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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)
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