V O L U M E 62, N U M B E R 25 PHYSICAL REVIEW LETTERS 19 J U N E 1989

Why is the Y ( 3 5 ) Different?

Harry J. Lipkin Department of Nuclear Physics, Weizmann Institute of Science, Rehovot 76100, Israel

and School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel

S. F. Tuan Department of Physics and Astronomy, University of Hawaii at Manoa, Honolulu, Hawaii 96822

(Received 9 March 1989)

The Y O ^ ) is much closer than lower Y{nS) states to BB and B"^B thresholds. These "5-channel singularities" may dominate Y(35) decay amplitudes, while '^/-channel gluonic states" dominant in con­ventional models are more important for other decays. An "^-channel" decay mechanism of sequential pion emission via a heavy intermediate state such as BB or B*B predicts a qualitatively different pion spectrum from that predicted by conventional "r-channel" models for Y(35)—* Y{nS)KK decays and the yet unobserved Y(35)—* YCP\)Kn decay and may explain the observed disagreement between experi­ment and previous predictions as well as the difference between the YCBS) and other states.

PACS numbers: 13.25.+m, 14.40.Gx

Recent experimental da ta ' for the decays Y(3»S) — Y(l5') + ;r+;r and Y ( 3 5 ) - ^ Y(25')-f-;r+;r show very different pion spectra from those of other heavy-quarkonium dipion decays and confirm earlier data^ showing that the two-pion invariant-mass distribution is largely flat with peaks in the high-mass and low-mass re­gions. This distribution cannot be fit by any of the previ­ously proposed conventional quark-gluon models for the decay, '̂̂ where the heavy quarkonium emits gluons which then either produce the two pions directly or via a bound state such as a glueball or a hadronic isoscalar

meson: . 3 - 5

Y ( « 5 ) - ^ Y/ + M(7/y-^ Y/-h ; r+; r , (1)

where MGH denotes either a gluon continuum or a bound gluonic or hadronic meson state and may even be any neutral isoscalar even-C even-/ state including new par­ticles. Y/ denotes any final state which can be reached by two-pion emission. We consider here the states Y C I ^ ) and Y ( 2 5 ' ) for which data are available and also the YCP\) for which predictions have been calculated.

An alternative model ^ treats these decays as sequen­tial pion emission via a heavy isovector intermediate state:

Y ( 3 5 ) — n^X-^ Y/ + ;r-h;r , (2)

where X can be any state containing a bb pair plus at least one isovector light-quark pair. One special case of interest is

Y{?>S)-^ Bi+B-^ Bj^n + B

-* Bk-^K-^-K-^-B—* Yf^n-\-n, (3)

where Bi.Bj.Bk denotes either a ^ or any polarization state of a ^ * .

This model predicts a qualitatively different pion spec­

trum and may explain the observed disagreement be­tween experiment and previous predictions. Simple dis­tributions predicted for the angle between the momenta of the two pions in the laboratory, rather than for invari­ant mass, include a forward-backward symmetry not easily explained by the other models where it implies a peculiar accidental symmetry between low-mass and high-mass gluonic states. Preliminary data for the Y ( 3 5 ' ) — • Y{\S) + 7r-^K decay show both high-mass and low-mass peaks as suggested by the model and agree with the predicted angular distributions.' The Y ( 3 5 ' ) — • Y(25') + ;r+;r decay has a rather flat mass dis­tribution. This paper considers the question of why Y ( 3 5 ) decays are different and generalizes the previous treatment^ to include the case of the Y ( 3 5 ' ) - > Y ( ' P i ) + ;r + ;T decay.

Since a reliable calculation from first principles is not feasible, we look for some insight into the difference be­tween the Y(3iS) decay and other decays by examining the analytic structure of the relevant scattering ampli­tude and the locations of the nearby singularities in the complex plane. The two types of transitions correspond exactly to the s- and ^channel descriptions of ;r-Y scattering, which is related to the decay process by cross­ing one of the pions. The variable s is the square of the invariant mass of a ;r-Y system; i.e., the mass of the in­termediate state X in Eq. (2). The variable t is the square of the invariant mass of a n-n system; i.e., the mass of the intermediate state MGH in Eq. (1). For the case where the Y mass is taken as very large, the mass of the state X is given by the pion energies, and the rest frame of X is just the laboratory frame. The Y ( 3 5 ' ) is much closer to Xh^BB and_i?i5* thresholds than the oth­er Y states. The BB and BB"*" cuts in the complex plane are thus very close to the physical region for the Y ( 3 5 ' ) decay. These 5-channel singularities might play a dom-

