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Inside the Quark

by John G. Cramer

Alternate View Column AV-80
Keywords: composite quark substructure evidence Fermilab CDF preon model mass paradox
Published in the September-1996 issue of Analog Science Fiction & Fact Magazine;
This column was written and submitted 2/5/96 and is copyrighted ©1996 by John G. Cramer.
All rights reserved. No part may be reproduced in any form without
the explicit permission of the author.


    The hot physics news for February 1996 was the composite nature of the quark. In a paper submitted to the journal Physical Review Letters, 450 members of the CDF group at Fermilab reported indications that the quark may have internal substructure. This is the first evidence that the quark is not a fundamental particle, but instead may be made of sub-particle components. This may be the breakthrough that transcends quantum chromodynamics (or QCD), the present Standard Model of particle physics. Experimental particle physics may have "struck gold", the first such strike in a long time.

    CDF (the acronym stands for Collider Detector at Fermilab) is the experiment that in 1994 and 1995 suggested and then confirmed the discovery of the top quark, using 1.8 TeV collisions of protons with antiprotons at the Fermilab Tevatron. To assemble convincing evidence for the top quark, the CDF group collected data from a large number of proton-antiproton collisions during the 1992-93 running period. Then, with the top quark safely salted away, the CDF group has been examining their accumulated data for other aspects of the p+p-bar collisions. One such study of the CDF group focuses on "jets" from the p+p-bar collisions. "Jet" is high-energy physics jargon for a cluster of high energy particles emitted in the same direction. Free unattached quarks are not permitted by the rules of QCD. Within the colliding protons, the constituent quarks are tied together with gluons that form "color strings" connecting the quarks. If a quark strikes another quark in a head-on collision and is ejected from its surrounding proton, its attempted escape from this confinement stretches the string until it breaks, with a new quark and anti-quark forming at the broken string ends. The resulting multitude of new quarks combine to form a multitude of new particles, all moving in the same direction as the original quark, thereby forming a "jet". When a very high energy quark is ejected from a collision, a jet is what actually reaches the detector.

    Seeing such jets are not new. They have become a standard feature of p+p-bar collisions at Fermilab. What is new is that the CDF data shows an unexpected excess of jets with energies above 200 GeV, an excess that cannot be explained by the best theoretical models. Analysis of such data is tricky, because a background from non-jets must be subtracted, and any mis- estimation of background could lead to effects like the one reported. Thus, delicate judgment calls within the CDF group were involved in analyzing the data and deciding to report the results. We would prefer confirmations from other experiments, but for the moment let's accept the result as reported. One interpretation of the surplus of jets with too much energy is that deep within quarks are even smaller particles with even larger masses which have collided. Thus, the CDF work suggests that there are particles more fundamental than quarks.

    This would be the next link in a chain of similar discoveries. In 1911 Ernest Rutherford, after his group at Manchester observed alpha particles scattered from a thin sheet of gold sometimes emerging at very large angles, concluded that atoms must have a heavy compact substructure which we now call the atomic nucleus. In 1990 Taylor and Kendall won the Nobel prize for the discovery, made by their group working at SLAC in the 1970's, that electrons scattered from protons show substructure within the proton. Their work supplied the convincing experimental confirmation of the quark model. Now quark-quark scattering by the CDF group shows evidence for substructure within the quark itself.

    The CDF work suggests that there are new and previously unknown particles from which quarks (and perhaps also electrons and neutrinos, i.e., leptons) are made, just as protons and neutrons are made of quarks, as nuclei are made of neutrons and protons, as atoms are made of nuclei and electrons, as molecules are made of atoms, as cells are made of molecules, and as we are made of cells. Is this hierarchy of wheels-within-wheels infinite, or does it stop somewhere?

