RADIATIVE and NONLEPTONIC HYPERON DECAYS in BROKEN SU(3) P. - - PowerPoint PPT Presentation

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RADIATIVE and NONLEPTONIC HYPERON DECAYS in BROKEN SU(3) P. - - PowerPoint PPT Presentation

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RADIATIVE and NONLEPTONIC HYPERON DECAYS in BROKEN SU(3) P. enczykowski Institute of Nuclear Physics Polish Academy of Sciences Krakw, Poland BEACH 2006 Lancaster July 6 Puzzle #1: S:P problem in NLHD 50 years old parity

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SLIDE 1

RADIATIVE and NONLEPTONIC HYPERON DECAYS in BROKEN SU(3)

  • P. Żenczykowski

Institute of Nuclear Physics Polish Academy of Sciences Kraków, Poland

BEACH 2006 Lancaster July 6

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SLIDE 2
  • P. Ż. - BEACH 2006 - Lancaster, UK

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Puzzle #1: „S:P problem in NLHD”

  • SU(3) amplitudes (f,d) -

Experimental values (Donoghue, Golowich, Holstein (DGH) 1986 review) : Parity viol. fS = 3.0 × 10 ─ 5 MeV dS = ─ 1.2 × 10 ─ 5 MeV Parity cons. fP = 4.7 × 10 ─ 5 MeV dP = ─ 2.6 × 10 ─ 5 MeV dP / dS ≈ 2.2 fP / dP ≈ ─ 1.8 fS / dS ≈ ─ 2.5

50 years old parity violating – parity conserving Non-Leptonic amplitudes Hyperon Decays (Σ+ → pπ0, etc.)

  • Current algebra (CA), PCAC, soft-pion theorems (1960’s):

fS = fP dS = dP

?

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  • P. Ż. - BEACH 2006 - Lancaster, UK

3

A) Hara’s theorem (1964): “Parity-violating amplitude D ( Σ+→pγ ) must vanish in SU(3) limit” For broken SU(3) (c.f. magnetic moments) expect small asymmetry:

| α ( Σ+ → pγ ) | ~ 0.2

Puzzle #2: „large negative asymmetry in Σ+→pγ”

40 years old WRHD - Weak Radiative Hyperon Decays

Λ→nγ, Ξ0 → Λγ, Ξ0→Σ0γ, Ξ−→Σ−γ

B) PDG now:

α ( Σ+ → pγ ) = ─ 0.76 ± 0.08

C) Theoretical conflicts between various approaches to parity-violating amplitudes (no deep problems with parity conserving amplitudes)

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  • P. Ż. - BEACH 2006 - Lancaster, UK

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Theoretical conflicts between various approaches to parity-violating amplitudes

1) Hadron-level pole model (Gavela et al. 1981):

  • agrees with Hara’s theorem in SU(3) limit

Negative α ( Σ+→ pγ ) ~ − 0.8 for broken SU(3) 2) Simple quark model (Kamal Riazuddin 1983):

  • violates Hara’s theorem in SU(3) limit

Negative α ( Σ+→ pγ ) ~ − 0.6 for broken SU(3) 3) Hadron-level VMD+SU(6) model (P.Ż. 1989):

  • violates Hara’ theorem in SU(3) limit

Negative α ( Σ+→ pγ ) ~ − 0.9 for broken SU(3)

Σ+ p

γ

½−

weak s u u W u u u d

Σ+ p γ ρωφ

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  • P. Ż. - BEACH 2006 - Lancaster, UK

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Experimental resolution of puzzle #2

NA48 – BEACH 2004

A) 1995 – J. Lach & P.Ż.: Status of Hara’s theorem may be clarified through measurement of α ( Ξ0 → Λγ ) asymmetry:

− + 0.8 + −

Hara’s - viol.

− − 0.8 − − (0)

Hara’s - OK

Ξ0→Σ0γ Ξ0→Λγ Λ→nγ Σ+→pγ

Process: B) 2004 – NA48, A.Lai et al..,Phys.Lett.B584,251(2004); BEACH 2004:

α ( Ξ0→ Λγ ) = − 0.78 ± 0.19

Small theory errors:

± 0.15

Large theory errors Experimentally hard

HARA OK HARA OK

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  • P. Ż. - BEACH 2006 - Lancaster, UK

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Theoretical resolution of puzzle #2

P.Ż. – BEACH 2002, Acta Phys. Pol. B34 (2003)

A) Quark model calculations violate confinement: in SU(3) limit intermediate quark enters its mass shell and propagates to infinity

s u u W u u u d

B) VMD+SU(6) calculation violates proper connection between weak couplings

  • f pseudoscalar and vector mesons:

Σ+ p γ ρωφ In VMD+SU(6) calculation (P.Ż.,1989) weak parity-violating couplings of vector mesons to hyperons and nucleons evaluated from Non-Leptonic Hyperon Decays (pseudoscalar couplings) as in Desplanques, Donoghue, Holstein (DDH,1980) calculations

  • f weak NNρ,… couplings (needed in nuclear parity violation)
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  • P. Ż. - BEACH 2006 - Lancaster, UK

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„DDH” versus „non-soft pion ↔ vector meson”