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VOLUME 62, N U M B E R 25 P H Y S I C A L R E V I E W L E T T E R S 19 J U N E 1989

inant role in the dynamics of the Y ( 3 5 ) decay. The hypothesis of 5-channel dominance can be tested

experimentally by noting that qualitatively different pion spectra are predicted by the two mechanisms (1) and (3), independently of the detailed dynamics. With sequential pion emission (3) from states near threshold, the intermediate heavy-meson states are nearly at rest in the laboratory system, and the momentum is transferred from the heavy-quark system to the final pions in two steps via an intermediate state. The natural variables for describing the pion spectrum are the energies of the pions in the laboratory and the angle between the two momenta. With pions produced by a decay (1), the momentum is transferred in one step from the heavy-quark system to an isoscalar system containing no heavy quarks which then decays into two pions. The natural variables here for describing the pion spectrum are the invariant mass of the pions and the angle in the n-K center-of-mass system between the pion momenta and the recoiling heavy-quarkonium final state.

A forward-backward symmetry about 90° in the angle between the two pion momenta in the laboratory arises naturally in a transition such as (3) where a ^ or ^ * meson at rest emits a pion and turns into another B and ^ * meson and the recoil of the high-mass heavy meson is neglected. This forward-backward symmetry is required by parity conservation in any transition where the two pions are emitted sequentially from a heavy object at rest in the laboratory and the intermediate state of the heavy object between the emission of the two pions has a definite parity. It also holds in general in any sequential model where there may even be contributions from inter­mediate states of both parities, but one of the pions is emitted in an S wave and has an isotropic distribution. This forward-backward symmetry is not expected for the decay mechanism (1).

A more detailed description of the angular distribution is obtainable from simple assumptions about the partial waves in which the pions are emitted. Pions emitted in the B-^ B* and B* -^ B"^ are in P waves in the center-of-mass system of the three-point function. For transi­tions to 15 and IS final states of type (3), where all the quark-antiquark bound states involved are S waves, there is no transfer of orbital angular momentum to the inter­nal degrees of freedom of the bound state, and no parity change in the heavy-quarkonium transition, it is reason­able to assume that the pions are in P waves also in the overall center-of-mass system. Calculations for the case where the two pions are emitted in P waves relative to the heavy-quarkonium state and the two P waves are coupled to a total angular momentum A / = 0 or 1 predict an angular distribution^ with a dominant ( A y = 0 ) con­tribution proportional to cos^^ and a smaller (A7 = l ) contribution proportional to sin^0 which vanishes when the two pion energies are equal and tends to flatten the angular distribution for large energy differences. The predicted energy and angular distributions provide a

reasonable test of this type of model. Neither the forward-backward symmetry nor the vanishing of the Ay = 1 component for equal pion energies is expected in the conventional model (1).

The /^-wave argument breaks down for the Y ( 3 5 ) — \OP\)nK transition because the Y C / ' I ) has a quark-antiquark state in a P wave and can be produced only via a transfer of one unit of orbital angular momen­tum to the heavy-quark system. Furthermore, the oppo­site parity of the YOP\) requires that in the approxima­tion where we consider the bottomonium as infinitely heavy, the two pions must be emitted in partial waves of opposite parity, e.g., one S ox D wave, one P wave, rather than with the same parity as in the Y ( 3 5 ' ) — • YCW^) transitions. There are now two different types of dia­grams, one in which the S- or /)-wave pion is emitted first, producing a 1+ or 2 + intermediate state, and one in which the P-wave pion is emitted first, producing a 1 ~ or 2 ~ intermediate state.

The two intermediate states now have opposite parity, in contrast to the \S case where all relevant states had the same parity. Thus there can be interference between contributions of different intermediate states with oppo­site parity and this might destroy the forward-backward symmetry. If, however, the S-P and PS transitions are dominant and the D waves are negligible, the -S-wave pion momentum has no correlation with anything else, and an isotropic distribution which includes forward-backward symmetry is predicted for the angle between the two pion momenta in the Y rest frame for all pion energies.

