left. As far goes formation of adducts between a baryon and an anti- quark, we have both kinetic and thermodynamic conditions. Even if nuclei bind a positive quark [26] with as high energy (say 0.5 to 5 GeV) as a negative quark, the former process has an activation energy of the order 0.1Z MeV (much like hydrochloric acid in a laboratory does not form argon) and positive quarks may remain loosely bound [21] to electrons in metals and anions, whereas negative quarks cas- cade down like negative muons [38]. Seen from this point of view, u2d~ of Eq. (1) is particularly easy to form. By the same token, the electrostatic attraction between a proton and a d-quark may provide the tetraquark u2d 2 probably best described as a bis

(diquark). Since the formation of a proton and an anti-proton in vacuo only costs 1.86GeV, a free d- quark may form such a tetraquark u2d 2 and eject an anti-proton, again-showing that unsaturated quarks may be much easier to conserve than free quarks. However, if a diquark is lighter than a tetraquark, the free d-quark may rather eject a proton, annihilate the anti-d-quark and produce an anti-diquark:

d + u2 d +(ff)2 d--+ u2 d +(ff) 2 (2)

This "Umlagerung" is a fascinating aspect of free quarks interacting with the vacuum. If each quark is ascribed the baryon number B=�89 (and each anti- quark -�89 the statement of decreasing energy q>q2>q3 can be re-written (1)>(2)>(0) for the rest (x) by division of 3]BI by 3. If q and q2 do not have comparable mass, as was suggested originally [17], switch reactions of the type Eq. (2) bring a member of class (1) into the lighter class (2). This scenario of wildly varying rest-masses has to some extent re-activated the "boot-strap" concept [39] that there are no privileged building-blocks, everything consists of everything else. However, the conservation of B and the (debatable) multiplication table of colour retains a certain "substantiability" of matter. It is clear that a magnesium atom at rest, and a proton with the kinetic energy 22GeV, are not equivalent in all respects, in spite of their identical energy content. It remains also valid that the amplitude of a mosquito in an elephant is almost as small as the amplitude of an elephant in a mosquito.

Nuclei as Quark Aggregates

For the chemist, a very important question is the constitution of nuclei. After the introduction of quarks, there has been some discussion of a phase transition from nucleon to quark matter at very high pressure [40, 41]. The predominant (or exclusive) occurrence of quark numbers divisible by 3 make people believe that the quarks are wrapped up, 3 at a time, in each nucleonic bag. The actual situation may very well be intermediate between nuclei of differing atoms (among which there is very little contact below 106 K) and the mobility of electrons between adjacent atoms. Though the quarks in mesons and baryons seem to have sufficiently small average speed to make a non-relativistic treatment a fair approximation [16, 17] they occupy their nucleonic volume to an extent the nucleus cannot do in an atom. If we are in an intermediate situation, it is a valid statement that the groundstate and the excited levels of the (Z, N) nucleus are stationary states

423

of a system of n u = ( 2 Z + N ) u-quarks and na=(Z +2N) d-quarks, neglecting the possibility of hyper- onic nuclei containing s,c,.., quarks. These linear relations allow the definition:

z=- nu- nd (3)

ascribing the Z-position in the Periodic Table to any nucleus having

n u = ~Z + �89 d (4)

