Volume 133B, number 1,2 PHYSICS LETTERS 8 December 1983

EVIDENCE FOR CHARMED-STRANGE EXOTIC MESONS? ~r

M. SUZUKI

Department of Physics and Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720, USA

and

S.F. TUAN

Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, HI 96822, USA

Received 13 September 1983

We suggest that the 1970 MeV state recently discovered in e÷e - annihilation at CESR is the F ÷ meson and the old 2020 MeV state is the (cgqCt)l= O state (q = u, d) ofJ P = 0 ÷. SU(3) analysis indicates a rich spectrum of charmed four-quark states. Semi-quantitative arguments are presented for the reason why the 2020 MeV state decays dominantly through weak inter- actions.

The discovery of a new state with narrow width at 1970 MeV decaying into ¢1r + [1] has generated a big puzzle in the charmed-strange meson spectroscopy. Is this for instance the F + (JP = 0 - of c~) meson? If so, what is the particle at 2020 MeV that was previously reported by a few experiments [2] and identified with the F+? The reported width of the 1970 MeV state is consistent with experimental resolution and the life- time of the 2020 MeV state is characteristic of weak decays. It is therefore very unlikely that either of these states is one of the glueball states, (qqg) states, or noncharmed four-quark states. In this letter we as- sume that the above states are really two distinct par- ticle states and address ourselves to this puzzle by iden- tifying the 1970 MeV state with F + and the 2020 MeV state with the isosingle c~qffl state. We work out the flavor SU(3) analysis of states, argue that weak decay can dominate for the 2020 MeV state, and point out that there should be two D-like four-quark doublets in the 2 GeV region, one of which may decay into Drr in S wave.

Systematics of four-quark states have been discussed by many authors [3,4], notably by Jaffe. Importance of charmed strange mesons was pointed out by Lipkin

This work was supported in part by the National Science Foundation under Grant No. PHY-8118547 and by the US Department of Energy under Contract DE-AM03-76SF00235.

0.031-9163/83/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)

[5]. We first describe the systematics of charmed four- quark states in the flavor SU(3) symmetry. According to empirical rules of light quark dynamics, two quarks (antiquarks) tend to be attracted more strongly in the color 3* (3) channel than in 6 (6*). The sp in-sp in force aligns quark spins in antiparallel configuration. Therefore, it is most likely that the lowest four-quark states of cq61~l, where q = u, d or s, are formed in the flavor SU(3) representations that result from 3 × 3, namely, 3* and 6 * ~. The quark contents of these states are given in fig. 1 and table 1. These states have JP = 0 +. As to which of 3* and 6 is the lighter multi- plet, this depends on the quark potential; A general guiding principle is that a multiplet of lower SU(3) representation is less heavy than that of the higher one. Accepting this rule the lowest four-quark state with the same charm and strangeness as the F + is the 1 = 0 state F'x ,2 of 3", a state which was called crypto-exotic by Jaffe [3]. The 6 representation is exotic and contains the 1 = 1 state F'I with C = S = +1 and the 1= 0 state F S with C= +1 and S = - 1 . The Gel l -Mann-Okubo mass formula for 6 is linear like m I = m(6) + Am I. However, the quark model further imposes that ml= 1

,1 The SU(3) flavor decomposition of cqqff does have pieces from 3 × 6", which are expected to appear as higher mass multiplets.

• 2 We follow the particle notations of ref. [5 ].

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Volume 133B, number 1,2 PHYSICS LETTERS 8 December 1983

-1

6

V ....... . . ~ : :- / mix

I I I

- i 0 1

S

° I /

. . . . . . . . ~" 0

-!

t I

-1/2 1/2

I3 I 3

Fig. 1.6 and 3* states of cq'~cl. See table 1 for quark content.

= ml= 0 since b o t h / = 1 and 0 states contain one s or quark. Therefore, we expect Am ~- 0 and degeneracy

of 6 states to the first order in SU(3) breaking. It _ 1 3 * should be noted that the I - 2 states of and 6 mix

with each other through SU(3) breaking to generate two mass eigenstates. The mass eigenstates are ex- pressed as

D ' = D(6) cos 0 + D(3*) sin 0,

= - ~ ( 6 ) sin 0 + ~ ( 3 " ) cos 0, (1)

1 where D(6) and D(3*) stand for the 1 - ~ states of 6 and 3", respectively, and 0 is the mixing angle related to the 6 - 3* transition mass m ( 6 - 3 " ) by

tan 20 = 2 m ( 6 - 3 " ) / [ m ( 6 ) - m(3*)] . (2)

The mass eigenvalues are given as *3

m ~ , + rn~ = m ~ l + ~ mF x ,

rn~, - m ~ = (rn~l - m~. x ) [1 + tan220] 1/2. (3)

The ideal mixing is realized with 0 = 45 ° such that D'

= cs~61 and D = {cqCtq~l- 1/2 like ~ and ~ , where q = u or d, and these states are likely candidates for the mass eigenstates in the naive quark model. It is interesting to note here that the ideal mixing 0 = 45 ° forces degeneracy of 6 and 3", as is evident from eq. (2). In this limit we predict masses of D and D' as

= ~ - = ~ +Amsq, (4) rn~ mFx Amsq , m~, mFx

where Amsq = m s - md, u = mF÷ - mD ÷,0. For values of 0 other than 45 °, m(6) is not necessarily equal to m (3") and. D' contains a (cq~]61)l= 1/2 component.

