1. Determination on F and D with SU(3) symmetry breaking effects and Δs distributions in the nucleon
Teruya Yamanishi

2. §１　Introduction
● Data used numerical analyses for polarized quark distribution functions
－ At LO QCD, first moment of pol. quark distribution functions
Since the EMC group has reported the value of the proton spin structure function g1p, many theorists and experimentalists made large efforts to understand the proton spin structure.
At present, a common recognition is that the first moment of the longitudinally polarized strange quark in the nucleon is a negative and large, and the amount of the quark carrying the proton spin is small.
However, these result is obtained by the values of SU(3) structure constants F and D with an assumption of SU(3) flavor symmetry for the octet baryon.
So, the real picture of the proton spin may be not implied.
Here I propose a new formula for F and D with SU(3) and/or SU(2) flavor symmetry breaking effects and attempt to estimate ones.
So far, there are several ideas.

3. Baryon semileptonic decays ;
－ F and D
Baryon semileptonic decays ;
F and D for SU(3) flavor symmetry
in these analyses
Δs : negative and large
ΔΣ : small
Since the EMC group has reported the value of the proton spin structure function g1p, many theorists and experimentalists made large efforts to understand the proton spin structure.
At present, a common recognition is that the first moment of the longitudinally polarized strange quark in the nucleon is a negative and large, and the amount of the quark carrying the proton spin is small.
However, these result is obtained by the values of SU(3) structure constants F and D with an assumption of SU(3) flavor symmetry for the octet baryon.
So, the real picture of the proton spin may be not implied.
Here I propose a new formula for F and D with SU(3) and/or SU(2) flavor symmetry breaking effects and attempt to estimate ones.
So far, there are several ideas.
Estimations of F and D with SU(3) and/or SU(2) breaking effects

4. §2 Baryon semileptonic decays
● Matrix element of V-A transition for M
where
Since the EMC group has reported the value of the proton spin structure function g1p, many theorists and experimentalists made large efforts to understand the proton spin structure.
At present, a common recognition is that the first moment of the longitudinally polarized strange quark in the nucleon is a negative and large, and the amount of the quark carrying the proton spin is small.
However, these result is obtained by the values of SU(3) structure constants F and D with an assumption of SU(3) flavor symmetry for the octet baryon.
So, the real picture of the proton spin may be not implied.
Here I propose a new formula for F and D with SU(3) and/or SU(2) flavor symmetry breaking effects and attempt to estimate ones.
So far, there are several ideas.

5. from N. Cabibbo et al., hep-ph/037298 .
●　Cabibbo model
In generally, from Ademollo – Gatto theorem, the ratio of the axial vector to vector coupling constant is expanded as like this.
from N. Cabibbo et al., hep-ph/

6. §3 F and D with SU(3)and SU(2) flavor breaking
●　In generally, g1(0) is expanded as
with
In generally, from Ademollo – Gatto theorem, the ratio of the axial vector to vector coupling constant is expanded as like this.
●　Here we take m = al + bl 3 8
as SU(2) and SU(3) breaking parameters.

7. Then, at Q2=0, one obtains for g1/ f1 :
Decay
A → B ν
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
Ξ０ → Σ＋
Σ－ → Λ
√(2/3) D
Σ＋ → Λ
Ξ－ → Σ０
Ξ－ → Ξ０ l
・ There are 8 variables ;

8. Experimental data of g1/ f1 :
Since the EMC group has reported the value of the proton spin structure function g1p, many theorists and experimentalists made large efforts to understand the proton spin structure.
At present, a common recognition is that the first moment of the longitudinally polarized strange quark in the nucleon is a negative and large, and the amount of the quark carrying the proton spin is small.
However, these result is obtained by the values of SU(3) structure constants F and D with an assumption of SU(3) flavor symmetry for the octet baryon.
So, the real picture of the proton spin may be not implied.
Here I propose a new formula for F and D with SU(3) and/or SU(2) flavor symmetry breaking effects and attempt to estimate ones.
So far, there are several ideas.

9. y and z are coefficients. CR is the radiative correction.
●　Total decay rate
where and
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 .

10. ●　Data of Baryon semileptonic decays used in fitting
A → B ν
Rate [ 106 s－1]
g1/f1
= e±
= μ
n → p
1.1291± *
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
Ξ０ → Σ＋
0.931±0.141
1.17±0.28±0.05
Σ－ → Λ
0.387±0.018
Σ＋ → Λ
0.249±0.062
Ξ－ → Σ０
0.53±0.10 l l l
* Rate in 10－3s－1

11. |Vud| |Vus| D F α χ2/ d.o.f. β a b c h 0.976±0.002 0.975±0.002
●　Results
Parameters
SU(3) symmetry
SU(3) breaking
SU(3) and SU(2) breaking
|Vud|
0.976±0.002
0.975±0.002
|Vus|
0.222±0.001
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

12. ●　SU(3) flavor symmetry case

13. ●　Both SU(3) and SU(2) flavor symmetry breaking case

14. n p Λ０ Ξ－ Ξ0 Σ0 Σ＋ Σ－ measured unmeasured not used in fit
●　Predictions　of the unmeasured n p Λ０ Ξ－ Ξ0 Σ0 Σ＋ Σ－
measured
unmeasured
not used in fit
no listed on PDG
g1 / f1
SU(3) symmetry
SU(3) breaking
SU(3) and SU(2) breaking
Ξ－ → Ξ０
－0.318±0.006
－0.148±0.082
－0.144±0.082
Ξ－ → Σ０
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 *
0.668±0.041
Taking into account the SU(2) flavor symmetry
breaking
* only g1 for Σ－→Λ and Σ＋→Λ

15. 016 . 572 cos ± = g q n p Λ０ Ξ－ Ξ0 Σ0 Σ＋ Σ－ measured unmeasured
●　Test of our results
measured
unmeasured
not used in fit
no listed on PDG
016 .
572
cos 1 = c g q
by M. Bourquin, Z. Phys. C12, 307 (1982) .
Σ－ → Λ
SU(3) symmetry
SU(3) breaking
SU(3) and SU(2) breaking
|Vud| ( = cosθc )
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

16. First moment of pol. quarks
§4　Δs content in the nucleon
●　Nucleon spin content from Δs quarks
●　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

17. §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
007 .
477 = F
010
572 / D
007 .
835 = D
compared with
004 .
475
SU(3) = F
005 .
793
SU(3) = D
006 .
599 /
SU(3) = D F .

18. symmetry case on the EMC result.
●　 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.