There's a story attributed to Freeman Dyson in which a physicist encountered a man who devoutly believed that the Earth is flat. The physicist was intrigued and asked what holds the Earth up. The man answered with great conviction that the Earth is a large flat disk supported on the back of a giant turtle. The physicist laughed and suggested that perhaps the turtle was in turn held up by an elephant or a dragon. "Oh no," the man whispered conspiratorially, "it's turtles, all the way down!" So the question is, has CDF turned up evidence for the fundamental ground structure of matter? Or have they simply reached the next layer of turtles?

    If the CDF discovery of quark sub-structure is confirmed by further experiments, it will not have caught theoretical physicists by surprise. The territory of quark sub-structure is already provisionally mapped, starting some 22 years ago when Salam and Pati proposed the first explicit model of quark substructure. They suggested that the quark is composed of pre-quarks which they called "preons".

    There are now a number of preon models, all attempting to explain the properties of quarks and leptons (electrons and neutrinos). These are: (1) quarks and leptons have three "generations" (e.g., up, charmed, and top) with escalating mass scales, (2) each generation has two "flavors" (e.g., up or down) with differing electric charges, and (3) within each flavor/generation the quark member has one of three strong-force "colors" while the lepton member is "colorless". In addition, each quark or lepton has an antimatter counterpart with opposite charge and color, each has an intrinsic spin of 1/2 an h-bar unit of angular momentum (h-bar = Planck's constant divided by 2pi = 197 MeV/c x 10-15 m), and each has a "parity" (positive or negative) describing its behavior under space-reversal (change the coordinate x to -x, etc.) Matter quarks and leptons have positive parity, meaning that their wave functions do not change sign after space reversal. Curiously, the anti-matter quarks have negative parity, meaning that their wave functions do change sign. The masses of the quarks and leptons span a very large range with the lightest lepton (the e-neutrino) having a mass close to zero, and the heaviest quark (the top) having a mass of about 180 GeV. If we consider quarks with different colors to be different particles then there are altogether 24 quarks and leptons plus 24 antimatter counterparts to explain.

    Most preon models describe each quark and lepton as a combination of three preons. In the preon model of Salam and Pati a quark or lepton contains one of three "somons" that determines its generation, one of two "flavons" that determines its flavor and electrical charge, and one of four "chromons" that determines its color (or lack thereof) and modifies its electrical charge. Somons are electrically neutral and colorless. Flavons have electric charges of either +1/2 or -1/2 of a proton charge and are colorless. Chromons that are red, green, or blue have a charge of +1/6, while the colorless chromon has a charge of -1/2. The possible combination of 3 x 2 x 4 preons gives all 24 quarks and leptons with appropriate generations, colors, and charges. The preon model make no attempt to explain the quark masses except to suggest that the higher generation somons are heavier, while the colorless flavon is particularly light.

    The preon model offers the bargain of "explaining" 24 particles as combinations of 9 preons, which can be viewed as not much of an economy. A more economic variation of the preon model is the rishon model of Harari and Seidberg, which describes all 16 of the particles and antiparticles in a particular generation as 3-particle combinations of "rishons". There are two rishon types, each type having three possible colors and hypercolors, with generations as excited states of the 3-rishon system, so that the rishon model uses only 2 preons and their antimatter counterparts to generate the 48 quarks and leptons.

    The show-stopper problem of all preon models of quark substructure is the so-called mass paradox. A composite particle may be either lighter or heavier than the sum of its components at rest. A nucleus (size about 10-13 m) is slightly lighter than the neutrons and protons from which it is made due to the strong- force binding energy that holds the nucleus together. It "costs" about 8 MeV of energy to pull each neutron or proton loose from its nuclear binding, so an assembled nucleus has about 1% less mass-energy than its disassembled components.

    On the other hand, the proton (size about 10-15 m) is much heavier than the combined masses of its three components (two up quarks and one down quark). The proton's mass in energy units is 938 MeV, while the up quark has a mass of only about 4 MeV and the down quark about 7 MeV. The majority of the proton's mass comes from the kinetic energy of its quark components. Within a proton the quarks are confined to a "box" only 10-15 m across. Heisenberg's uncertainty principle dictates that the product of uncertainties in position and momentum must be greater than h-bar, so a quark localized to 10-15 m must have a momentum uncertainty of at least 197 MeV in energy units. The energy contributions from three quarks having about this momentum in each of three space directions approximately equals the proton mass. The proton thus derives its net mass energy mainly from the internal motions of its constituent quarks, not from their rest masses.