P.Ż. – BEACH 2002, Acta Phys. Pol. B34 (2003) Par.viol. A(NLHD) = commutator term + non-soft-pion correction term DDH: P.Ż.: SU(6) neglect sizable sizable dominates (standard assumption) Hara’s theorem: Contributions to vector meson couplings: full zero zero full VMD violates satisfies α(Ξ0→Λγ) + 0.8 − 0.8

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  • P. Ż. - BEACH 2006 - Lancaster, UK

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NLHD & WRHD for broken SU(3)

P.Ż. – Phys. Rev. D73, 076005 (2006) Parity-conserving NLHD (data + ½+ pole model) Parity-violating WRHD (data on asymmetries, B.R. + parity conserving WRHD + ½− pole model) − VMD → Parity-violating vector meson couplings (predicted)

↓ SU(6)

Non-soft-pion correction term in parity-violating NLHD (predicted) SU(3) broken Parity-conserving WRHD (predicted)

→

+SU(6) +VMD

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SLIDE 9
  • P. Ż. - BEACH 2006 - Lancaster, UK

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Parity- conserving amplitudes

N D F d f p B

P P

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = → Σ

+

1 1 2 1 ) ( π

s P

m Dd F m N Δ =

π 8

2 MeV F 94 =

π

details NLHD

…

MeV m MeV m

s

190 1130

8

= Δ =

81 . 44 . = = D F

P.Ż. dP= −3×10−5 fP= 5.8×10−5 DGH review: dP= −2.6×10−5 fP= 4.7×10−5 (kaon poles) 15.4 18.8 0.9 41.3 28.6 P.Ż. 16.6±0.8 22.1±0.5

  • 1.4±0.2

42.4±0.4 26.6±1.3 data

Ξ−

−

Λ0

−

Σ−

−

Σ+

+

Σ+

) ( 2 ) ( 1 ) ( U B B B m m g e B B C

f i f i f i

→ + = → γ

( )

D N d f pU B

p p P P

µ µ µ − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ − = → Σ

+ Σ +

1 2 ) ( WRHD …

e/g - VMD factor; g = 5.0

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  • P. Ż. - BEACH 2006 - Lancaster, UK

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Parity-violating amplitudes

) ( 2 ) ( 1 ) ( U B B A m m g e B B D

f i f i f i

→ − = → γ

R R

s b x x x pU A 2 3 1 1 ) 1 )( 1 ( 6 2 9 1 ) (

2

+ − − − + = → Σ

+

ε

bR cR

3 1 570 190 ≈ ≈ Δ Δ = MeV MeV m x

s

ω

ε – additional SU(3) breaking (as in magnetic moments)

bR ≈ +5.3 ×10−7 sR ≈ −0.75×10−7 WRHD Correction terms in NLHD (fR, dR) b = 4d/Fπ c = 6(f+d)/Fπ Data on B.R. & asymmetries + parity conserving WRHD amplitudes

sR contains cR

cR≈0 B.R. ( Ξ− → Σ−γ ) small

Corections fR, dR to fS,dS

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  • P. Ż. - BEACH 2006 - Lancaster, UK

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Sensitive to SU(3) breaking in par.cons. amplitudes

Results

0.16 0.127±0.023 Ξ−→Σ−γ 4.42 3.33±0.10 Ξ0→Σ0γ 1.02 1.16±0.08 Ξ0→Λγ 0.77 1.75±0.15 Λ→nγ 0.72 1.23±0.05 Σ+→pγ this approach data +0.80 + 1.0±1.3 Ξ−→Σ−γ −0.92 −0.63±0.09 Ξ0→Σ0γ −0.97 −0.78±0.19 Ξ0→Λγ −0.93 Λ→nγ −0.67 −0.76±0.08 Σ+→pγ this approach data

Branching ratios Asymmetries

uncertain reliable

−0.5 −0.333 Ξ0→Σ0γ −0.128 −0.192 Ξ0→Λγ 0.048 0.192 Λ→nγ 0.196 Σ+→pγ SU(3) broken x=1/3, ε=2/3 SU(3) x=0,ε=1

Resolution of PUZZLE #2

Coefficients at bR (relative size of two-quark contribution)

20% errors at amplitude level

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  • P. Ż. - BEACH 2006 - Lancaster, UK

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Resolution of puzzle #2 (S:P in NLHD)

bS = bP+bR/(1+x) cS ≈ cP fS = fP dS = dP Commutator contribution in p.v.

  • nly:

bS = bP cS = cP With non-soft pion contribution (in units of 10−7) − 5 ≈ − 11.1 12 ≈ 13.4 With x =1/3 (in units of 10−7) − 5 ≈ − 6.6 12 ≈ 13.4 Differences between S and P waves mainly from two-quark contributions If x: ≈ 0 dP/dS ≈ 2 fP/dP ≈ −1.8 fS/dS ≈ −2.6

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  • P. Ż. - BEACH 2006 - Lancaster, UK

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Conclusions:

simultaneous description of WRHD and NLHD

in SU(3)-breaking VMD model Commutator + non-soft-pion correction All WRHD described In particular: large negative Σ

+

→p γ asymmetry through SU(3) breaking Simultaneous resolution

  • f the dominant part
  • f the S:P problem in NLHD

Questions: relation to nuclear parity-violation (Desplanques, Donoghue, Holstein paper)