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

Baryon-Baryon Interactions

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

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

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

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

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

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!

Saclay pp+(pn) 1000 MeV

pp(pn)

dpp(pn)

triplet (from fit to all)

singlet (from deuteron)

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

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

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

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

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)

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

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

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

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

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

-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)

Peak analysis

K d p lower mass peak at +n threshold

higher mass peak or shoulder =???

Flatté analysis

Elastic p scattering

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

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

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

p(p,X) Pbeam =2735 MeV/c

vetoed with cherenkov signalcherenkov signal