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Charm and Beauty in Particle Physics

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Charm and Beauty in Particle Physics CORE Metadata, citation and similar papers at core.ac.uk Provided by CERN Document Server EFI-95-02 January 1995 hep-ph/9501291 1 CHARM AND BEAUTY IN PARTICLE PHYSICS Jonathan L. Rosner EnricoFermi Institute and Department of Physics University of Chicago, Chicago, IL 60637 ABSTRACT The sp ectra of states containing charmed and b eauty quarks, and their regularities, are reviewed. I. INTRODUCTION More than 20 years ago, two exp erimental groups announced the discovery of the rst in a series of charm-anticharm b ound states [1, 2]. During the rst year in which the prop erties of these cc,orcharmonium, states were mapp ed out, this system b egan to display exp erimental p ossibilities as rich as those in p ositronium. However, an imp ortant di erence from p ositronium was predicted by theory and so on veri ed exp erimentally. Whereas the 2S and 1P p ositronium levels are nearly 2 degenerate, the 1P charmonium level lies signi cantly b elow the 2S state. What do es this say ab out the interquark force? M. A. Baqi Beg asked this question of Andre Martin during Martin's visit to Ro ckefeller University in 1975. The result was the rst [3] in a series of lovely theorems ab out the order of energy levels in nonrelativistic p otentials [4, 5 , 6], and a simple form of p ower-law p otential [7] which has proved remarkably successful in predicting the masses of new states containing not only charm and b eauty, but also strangeness. My own involvement in similar questions b egan with the discovery of the up- silon (b b) levels [8], for which the 2S 1S spacing app eared close to that in 1 Presented at CERN on Septemb er 28, 1994, at a symp osium in honor of Andre Martin's retirement. This article is dedicated to the memory of M. A. Baqi Beg. 2 HEP-PH-9501291 We lab el levels by n + 1, where the radial quantum number n is the numb er of no des of r r the radial wave function b etween 0 and 1. 1 charmonium. Chris Quigg and I asked what kind of p otential would give a level spacing indep endent of mass [9]. The result, a p otential V (r ) ln r whose prop- erties had b een investigated even b efore the discovery of the upsilons [10], was surprisingly simple, and led us to numerous related investigations of general prop- erties of p otential mo dels [11 , 12 ] and our own attempts at p ower-law ts [13]. It also stimulated work in the inverse scattering problem [14] as an outgrowth of attempts to construct the interquark p otential directly from data. These parallel e orts have b een marked by a go o d deal of corresp ondence b e- tween the resp ective groups. Wehave greatly enjoyed hearing ab out each other's results. It now app ears that the rst actual collab orative pap er involving b oth our groups [15 ] will emerge as a result of this Symp osium. For this, and for the opp ortunity to honor Andre, I am very grateful. We b egin in Section I I by reviewing quarkonium sp ectra and their regularities. We next discuss the predictions of p ower-law p otentials for level spacings in Sec. I I I and for dip ole matrix elements in Sec. IV. Some inverse scattering results and the key role of information on the wave function at the origin are mentioned in Sec. V. We discuss hadrons with one charmed quark in Sec. VI, and relate their prop erties to those of hadrons containing a single b quark using heavy quark symmetryin Sec. VI I. An overview of the prop erties of hadrons with b eauty o ccupies Sec. VI I I. These hadrons (particularly the mesons) are a prime lab oratory for the study of the Cabibb o-Kobayashi-Maskawa (CKM) matrix (Sec. IX) and of CP violation (Sec. X). We note some issues for further study and conclude in Sec. XI. I I. QUARKONIUM SPECTRA AND THEIR REGULARITIES Of all the known quarks, the charmed quark c and the b eauty quark b o er the b est opp ortunity for the study of b ound states and for insights into the strong interactions using simple metho ds. Since the scale at which the interactions of quantum chromo dynamics (QCD) b ecome strong is several hundred MeV, the masses of the u, d, and s quarks are overwhelmed in b ound states by QCD e ects. The top quark is so heavy that it decays to W + b b efore forming b ound states. Leptons, of course, b