1

S. Wycech (Warsaw, Poland), B. Loiseau

Antiproton-proton resonant like Antiproton-proton resonant like channels in decayschannels in decays

J / p p

Beijing09/2004

Scattering lengths for 2I+1,2S+1LJ states from low energy scattering experiments but clear separation of quantum state difficult.

Introduction• Existence of quasi-bound, virtual or resonant antinucleon-nucleon states ?

(N N)

Complementary X rays transitions in -hydrogen if fine structure of level resolved e.g. 1S states : M. Augsburger et al., PLB461 (1999) 417, « Measurement of the strong interaction parameters in antiprotonic deuteriuim »

and partly 2P states :M. Augsburger et al. NPA658 (1999) 149, « Measurements of the strong interaction parameters in antiprotonic hydrogen and probable evidence for an interface with inner bremsstrahlung »

p

2

Collaboration, J.Z. Bai et al. PRL91 (2003) 022001,

« Observation of a near-threshold enhancement in the mass spectrum from radiative decay » .

pp

J / pp

On the other hand clear threshold suppression in .

J / 0 p p

But fine structure resolution not achieved yet.

Possible understanding from subthreshold energy region like in low- or zero - energy reactions cf. atomic experiments : D. Gotta et al. NPA660 (1999) 283, « Balmer and transitions in antiprotonic hydrogen or deuterium ».

p D

Formation experiments : resonant-like behaviour in BES

3

Physics of slow pairs produced in J/ decay :

p p

JPC conservation several final states possible Close to threshold different behavior

p p

p p

Some recent approaches to interpret BES Collaboration results B. S. Zou, H. C. Chiang, PRD69 (2004) 034004, « One-pion-exchange final state interaction and the near threshold enhancement in decays », B. Kerbikov, A. Stavinsky, V. Fedotov, nucl-th/0310060, « Low-mass proton-antiproton enhancement : Belle and BES results, premises of LEAR and expectations from CLAS », Chong-Shou Gao and Shi-Liu Zhu, hep-ph/0308204, « Understanding the Possible Proton Antiproton Bound State Observed by BES Collaboration ».

p p

J / p p

4

Use of Paris potential model.

NN

r > 1 fm from G-parity transformation from Paris NN potential based on dispersion theoretic treatment of 2 exchange.

UNN (r)

r < 1 fm fit to data.

UNN (r)

NN

State dependent optical potential :

VNN (r) UNN (r) iWNN (r)

phenomenological short range with a form suggested by calculation of mesons or resonances.

WNN (r)

NN 2

Paris model : parameters of short range readjusted by fitting to new data.

We here shall rely on elastic and inelastic NN scattering experiment.

5

Paris 82 : J. Côté, M. Lacombe, B. Loiseau, B. Moussallam, R. Vinh Mau, PRL48

(1982) 1319, « On the nucleon-antinucleon optical potential » pre-LEAR (CERN) data mainly (T=0 + T=1), 2/data=2.80 for 915 data.

p p

Paris 99 : B. El-Bennich, M. Lacombe, B. Loiseau, R. Vinh Mau, PRC59 (1999)

2313, « Refining the inner core of the Paris potential » previous data + more recent LEAR : 2/data=2.95 for 3814 data.

p p n n

NN

Paris 03 : M. Lacombe, B. Loiseau, R. Vinh Mau, S. Wycech, in preparation, data used in Paris 99 + scattering lengths (antiprotonic hydrogen and deuterium,

M. Auberger et al. (1999)) + «Antineutron-proton total cross-section from 50 to 400 MeV/c » F. Iazzi et al. PLB475 (2000) 378.

Paris 03 : 2/data = 3.19 for 3934 data.

Paris antinucleon-nucleon potentials

Paris 94 : M. Pignone, M. Lacombe, B. Loiseau, R. Vinh Mau, PRC50 (1994) 2710, « Paris potential and recent proton-antiproton low

energy data » + LEAR data in particular (T=1 - T=0), 2/data=2.46 for 3295 data.

