meson assisted baryon-baryon interaction hartmut machner fakultät für physik universität...
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Meson Assisted Baryon-Baryon Interaction
Hartmut Machner
Fakultät für Physik
Universität Duisburg-Essen
Why is this important?
•NN interactions Nuclear potential, nuclear structure
•NY interactions Hypernuclear potential, hypernuclear structure, neutron stars
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Baryon-Baryon Interactions
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Baryon-baryon interaction
Fäldt & Wilkin derived a formula ( for small k)
2 2
2 2
2| ( ) | | ( ) |k r r
k
From this follows, that from a the cross section of a known pole (bound or quasi bound) the continuum cross section is given [N({1+2})N(1+2)tN(1+2)s].
The fsi is large for excitation energies Q of only a few MeV.
a b a b Standard method: elastic Scattering:
Often it is impossible to have either beam or target. Way out FSI in (at least) three body reaction. If the potential is strong enough one has resonances or even bound states.
1 2 3
or
a+b 1+2 +3
a b
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Example: neutron-neutron scattering
Bonn
16.1 0.4fmnna
neutron and proton coincidences
different sides of the beam
TUNL
neutron-neutron coincidences
same side of the beam
18.7 0.6fmnna
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neutron-neutron scattering
Bonn equipment at TUNL yielded:
16.8 0.3 0.4fmnna
Obviously ist the geometry which makes the difference. Three body effects?
Better method: a meson in the final state: d nn
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Problem
22
2
dU q
dr
( ) ( ) ( ) ( ) ( ) ( )p np n r r q p nr r
Why meson assisted?
( 0) BT q T
factorisation:with
leads to
baryon-baryon interaction strong
meson-baryon interaction weak
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resonances
Strategy: choose beam momentum so that no resonance is close to the fsi region.
2 1 2
2 12 2
0
1 1cot
2
tan
q rqa
qq q
Note: different sign conventions in a. a<0 unbound
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The pp0pp case
Elastic pp scattering, Coulomb force seems to be well under controle: app=-7.83 fm
However: an IUCF groupClaimed „…the data require app=-1.5 fm.“ They questioned the validity of the factorization.
Experiment at GEM, differential and total cross sections.
10-6
10-5
10-4
10-3
10-2
10-1
100
( m
b)
0.1 0.1 0.5 1.0
BilgerBondarMeyerZlomanczukFlaminioShimizuStanislausRappeneckerGEM
FIT Ss, Pp (Ps from polarisation experiments)
no resonance
with resonance, usual fsi
with but fsi with half the usual pp scattering length
No need to change the standard value!
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Saclay pp+(pn) 1000 MeV
pp(pn)
dpp(pn)
triplet (from fit to all)
singlet (from deuteron)
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Data from Uppsala and GEM
p=1642.5 MeV/c
102
103
104
cou n
t s
-10 -5 0 5 10 15 20
(MeV)
Betsch et al.30 deg.
102
103
104
cou n
t s
-10 0 10 20 30 40
Q (MeV)
Uppsala 30 degreeGEM 0 degree
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Triplet FSI absolute
0
20
40
60
80
100
120
140
160
180
200
220
cou n
t s
0 5 10 15 20 25 30Q (MeV)
datatriplet +bg
at and rt close to literature values
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Singlet FSI absolute
0
100
200
300
400
c ou n
ts/ 0
. 2 M
eV
-2 0 2 4 6 8 10 12 14 16 18 20 22 (MeV)
No singlet state!
singlet fraction Ref.
0.40±0.05 Boudard et al.
< 0.10 Betsch et al.
<0.10 Uzikov & Wilkin
< 0.10 Abaev et al.
