Transcript

Volume 131B, number 1,2,3 PHYSICS LETTERS 10 November 1983

COMMENTS ON "GLUEBALLS, MULTI-QUARK STATES AND THE OZI RULE" e

S.J . L I N D E N B A U M

Brookhaven National Laboratory, Upton, N Y 11973, USA and City College of New York', New York, N Y 10031, USA

Received 5 July 1983

Arguments in regard to the OZI rule by Lipkin are shown to be erroneous, especially in regard to the reaction ~--p ~ ~b~n and ~0'(3685)--* J/~0(3100)+ 2~" which he concludes are OZI allowed or only suppressed by a much smaller factor. His conclusions in regard to our glueball arguments are also erroneous. The reasons for these errors are discussed in this paper.

Ref. [1] erroneously concludes that: (a) The 0(3685)--, J /0(3100)+ 27r is OZI al-

lowed or only suppressed by a much smaller factor.

(b) r r - p ~ ~bqSn is either not an OZI sup- pressed process or has a much smaller sup- pression factor.

(c) That the successful version of OZI, which is in remarkable agreement with experiment and has a handwaving QCD justification, refers only to hairpin-type diagrams in which two quark lines from a single hadron come together to form a hairpin-like loop disconnected from the remainder of the diagram (like those which occur in the production and decays of stran- geonium or charmonium mesons when there are no other strange or charmed quarks present in the reaction).

(d) The experimental observation of 7 r -p~ q~bn is thus adequately explained as a crossed pomeron process without assuming new kinds of particles. (We assumed the intervention of glueballs for explaining the breakdown of the OZI suppression [24] . )

In regard to point (a), if 0 ' ~ 0 + 2zr has no or only relatively small OZI or Zweig sup- pression, why is the 0 ' (3685) with F = 0.215 MeV so narrow; a factor only ~3 times wider than the J /0? The only explanation for

~'This research was supported by the US Department of Energy under Contract Nos. DE-AC02-76CH00016 (BNL) and DE-AC02-79ER10550A (CCNY).

the narrowness of the ~b' (3685) is the Zweig suppression. Fig. la shows reaction (7a) of ref. [1] diagrammatically, including the decay of the J/0(3100) to hadrons.

This is a doubly disconnected Zweig diagram where the upper disconnection has two hadrons forming two hairpins and also providing striking Zweig suppression or else the 0'(3685) would be orders of magnitude wider.

Ref. [1] states in relat ion to this reaction, the reaction q / ~ 0 + 27r, {e.g., (7a) of ref. [1]} is related by crossing to the diffractive excitation of the q / i n zr0 scattering {(76) of ref. [1]}

0 + z r ~ q / + 7r

and this non-hairpin diagram containing two disconnected pieces, each with two hadron lines, is several orders of magnitude stronger than all other hadronic forbidden hairpin diagrams, and thus ref. [1] concludes it has either a much smaller suppression, as in the reaction (7a) or no suppression at all.

It is an experimental fact that the q/(3685) is 103 narrower than would correspond to non-

Zweig suppressed decay, and thus the con- clusions in points (a) and (c) are in striking disagreement with experimental fact, and thus erroneous. This case of Zweig suppression was pointed out in several papers [3,4]. Actually the factor - 1 0 0 by which this final state has a rela- tively greater decay rate than others is probably at least partly due to the fact that there is rela-

0 031-9163/83/0000--0000/$03.00 © 1983 North-Holland 221

Volume 131B, number 1,2,3 PHYSICS LETTERS 10 November 1983

8 ~ ( 3 6 8 5 ) r = 0 . 2 1 5 ~0.040 MeV

J/~ r:o.o6: ~0.00! MeV

[ . . . . 1 I

I i I I

HADRONS

c ~ u

< d

\ d /

<u

+

TI

b

1 ( 10 ,020 I r=o.030

b -+0.010 MeV

T(9460) F=0.042 -+0.015 MeV

r - - - ] I I I I j I

HADRONS

b d

L ) d _

<o

Fig. 1. Only the ~-+~r- decay mode is shown in the first decay. There is obviously an accompanying rr°rr ° decay mode.

tively less Zweig suppression since it involves only two relatively softer gluons, and is also the most probable reaction when kinematic and other factors are considered. The other typical cases involve three harder gluons, and have available many final states which compete for the three gluon decay partial width.