NN

p p n n

6

Allowed final states of pairs

p p

JPC conservation limits number of slow final states -i.e. for small - JPC(J/) = 1- -.

M pp 2m p

pp

e+e- collision being angle of final photon with direction of the beam, BES Collaboration favours 1 + cos2 over sin2 angular distribution pseudoscalar (1S0) or scalar (3P0)

decay mode analogue JPC or JPC or h pp relative

pp 1S0 (1444) 1 0 pseudoscalar 1

pp 3P0 f0(1710) 1 0scalar 0

pp 3P1 f1(1285) 1 1pseudovector 0

0 pp 31P1 0 1pseudovector 0

0 pp 33S1 0 0 1 vector 1

7

In channel f :

Tff A ff

1 iq f A ff

Large ReAff > 0 possiblity bound (quasi-bound) state.

Large ReAff < 0 virtual state likely.

Needs to extrapolate below threshold.

S-wave K-matrix low-energy multichannel system :

See H. Pilkuhn, « Interaction of hadrons », North Holland P.C., 1967.

Tif Aif

1 iq f A ff ,

Aif transition length, A ff scattering length, functions of q f2

Final state interaction

8

For P wave

A ff A ffP q f

2 ; Aif AifP q f ; A ff scattering volume

Here formation amplitude unknown, but up to terms

q f2

Tif Aif

A ff Tff

CTff

q fL

final state interaction factor in an appropriate partial wave

t 2 Tff

q fL

2

p p

p p

In many open annihilation channels : ImAff large.

p p

: formation amplitude, L angular momentum.

C Aif q f

L

A ff

Formation amplitude

9

Paris potential for

tL SL 1

2iq2L1, with SL Le2iL

tL 1

2q2L1L sin2L i 1 L cos2L

Tlab 2q2

m p, x M p p 2m p

Tlab

2

4m p

M p p 2m p

Close to threshold (at Tlab = 300 MeV, x = 289.2MeV)

x Tlab

2

Final state interaction factor

10

Solid curve : fit by background (dashed curve) plus S-wave Breit- Wigner (1S0) :

MR 1859 103 (sta) 25

5 (syst) MeV/c2

and width R < 30 MeV/c (2/d.o.f. = 56.3/56). Note : If P-wave (3P0) Breit-Wigner 2/d.o.f. = 59/56 and MR = 1876.4 0.9 MeV/c2, width = 4.6 1.8 (sta) MeV/c2.

Fig. 1: (a) From BES Collaboration : the near threshold distribution

for the event sample.

M p p 2m p

pp

Experimental results for

J / p p

11

J / p p

The unknown formation amplitude C parametrized as

C (x) 2 c0 xc1, x M pp 2m p

Numbers of Events =

For Paris 03 at x = 7 MeV and x = 66.2 MeV c0 and c1

T (x) 2 c0 c1x t(x) 2

11S0 +31S013P0 +33P0

13P1 +33P1

c0 87.70 96.46 138.63

c1 2.87 14.12 9.78

p p I 0 I 1

Experimental points and errors extrapolated from figures of BES Collaboration PRL91 (2003) 022001.

Model fit for

12

Comparison of the result to the BES event sample,

data from Fig. 3 of J. Z. Bai et al. PRL91 (2003) 0022001).

p p 11S031S0

Fig. 2

13

Weighted events compared to data.

p p 1S0

M p p2 4 q2 m2

M p p2 4 GeV2 4 q0

2 m2

Weighted events = T(x) 2 q0

q

Fig. 3

14

Bound states in 11S0

Re E (MeV)

Width(MeV)

Paris 03 : -4.8 52.5

Paris 99 : -69 46

Paris 94 : none

Paris 82 : none

final state factor compared to data.

p p 11S031S0

Fig. 4

15

Comparison of the result to the BES event sample.

p p 13P033P0

Fig. 5

16

M p p2 4 q2 m2

M p p2 4 GeV2 4 q0

2 m2

Weighted events = T(x) 2 q0

q

Weighted events compared to data.

p p 3P0

Fig. 6

17

p p 13P033P0 final state factor compared to data

Resonances in 13P0

Mass (MeV)