without making any specific reference to protons and neutrons then becoming the simplest nuclei. However, if Z and N are allowed to have opposite sign, systems such as u 3 and d 3 are also included, in spite of being 0.3 GeV excited (relative to a nucleon) and having 3=3/2. It may be noted that A + +(u 3) has two positive charges, but only a-third of the mass of the c~-particle. It is a rather arbitrary choice to say that it is a light, short-lived isotope of helium, without d-quarks, and hence N = - 1 in Eq. (3). In monatomic entities, it is well-known that the classification of energy levels according to J and parity (and in the frequent case of approximate Russell-Saunders coupling, also S and L) allows a bunching in electron configurations [33, 42] though the total wave-function definitely cannot be a single Slater determinant. The moderate effects of intermix- ing of configurations show up in some characteristic details, but is a second step in a refined description. If the picture of the nucleus suggested by Eqs. (3) and (4) is useful, the tendency toward clustering of the quarks is the first-order effect, and the energy dependence on other quantum numbers (such as I and parity [25]) is a small correction. In the quantum mechanics of the groundstate, it is important to discuss the instantaneous picture ob- tained by very rapid (and hence violent) measurements. The statistical interpretation of the wave- function according to Born is the probability distribution of such pictures, and many legitimate diver- gencies [7] occur between the time-average picture of compounds in crystallography and the short time- scales of various spectroscopic techniques. It would resolve many ambiguities (that a nucleus shows many of the properties of a liquid drop with high surface tension [43] but also of a nucleonic shell model [25] reminiscent of electron configurations) if the "constituents" were the 3A quarks of Eq. (3). Then, the instantaneous picture is assumed to show a strong tendency toward clusters u2d and ud 2 but probably also a high concentration of u6d 6 at short mutual distances. This would explain the tendency of 4He clustering most eminent in c~-radioactivity (like with /~-radioactivity, where the pre-existence of

the electron in the nucleus cannot be concluded) though from a strict quantum-mechanical point of view, we are only observing a transmutation from (Z, N) to ( Z - 2 , N - 2 ) . On the other hand, big clusters such as /,/18d18(12C) or u24-d24(160) should be much less pronounced. The inter-nucleon attraction is a residual result of the inter-quark interaction (much stronger at shorter distance). As said by Gla- show [44]: "The nuclear force must be a secondary consequence of the fundamental force that binds quarks into nucleons, just as the chemical force between neutral atoms is a secondary consequence of the Coulomb force that binds the atom". The unexpected (negative) sign of the spin-orbit coupling in the nucleonic shell model seems to be due to the longer-range tail of the inter-quark forces [45]. The main conclusion is that nearly all matter outside high-energy laboratories consists of electrons sur- rounding high-density, grey u- and d-quark aggregates.

Quark-Lepton Generations, Rishons and Technicoloured Hadrons

The link between leptons (including electrons and neutrinos) and quarks is most conspicuous in the common value of e for electrons (with opposite sign) and protons agreeing better than one part in 10-19 Whereas quantum mechanics is adamant about the choice between fermion and boson characteristics, there is no obvious reason why e or (e/3) should be a smallest quantum of electric charge. Several authors [14, 19] propose to define three generations (here called fi, # and r). Figure 1 gives the sixteen members of the fl generation having charges (in- creasing in steps of a-third) from - 1 to 1, the integers represented by the electron, anti-neutrino, neutrino and positron, and the four fractional charges by ~, d, d and u quarks (each in three colours). Figure 1 gives a trigonal Aufstellung (Klein's Vierergruppe) and a hexagonal arrangement (anti-quarks having anti-colours). There is general agreement that the second generation has exactly analogous members, the leptons being the positive and negative muons, and the muonic neutrino and anti-neutrino, and the quarks being c and s (rather than u and d). It is not certain [463 that ~ and b are connected with a sixth quark. Veltman [473 has discussed the relations between such generations, and the severe higher limit on their number (four would still be conceivable). We may be stuck for many years with the three generations containing 48 leptons and quarks, rather similar in ordering to the Periodic Table before

424

-1 -2/3 -1/3 0 +1/3 +2/3 +1 I I L I I I I

o

V e- u d v- d u e +

Q

Fig. 1. The first generation of quarks and ieptons arranged according to electric charge Q. The rishon structure proposed by Harari [48] is shown in vertical cartouches. The figure [23] is reproduced with permission from "Gamma"

