FFukui ukui UUniversity of niversity of TTechnology echnology
Determination on F and D with SU(3) symmetry breakDetermination on F and D with SU(3) symmetry breaking effects and Δs distributions in the nucleoning effects and Δs distributions in the nucleon
Teruya YamanishiTeruya Yamanishi
Fukui University of Technology
● Data used numerical analyses for polarized quark distribution functions
§ １ Introduction
,,,),( 2,,1 DFA Qxdnp
－ At LO QCD, first moment of pol. quark distribution functions
)}/1/(12/3){(9 1 DFDFp
)}/1(3/52/3){(3 1 DFDFs p
)9
1
9
1
9
4(
2
1)(
1
0 11 sduxg pp
DFdu
DFsdu 32
Fukui University of Technology
Estimations of F and D with SU(3) and/or SU(2) breaking effects
Δs : negative and largeΔΣ : small
F and D for SU(3) flavor symmetryin these analyses
－ F and D
Baryon semileptonic decays ;
015.0718.03/: DFeep
05.025.03/: DFee
017.0340.0: DFeen
0035.02670.1: DFeepn
008.0463.0 F008.0804.0 D
Fukui University of Technology
where
§2 Baryon semileptonic decays
● Matrix element of V-A transition for BA
uuuOOu AAV
BsG )1()( 52
M
qMqfq
MqfqfO
AA
V )()()(2
32
221
5
23
222
1 ))()()((
qMqgq
MqgqgO
AA
A
sG 0for SVG udF1SVG usF
Fukui University of Technology
● Cabibbo model
from N. Cabibbo et al., hep-ph/037298 .
Fukui University of Technology
wwh
www
ww
g
DCFCg
c
baDF
BTr'BTrBTr'BTr
TrB'BTrB'BTrB'BTr
B,'BTr,B'BTr1
－
● In generally, g1(0) is expanded as
with
BBTr ,WFC
BBTr ,WDC
● Here we take
as SU(2) and SU(3) breaking parameters.
§3 F and D with SU(3)and SU(2) flavor breaking
83
Fukui University of Technology
Then, at Q2=0, one obtains for g1/ f1 :
・ There are 8 variables ; .and,,,,,, hcbaDF
)(2 cbDF
hcbaD
F 2)3(3
1)2)((
3
1
3
))(( caDF
hcbaD
F 2)3(3
1)2)((
3
1
3
))(( cbDF
hcbaD 3)(3
2
)(2 caDF
hcbaD 3)(3
2
DecayA → B SU(3) symmetry SU(3) and SU(2) breaking
n → p F + D
Λ → p F + D/3
Σ － → n F － D
Ξ － → Λ F － D/3
Ξ ０ → Σ ＋ F + D
Σ － → Λ √(2/3) D
Σ ＋ → Λ √(2/3) D
Ξ － → Σ ０ F + D
Ξ － → Ξ ０ F － D
Fukui University of Technology
Experimental data of g1/ f1 :
015.0718.0: eep
05.025.0: ee
017.0340.0: een
0029.02695.1: eepn
05.028.017.1:0 ee
Fukui University of Technology
● Total decay rate
]},[],[],[],[{,
jijijijiR zbyaCji
where and
)}0()0(Re{],[ jijia
,,,, 11 gfji
]})[0()0(Re{],[jijijib
y and z are coefficients. CR is the radiative correction.
● In our calculations
― omit the form factors f3 and g3 due to have terms of m/M.
― exclude g2 in the framework of standard model because g2 arise from a “second class current”.
― express f2 in term of the anomalous magnetic moments of relevant baryons .