For the case where the Y ( 3 5 ) is produced by polarized e^e~ beams, simple predictions are given by this model for the angular distributions of the two pions with respect to the direction of the polarization axis. Let m,, m/, and m„ denote, respectively, the projections on the polarization axis of the angular momenta of the initial Y state, the final Y state, and an emitted pion. An iS-wave pion always has an isotropic distribution. A P-wave pion can be emitted with m;r = l, 0, and — 1, with an angular distribution given by the square of the spherical harmon­ic I Fiw I ^ which is (3/4;r)cos^^ for m;r=0 and (3/8;r)sin^^ for mj,=^±\. The relative strengths of these components depend upon the initial polarization m/ and angular momentum couplings.

For the case of the decay to YOP\) final state with one 5-wave and one P-wave pion, the /^-wave distribu­tion is determined uniquely by mt and the Clebsch-Gordan coeflScients for coupling three angular momenta of one with projections m,, m/, and ntn- For the case of antiparallel polarization of the electron and positron, AW/=0; the Clebsch-Gordon coefficient vanishes for m/=m/=m;r = 0 and the angular distribution is that for m ; r = ± 1,

W{e),n., =0 = (3/87r)sin 6̂̂ . (4a)

For the case of parallel polarization, m, = ± 1 depend-

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VOLUME 62, NUMBER 25 P H Y S I C A L R E V I E W L E T T E R S 19 JUNE 1989

ing upon whether the electron and positron are both po­larized "up** or "down." The two possible final states for each case, |m;r~0;m/= ± 1) and | m;r= ± l;m/==0), have equal Clebsch-Gordan coefficients, which can be seen from the symmetry. The two contributions are equal and incoherent if the ^P\ polarization is not mea­sured. The angular distribution is thus

w(e) nii •• = (3/16;r)(l+cos2^) (4b)

Since it is not clear a priori which pion is S wave and which is P wave, the angular distributions of the higher-energy and the lower-energy pions should be plotted sep­arately and deviations from isotropy should be sought in each case.

Discussions with Ian C. Brock, Sheldon Stone, and T. M. Yan are gratefully acknowledged. This work was supported in part by the U.S. Department of Energy at Honolulu, DOE Contract No. DE-AMO3-76SF00235.

4 . C. Brock et ai, Cornell University Report No. CBX-88-22, 1988 (to be published).

2T. Bowcock et ai, Phys. Rev. Lett. 58, 307 (1987); Ian C

Brock, in Hadrons, Quarks and Gluons, Proceedings of the Hadronic Session of the Twenty-Second Rencontre de Moriond, edited by J. Tran Thanh Van (Editions Frontieres, Gif-sur-Yvette, France, 1987), p. 115.

^Y. P. Kuang, S. F. Tuan, and T. M. Yan, in Hadron '87, Proceedings of the Second International Conference on Had­ron Spectroscopy, KEK Tsukuba, Japan, 1987, edited by Y. Oyanagi, K. Takamatsu, and T. Tsuru (KEK Report No. 87-7, 1987), p. 213; Y. P. Kuang, S. F. Tuan, and T. M. Yan, Phys. Rev. D 37, 1210 (1988); T. M. Yan, Phys. Rev. D 22, 1652 (1980); Y. P. Kuang and T. M. Yan, Phys, Rev. D 24, 2874 (1981).

"^M. Voloshin and V. Zakharov, Phys. Rev. Lett. 45, 688 (1980); M. Voloshin Yad. Fiz. 43, 1571 (1986) [Sov. J. Nucl. Phys. 43, 1011 (1986)1; M. Novikov and M. A. Shifman, Z. Phys. C 8, 43 (1981).

^For a discussion of a failed attempt to find an explanation of these KK spectra within the standard picture, see G. Belanger, T. DeGrand, and Peter Moxhay, Phys. Rev. D 39, 257 (1989); P. Moxhay (private communication).

^Harry J. Lipkin and S. F. Tuan, Phys. Lett. B 206, 349 (1988); University of Hawaii Report No. UH-511-664-88 [in Proceedings of the Twenty-Fourth International Conference on High Energy Physics, Munich, Germany, August 1988 (to be published)].

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