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Charmed Baryons CHARMED BARYONS S. Fleck and J.M. Richard Abstract A review of the spectroscopy and decay properties of charmed baryons is presented, with emphasis on the double—charm and triple—charm sectors, which have been studied recently. 1. Introduction It is hardly necessary to underline the importance of charm The discovery of hidden charm in 1974 and naked charm in for weak interactions. The charmed quark was in fact predicted 1976 opened a new era in hadron spectroscopy [1, 2]. All new by GIM [4] to solve a long—standing problem related to the decay heavy mesons and baryons [3] have been described simply by properties of neutral kaons. Charmed particles themselves have adding a new quark, c, to the series of the constituents d, u and 3, revealed intriguing decay properties: in particular, the ratio of thus reinforcing the quark model. meson lifetimes, T(D+)/T(D0), is different from 1, showing that This qualitative success stimulated detailed dynamical the decaying charmed quark does not ignore its environment. calculations of quark binding, based on models of confinement. The dynamics of the weak decay of charmed mesons nowadays Several bag or potential models were very efficient in repro- seems better understood [5]. We shall show that charmed baryons ducing the static properties of hadrons. Meanwhile, some permit us better to determine the relative importance of progress has been made in non-perturbative QCD, thanks, for W emission, W exchange and final—state interactions in weak instance, to lattice simulations, which provide some basis for decays [6, 7]. empirical models. In this framework, we shall show that Throughout this review, we shall very often use the baryons with single, double, or triple charm provide very convenient language of the non—relativistic quark model. Most of interesting opportunities to test the dynamics of quark the physics discussion on charmed baryons holds, however, confinement. beyond this particular approximation. We shall give references to In charmonium, the heavy quarks move slowly in the alternative studies based on bag models or relativistic wave short—range QCD potential, and form several narrow levels, equations, and emphasize the need for relativistic corrections with interesting cascades from one to another. In charmed when discussing electromagnetic mass differences. mesons, the light antiquark is accelerated by the presence of a heavy static colour source, so that relativistic effects are enhanced. 2. The experimental situation These two aspects of quark dynamics also enter in the We adopt here the notation of the Particle Data Group [1] charmed baryon sector, where they are sometimes intimately which now replace the naming scheme of ref. [8]: AC, for instance combined. Triple—charm baryons are the analogues of charmonia, is a A (sud) state where the strange quark s has been replaced by a with even narrower levels and the subtleties of the three—body l Llllllllk. 1n tln- tun] kuctur [qr : n m if]. wt‘ (it‘llUlt' by E, lln- systems. In double—charm baryons, we see the slow relative hurynn where the Lug) pair is must ul'tcn inn spin it slate. EL thr- motion of the two heavy quarks together with the relativistic Inn‘ytin with lulzll spin US and Iht'. 1w! p:tir IInmtly in [l spin | motion of a light quark around a coloured centre. Single—charm Hltllt'. E: t' lowest Spill 3/9, hnrynn. and El ..: any higher rmhul baryons look more like charmed mesons, but some details such as or nrhital t'M‘iiHlil‘ll. Nut: that 12‘ is :1 spin 1,"). bury-nu with [M's] hyperfine structure allow one to disentangle the heavy—light from content, while Q: is its spin 3/2 partner. The ground states of the light—light type of interquark forces. charmed mesons and baryons are listed in table 1. Table 1 Ground—state hadrons with charm (q denotes u or d quark) | Charmed mesons Charmed baryons ‘ Quark content cq CE cqq cqq csq ccq css ccs ccc Isospin 1/2 0 0 1 1/2 1/2 0 0 0 Spin 0 1 0 1 1/2 1/2 3/2 1/21/2 3/2* 1/2 342 1/2 3/3 1/2 3/3 3/2 ~ ... ‘ n-t '3' u 67 lName D 13* D D AC EC 22‘ “'“C— “C “‘— C h'CC “"—' CC QC QC QCC QCC QCCC © 1989 Gordon and Breach Science Publishers S A Photocopying permitted by license only Particle Wotld, Vol I, No 3, p 67773, l900 S Fleck and J.M Richard The experimental masses and lifetimes of charmed baryons M(m|,m|,m|) + M(mz,mz,mz) + seen in 2 are summarized in table 2. These baryons