It is natural to assume that fix (-csqcl) is no lighter than F+(cg) since addition of (q(l)l=0 should cost some positive energy;,Therefore, F ÷ is assigned to the 1970 MeV state and F x is assigned to the 2020 MeV state. The absence of a peak around 2 0 2 0 - 2 0 5 0 MeV [6] in the Cp0 invariant mass plot does not allow us to iden- tify the 2020 MeV state with F'I" With our assignment, the F + - D + mass difference comes out on the smaller side (1970 M e V - 1869 MeV = 101 MeV) as compared with A - N mass difference and Y ~ - A mass difference, but it is comparable with the K * - p mass difference (123 MeV) and the K* (2÷ ) -A 2 mass difference (116 MeV). With this value of Amsd = 101 MeV, eq. (4) leads to

mg+ = 1915 MeV, ml~o = 1919 MeV,

Table 1

if7 + = (1/21/2) cu (ds - "sd)

~/+ = (1/2) c u f u -fis-) + (1/2) cd (d's -~,d)

F'~ = (1/21/2) cd6u - fi's)

5÷(6, 3*) = (1/2) cs(d'~ - ~d) + (1/2) cu(fid - dt~)

5 ° (6, 3*) = (1/2) cs(st~ - fis-) + (1/2) cd(t~d - dt~)

rag,+ = 2125 MeV, rns~o = 2121 MeV. (5)

A problem subject to more debate is whether the added q61 pair can cost only 50 MeV (= 2020 MeV-1970 MeV). We do not find a convincing argument to the contrary, so we proceed by assuming that this is pos- sible.

Next we discuss the decays of these particle states. The most important problem is obviously whether the F~ x lifetime can be as long as 2 X 10 -13 s or not. F'x can decay into F + by emitting two ")" since one ~' emis-

v~ = (1/21/2) cs(6~ - ~6)

Fx = (1/2) cuG~ - fi~) - (1/2) cd(d~ -~d)

.3 In the naive quark model, we expect m~(3. ) = m~x by s quark counting, so m (3*) has been replaced by m]~ x in eq. (3).

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Volume 133B, number 1,2 PHYSICS LETTERS 8 December 1983

sion is forbidden by the 0 - 0 transition rule. To be consistent with the observed lifetime, the radiative de- cay F x ~ F + + 77 has to be suppressed enough to be dominated by the weak decay of the c quark in F'x" One might make a naive estimate in analogy with 2S

IS + 3'3' in hydrogen, which leads to the expression I'F.rv ~- (1/121r) a2(A/M)aA [7] where A = m~" x - m F = 50 MeV and 1/M is the size o f the spread of light quarks. With M -~ constituent mass of u, d, this formu- la would give

FF~/Fc- - , suc~ ~ ( 327r2a2 A/3 GF 2 mc 5 ) (A/mq)4

= 1 × 102. (6 )

However, this is probably a gross overestimate because the formula applies to the 23' emission of the type shown in fig. 2a, not to the process of our present in- terest, as depicted in fig. 2b, where a light quark pair must annihilate to produce two 7's. Estimate of such a matrix element needs a detailed knowledge of wave-

C '~

g ,,

q

Ca

C

g ,c

(b)

q ~, y

(c)

functions of light quarks inside F'x. One way to ap- proach this problem is to estimate through

Fx -+ F + "r/" ( 7 ) t-,77'

Current algebra sets a constraint that the matrix ele- ment should vanish at p~ ~ O. Evaluating the matrix element including this condition, one finds an order of magnitude estimate

YFv,r "~ (1/192rr3)(e2/327r2frr)2 A9/f~rmn 4 (8)

leading to

I 'F~v/I 'c~ suci ~ (~2/96rt2) A9/GFmcf~r2 5 4mn4

= 1 × 10 -5. (9)

The large reduction of I-'F77 in eq. (9) relative to I'F.r. r in (6) is due to the current algebra zero characteristic of light 0 - states and to (1/32rr2) 2 in 77 -+ 73'. Another possible decay mechanism is to emit 23' from ~ quark with a qc] pair annihilating into two gluons that even- tually are absorbed by c and/or g. (See fig. 2c.) The suppression of this process relative to that of fig. 2a is the s quark charge to the fourth power ( - 1 / 3 ) 4, replace ment of mq in eq. (6) by constituent s quark mass, and whatever factor that costs to annihilate q61 through two gluons. Taking the last factor rather arbitrarily to be 1/10, we find a suppression factor o f ( l / 3 ) 4 (300/ 500) 4 X (1/10) -~ 1.6 × 10 -4 , which is sufficient to reduce the FF.r.r/I'c~ sud ratio to less then unity. The estimate of the decay rate I'F.r. r is crucial to our pres- ent assignment of particle states and improvement in accuracy of estimate is in pr.~ogress. It is quite possible that the radiative decay.,of F x is strongly suppressed and the main decay of F x is through the weak interac- tions. In the weak decays, final states ofF" x consist of three quarks and three antiquarks, which, some people argue, form more likely multi-hadron states rather than two-body states because pair annihilation into gluons is hindered. The 2020 MeV state was seen in q~Tr + and r/rr + as well as in r/37r and r/'37r, there is also some evidence [6] of the ~bp mode. It is yet to be seen whether the branching ratios into two-body final states receive suppression or not.