< 0.003 GEM
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More experiments
10-1
100
101
102
103
101
102
103
104
d2 /d
d b/
sr M
eV) 10
0
101
102
103
-5 0 5 10 15 20 25
(MeV)
p+p++X
pp
=955 (MeV/c)
0.70±0.04
pp
=1220 (MeV/c)
1.32±0.02
pp
=1640 (MeV/c)
1.92±0.03
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
norm
aliz
atio
n fa
cto r
R
300 400 500 600 700 800 900 1000Tp (MeV)
this workGEM PLBPleydon
Fäldt-Wikin relation
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Full 3 body calculation
Relativistic phase space
Reid soft core potential
10-1
100
101
102
103
101
102
103
104
d2 /d
d b/sr
Me
V)
100
101
102
103
-5 0 5 10 15 20 25
(MeV)
p+p++X
pp
=955 (MeV/c)
pp
=1220 (MeV/c)
pp
=1640 (MeV/c)
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p elastic scattering
378+224 events in a 82 cm bubble
chamber
fit as rs at rt
A -2.0 5.0 -2.2 3.5
B 0 0 -2.3 3.0
F -8.0 1.5 -0.6 5.0
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pppK+
Simultaneous fit:
only spin singlet
only spin
2.43fm
r 2.21fm
a 1.56fm
r 3
triplet
.7fm
s
s
t
t
pp pK
p p
K d p
a
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production
10-2
10-1
100
101
102
b
)
10-1
100
101
102
0 500 1000 1500 2000 (MeV)
COSY-11Sibirtsev et al.ANKEHIRESShyamFlaminioppK0+p (*0.4)ppK0+p (*2.5)
TOF07FlaminiofitShyam
ppK+n
ppK0p
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Resonances
0
20
40
60
80
100
120
140
160
180
d2 /d
m d
( nb/
MeV
/ sr )
2.04 2.05 2.06 2.07 2.08 2.09 2.10 2.11
m(p) (GeV)
HIRESfitSATURNE 4 (-0.002 GeV)
without/with resolution folding
Upper limits (99%)
solid =1 MeV
dashed 0.5 MeV
dotted 0.1 MeV
Aerts and Dover
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deuteron?
0
20
40
60
80
100
120
140
160
180
d2
/dm
m d
( nb /
Me V
/sr )
2.045 2.050 2.055 2.060 2.065 2.070 2.075
missing mass (GeV/c2
)
HiresSaclay*2
FW-theorem: nb
Exp.: 75±3 nb
2/dof = 1.3
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-20
-10
0
10
20
30
d2 /d
m d*
(p
) (n
b/M
e V s
r)
m(p) (GeV)
peak
Peak below threshold:
-deuteron
Peak at threshold:
cusp
Peak above threshold:
Resonance (dibaryon?)
Shaded: HIRES only p; dots TOF (submitted)
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Peak analysis
K d p lower mass peak at +n threshold
higher mass peak or shoulder =???
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Flatté analysis
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Elastic p scattering
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Potential models
- bound state (deuteron like N):
3D1 phase passes through 90°:
Nijmegen NSC97f, Nijmegen NF, Jül89
S1 phase passes through 90°:
Nijmegen ESC04, Toker&Gal&Eisenberg
- inelastic virtual state = peak direct at threshold = genuine cusp, none of the relevant phases passes through 90°:
Nijmegen NSC89, ND, ESC08, Jülich05, EFT
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Summary
Meson assisted baryon-baryon interaction is a powerful tool to study bb-potential.
Low energy interaction can be studied via fsi and resonances as well as bound states.
pp0pp: indicates factorization is valid. No different parameters than in pppp.
pp+pn: only triplet scattering. Why?
ppp: mostly singlet scattering. Why? The potential is to week to form a bound state. No dibaryon resonance! Strong enough to form a resonance?
ppK+N: potential strong enough to bind? But no fsi visible.
Thank you to
GEM & HIRES
Johann Haidenbauer, Frank Hinterberger, Jouni Niskanen, Andrzej Magiera, Jim Ritman, Regina Siudak
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FSI approaches
A lot of studies made use of a Gauss potential. However the Bargman potential is the potential which has the effective range expansion as exact solution: a, r . defines the pole position (positive ↔ bound, negative ↔ unbound). 2
2
1
2 22
2
2
1| |
( )
2| |
| |
ER
FW
pp p
Jost
T ka k
TQ
k iT
k i
m
All with Gamow factor
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p(p,X) Pbeam =2735 MeV/c
vetoed with cherenkov signalcherenkov signal