Antibaryon interactions with the nuclear medium
Jaroslava Hrtánková
Nuclear Physics Institute, eº, Czech Republic
INPC, Adelaide, September 11 - 16, 2016
1
Introduction
Introduction
study of
B̄ (p̄, Λ̄, Σ̄, Ξ̄) bound states in selected nuclei:
behavior of B̄ in the nuclear medium including its absorption
core polarization eect due to B̄
testing models of (anti)hadronhadron interactions
knowledge of B̄ nucleus interaction for future experiments
(PANDA@FAIR)
2
Model
RMF approach
Nucleons Dirac elds interacting via the exchange of meson elds
Dirac equation for nucleons and antibaryon
~ + β(mj + Sj ) + Vj ]ψjα = αj ψjα ,
[−i α
~∇
S = gσj σ, Vj = gωj ω
0
+ gρ j ρ 0 τ 3 + e j
Klein-Gordon equations for meson elds
j = N , B̄
,
1 + τ3
A0 ,
2
(−4 + mσ2 )σ = −gσN ρS −gσB̄ ρS B̄
(−4 + mω2 )ω0 = gωN ρV +gωB̄ ρV B̄
(−4 + mρ2 )ρ0 = gρN ρI +gρB̄ ρI B̄
−4A0 = e ρp +eB̄ ρB̄ .
3
Model
Baryon-nucleus interaction
Nucleon-meson couplings obtained by tting nuclear matter and nite
nuclei properties
Hyperon-meson coupling constants:
for ω and ρ eld obtained from SU(6) symmetries,
for σ eld obtained from ts to experimental data (Λ hypernuclei, Σ
atoms, Ξ production in (K + , K − ) reactions)
gσΛ = 0.621gσN ,
gσΣ = 0.5gσN ,
gσΞ = 0.299gσN ,
gωΛ = 2/3gωN ,
gωΣ = 2/3gωN ,
gωΞ = 1/3gωN ,
gρΛ = 0 ,
gρΣ = 2/3gρN
gρΞ = gρN
,
4
B̄ -nucleus interaction
B̄ -nucleus interaction
BN
→
BN
interaction G-parity transformation
Ĝ
= Ĉe i πI1
gσB̄ = gσB , gωB̄ = −gωB , gρB̄ = gρB
G-parity valid for the long and medium range
→ 750 MeV deep p̄ potential in the nucleus
B̄N
potential
Nuclear medium + short range interaction possible deviations from
the G-parity
Antiprotonic atoms and p̄ scattering o nuclei at low energies
→ ReVp̄ ∼ 100 − 300 MeV deep
Reduced
B̄
coupling constants
gσB̄ = ξ gσB , gωB̄ = −ξ gωB , gρB̄ = ξ gρB
,
where parameter ξ = 0.2 − 0.3
5
B̄ -nucleus interaction
Antibaryon potential
0
20
TM2
ξ=0.2
-50
S+V (MeV)
0
-100
-20
-150
16
-40
16
16
-60
16
0
2
4
r (fm)
Fig.1: The
16
Op
16
OΛ
16
OΣ0
16
OΞ0
6
Op
-200
OΛ
OΣ0
-250
OΞ0
4
2
0
r (fm)
B nucleus (left) and B̄ nucleus (right) potentials in
16
O.
6
B̄ -nucleus interaction
Antibaryon spectrum
TM
200
ξ=0.2
12
6
BΒ (MeV)
150
Li
C
16
p
O
40
100
208
Ca
90
Zr
Pb
Λ
0
Σ
50
0
Ξ
0
10
20
(-)
30
40
2/3
A
Fig.2: The A dependence of
model for ξ = 0.2.
B̄
1s binding energies, calculated dynamically in the TM
7
p̄ absorption
p̄ absorption
p̄nucleus potential:
1.0
2π
channel
s = (EN +Ep̄ )
ηω
0.6
3π
0.4
ξ = 0.2, Imb0 = 1.9 fm
2
fs
ReVp̄ =ξ VRMF
X
ImVp̄ =
fs (√s )Br Imb0 ρ
KK
0.8
5π
πρ
2ω
2πρ
2πη
2πω
6π
ρω
0.2
−(~pN +~pp̄ )
7π
πω
πKK
2
ωKK
4π
0.8
1
1.2
1.4
1/2
s
1.6
1.8
(GeV)
Fig.3: The phase space suppression factor √
fs
as a function of the center-of-mass energy s .
