The term "hadron" refers to a bound state of quarks, and a heavy hadron is a bound state that contains at least one heavy quark. Of the six quarks that are known to exist, three (up, down, strange) are considered to be light because their masses are much smaller than the mass of the proton. The other three (charm, bottom, top) are the heavy quarks. The lifetime of the top quark is too short for it to have time to form a bound state with other quarks, so it is charm and bottom quarks which are found in heavy hadrons. Because both of these quarks live for only about 10-12 seconds before they decay, heavy hadrons are found in nature only when they are produced in high-energy collisions.
There are two primary types of hadrons: mesons, which contain a quark and an antiquark, and baryons, which contain three quarks. For example, there is the Λc baryon, made of a charm, an up and a down quark; the B+ meson, made of a bottom antiquark and an up quark; and the charmonium state J/ψ , made of a charm quark and a charm antiquark. The most exotic of the heavy hadrons, discovered by the CDF Collaboration at Fermilab in 1998, is the Bc, made of a bottom antiquark and a charm quark.
Heavy Quark Decays
Heavy quarks are interesting primarily because the pattern of their decays to lighter quarks can help physicists understand the mechanism responsible for the masses of the fundamental particles. The vacuum through which particles move is not empty; rather it is filled with a background energy density known as the Higgs condensate. Some of the properties of this condensate are known, although the reason for its existence is not yet understood. In a true vacuum quarks would move at the speed of light and therefore would be massless. They appear to have masses only because interacting with the Higgs condensate slows them down. The more strongly a quark interacts with the condensate, the larger its mass.
Quark decays also are governed by their interactions with the Higgs background. For example, 99 percent of the time a bottom quark decays to a charm quark (plus other particles), while only 1 percent of the time does it decay to an up quark. Understanding the origin of this ratio would provide clues to the physics of the bottom quark mass because both properties depend on the Higgs condensate.
An important feature of quarks is that they are never observed in isolation. They are always found in hadrons, which are complex bound states of quarks, antiquarks, and gluons (the force carrier which holds the quarks together). This complicates the problem of studying quarks, since what physicists observe in experiments are not transitions of quarks but transitions of hadrons. For example, the decay of a bottom quark into a charm quark manifests itself as the decay of bottom meson (B ) into a charm meson (D ). Because the mathematics is so difficult, it is still not known how to compute the structure of hadrons from first principles, and one must use tools more sophisticated than brute force to disentangle information about quarks from experimental data on hadrons.
Heavy Quark Symmetry
An important example of such a tool is heavy quark symmetry. This is an analog of the isotopic symmetry famous in chemistry, namely, that the chemical properties of an element depend only on the charge but not on the mass of the nucleus. The reason is that the nuclear charge determines the number of electrons, and the electrons in turn are so light that the nucleus appears infinitely heavy by comparison, whatever its precise mass may be. For example, the chemistry of deuterium is essentially identical to that of hydrogen, even though the nucleus of deuterium (a deuteron) is twice as heavy as that of hydrogen (a proton). What matters is that a deuteron and a proton have the same electric charge. Similarly, a heavy hadron consists of (1) a bottom or charm quark and (2) light quarks, antiquarks, and gluons, collectively known as the "brown muck" (a term coined by Nathan Isgur). Since the brown muck is much lighter than the heavy quark, it is insensitive to whether it is bound to a charm or a bottom. Therefore there is a symmetry, which is that every charm hadron has a bottom hadron analog for which the brown muck is exactly the same. (There is an equally useful symmetry among the three light quarks, known as SU(3) flavor, which originates in their masses being much less than the proton's, rather than much greater.)
The most important application of heavy quark symmetry is to measure the fundamental quantity Vcb. This parameter, which gives the probability for a bottom quark to decay to a charm quark, is one of a collection of nine parameters (the CKM matrix) which determine the transition rates between each of the down-type quarks (down, strange, bottom) and each of the up-type quarks (up, charm, top). Along with the masses of the quarks, the CKM matrix contains all the information about the interaction of the quarks with the Higgs condensate, so its elements must be measured as accurately as possible. The best process for measuring Vcb is the semileptonic bottom quark decay b- → cev , which produces a charm quark, an electron, and a neutrino. Unfortunately the physical hadronic transition B → Dev depends both on Vcb and on the unknown probability for the brown muck initially in the B meson to reassemble itself around the recoiling charm quark to make a D meson. The problem would be intractable, except that there is a special configuration: occasionally the lepton and the neutrino are emitted with equal and opposite momenta, with the charm quark left at rest (Figure 1). For the brown muck, all that happens then is that the motionless bottom quark is replaced by a motionless charm quark. By heavy quark symmetry, the two situations are indistinguishable. Since the brown muck does not have to rearrange itself at all, a D meson will always be produced, and the observed probability for B → Dev is exactly the same as for the quark decay b → cev . The power of heavy
quark symmetry is that even though the properties of the brown muck are almost entirely unknown, physicists can measure Vcb to a precision of better than 5 percent.
Heavy quarks, especially bottom quarks, are also of interest because their transitions can manifest CP asymmetry, which is a difference in behavior between a particle and its antiparticle. For example, both a B0 meson (made of a bottom antiquark and a down quark), and the anti-B0 (made of a bottom quark and a down antiquark) can decay to the final state J/ψΣKS, where a ΚS is a combination of strange and down quarks and antiquarks. If CP symmetry were respected in nature, the probability for a B0 to decay in this way would be exactly the same as the probability for an anti-B0 to do so. In 2001, experiments at the B Factories at the Stanford Linear Accelerator Center (SLAC) in California and the Japanese High-Energy Research Organization (KEK) showed conclusively that this equality does not hold and therefore that CP is violated strongly in bottom quark transitions. On the other hand, CP violation has never been observed in charm quark transitions. These properties are another important clue to the incompletely understood nature of heavy quark interactions with the Higgs condensate.
Bigi, I. I., and Sanda, A. I. CP Violation (Cambridge University Press, Cambridge, UK, 2000).
Brando, Gustavo C.; Lavoura, L.; and Silva, J. P. CP Violation (Oxford University Press, Oxford, UK, 2000).
Manohar, A. V., and Wise, M. B. Heavy Quark Physics (Cambridge University Press, Cambridge, UK, 2000).
Adam F. Falk