QUARKONIUM PHENOMENOLOGY

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QUARKONIUM PHENOMENOLOGY

A. Martin

To cite this version:

A. Martin. QUARKONIUM PHENOMENOLOGY. Journal de Physique Colloques, 1982, 43 (C3), pp.C3-96-C3-101. �10.1051/jphyscol:1982322�. �jpa-00221875�

JOURNAL DE PHYSIQUE

CoZZoque C3, suppZ6ment au n o 12, Tome 43, d6cembre 1982 page C3-96

QUARKONIUM PHENOMENOLOGY

A. Martin

TH Division, CERiV, CH-1211, Geneva 23, SwitzerZmd

L e t me q u i c k l y s t r e s s t h e main e x p e r i m e n t a l news i n quarkonium.

1) There h a s been a n a b s o l u t e measurement o f t h e mass o f t h e u p s i l o n a t Novosibirsk which i s : M = 9.4596 r 0.0007 GeV.

T h i s measurement a g r e e s w i t h t h e DESY v a l u e . C o n s e q u e n t l y , t h e numbers I s h a l l q u o t e w i l l b e u s i n g t h i s s c a l e .

2 ) The f i r s t r a d i a l e x c i t a t i o n o f t h e P s t a t e s o f t h e u p s i l o n system was

o b s e r v e d a t CESR by CUSB. The mass o f t h e c e n t r e of g r a v i t y is : MZp = 10.247 GeV.

The p r o b a b l e s e p a r a t i o n between t h e J = 2 and J = 0 s t a t e s i s o f t h e o r d e r o f 3 2 MeV.

3 ) We h a v e , from O r s a y , c o n f i r m a t i o n o f t h e e x i s t e n c e o f t h e @ I .

4 ) The fl; h a s been found by C r y s t a l B a l l , and M _{s t} - ^M rl:,

-

M - M , ² 92 MeV.

rl' ilc

5 ) R a d i a t i v e E l and M 1 b r a n c h i n g r a t i o s , a s w e l l a s h a d r o n i c b r a n c h i n g r a t i o s have been o b t a i n e d o r c o n f i r m e d ,

T h e r e a r e t w o k n o w n a p p r o a c h e s f o r d e s s r i b i n g theoreticallythequarkonium s y s t e m , i . e . , b6, c ? , a n d , w i t h some d a r i n g , ss, t h e p o t e n t i a l approach and t h e QCD sum r u l e s o f t h e ITEP-Novosibirsk group. A t t h i s Conference " d e r i v a t i o n s " o f a s t a t i c p o t e n t i a l f o r i n f i n i t e l y heavy q u a r k s have a l s o been proposed. D i r e c t , l a t t i c e QCD c a l c u l a t i o n s o f h a d r o n i c masses a r e s t i l l i n i n f a n c y .

The t h e o r e t i c a l problems a r e :

-

-

-

-

- ^{E l} t r a n s i t i o n r a t e s

- ^MI t r a n s i t i o n r a t e s

- h a d r o n i c d e c a y r a t e s ( a b o u t which I s h a l l n o t s p e a k ) .

1. The P o t e n t i a l Models.- What a r e t h e a d v a n t a g e s o f t h e p o t e n t i a l models? F i r s t of a l l t h e i r s i m p l i c i t y , t h e i r h i s t o r i c a l s u c c e s s i n p r e d i c t i n g t h e P s t a t e s o f c?, t h e D s t a t e s , t h e r e l a t i v e l e p t o n i c w i d t h s and t h e i r a b i l i t y t o p r e d i c t h i g h r a d i a l e x c i t a t i o n s . I n p a r t i c u l a r , t h e number o f n a r r o w R = 0 s t a t e s i s c o r r e c t l y g i v e n by

~ = L + I = , ^{4 4} mc

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982322

A. Martin C3-97

which even almost works for the ss system, since it gives n

-

systems I), The theoretical prejudice is that V(r) behaves like l/r log(l/rl for r -t 0 and like r for r + a. This is the case for a certaln number of theoret- ically motivated potentials 2, as well as certain potentials derived from QCD like the one of Adler and Pirani 3) or of Stack (using SU2 colour) 4 ) . On the other hand, I have proposed a simple phenomenological potential 5)

with m = 5.174, m = 1.8, m = 0.518 (all units are powers of Gev's), which gives a good kit to the e$ergy levefs and the relative leptonic widths. The recently announced 2P state of the T system agrees with all potential models :

Theory Experiment 7

10.24 (Martin 5, )

10.25 (Buchmiiller et al. 2 ) ) 10.247 10.27 (Cornell 1978 6, )

Quigg has noticed that if one tries to find directly what a is in V = A + ~r~

from this new measurement, one gets

as shown on Fig. 1.