have been + M(m3,m3,m3) S 3 M(n11,m2,I113). ( ) several experiments, using hadronic or leptonic beams. There is an urgent need for high—precision and high~statistics This provides a limit on the mass of (cc-c) from that of (qqq), (sss) measure-ments of these baryons. This will hopefully be and the recently discovered (csq) [l, 2]. With a plausible estimate achieved in future experiments with hyperon beams or at of hyperfine corrections for (csq), one obtains flavour factories. M(ccc) S 5.08 GeV . (3) Table 2 The inequality (1) holds for any interquark potential, Experimental masses and liftetimes of charmed baryons provided it does not depend on flavour. The following inequality like (2), requires that the potential does not grow too sharply [11], 'Baryon | Mass (GeV) . 1(10—13 5) Ref. a condition easily fulfilled by realistic models. It reads 9 2.285 I (1.8 i 0.2) [1] M(M, M, m)+.'M(m,m, m)S 2M(M, m, m) , (4) (5‘1 2.455 i unstable (—> AC + 71’) [I] and gives a limit on double—charm baryon masses. When ell-f— 2.460 (4.3 i 1.5) [1] hyperfine corrections are omitted, one obtains «13 2.471 [2] M(ccq) S 3.72 GeV . (5) .52 2.740 [1] 3.2 Inequalities relating mesons and baryons There are good reasons to believe that the potential that links 3. Charmed baryon spectroscopy the three quarks of a baryon can be simulated by a sum of 3.1 Baryon mass inequalities two—body terms, each of these being half of the quark—antiquark In QCD, gluons are coupled to the colour rather than to the potential binding mesons [12] flavour of quarks. The interquark potential is thus, in first approximation, flavour—independent. Likewise, in QED, the V01, r2, r3) :2 q(rij) =§Z va'ij) . (6) same electrostatic potential e2/r binds e+e_ as well as (:77. Flavour independence leads to interesting inequalities among If one takes seriously this “1/2 rule”, one gets for equal—mass hadrons. quarks [l3] Let M(ml, m2) be the mass of a (c1152) meson in its ground 2M<QQQ> > 3M(QQ) (7) state. Neglecting spin corrections, one gets [9] as a direct consequence of the variational principle. This means M(M,M)+fM(m,m)S29l/[(M,m) (1) that a quark feels itself heavier in a baryon than in a meson(*). If from the variational principle or the observation that the the potential of eq. (6) is considered as acting between quarks reduced Hamiltonian depends linearly on the inverse reduced with parallel spins, one may apply the inequality (7) between a mass A and that, if H = A + AB, its ground—state energy is a spin 3/2 baryon and a vector meson. In the strangeness sector, one concave function of A. The inequality (1) can be extended to checks that 2 M(.Q_) > 3 M (¢). In the charm case, one predicts the sum of the first It levels or applied as it stands to the lowest mom ) > ifMU/w) : 4.65 GeV . (8) state in a sector of a given parity or orbital angular momentum. Applying the inequality (1) to charmed and strange quarks Various generalizations of the inequality (7) can be elabo- gives rated, involving the sum of the first levels, or different flavours, or spin 1/2 baryons. If one neglects spin effects or considers only MUN/l) +M(¢)S 2M(DS) (1') parallel spins, one may write [14] which is indeed true [1]. 2 M(Q1Q2Q3)> M(Q1é2) + M<Q2Q3) + M(Q3Ql)a (9) In a first generalization to baryons, one may study the ground—state binding energy E0(m|, m2, m3) as a function of m", whereas incorporating hyperfine effects for spin 1/2 baryons and the inverse mass of the first quark, and constrain the mass of Ab for mesons, in the single—charm sector, leads to [10] in terms of the masses of AC and A [10]. However, the resulting inequalities for baryons depend on the quark masses. On the other hand, there are simple convexity relations 68 (*) In the Coulomb case, in a very different context, an equivalent equality is involving the three inverse masses and leading to inequalities discussed by J.M. Lévy—Leblond (ref. [13]). We thank A. Martin for an such as interesting discussion on this point. S. Fleck andJ M Richmd model—dependent. The E; — EC splitting is always found to be M(AC)>;—M(fl)+%M(D*)+i9t/[(D)(2.28 > 2.04 GeV) less than 140 MeV, so that the E‘c should be rather narrow. On the other hand, the transition 5: —> SC + 7: is_either easily [18] or > 2.29 GeV) so that the E: is either broad or M(EC)>l—M(P)+3—EM(D)+LM(D*)(2.454 (10) marginally [19] allowed, 2 * 4 relatively narrow, depending on the model.
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