sorakrai srisuphaphon role of pentaquark components into meson production meson production...
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Sorakrai SrisuphaphonSorakrai Srisuphaphon
Role of pentaquark components intoRole of pentaquark components into meson productionmeson production
proton-antiproton annihilation reactionsproton-antiproton annihilation reactions
OutlineOutline
IntroductionIntroduction The proton wave functions with pentaquark The proton wave functions with pentaquark
componentcomponent The transition amplitude for The transition amplitude for meson meson
production in proton-antiproton annihilation production in proton-antiproton annihilation reactionsreactions
Results and ConclusionsResults and Conclusions
Introductionuu uu
dd
protonproton
Baryons being bound states of three quarks.
The proton might contain a substantial strange quark-antiquark component
The proton might contain a substantial strange quark-antiquark component
Deep Inelastic Scattering
The non-zero strange spin of the proton
03.010.0 s
The strangeness magnetic moment can be extrapolated from the strange magnetic form factor
sSM QG )0(
Several experimental measurements suggest a positive value forSeveral experimental measurements suggest a positive value for s
?proton ?proton
uuuu
dd
ss
0s 0s
The presence of a uudss piece in the proton wave function.suuds
),,,( 0 XXpp
The proton wave functions with 5q componentThe proton wave functions with 5q component
suudsBuudAp
122 BA 22 BA with
pentaquarkpentaquark
0s 0s
022 SFFS FFS
suuds
uuds
2
1,
2
1,2
10
2
1,
2
1
55
1
q
siq mmjS
uuds
msuudssuuds
Orbital]31[
The correspondingspatial state labeled by
spin
flavor
flavor-spin
orbital
colororbital-flavor-spin]211[uuds ]11[ s ]222[ suuds
color singlet
))()()((3
1]211[]211[]211[ BGRBGBRGRBGRC
jjjj
Construction of multiquark states in group theory. Y. Yan, S. Srisuphaphon
Prog.Part.Nucl.Phys. 67 (2012) 496-501
)(]211[ RBG
orbital-flavor-spin
color
)2
( 21,11
qqY
)6
2( 321
,12
qqqY
)12
3( 4321
,13
qqqqY
orbital1
2
3 4
1
3
2 4
1
4
2 3
]211[]31[
21
22,2222 SSS 00
43
0
21
2
1
2
1
2
1
2
122
1
S
}
2222{24
1211
1
udsuusuddususuud
usdusuduudusduus
sduudsuuuusduudsF
flavor
spin
)6
2(
)20
4(
2exp
]}312
12
6
1
2
1[
2exp{)(
321,1
2543212
24321
2321
221
2
5,..,1
qqqY
qqqqqR
qqqqqqqqqR
Nqq
B
Bsuudssuuds
spatial
),,,( 0 XXpp ),,,( 0 XXpp
ppX OT ˆTransition amplitudeTransition amplitude
suudsBuudAp 22 BA
duusuudsOXABT ˆ2
)()(......ˆ...
.........
81811
4143
13
83
13
duusuudsqqqqOqq
qqXqdqdqdqdT
I
I
A
A
)()(......ˆ...
.........
81811
4143
13
83
13
duusuudsqqqqOqq
qqXqdqdqdqdT
I
I
A
A
duusuudspp
The transition amplitude for The transition amplitude for meson production in meson production in proton-antiproton annihilation reactionsproton-antiproton annihilation reactions
03 P
)()()()( 48)3(
33)3(
22)3(
11)3(
qqqqqqqq
1AO 4756VV
duusuudsOXABT ˆ2
ijC
ijFjiji
ijij qqqqYV 11)1)(()( 1)3(1
)()(......ˆ...
.........
818141
4143
13
83
13
duusuudsqqqqOqq
qqXqdqdqdqdT
I
I
A
A
Choosing the plane wave basis for the relative motion of the proton and antiproton
suuds )( 54321)3( kqqqqq
)( 876)3( kqqq
p
k
k
zSSpsuudspsuudsduusuudsqq ,,81 ][)()(...