1913. In both cases, there is no striking answer to the question about their origin. However, in analogy to Prout's heuristic, but partly erroneous, hypothesis, there may be "constituents" at a deeper stratification explaining the structure of, at least, the /~ generation. Figure 1 illustrates one such proposal, the rishons of Harari [48]. Each "elementary" fermion "contains" three rishons, T(+ e/3), V(neutral), or T(-e/3) and V(neutral). The grey leptons have three identical rishons, whereas the coloured quarks "contain" two and one of the T or V categories. DeRfijula [49] and Sikivie [50] have written high- spirited reviews on conceivable forms of rishons and other sub-quarks. Although high-energy physicists instinctively think about inter-rishon distances [49, 51] below 10-2~ it may very well be that rishons are much more like quantum numbers than like Lego bricks. Anyhow, we may experience today one extreme turning-point of the pendulum, the rishons of 1979 corresponding to the protons and electrons of 1928. The other extreme is a heterogeneous col- lection of a hundred "elementary" particles or elements. The description of matter, using leptons and quarks, has taken a surprisingly coherent form within a few years. However, it has active growth areas in two directions. Glashow [46] recommended "passive ex- perimentation" as a needed alternative to high-energy physics. He points out that 1% of the unexpected element argon was found in the atmosphere 1894, that radioactive isotopes extracted from uranium

and thorium minerals provided all nuclear data the following 38 years, and that cosmic rays were the precursors of the huge accelerators. The geochemical predictions of the chemistry of species containing unsaturated quarks [21, 25] are interesting, because new "elements" (Z+~) and/or (Z+~), which cannot be completely neutralized by electrons, are interca- lated in the Periodic Table. Fairbank and collaborators in Stanford reported in 1977 [52] that 10-~g samples of superconducting niobium (suspended in a magnetic field) in about half the cases show charges close to +0.34e (or -0.66e) by Millikan-measurements and they still maintain [53] that about one unsaturated quark is observed per 10 is nuclei of 93Nb or per 102o nucleons. Some of the carriers of fractional charge are remarkably mobile, and as discussed by Orear [54] and Schiller [55] look like (+ e/3), perhaps bound to an electron. The positive species is not necessarily d but could be a tightly bound diquark ud of hadronic radius, similar to proton-quark adducts [21]. It may also bind halide anions, water, ammonia and, of course, metallic samples. If the positions of spectral lines of quarked atoms were well known, techniques are available [56] for detecting a few atoms. Many other investigators have reported negative results, with very low higher limits of detection [57, 58] including careful work [59] on mercury containing altogether 102o nucleons. It is likely that any unsaturated quarks originated very shortly after the Big Bang, and Wagoner and Steigman [60] calculat- ed that they froze out of equilibrium during the quark-hadron transition at kT somewhere between 200 and 400MeV (i.e. T close to 3.10~2K). This range is compatible with a surviving concentration 10 -2o per nucleon, if their rest-mass is between 15 and 30 GeV, and 10-30 in the interval 20 to 38 GeV. The surviving unsaturated quarks may not only be diquarks like ud, or nuclei bound to a quark [21, 26] but might also be exotic quarks protected by very strong selection rules of the type of B conservation. The question of quarks outside the three generations has close connections with grand unified theories (GUT) where the unification of electrody- namic and weak (parity non-conserving) interactions by Weinberg and Salam [19] is extended to the strong interactions. For a few years, there was a general consensus that no new particles would show up in the range between 200 and 1014GeV, and that the proton has a half-life close to 10 31 years [e.g. due to the slow rishon disproportionation 2TTV-+(TTT)+(TVV) of Fig. 1]. Since the characteristic Planck mass is 1.22.1028 eV =l .3 .1019amu=22gg, there have been expressed some hopes of a super-unification with gravitation

