Phenomenological study for the and two-meson couplingtetsuo.hyodo/old/publication/06_06KEK.pdf ·...
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1 2006, Mar . 1st Phenomenological study for the Θ + and two-meson coupling Tetsuo Hyodo a RCNP, Osaka a and A. Hosaka a
Transcript of Phenomenological study for the and two-meson couplingtetsuo.hyodo/old/publication/06_06KEK.pdf ·...
12006, Mar. 1st
Phenomenological study for the Θ+ and two-meson coupling
Tetsuo Hyodoa
RCNP, Osakaa
and A. Hosakaa
2
IntroductionPure antidecuplet case8–10 mixing case
Mass spectraDecay widths
Two-meson couplingCoupling constantsMeson induced Θ production
Summary
Contents
3
Introduction : Flavor SU(3) symmetry
Existence of Θ+ + Flavor SU(3) symmetry
Existence of flavor partners of Θ+
Phenomenological but model independent analysis up to O(ms)
Assuming the flavor multiplet that Θ+ belongs to, we examine its propertiesby symmetry relation, in connection with known baryon resonances.
to determine the JP of Θ+
4
Pure antidecuplet case
Simplest assignment for Θ+
Test the masses and widths of partnersvia flavor SU(3) symmetry relations
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Pure antidecuplet case
Mass : Gell-Mann—Okubo formulaM(10;Y ) = M10 − aY
gΘKN =√
6gN∗πN
ΓR = g2RFI
p2l+1
M2lR
Width : SU(3) symmetric coupling
Two parameters <— Mass of Θ and N*
One parameter <— Width of N*
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Pure antidecuplet caseMass and width [MeV]
JP MΘ MN MΣ MΞ ΓΘ
1/2- 1540 1647 1753 1860 156.1 exp. Θ(1540) N(1650) Σ(1750) Ξ(1860)
1/2+ exp.
3/2+ exp.3/2- exp.
M(10;Y ) = M10 − aY, gΘKN =√
6gN∗πN , ΓR = g2RFI
p2l+1
M2lR
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Pure antidecuplet case
JP MΘ MN MΣ MΞ ΓΘ
1/2- 1540 1647 1753 1860 156.1 exp. Θ(1540) N(1650) Σ(1750) Ξ(1860)
1/2+ 1540 1710 1880 2050 7.2 exp. Θ(1540) N(1710) Σ(1880) Ξ(2030)
3/2+ exp.3/2- exp.
Mass and width [MeV]M(10;Y ) = M10 − aY, gΘKN =
√6gN∗πN , ΓR = g2
RFIp2l+1
M2lR
8
Pure antidecuplet case
JP MΘ MN MΣ MΞ ΓΘ
1/2- 1540 1647 1753 1860 156.1 exp. Θ(1540) N(1650) Σ(1750) Ξ(1860)
1/2+ 1540 1710 1880 2050 7.2 exp. Θ(1540) N(1710) Σ(1880) Ξ(2030)
3/2+ 1540 1720 1900 2080 10.6 exp. Θ(1540) N(1720)3/2- exp.
Mass and width [MeV]M(10;Y ) = M10 − aY, gΘKN =
√6gN∗πN , ΓR = g2
RFIp2l+1
M2lR
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Pure antidecuplet case
JP MΘ MN MΣ MΞ ΓΘ
1/2- 1540 1647 1753 1860 156.1 exp. Θ(1540) N(1650) Σ(1750) Ξ(1860)
1/2+ 1540 1710 1880 2050 7.2 exp. Θ(1540) N(1710) Σ(1880) Ξ(2030)
3/2+ 1540 1720 1900 2080 10.6 exp. Θ(1540) N(1720)3/2- 1540 1700 1860 2020 1.3 exp. Θ(1540) N(1700) Ξ(2030)
are not reproduced simultaneously.
Mass and width [MeV]M(10;Y ) = M10 − aY, gΘKN =
√6gN∗πN , ΓR = g2
RFIp2l+1
M2lR
10
Octet-antidecuplet mixing
Second simplest assignment for Θ+
Mixing is induced by the SU(3) breakingin mass term.
mix
mix
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MΣ1 = (M8 + 2c) cos2 θΣ + M10 sin2 θΣ − δ sin 2θΣ
MΣ2 = (M8 + 2c) sin2 θΣ + M10 cos2 θΣ + δ sin 2θΣ
MΞ8 = M8 + b +12c
MΞ10= M10 + aMΘ = M10 − 2a
MN1 =(
M8 − b +12c
)cos2 θN + (M10 − a) sin2 θN − δ sin 2θN
MN2 =(
M8 − b +12c
)sin2 θN + (M10 − a) cos2 θN + δ sin 2θN
MΛ = M8
Octet-antidecuplet mixing
Mass formulae : GMO + mixing (N,Σ)
8 masses v.s. 6 parametersJP = 1/2— : too wide widthJP = 3/2+ : states are not well established
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π−p
K+
n
K+
π+
p
K+
n
K+
π+
∆+
ρ0
p
K+
n
π+
K+
Mass spectra2000
1900
1800
1700
1600
1500
1400
Mas
s sp
ectr
um
[M
eV]
2000
1900
1800
1700
1600
1500
1400
Mas
s sp
ectr
um
[M
eV]
1/2+
3/2—
N8
N10
N(1440)
N(1710)
N8
N10
N(1520)
N(1700)
10 (1540) 10
(1540)
10
(1860)
10 (1860)
10
(1690)
10
(1660)
8
(1880)
8
(1670)
8
(1690)8
8(1820)
8
8 10 Theory Exp. 8 10 Theory Exp.