    We know from scattering experiments that quarks and leptons are "pointlike" down to distance scales of less than 10-18 m (or 1/1000 of a proton diameter). The momentum uncertainty of a preon (of whatever mass) confined to a box of this size is about 200 GeV, 50,000 times larger than the rest mass of an up-quark and 400,000 times larger than the rest mass of an electron. Thus, the preon model represents a mass paradox: How could quarks or electrons be made of smaller partcles that would have many orders of magnitude greater mass-energies arising from their enormous momenta?

    One way in which the huge mass from internal momentum can be "nulled out" is to postulate a new and extremely strong force (or hyperforce) which would tightly bind preons inside a quark or lepton. Such a hyperforce would have to be at least 100,000 times stronger than the strong interaction. It is also somewhat unwelcome because it would add considerable complication to the Standard Model, which already has too many arbitrary parameters [see my column in the May-1996 issue of Analog]. With such a hyperforce acting, the preons would be so tightly bound inside a quark that the energy contribution from their large momentum would be canceled by the large binding energy. This approach has some appeal, but it has not been used successfully to explain the masses and other properties of quarks and leptons, particularly the large mass differences between generations and between quarks and neutrinos.

    Since this is a science fiction magazine, it's amusing to speculate on an alternative approach which I propose here for the first time. Suppose we solve the momentum problem by giving preons a tachyonic rest mass. Tachyons [see my column in the October-1993 issue of Analog] are particles that have a rest mass that is imaginary (like [-1]1/2) and if moving freely travel with faster-than-light speeds. Bound tachyonic preons in a quark would not be of interest as faster-than-light particles, but would have a negative mass-squared that would subtract from and even cancel the large mass-energy contribution from the large momentum. By a suitable choice of tachyonic masses for preons and moderate binding forces, the observed masses of quarks and leptons should be accommodated. Moreover, tachyonic mass that did not quite cancel for the lightest particles would even explain recently published experimental evidence (not taken seriously in the physics community) that the electron neutrino is tachyonic, with a mass-squared of -130 ± 20 eV2 (see ref).

    In any case, this is a new and exciting time for high energy physics. The well tested QCD Standard Model of particle physics shows signs of being broken and in need of closer examination by new experiments and of repair by theorists. Yesterday's fundamental particle, the quark, may be a composite object assembled from even more fundamental preons. And who knows what particles preons are made of? I'm reminded of a modern poem, derived from Swift, that my late father was fond of quoting: "Great fleas have lesser fleas, upon their backs to bite 'em, and the smaller one have smaller ones, and so on, ad infinitum.."

John G. Cramer's 2016 nonfiction book (Amazon gives it 5 stars) describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at: or

SF Novels by John Cramer: Printed editions of John's hard SF novels Twistor and Einstein's Bridge are available from Amazon at and His new novel, Fermi's Question may be coming soon.

Alternate View Columns Online: Electronic reprints of 212 or more "The Alternate View" columns by John G. Cramer published in Analog between 1984 and the present are currently available online at: .


Evidence for Quark Sub-structure:
F. Abe, et al., FERMILAB-Pub-96/020-E CDF, and Physical Review Letters (to be published, 1996).

Preon Models:
H. Harari, Scientific American, pp. 56-68, (April, 1983).

Neutrino Mass:
Wolfgang Stoeffl and Daniel J. Decman, Physical Review Letters 75 #18, pp. 3237-3240 (1995).

Note (11/18/2014):  The CDF results were not confirmed by other experiments, and there is presently no evidence for quark substructure.  The current standard model describes quarks an leptons as "pointlike", with no substructure.

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This page was created by John G. Cramer on 7/12/96 and revised in 11/18/2014.