A distinction between various potentials comes from the comparison of the T

and J$ leptonic widths. If one believes that the ratio rv/r;f is given by the Weisskopf-Van Royen formula, Miller and Olsson 8, point out that his favours a po- tential singular at the origin as opposed to a non-singular one. This is good since it agrees with QCD expectations. There are, of course, relativistic correc- tions which have been discussed in various contributions to this Conference 9)710).

What are the problems of potential models that can be fixed up? The naive cal- culations of the El electromagnetic transition from $' to x's and from the

X'S to @ give partial widths which are, respectively, about 2 times and 1.5 times too large when compared with experiment. This problem cannot be solved by changing the potential because any good potential must reproduce the energy levels and the El matrix elements are constrained by exact sum rules 11). It is, basically, rela- tivistic effects which reduce the magnitude of the matrix elements (the wave function shrinks towards the origin), and the $' + x matrix element, XU$, UX rdr,

which contains a positive part for r large and a negative part for r small (the positive part wins 13)), is particularly unstable. These effects had already been

c3-98 JOURNAL DE PHYSIQUE

accounted for by a Bethe-Salpeter calculation of Henriques et al. l3). A new estima- tion of relativistic effects by 14cClary and Byers lo) reconciles theory and experi- ment. In the case of the recently observed transitions 7) _{yn +} XL + y: and yll + ~6 + Y, where quarks move much more slowly, the global rates are In accordance with expectations. However lo), relativistic corrections are still important in the transitions involving the J = 0 states. The rates y" ^-t xb + y, very sensitive to the detailed shape of the potential, are difficult to predict.

A seemingly more serious problem is that of the M1 transition JJ1 + yqc. The experimental branching ratio is 14)

while the nafve theory

leads to 2.5% with mc = 1.84 GeV.

However, Sucher, Feinberg and Kang 15) ,16) have pointed out that "1" should be replaced by

where Vs is the llscalarll part of the potential. Updating their figures, one gets :

- ^{for m} _C ^{= 1.8}

1% scalar confinement < branching ratio < 2% vector confinement

- ^{for m z 1.6}

1.3% scalar confinement < ', branching ratio < 2.7% vector confinement.

So there is no contradiction between theory and experiment. However, the theory does not make a strict prediction since nobody knows the exact amount of the presumably dominant scalar part of the confining potential.

One might worry that mc could be much smaller than 1.6 MeV. We argue that the c o n s t i t u e n t mass cannot go below 1.5 GeV. There are good reasons to b e l i e v e that the binding energy of a QB system becomes more negative when the quark mass increases. Therefore

with the constituent quark mass mu = md = 0.3 GeV.

We come now to the major c r i t i c i s m s of the potential approach. The main one is that the potential is a r b i t r a r y . However, we see that the central part has not much flexibility since all the predictions of the 2P state of the T system agree with each other and with experiment! Perha s the most comfortin news of this Conference is that, in a number of papers, Flory P7), Soni and Tran '8, Adler and Pirani 3, and Stack 4 ) , show ways of deriving a static potential from QCD (lattice, analytic, or QCD sum rules) and this potential, for instance 1 1 ~ Ref. 3), agrees with the phenome- nological potential describing the heavy quark-antiquark spectrum and has a linear part in agreement with the Regge slope.

A . Martin

Perhaps the most violent criticism concerns the spin dependent part of the po- tential. It is a fact that when it was believed that the nc had a mass 2.83 GeV, a few physicists tried to account for this by an ad hoc potential. However, the views of the majority were well expressed by Krasemann and Krammer, in Schladming in the winter of 1979 11) :

''Up to now, we do not know any quarkonium pseudoscalar state definitely.