425

[193 and the best group-theoretical model is super- symmetry [61] involving one graviton (J=2) and eight gravitinos (J=~) which may be almost im- possible to detect. However, Pauli may be right that unification with gravity is intrinsically excluded; the geometry of the space (expressing the gravity) may be the stage of the theatre, where the Schr6dinger or relativistic wave-functions are played. The Universe may also be a 4 (Minkowski)-dimensional soap-bub- ble in a 11-dimensional space [62]. Anyhow, the conventional GUT have lost some sup- porters [47, 51, 633 and arguments given for "new physics" in the teravolt (1012eV or 1000ainu) range [64]. A prominent candidate are the technicoloured fermions proposed by Dimopoulos and Susskind [65, 66] providing long-lived hadrons, as well as ditech- niquarks around a few hundred GeV. If such had- tons X- are remnants of the Big Bang, they form strong adducts [67, 683 with the nucleus Z becoming super-heavy isotopes of ( Z - l ) . The very low concentration of actinium in minerals might serve as carrier for 232ThX, and it might be worthwhile looking at the very high A-region (400 to a million) in big mass spectrometers (such as Oak Ridge calut- rons). Cahn and Glashow [68] argue that adducts of X- with heavy elements were formed shortly after the Big Bang because 8BeX is not a-radioactive (like 8Be) opposing no bottleneck to nucleosynthesis [69]. Such heavy isotopes might help condensation of galaxies, a job sometimes assigned [23 to slow (braked) neutrinos, if they have a rest-mass of a few eV. Another astrophysical consequence of technicoloured hadrons is that the neutral adducts tHX and 2DX may polymerize to a metallic liquid (with conduction protons) and catalyze nuclear fusion at room temperature [67] as proposed by Zweig [70] for long-lived exotic quarks (-4e/3), or (~)2 of Eq. (2). This might explain that Jupiter and Saturn ir- radiate about twice as much heat as they absorb from solar light. As Mouloudji sings, nostalgia is no longer what it used to be. The fundamental problem of analytical chemistry, the "constituents", may have entered a decisive phase with a happy end, as also reviewed by Schopper [71] in this journal. It seems to be a wrong interpretation of Hermes Trismegistos that Nature just repeats the same structures on different scales of size. Galaxies, animals and coins are similar, but not identical, whereas the objects of quantum mechanics are thoroughly identical [72]. One may even suspect [73, 743 that quantum mechanics is only applicable to small systems, which can be reproduced identically. This review treats two strati- fications suggesting that we may be touching the bottom of the ocean of undulating theories. The

binding-energy ratio R is still below 0.01 for nuclei relative to nucleons, but seems to be above 50 for baryons relative to quarks. We have here lost an essential aspect of "constituents" in earlier thinking, but conserved a (unexplained) quantum of charge (e/3). This is also true for the deeper stratification of rishons, which may be science-fiction, or may be the ultimate solution. Rishons may be dogmatically confined in quarks and leptons in a way that quarks cannot be confined in baryons, because rishons are in no sense "partons" you can hit in a collision, and may not even be full-fledged fermions. Their local fields must be impressive, since (TTV) and (TVV) are some 105 times heavier than (TTT), whereas (VVV) may lack rest-mass. For the chemist, it is fascinating that the temperature is so low now, 10 l~ years since the Big Bang, that positive rest-mass has precipitated out in ashes of a most brilliant fire-work. The first few minutes [753 a-fifth of all protons formed helium. It is the business of normal stars (such as our Sun) to con- tinue this process on a slow rate at some 15 mega- kelvin [69]. Only during supernova explosions, the heavier elements are formed close to 109 K (kT~0.1MeV) and the inorganic chemists are in- deed fortunate that 0.15% of the Earth's crust are elements with Z from 31 to 92 collected from supernova dust, a much higher concentration than in most stellar atmospheres. The emphasis on total symmetry [25] (including grey colour) of quark aggregates (nuclei) reminds the chemist of diamagnetic organic compounds. But groundstates of lanthanide compounds [76, 77] show J-levels up to 8 and S up to 7/2 and it is possible that a residual concentration around 10 20 (if not 10 - 1 6 in certain minerals, to be compared with 10 12 radium and 10 -1~ radon in most rocks) of analogous exotic materials involving unsaturated quarks and/or technicoloured hadrons remains to be detected. We cannot make the furnaces for 1013 K, but we can look at minerals with an open mind.