2,
22,
AVM
qji
Fukui University of Technology
● Data of Baryon semileptonic decays used in fitting
DecayA → B
Rate [ 106 s － 1]g1/f1
= e± = μ
n → p 1.1291±0.0010 * 1.2695±0.0029
Λ → p 3.161±0.058 0.597±0.133 0.718±0.015
Σ － → n 6.88±0.24 3.04±0.27 － 0.340±0.017
Ξ － → Λ 3.35±0.37 2.13±2.13 0.25±0.05
Ξ ０ → Σ ＋ 0.931±0.141 1.17±0.28±0.05
Σ － → Λ 0.387±0.018
Σ ＋ → Λ 0.249±0.062
Ξ － → Σ ０ 0.53±0.10
* Rate in 10 － 3s － 1
Fukui University of Technology
● Results
Parameters SU(3) symmetry SU(3) breakingSU(3) and SU(2)
breaking
|Vud| 0.976±0.002 0.976±0.002 0.975±0.002
|Vus| 0.222±0.001 0.221±0.002 0.221±0.002
D 0.793±0.005 0.770±0.004 0.835±0.007
F 0.475±0.004 0.499±0.001 0.477±0.007
α － － － 0.949±0.200
β － － 0.205±0.105 － 1.301±0.211
a － 0.454±0.213 0.099±0.049
b － 0.067±0.049 0.072±0.005
c － 0.065±0.055 0.043±0.005
h － － 0.099±0.050 － 0.031±0.010
χ2/ d.o.f. 2.77 1.02 0.89
Fukui University of Technology
004.0475.0 F
005.0793.0 D
006.0599.0 D
F
77.2dof/2
eepn
eep0
ee ＋0
ee 0－
een－
● SU(3) flavor symmetry case
Fukui University of Technology
007.0477.0 F
007.0835.0 D
010.0572.0 D
F
eep0
ee ＋0
ee 0－
een－
89.0dof/2
● Both SU(3) and SU(2) flavor symmetry breaking case
eepn
Fukui University of Technology
● Predictions of the unmeasured 11 / fg
n p
Λ ０
Ξ － Ξ0
Σ0Σ ＋Σ －
measuredunmeasured
g1 / f1 SU(3) symmetry SU(3) breakingSU(3) and SU(2)
breaking
Ξ － → Ξ ０ － 0.318±0.006 － 0.148±0.082 － 0.144±0.082
Ξ － → Σ ０ 1.269±0.006 1.270±0.011 1.283±0.033
Σ － → Λ * 0.648±0.004 0.607±0.039 0.601±0.041
Σ ＋ → Λ * 0.648±0.004 0.607±0.039 0.668±0.041
not used in fitno listed on PDG
* only g1 for Σ －→ Λ and Σ ＋→ Λ
Taking into account the SU(2) flavor symmetry
breaking
Fukui University of Technology
● Test of our results n p
Λ ０
Ξ － Ξ0
Σ0Σ ＋Σ －
measuredunmeasurednot used in fitno listed on PDG
Σ － → Λ SU(3) symmetry SU(3) breakingSU(3) and SU(2)
breaking
|Vud| ( = cosθc ) 0.976±0.002 0.976±0.002 0.975±0.002
g1 0.648±0.004 0.607±0.039 0.601±0.041
g1 cosθc 0.632±0.004 0.593±0.038 0.586±0.040
by M. Bourquin, Z. Phys. C12, 307 (1982) .
016.0572.0cos1 cg
Fukui University of Technology
§4 Δs content in the nucleon
)GeV7.10(015.0010.0126.0
91
91
94
21
)(
22
1
0 11
Q
sdudxxg pp
● Nucleon spin content from Δs quarks
9
1
2
33 1 D
FDs p
● ΔΣand Δs content from our results on F and D
First moment of pol. quarks SU(3) symmetry SU(3) breaking
SU(3) and SU(2) breaking
Δs － 0.203±0.054 － 0.243±0.054 － 0.188±0.054
ΔΣ 0.024±0.162 0.000±0.162 0.037±0.162
Fukui University of Technology
§5 Summary
● We have suggested a new formula for SU(3) structure constants F and D including SU(3) and SU(2) flavor symmetry breaking effects.
● Using present experimental data, g1/ f1 and decay rates, the numerical results for both SU(3) and SU(2) flavor symmetry breaking were
compared with
007.0835.0 D007.0477.0 F
010.0572.0/ DF
004.0475.0SU(3) F 005.0793.0SU(3) D
006.0599.0/ SU(3) DF .
Fukui University of Technology
● The value of ( g1cosθc) for Σ －→ Λ obtained from our results F and D with both SU(3) and SU(2) flavor symmetry breaking is consistent with the experimental data. ● At the LO of QCD, Δs becomes － 0.188±0.055 for both SU(3) and SU(2) flavor symmetry breaking case, while that is － 0.203±0.054 for SU(3) flavor symmetry case on the EMC result.