N1
N2
10
1
2
8
N1
N2
10
1
2
8
predicted predicted
13
π−p
K+
n
K+
π+
p
K+
n
K+
π+
∆+
ρ0
p
K+
n
π+
K+
Decay width of Θ
JP θN [deg] ΓΘ [MeV]
1/2+ 29 29.1
3/2- 33 3.1
gΘ =√
6(gN2 cos θN − gN1 sin θN )
ΓR = g2RFI
p2l+1
M2lR
N* decay
from masses
Narrow width
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π−p
K+
n
K+
π+
p
K+
n
K+
π+
∆+
ρ0
p
K+
n
π+
K+
Two-meson coupling
π+π−
K+
K−
p Θ+
the cross section of
SU(3) relation enable us to calculate
from the decay of N* —> π π N
Then, what about two-meson coupling?
: large branching ratio of N* —> π π N: π K N molecule picture for the Θ
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π−p
K+
n
K+
π+
p
K+
n
K+
π+
∆+
ρ0
p
K+
n
π+
K+
Two-meson coupling
s s v v
Hosaka, Hyodo, Estrada, Oset, Peláez, Vacas, PRC71, 074021 (2005).The structure of the two-meson coupling
• These terms provided a sizable contribution.
• The effect of the two-meson coupling was studied by evaluating the self-energy.• We examined possible structures, and found that two types of the interaction Lagrangians were important.
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π−p
K+
n
K+
π+
p
K+
n
K+
π+
∆+
ρ0
p
K+
n
π+
K+
Two-meson coupling
JP state πN ππN(s) ππN(v)1/2+ N(1440) 65 7.5 <8
N(1710) 15 25 153/2- N(1520) 55 25 20
N(1700) 10 <85-95 <35
Branching fraction [%]
5
4
3
2
1
0
|gs |
5
4
3
2
1
0
|gv|
phase 1 phase 1phase 2 phase 2
5
4
3
2
1
0
|gs |
5
4
3
2
1
0
|gv|
phase 1 phase 1phase 2 phase 2
Still large uncertainty
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π−p
K+
n
K+
π+
p
K+
n
K+
π+
∆+
ρ0
p
K+
n
π+
K+
Constraints on the coupling
π-p -> K-Θ+ at KEK : upper limit is ~ 4.1 μb
Self-enefgy : not too large, but not too small
p Θ+
π− K−
< 4.1 μb
~ 100 MeV
We impose phenomenological constraints.
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π−p
K+
n
K+
π+
p
K+
n
K+
π+
∆+
ρ0
p
K+
n
π+
K+
Constraints on the coupling
Two structures should be added coherently.
p Θ+
π− K−
—> interference effect among s and v.
p Θ+
π− K−
s v
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π−p
K+
n
K+
π+
p
K+
n
K+
π+
∆+
ρ0
p
K+
n
π+
K+
Θ production12
10
8
6
4
2
0
[b
]
260024002200200018001600s [MeV]
s v Total
200
150
100
50
0
[b
]
260024002200200018001600s [MeV]
s v Total
-p -> K- + K+p -> + +
20
15
10
5
0
[ b]
260024002200200018001600s [MeV]
s v Total
140
120
100
80
60
40
20
0
[ b]
260024002200200018001600s [MeV]
s v Total
-p -> K- + K+p -> + +
1/2+
3/2-
largeinterference
σ(K+)σ(π−)
∼ 50
smallinterference
σ(K+)σ(π−)
∼ 3
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Summary 1 : mixing scheme
Masses of Θ(1540) and Ξ(1860) are well fitted in the 8–10 mixing scheme with JP = 1/2+ or 3/2— baryons.A very narrow width of Θ can be obtained for the JP = 3/2— case.For both JP, the mixing angle is close to the ideal angle.T. Hyodo and A. Hosaka, Phys. Rev. D71, 054017 (2005)
We examine 8–10 mixing scheme for the exotic and non-exotic baryon resonances.
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/1/2+ 1.59 -0.27 50 -78 MeV3/2− 0.104 0.209 3 -23 MeV
Summary 2 : Two-meson coupling and Θ producion
There is an interference effect between two amplitudes, which is prominent for 1/2+ case and rather moderate for 3/2- case
T. Hyodo and A. Hosaka, Phys. Rev. C72, 055202 (2005)
Based on the mixing scheme, we evaluate the two-meson coupling of Θ, and calculate the reaction process for Θ production
gs gv σπ−σK+ ReΣΘJP
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