1. Feynman, R.P.: Science 183, 601 (1974) 2. B6rner, G.: Naturwissenschaften 68, 458 (1981) 3. Mulvey, J.: Nature 278, 403 (1979) 4. Marciano, W., Pagels, H.: ibid. 279, 479 (1979) 5. Weeks, M.E.: The Discovery of the Elements. Easton, Penn.: J.

Chem. Educ. Publ. 1968 6. Jorgensen, C.K.: Centenaire de l'Ecole de Chimie 1879-1979,

Geneva: Section de Chimie de l'Universit6 1979 7. Jorgensen, C.K.: Modern Aspects of Ligand Field Theory.

Amsterdam: North-Holland 1971 8. Gell-Mann, M.: Phys. Rev. Lett. 8, 241 (1964) 9. Hussar, P.E., Kim, Y.S., Noz, M.E.: Am. J. Phys. 48, 1043

(1980) 10. Olashow, S.L., Iliopoulos, J., Maiani, I.: Phys. Rev. D2, 1285

(1970)

426

11. Galliard, M.K., Lee, B.W., Rosner, J i . : Rev. Mod. Phys. 47, 277 (1975)

12. Richter, B.: ibid. 49, 251 (1977) 13. Brandt, S.: Naturwissenschaften 64, 229, 356 (1977) 14, Proc. 1979 Int. Symp. on Lepton and Photon interactions at

High Energies (eds. T.B.W. Kirk, H.D.I. Abarbanel). Batavia, Illinois: Fermi National Accelerator Laboratory 1979

15. Schopper, H.: Naturwissenschaften 67, 161 (1980) 16. Franklin, J.: Phys. Rev. D20, 1742 (1979) 17. Close, F.E.: An ~ntroduction to Quarks and Partons. London:

Academic Press 1979 18. Brodsky, S.J., Drell, S.D.: Phys. Rev. D22, 2236 (1980) 19. Ne'eman, Y. (ed.): To Fulfill a Vision - Jerusalem Einstein

Centennial Symposium on Gauge Theories and Unification of Physical Forces. Reading, Mass.: Addison-Wesley 1981

20. Hoshino, M.: Am. J. Phys. 47, 573 (1979) 21. Jorgensen, C.K.: Structure and Bonding 34, 19 (1978) 22. Jorgensen, C.K.: Arch. Sci. (Geneva) 32, 201 (1979) 23. Jorgensen, C.K.: Gamma (Copenhagen) 45, 30 (1980) 24. Jorgensen, C.K.: Naturwissenschaften 67, 35 (1980) 25. Jorgensen, C.K.: Structure and Bonding 43, 1 (1981) 26. DeRfijula, A., Giles, R.C., Jaffe, R.L.: Phys. Rev. D17, 285

(19783 27. King, M., Rohrlich, F.: Phys. Rev. Lett. 44, 621 (1980) 28. Lipkin, H.J.: Phys. Rep. (Phys. Lett. C) 8, 173 (1973) 29. Wills, J.G., Lichtenberg, D.B., Kiehl, J.T.: Phys. Rev. DI5,

3358 (1977) 30. Schoen, R., Yau, S.T.: Phys. Rev. Lett. 48, 369 (1982) 31. Horowitz, G.T., Perry, M.J.: ibid. 48, 371 (1982) 32. Jt3rgensen, C.K.: Adv. Quantum Chem. II, 51 (1978) 33. Jorgensen, C.K.: Int. Rev. Phys. Chem. 1,225 (1981) 34. Fredriksson, S., J~indel, M.: Phys. Rev. Lett. 48, 14 (1982) 35. Close, F.: Nature 296, 305 (1982) 36. Weinstein, J., Isgur, N.: Phys. Rev. Lett. 48, 659 (1982) 37. Litke, A.M.: Proc. Int. Symp. on Lepton and Photon In-

teractions at High Energies, Bonn, August 1981 38. Daniel, H.: Naturwissenschaften 68, 590 (1981) 39. Capra, F.: Am. J. Phys. 47, 11 (1979) 40. Fechner, W.B., Joss, P.C.: Nature 274, 347 (1978) 41. Pati, J.C.: [19], p. 221 42. Jorgensen, C.K.: Oxidation Numbers and Oxidation States.