The experimental candidates can hardly be understood. Especially, their M1 transitions and gluon annihilation properties should be much dif- ferent from what is observed."

In fact, before the discovery of the true qc, Beavis et al. 19) predicted a

$-nc mass difference of 84 MeV and, later on, Buchmiiller et al. 2, got 99 MeV.

From a fit to $-n = 112 MeV they predicted +'-I$ = 80i10 MeV, to be compared with the experimental value of 92 MeV.

The comparison of +-nc and $ ' - Q ; mass difference is very informative on the nature of the spin-spin forces. J.M. Rrchard and I 20) have shown that in the simple potential approach it favours a very short-range force, for instance a Fermi type term. However, problems arise if one tries to take into account the coupling to charmed meson pairs because the Q' is much more affected than the q; by this cou- pling. However, the calculations exhibit a great instability with respect to parame- ters and it is not clear that we should be worried by the results of this too sophis- ticated model.

Concerning the fine structure, I can quote the results of Buchmiiller 21) (see also Ono 22)) :

Theory Experiment

3553 3551 MeV

3502 3507

3419 3414

Xb (J = 2)

-

depending on as. For the ( ~ 6 ) 's states, experiment 7, seems to indicate an over- all spacing of 31 MeV.

2. The QCD Sum Rules.- This very ingenious method, invented by the ITEP and

Novosibirsk theorists 23) has the major advantage that it contains, in principle, very few parameters : as, current quark masses, magnitude of the gluon condensate.

The starting point is also more fundamental. However, the power of the method is limited to the prediction of the masses and properties of ground states _$, nc,

xo, x,, x P , T, nb, xb, but not of the radial excitations.

The most spectacular success of the sum rules was the prediction

9

= 100 MeV by Shifman et al. A more recent achievement has been the pre iction of the P state splittings by Reinders et al. 24) using power moments. However, Bertlmann 25), using exponential moments, does not get as spectacular a success:

JOURNAL DE PHYSIQUE

It i s d i f f i c u l t t o judge from t h e o u t s i d e who i s r i g h t . According t o Broadhurst 2 6 ) , t h e method might have some b a s i c i n s t a b i l i t y .

There i s , however, a d e c i s i v e and f e a s i b l e t e s t which i s t h e measurement o f t h e mass o f t h e 1P s t a t e o f t h e T system.

R e i n d e r s , R u b i n s t e i n and Yasuki

3.01 3.10 3.40 3.50 3.56

1

The p r e d i c t i o n s o f t h e QCD sum r u l e s f o r t h e c e n t r e o f g r a v i t y o f t h e P s t a t e s a r e :

Bertlmann

3.04 3.10 3.48 3.52 3.56 qc

J'$

x o

x ¹

x2

9.83 k 0.03 (Voloshin 27) )

9.80 + ^0.01 (Bertlmann 25) ) Experiment

2.98 3.10 3.41 3 . 5 1 3.55

with presumably v e r y s m a l l f i n e s t r u c t u r e s p l i t t i n g s ( t h i s s h o u l d be checked!), w h i l e t h e p o t e n t i a l models p r e d i c t 9.86 ( M a r t i n 5 ) , BuchmCiller 2 ) ) t o 9.92 ( C o r n e l l 6 ) ) GeV.

I s h o u l d add t h a t QCD sum r u l e s g i v e good p r e d i c t i o n s f o r t h e l e p t o n i c widths.

The E l and M 1 t r a n s i t i o n r a t e s a r e c o r r e c t w i t h i n a f a c t o r o f t o 2, b u t t h e c a l c u l a t i o n s a r e s u b j e c t t o improvement 2 8 ) .