The erroneousness of points (a) and (c) are shown even more dramatically in the Y system (fig. lb) where the Y(10,020) ~ Y(9460) + 2~r and has a F = (0.030_+ 0.01) MeV which is within the errors equal to the width of the ground state Y(9460) thus showing a very strong Zweig suppression. If we use the naive approach of ref. [1], we can cross the Y(10,020)~ Y(9460) + 27r to 7r + Y ~ Y' + ~" and argue erroneously, as ref. [1] does, that it is an un- suppressed process, or is only suppressed by a much smaller factor. But then how do we explain its narrow width without the Zweig suppression?

We now get to point (b), Lipkin's approach to ~ - p ~ ~b~bn (see fig. 2) which we have claimed [2--4] is, in the absence of glueballs, an OZI suppressed process. Thus the observed break- down of the OZI suppression gives very strong evidence for glueballs.

Ref. [1] points out that this process is related by crossing to the reaction ¢ + n ~ ~b + 7r- + p, which is just elastic C-nucleon scattering with additional pion production, and there is no reason to believe that this process is forbidden.

From the previous examples I gave in the $'(3685) and the Y', it is clear that the approach used in ref. [1] is no more justified here, and is erroneous. What is overlooked in ref. [1] is that when you use crossing, you get into different physical and kinematic regions than the original reaction was and you cannot simply relate the two reactions unless you know and calculate everything about the analytic continuation, the singularities involved, etc. which was not con-

< u ,;..

i > u

P >u ) > u n >a >d

Fig. 2. The Zweig diagram for 7r-p--~ ( ~ n .

222

Volume 131B, number 1,2,3 PHYSICS LETTERS 10 November 1983

sidered at all in ref. [1]. For example, the high cross sections one associates with elastic scat- tering or diffractive dissociation occur at low momentum transfers, and the crossed reaction ~b + n ~ th + ~r- + p involves high momentum transfer where elastic scattering and diffractive dissociation are likely very small. Furthermore, the previous experimental evidence that I have cited is enough by itself to show that the ap- proach used in ref. [1] is wrong. It should be noted that the total cross section for z r - p ~ ~b~bn is ~20 nb compared to ~10 mb for elastic scat- tering. The difference of a factor - 1 0 6

emphasizes the points made here. In the 7 r - p~ ~b~bn case, the change from the

physical and kinematic regions when you cross is much greater than for the ~b'(3685) ~0(3100) + 2~- and the Y(10,020) ~ Y(9460) + 27r, and thus Lipkin's approach is even less valid. It fur thermore has to be noted that crossing has not even been demonstrated experimentally to be a correct approach in those Zweig discon- nected processes.

Finally, the conclusions in ref. [1] on p. 511, that the experimental observation of the reac- tion (6a) (i.e. 7 r -p~ ~b~bn) is thus adequately explained without assuming new kinds of parti- cles {refs. [10-11] of ref. [1]} 51 unless it proceeds by an intermediate resonance {e.g. (5b) of ref. [1]} (~ ' - p~ M0 + n ~ ~b + 4) + n) where M0

,1Ref. [10] of ref. [11 in this paper is my ref. [2].

denotes any ideally mixed quarkonium state, is based on the previously discussed erroneous arguments, and is thus also erroneous.

Hence in ref. [1] most of the statements in regard to the BNL/CCNY paper [2] and others I have written [3,4] are erroneous and do not apply to the papers [2--4].

Finally, it should be noted that ref. [1] is addressing an important point albeit incorrectly.

I have concluded [3,4] that given the very simple input axioms,

(1) QCD is correct. (2) The OZI rule is universal for weakly

coupled glue in Zweig disconnected diagrams where the disconnection is due to the intro- duction of new types (i.e. flavors) of quarks, that we have discovered one or more glueballs.

These axioms are essentially just modern QCD practice, thus we have very probably dis- covered one or more glueballs.

References

[1] H.J. Lipkin, Phys. Lett. 124B (1983) 509. [2] A. Etkin et al., Phys. Rev. Lett. 49 (1982) 1620. [3] S.J. Lindenbaum, Evidence for Glueballs, AIP Conf.

Proc. No. 98, Particles and fields (1982), Particles and Fields Subseries No. 29, eds. W.E. Caswell and G.A. Snov (APS/DPF University of Maryland) p. 218.

[4] S.J, Lindenbaum, Glueballs in the reaction ~ - p ~ ~bn , Invited Lecture XVIII Rencontre De Moriond Elemen- tary particle physics Meeting (Savoie, France, January 1983), to be published; also BNL 32855.

223


Recommended