Berlin-Heidelberg-New York: Springer 1969 43. Bohr, A., Mottelson, B.R.: Nuclear Structure. New York:

Benjamin, Vol. 1: 1969, Vol. 2:1975 44. Glashow, S.L.: [19], p. 160

45. Pirner, H.J.: Phys. Lett. 85B, 190 (1979) 46. Glashow, S.L.: Rev. Mod. Phys. 52, 539 (1980) 47. Veltman, M.: [14], p. 529 48. Harari, H.: Phys. Lett. 86B, 83 (1979) 49. DeRfijula, A.: ibid. 96B, 279 (1980) 50. Sikivie, P.: ibid. I03B, 437 (198l) 51. Harari, H., Seiberg, N.: ibid. 98B, 269; IOOB, 41, 102B, 263

(1981) 52. LaRue, G.S., Fairbank, W.M., Hebard, A.F.: Phys. Rev. Lett.

38, 1011 (1977) 53. LaRue, G.S., Phillips, J.D., Fairbank, W.M.: ibid. 46, 967

(1981) 54. Orear, J.: Phys. Rev. D20, 1736 (1979) 55. Schiffer, J.P.: Phys. Rev. Lett. 48, 213 (1982) 56. Hurst, G.S., et al.: Rev. Mod. Phys. 51. 767 (1979) 57. Jones, L.W.: ibid. 49, 717 (1977) 58. Ogorodnikov, D.D., Samoylov, LM., Solntsev, A.M.: Soviet

Phys. JEPT 49, 953 (1979) 59. Hodges, C.L., et aI. : Phys. Rev. Lett. 49, 1651 (1981) 60. Wagoner, R.V., Steigman, G.: Phys. Rev. D20, 825 (1979) 61. Wess, J.: Naturwissenschaften 67, 484 (1980) 62. DeWit, B., Van Nieuwenhuizen, P., Van Proeyen, A.: Phys.

Lett, I04B, 27 (1981) 63. Politzer, H.D.: Phys. Scripta (Stockholm) 23, 1017 (1981) 64. Pagels, H., Prima&, J.R.: Phys. Rev. Lett. 48, 223 (1982) 65. Dimopoulos, S., Susskind, L.: Nucl. Phys. B155, 237 (1979) 66. Dimopoulos, S., Ellis, J.: ibid. B182, 505 (1981) 67. Jorgensen, C.K.: Nature 292, 41 (1981) 68. Cahn, R.N., Glashow, S.L.: Science 213, 607 (198l) 69. Trimble, V.: Rev. Mod. Phys. 47, 877 (1975) 70. Zweig, G.: Science 201,973 (1978) 71. Schopper, H.: Naturwissenschaften 68, 307 (1981) 72. Jorgensen, C.K.: Theor. Chim. Acta 34, 189 (1974) 73. Ballentine, L.E.: Rev. Mod. Phys. 42, 258 (1970) 74. Primas, H.: Chemistry, Quantum Mechanics and Reduc-

tionism (Lecture Notes in Chemistry, Vol. 24). Berlin-Heidel- berg-New York: Springer 1981

75. Weinberg, S.: The First Three Minutes. New York: Bantam Books 1979

76. Reisfeld, R., Jorgensen, C.K.: Lasers and Excited States of Rare Earths. Berlin-Heidelberg-New York: Springer 1977

77. Jorgensen, C.K., Reisfeld, R.: Topics Curr. Chem. i00, 127 (1982)

Received April 19, i982

427

Documents

More news about quarks