Width(MeV)

Paris 03 : 1873 10.7

Paris 99 : 1876 4.8

Paris 94 : 1876 10.4

Paris 82 : 1880 11

Fig. 7

18

J / 0 pp

Fig. 8 (a) From BES Collaboration : the distribution

events for the selected decay.

x M p p 2m p

J / 0 pp

Solid curve fit by

fbkg N x1/ 2 a1x3 / 2 a2x 5 / 2

Experimental results for

19

As for 33S1, t(x) does not vanish at threshold choice of

C (x) 2 c1x c2 x 2

For 31P1

C (x) 2 c0 c1x

For 33S1 and 31P1 : N events =For Paris 03 at x = 7 MeV and x = 41.7 MeV ci, i=0,1.2

T (x) 2 C (x) 2 t(x) 2

The pair has to be in I=1 (J/ is I=0)

p p

J / 0 pp

33S131P1

c0 0 20.29

c1 7.42 19.69

c2 0.012 0

p p [I 1]

Model for

20

Comparison of the result to the BES event sample

p p 31P1

Fig. 9

21

final state factor compared to data.

p p 31P1 Bound states in 31P1

ReE (MeV)

Width(MeV)

Paris 03 : -15.4 118.4

Paris 99 : -60 130

Paris 94 : none

Paris 82 : none

Fig. 10

22

For Paris 03 : 11S0 (ReE = -4.8 MeV, Width = 52.5 MeV) and 33P1 (ReE = -4.5 MeV, Width = 18.1 MeV). Existence of these states needs confirmation. For Paris 03 the resonance 13P0 (ReE = 1873 MeV, Width = 10.7 MeV). This well-established resonance orginates from the strong attraction from one-pion exchange.

Such a model predicts quasi-bounds states close to the threshold in particular and and a resonance in .

p p 11S0

p p 33P1

p p 13P0

New results of BES Collaboration : natural explanation from a traditional model of interaction based on G transformation, dispersion theoric treatment of two-pion exchange and semi-phenomenological absorptive and short range potentials.

p p

Each of these states gives a reasonable representation of the BES decay data.

J / p p

Some concluding remarks

23

33S1 or 31P1 waves occuring in the decays.

J / 0 pp

p p

Here isospin conservation forces the pair to be I = 1. Our final state emission model gives ratio of branching of the and 0 channels of order 1 as in the experience (1/4 from isospin conservation).

p p

/( fNN2 /4)

OUTLOOK

Needs the experimental data points to be more quantitative (2/d.o.f.)

- in progress - a more specific semi-quantitative (dominance of magnetic transition) favors and

Final state off-shell effects.

Microscopic quark model of the annihilation followed by pair creations and then or emission could generate some formation amplitude C.

J / 0 p p (31P1) .

J / p p (1S0 )

cc (3S1)

qq

0 (qq )

No narrow quasi-bound states or resonance close to the threshold

24

Other antiproton-proton graphs

25

Comparison of the result to the BES event sample.

p p 13P133P1

Fig. 11

26Fig. 12

Weighted events (3P1) compared to data

27

final state factor compared to data

p p 13P133P1 Bound states in 33P1

ReE (MeV)

Width(MeV)

Paris 03 : -4.5 18.1

Paris 99 : -20 24

Paris 94 : -29 9.4

Paris 82 : -71 244

Fig. 13

28

Comparison of the result to the BES event sample from

Fig. 2 of J. z. Bai et al. PRL91 (2003) 002001

p p 33S1

Fig. 14

29

p p 33S1 final state factor compared to data Bound states in 33S1

ReE (MeV)

Width(MeV)

Paris 03 : -111.7 45.8

Paris 99 : -168 50

Paris 94 : -114 1

Paris 82 : - 84 272

Fig. 15

30

tot p bar p

31

ann 10-190 p bar p

32

ann 0-50 p bar p

33

Alston

34

ann n bar p

35

d/d elast

36

P elast

37

Cex

38

d/d Cex 147

39

P Cex

40

d/d Cex 206

41

d/d Cex 344