eing colorless, do not participate in this richphysics at all. In this Section we give a brief overview of levels containing only c and b quarks. A. Charmonium The charmonium sp ectrum is shown in Fig. 1. Masses of observed levels are based on the averages in Ref. [16]. The prediction of the (2S ) is based on Ref. [17]. c Arrows are lab eled by particles emitted in transitions. States ab ove the horizontal dashed line can decay to pairs of charmed mesons (D D ) and are consequently broader than those b elow the line, which decay b oth electromagnetically and with appreciable branching ratios to non-charmed hadrons (not shown). + For manyyears, the ma jor source of charmonium was the reaction e e ! ! (cc), which can pro duce only states with spin J = 1, parity P = , and 2 Figure 1: Charmonium (cc) sp ectrum. Observed and predicted levels are denoted by solid and dashed horizontal lines, resp ectively. 3 3 charge-conjugation eigenvalue C = , namely the S and D levels. Other levels 1 1 PC were reached by electric or magnetic dip ole transitions from the J =1 states, as indicated by the arrows lab eled by in the gure. More recently, starting with an exp eriment in the CERN ISR [18] and continuing with studies in the Fermilab antiproton accumulator ring [19], it has b een p ossible to p erformpp collisions with carefully controlled energy, forming charmonium states in the direct channel. The observation of the h (1P ) level has b een one b ene t of these studies, which are c exp ected to continue. B. Upsilons We show(bb) levels in Fig. 2. The observed levels are as quoted in Ref. [16], PC + while the J =0 levels are shown with masses predicted on the basis of PC + Ref. [17]. The J =1 (\h ") levels are taken to have the spin-weighted average b masses of the corresp onding levels. Since avor threshold lies higher than for b charmonium, there are two sets of narrow P-wave levels, and consequently a rich 3 Figure 2: Sp ectrum of bb states. Observed and predicted levels are denoted by solid and dashed horizontal lines, resp ectively. In addition to the transitions lab eled by arrows, numerous electric dip ole transitions and decays of states b elow B B threshold to hadrons containing light quarks have b een seen. set of electric dip ole transitions b etween the and states, e.g., 3S ! 2P ! b 2S ! 1P ! 1S ,3S !1P (very weak), and 2P ! 1S . The systematics of these transitions has b een a sub ject of recentinterest to Andre, our colleagues, and me [20, 21 ], which will b e describ ed in Sec. IV. C. Quarkonium and QCD As anticipated [22], quarkonium has proved a remarkable lab oratory for the study of quantum chromo dynamics. 1. Forces between a quark and an antiquark are b est visualized with the help of Gauss' Law. At short distances, the interquark p otential is describ ed byan e ective p otential V (r )=(4=3) (r )=r , where the 4/3 is a color factor and the s strong ne structure constant decreases as 1= ln r at short distances as a result s of the asymptotic freedom of the strong interactions [23]. Lines of force b ehave 4 approximately as they do for a Coulomb p otential. They spread out in a typical dip ole pattern; one cannot tell the scale of the interaction by lo oking at them. At long distances, on the other hand, the chromo electric lines of force bunchup into a ux tub e of approximately constant area, much as magnetic ux in a typ e- I I sup erconductor forms tub es. The force b etween a quark and antiquark at long distances is then indep endent of distance [24], so the p otential V = kr rises linearly 2 with distance. Exp erimentally k is ab out 0.18 GeV . 2. Decays of quarkonium states are a source of information ab out the strength + of the strong coupling constant. For example, the ratio of the three-gluon and 3 2 decay rates of the is prop ortional to = , where is the electromagnetic ne- s structure constant, and leads [25] to a value of (M )= 0:108 0:010 consistent s Z with many other determinations. (It has b ecome conventional to quote at M s Z even though the decay of the prob es at m ' 5 GeV.) s b 3. Lattice QCD calculations [26 ] deduce the value of from the observed s 1P 1S level spacing in the system (Fig. 2), leading to (M )=0:110 0:006. s Z Both this value and that determined from decays are consistent with the world average [27] (M )=0:117 0:005.
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