The other particles in 3* and 6 decay as follows:

Fig. 2. (a) Two-photon transition between four-quark states. (b) Two-photon emission by pair annihilation. (c) Two-photon emission from ~ quark.

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Volume 133B, number 1,2 PHYSICS LETTERS 8 December 1983

F'~+ -~ uudds~ [weak], F'~+ ~ (F + + lr +) [strong],

F"~ ~ uufids~ - uddds~ [weak],

F + + 77 [electromagnetic],

(F + + zr 0) [strong],

F'O -+ ut~dcls~ [weak], F'O -+ (F+ +r r - ) [strongl,

F'S ~ ufiddss [weak],

~ D + 3'3' [electromagnetic],

D' ~ D + 77 [electromagnetic],

(D + rr) [strong], (10)

where the final states designated by quarks and anti- quarks mean hadronic states made up of them including possible pair annihilation and the decay modes in paren- theses are allowed only when enough phase space is available. As we have argued above akeady for Fx, the weak decay may compete with or dominate over the radiative decay for F'~- too, if the mass of F'~ is not much higher than 2020 MeV. The strong decay D' ~ D + zr is OZI forbidden in case o f ideal mixing.

Finally, let us propose several searches to be done in experiments.

(1) Look ~++ for F T- and F 0 (~'O) near 2020 MeV or above in modes like ~X and rTX, where X are particles of zero strangeness (e.g. lr+rr +, rr+rr+rr 0 etc.).

(2) Look for F S (Fs) near 2020 MeV or above in modes (K ~ K; X + -+).

(3) Look for D' just above m D + mrr in Dlr. Though 3P 0 o f c~ has the identical quantum numbers, the de- cay width of D' is narrower because of perfect or par- tial OZI suppression. There has so far been no evidence for D' in the Drr invariant mass plot, while D* shows up as a prominent peak. The D' being a four-quark state, its production rate is expected to be much lower than that of D*, so failure to find D' in data so far taken is not considered as a negative evidence.

(4) Look for F'~-+ and ~'0 in the invariant mass plot of F+rr + and F+lr - , which should show up if their masses are higher than m F + mrr.

(5) It is desirable to explore 27 emission decays with good photon detectors. However, such a measurement looks very difficult to carry out at this moment.

(6) If our present interpretation is correct, we ex- pext an SU(3) nonet of (c~q~) states in the J /~ region. The lightest ones might appear at 50 MeV above r/c (2981 MeV). However, the radiative transitions like if'

(ccq61) + 7 may be suppressed to the extent that a qCt pair has to be created.

In conclusion, careful search for F'~-+, ~'0 (T0), and ~,+,0 may expose a surprisingly rich spectrum of four- quark states, leading to the firm establishment of the existence of such states which have hitherto been re- garded by many people as ambiguous in the meson spectroscopy of light quarks. Furthermore if our pre- diction of a new harvest o f hadronic states in the 2 GeV domain (some with distinctive signatures) is cor- rect, a case can yet be made for a high luminosity e+-e - storage ring facility even at modest CM energy (e.g. the proposed 5 GeV Beijing machine).

One of us (S.F.T.) would like to thank Professor Sandip Pakvasa for suggesting the problem, and Profes- sor Harry J. Lipkin for a helpful discussion.

References

[ 1] CLEO Collab., A. Chen et al., Phys. Rev. Lett. 51 (1983) 634.

[2] R. Brandelik et al., Phys. Lett. 80B (1979) 412; D. Aston et al., Phys. Lett. 100B (1981) 91; Nucl. Phys. B189 (1981) 205; M. Atkinson et al., Z. Phys. C17 (1983) 1.

[3] R.L. Jaffe, Phys. Rev. D15 (1977) 267,281. [4] A. Hendry and I. Hinehliffe, Phys. Rev. D18 (1978) 3453. [5] H.J. Lipkin, Phys. Lett. 70B (1977) 113;

see also K. Izawa, M. Matsuda, M. Nakagawa and S. Ogawa, Prog. Theor. Phys. 67 (1982) 1495.

[6] K. Berkelman, in: Proc. Ninth Hawaii Topical Conf. in Particle physics (1983) (University Press of Hawaii,

Hawaii), to be published. [7] G. Breit and E. Teller, Astrophys. J. 91 (1940) 219;

J. Sucher, Rep. Prog. Phys. 41 (1978) 41; Y. Tomozawa, Phys. Rev. D25 (1982) 1448.

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