41...qqX ( )
mjX i ,][ )( '2'1)3( qqq
)( '4'3)3( qqq
q q
duusuudsOXABT ˆ2
iMmffiOf fCCFFA
,
475647564756 ),,,,(1111)1(1
iOfIA spin-color-flavor weight
StoP
PtoSMmf
MPS
MPS
MPS
mSP
mSP
mSP
ffff
;)1()1()1(
;)1()1()1(),,,,(
,,3,,2,,1
,,3,,2,,1
iOfkQqQkqTIAkqfi }exp{),( 2222
)(22 , PSSPnkq andQQ
MB RR , are geometrical constants depending on the radial parameters
Including the initial state interaction for the atomic state of the systempp
)(),()(),( 3, kkqTkdqTkqT I
LSJfiLSJfif
)()(...)()(... 813
81 duusuudskkqqkdduusuudsqq
pp )(kILSJ
The protonium wave function in mo
mentum space for fixed isospin I
iOfkQqQkqTIAkqfi }exp{),( 2222
),(),(22
1JIiOfXf
IAAXpp
0,00 J
1J 0,1
1,1
1,1
2
,)3(
33
)()()(22
qTEEEppE
pd
E
pdLSJfXX
X
XXpp
The partial decay width for the transition of the state to the two-meson state
2;
12
)12(
1;4
)12(
)(
JJ
JJ
JWstatistical weight
BBranching ratioranching ratio the partial decay width divided by the total widththe partial decay width divided by the total width
)()(),( ,
JJWXBR
total
Xpp
)(
)(),(
J
JWXBR
total ),(),(
22 JIiOfXfII AA
q q
RReduceducinging tthe model dependencehe model dependence
2/1222/122 )()( qmqms X
})(2.1exp{),( 2/11XssGeVqXf
Choosing a simplified phenomenological approach that has been Choosing a simplified phenomenological approach that has been applied in studies of two-meson branching ratios in nucleon-applied in studies of two-meson branching ratios in nucleon-
antinucleon and radiative protonium annihilation.antinucleon and radiative protonium annihilation.
we use a kinematical phase-space factor of the phenomenological form
The initial-state interaction coefficients
are related to the probability for a protonium state to have
isospin I and spin J
}exp{)(),( 223 kQkkdJI kILSJ
Transition
011 S
01
33 S
00
31 S
udS 113
XLNN )0(
Results
.exp
104BR
3.23.6
7.05.5
0.14.3
3.09.0
410BR
]22][22][4[ ]22][22][22[ ]22][31][31[ ]22][211][31[]22][211][211[
]22][31][211[
3.6
4.5
8.3
8.14.1
84.0
0
8.62.5
3.7
9.3
0.179.0
3.4
7.3
4.29.1
84.0
5.3
8.62.5
The effective strength parameter has to be adjusted to data
Transition
.exp
104BR410BR
]22][22][4[ ]22][22][22[ ]22][31][31[ ]22][211][31[]22][211][211[
]22][31][211[
2,1,013 P
01
31 P
02,1,0
33 P
udP 111
9.07.3
4.19.2
3.00.0
2.04.0
7.3
31.0
7.1
12.010.0
0029.0
13
0080.00061.0
21.0
5.2
087.0066.0
48.0
3.1
22.017.0
13
0029.0
0080.00061.0
XLNN )1(
ConclusionsConclusions
suudsBuudAp
2
1,
2
1,2
10
5
1
q
sim
mjS suuds 0s 0s
The The model prediction model prediction only only in the in the configuration of configuration of
is agree well with the is agree well with the experimental data.experimental data.
SFFS 22224
]22][22][4[
]22][22][22[]22][31][31[
]22][211][31[
]22][31][211[]22][211][211[
),,,( 0 XXpp
03 P
BBranching ratioranching ratioss
Thank you Thank you for your attentionfor your attention