p̄ absorption
Energy available for annihilation
CMS frame →
√
s = mp̄ + mN − Bp̄ − BN
(M)
p̄ absorption in a nucleus → ~pN + ~pp̄ 6= 0
(A. Cieplý, E. Friedman, A. Gal, D. Gazda, J. Mare², PLB 702, 402 (2011))
√
s = Eth
1/2
2(Bp̄ + BNav ) (Bp̄ + BNav )2
1
1
1−
+
−
T
−
T
, (J)
p̄
Nav
Eth
Eth2
Eth
Eth
where
Tj = −
~2
mj∗ 4 and
2
mj∗ = mj − Sj , j = N , p̄
9
p̄ absorption
1s
p̄ energies and widths in nuclei
280
M
J
320
Pb
240
Ca
Γp (MeV)
Bp (MeV)
280
200
160
Ca
Pb
Zr
Zr
240
200
TM1
120
TM1
10
20
2/3
A
30
40
10
20
2/3
A
30
40
Fig.4: Binding energies (left panel) and widths (right panel) of 1s p̄ -nuclear
√ states in
selected nuclei, calculated dynamically using the TM1 model for dierent s .
10
Paris
Paris
N̄N
N̄N potential
potential
Microscopic N̄N Paris potential constrained by scattering and
antiproton atom data
(B. El-Bennich, M. Lacombe, B. Loiseau, S. Wycech, PRC 79 (2009) 054001.)
Recently used to describe the p̄ -atom data and low energy
o nuclei
p̄ scattering
(E. Friedman, A. Gal, B. Loiseau, S. Wycech, NPA 934 (2015) 101)
S-wave p̄ -nucleus optical potential in a 'tρ' form
√ 1
s
1
2Ep̄ Vopt = −4π
ρ +ρ
F ρ +F
mN 0 2 p 1 2 p n
11
Paris
N̄N potential
In-medium Paris S-wave amplitudes
In-medium amplitudes F0 and F1 obtained from free-space amplitudes
by multiple scattering approach (WRW)
(T. Wass, M. Rho, W. Weise, NPA 617 (1997) 449)
√
√
√
fp̄n√(δ s )
[2fp̄p (δ s ) − fp̄n (δ s )]
√
F1 =
, F0 =
,
√
√
√
s
1
1
1 + 4 ξk mN fp̄n (δ s )ρ
1 + 4 ξk mNs [2fp̄p (δ s ) − fp̄n (δ s )]ρ
√
√
R ∞ dt
2
t exp(iqt )j1 (t )
0
where δ s = s − Eth , ξk = 9pπ2 4
f
and q = p1
f
q
Ep̄ − mp̄
2
2
12
Paris
N̄N potential
In-medium Paris S-wave amplitudes
10
10
ρ0
free
8
8
6
Im FpN (fm)
Re FpN (fm)
6
4
2
4
2
0
0
-2
-2
-4
-200
-4
-150
-100 -50
E - Eth (MeV)
0
50
-200
-150
0
-100 -50
E - Eth (MeV)
50
Fig.5: Energy dependence of the Paris 09 p̄N S-wave amplitudes: Pauli blocked
amplitude for ρ0 = 0.17 fm−3 (solid lines) compared with free-space amplitude (dotted
lines).
Paris
1s
N̄N potential
p̄ energies and widths
240
260
220
240
Paris 09
Pb
200
Γp (MeV)
Bp (MeV)
NL-SH
Zr
O
Ca
C
180
Paris 09
220
200
Ca
NL-SH
C
160
Pb
Zr
O
180
0
10
20
2/3
A
30
40
0
10
20
2/3
A
30
40
Fig.6: Binding energies (left panel) and widths
√ (right panel) of 1s p̄ -nuclear states in
selected nuclei, calculated dynamically for s = J using the Paris N̄N S-wave potential
(red) and phenomenological approach within the NL-SH model (black).
Paris
N̄N potential
p̄ spectrum in 16O
Bp (MeV)
280
16
O+p
phenom. Vopt
16
1s1/2
1p3/2
1p1/2
O+p
S-wave Paris 09
320
280
240
240
200
200
160
160
120
120
80
80
40
40
Bp (MeV)
320
16
Fig.7: 1s and 1p binding energies (lines)
√and widths (boxes) of p̄ in O calculated
dynamically within the TM2 model for s = J with phenomenological p̄ optical
potential (left) and S-wave Paris potential (right).
15
Conclusions
Conclusions
Antibaryons deeply bound in the nuclear medium within the RMF +
G-parity approach
p̄ absorption in a nucleus p̄ widths are reduced due to signicant
contribution from Tp̄ and TN to Γp̄ , but still remain large for
potentials consistent with p̄ atom data
p̄-nucleus quasibound states calculated with the Paris N̄N potential
S-wave potential yields smaller 1s p̄ energies and larger p̄ widths then
the RMF approach
the P-wave interaction to be included
16