F i n a l l y , I would l i k e t o g i v e a l i s t o f p r e d i c t i o n s f o r t h e T-qb mass d i f f e r e n c e :

60 MeV R e i n d e r s , R u b i n s t e i n , Yasuki (QCD sum r u l e s ) 24 ) 30 MeV Voloshin (QCD sum r u l e s , confirmed)

60 MeV Martin ( n a f v e p o t e n t i a l , n a I v e Fermi term) 5 30-40 MeV Buchmiiller 2 9 )

1 0 0 MeV McClary-Byers 10 )

I want t o f i n i s h w i t h a p r e d i c t i o n which r e s u l t s from a p u r e l y e m p i r i c a l o b s e r v a t i o n . I f we c a l c u l a t e ( m ( J = 1 ) ) - ^{(m(Jz0) ) 2 ,} we f i n d m i

-

-

; mk,

-

( ~ ~ * ) 2 - ( ~ ~ ~ ) 2 -0.67 ( G ~ v ) ~ and I e x p e c t t h a t t h i s t r e n d w i l l c o n t i n u e f o r h e a v i e r quarks. From M$ - ^{MGb > 0.67} we g e t MT - ^Mqb ' ^{36 MeV}

Apologies.- I a p o l o g i z e f o r n o t s p e a k i n g on : - h a d r o n i c t r a n s i t i o n s and 2-3 gluon decays,

-

A . Martin

References

1) MARTIN A., Talk at the EPS Conference on High Energy Physics, Lisbon (19811, to be published.

2)

BUCHMLLER

BUCHMULLER W. and TYE S.H.H., Phys.Rev. 93B (1980) 338.

3) ADLER S. and PIRANI S., Institute for Advanced Study Preprint, submitted to this Conference (0332), to appear in Phys.Letters B.

4) STACK J.D., Preprint, University of Illinois, paper submitted to this Conference (0406).

5) MARTIN A., Phys.Letters 9 (1980) 511.

6) EICHTEN E. et al., Phys.Rev. (1980) 203, note added in proof.

7) LEE FRANZINT J., Invited talk at this Conference. We have corrected the scale difference between CESR and the absolute measurement of Novosibirsk.

8) MILLER K.J. and OLSSON M.G., Preprints, University of Wisconsin, Madison, papers submitted to this Conference (060, 061, 062).

9) IF0 H., Preprint, Kinki University, Osaka, paper submitted to this Conference (0274).

10) McCLARY R. and BYERS N., Preprints UCLA/80/TEP/2O1 and UCLA (1982).

11) KRAMMER M. and KRASEMANN H., Acta Phys. Austriaca Suppl. XXI (1979) 259.

12) MARTIN A , , Proceedings of the I1 International Symposium on Hadron Structure and Multiparticle Production, Kazimierz (1979), p. 291, 2. Ajduk Editor, Institute of Nuclear Research, Warsaw.

13) HENRIQUES A.B. et al., Phys.Letters 64B (1976) 85.

14) BLOOM E., Rapporteur's talk at this Conference.

15) FEINBERG G. and SUCHER J., Phys.Rev.Letters 2 (1975) 1740.

16) KANG K.S. and SUCHER J., Phys.Rev. 2 (1978) 2698.

17) FLORY C., Phys.Letters (1982) 263.

18) SON1 A. and TRAN M.D., Phys.Letters (1982) 393.

19) BEAVIS D. et al., Phys.Rev.= (1979) 743 and 2345.

20) MARTIN A. and RICHARD J.M., CERN Preprint TH. 3296 (19821, to appear in Phys.Letters B.

21) BUCHM~~LLER W., Phys.Letters g (1982) 479.

22) ON0 S. and SCH~BERL F., Preprint, University of Vienna UWThPh-1982-24.

23) Rather than giving the origlnal references, we refer to the excellent review of SHIFMAN M.A., Proceedings of the 1981 International Lepton-Photon Symposium, Bonn, p. 242, W. Pfeil Editor (Universitzt Bonn, Physikalisches Institut).

24) REINDERS L.J., RUBINSTEIN H.R. and YASUKI S., Nuclear Phys. B186 (1981) 109.

25) BERTLMANN R., CERN Preprint TH. 3192 (1981), to appear in Nuclear Phys. B, and Preprint, University of Vienna, UWThPh-1982-14.

26) BROADHURST D.J. and GENERALIS S., Preprint, The Open University, Milton Keynes, OUT-4102-8.

27) VOLOSHIN M.B., Preprint ITEP 21 (1980).

28) KHODJAMIRIAN A.Yu., Preprint, Erevan.Physics Institute, EPI 427(34)-80 (19801.

29) BUCHM~LLER W., NG J.Y. and TYE S.H.H., Phys.Rev. D24 (1981) 132.