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

RADIATIVE and NONLEPTONIC HYPERON DECAYS in BROKEN SU(3) P. Ż enczykowski Institute of Nuclear Physics Polish Academy of Sciences Kraków, Poland BEACH 2006 Lancaster July 6

Puzzle #1: „S:P problem in NLHD” 50 years old parity violating – parity conserving Non-Leptonic amplitudes Hyperon Decays ( Σ + → p π 0 , etc.) SU(3) amplitudes (f,d) - � Experimental values (Donoghue, Golowich, Holstein (DGH) 1986 review) : f S = 3.0 × 10 ─ 5 MeV d S = ─ 1.2 × 10 ─ 5 MeV Parity viol. f P = 4.7 × 10 ─ 5 MeV d P = ─ 2.6 × 10 ─ 5 MeV Parity cons. f P / d P ≈ ─ 1.8 f S / d S ≈ ─ 2.5 d P / d S ≈ 2.2 Current algebra (CA), PCAC, soft-pion theorems (1960’s): � f S = f P ? d S = d P P. Ż . - BEACH 2006 - Lancaster, UK 2

Puzzle #2: „large negative asymmetry in Σ + → p γ ” 40 years old WRHD - Weak Radiative Hyperon Decays Λ→ n γ , Ξ 0 → Λγ , Ξ 0 →Σ 0 γ , Ξ − →Σ − γ A) Hara’s theorem (1964): “Parity-violating amplitude D ( Σ + → p γ ) must vanish in SU(3) limit” For broken SU(3) (c.f. magnetic moments) expect small asymmetry: | α ( Σ + → p γ ) | ~ 0.2 α ( Σ + → p γ ) = ─ 0.76 ± 0.08 B) PDG now: C) Theoretical conflicts between various approaches to parity-violating amplitudes (no deep problems with parity conserving amplitudes) P. Ż . - BEACH 2006 - Lancaster, UK 3

Theoretical conflicts between various approaches to parity-violating amplitudes γ 1) Hadron-level pole model (Gavela et al. 1981): ½ − Σ + - agrees with Hara’s theorem in SU(3) limit Negative α ( Σ + → p γ ) ~ − 0.8 for broken SU(3) p weak 2) Simple quark model (Kamal Riazuddin 1983): s u u - violates Hara’s theorem in SU(3) limit u W d Negative α ( Σ + → p γ ) ~ − 0.6 for broken SU(3) u u γ 3) Hadron-level VMD+SU(6) model (P. Ż . 1989): ρωφ - violates Hara’ theorem in SU(3) limit Σ + Negative α ( Σ + → p γ ) ~ − 0.9 for broken SU(3) p P. Ż . - BEACH 2006 - Lancaster, UK 4

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 ( Ξ 0 → Λγ ) asymmetry: Process: Σ + → p γ Λ→ n γ Ξ 0 →Λγ Ξ 0 →Σ 0 γ Hara’s - OK − (0) − − 0.8 − Hara’s - viol. − + + 0.8 − Large theory errors Small theory Experimentally hard errors: ± 0.15 B) 2004 – NA48, A.Lai et al..,Phys.Lett.B584,251(2004); BEACH 2004: α ( Ξ 0 → Λγ ) = − 0.78 ± 0.19 HARA OK HARA OK P. Ż . - BEACH 2006 - Lancaster, UK 5

Theoretical resolution of puzzle #2 P. Ż . – BEACH 2002, Acta Phys. Pol. B34 (2003) A) Quark model calculations violate confinement: s u u in SU(3) limit intermediate quark enters its mass shell u W d and propagates to infinity u u γ B) VMD+SU(6) calculation violates proper ρωφ connection between weak couplings Σ + p of pseudoscalar and vector mesons: 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 of weak NN ρ ,… couplings (needed in nuclear parity violation) P. Ż . - BEACH 2006 - Lancaster, UK 6

„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 dominates neglect DDH: (standard assumption) SU(6) sizable sizable P. Ż .: Contributions to vector full zero meson couplings: full zero VMD Hara’s theorem: violates satisfies α ( Ξ 0 →Λγ ) + 0.8 − 0.8 P. Ż . - BEACH 2006 - Lancaster, UK 7

NLHD & WRHD for broken SU(3) P. Ż . – Phys. Rev. D73, 076005 (2006) Parity-conserving NLHD → +SU(6) Parity-conserving WRHD (data + ½ + pole model) +VMD (predicted) Parity-violating WRHD Parity-violating − VMD → (data on asymmetries, B.R. vector meson couplings + parity conserving WRHD (predicted) + ½ − pole model) ↓ SU(6) Non-soft-pion correction term SU(3) broken in parity-violating NLHD (predicted) P. Ż . - BEACH 2006 - Lancaster, UK 8

Parity- conserving amplitudes NLHD WRHD details 2 ⎛ ⎞ ⎛ − ⎞ 1 m Dd 0 . 44 1130 f F m MeV F = = ⎜ ⎟ 8 ( 0 ) 1 ⎜ 1 ⎟ N = P + 8 B Σ → p π = P − N ⎜ ⎟ 2 ⎝ ⎠ F Δ m 190 ⎝ ⎠ 0 . 81 d D Δ m = MeV D = π s P s … 94 F = MeV π P. Ż . d P = − 3 × 10 − 5 Σ − Ξ − Σ + Σ + Λ 0 − − − 0 + f P = 5.8 × 10 − 5 data 26.6±1.3 42.4±0.4 -1.4±0.2 22.1±0.5 16.6±0.8 DGH review: P. Ż . 28.6 41.3 0.9 18.8 15.4 d P = − 2.6 × 10 − 5 f P = 4.7 × 10 − 5 (kaon poles) 1 e ( ) ( 0 ) C B → B γ = B B → B U i f ( ) 2 i f g m + m i f … ⎛ ⎞ f N ⎜ ⎟ ( ) ( 0 ) 2 1 e/g - VMD factor ; g = 5.0 + P B Σ → pU = ⎜ − ⎟ µ − µ Σ + p ⎝ ⎠ d µ D P p P. Ż . - BEACH 2006 - Lancaster, UK 9

Parity-violating amplitudes WRHD Correction terms in NLHD (f R , d R ) 1 e ( ) ( 0 ) b R D B B A B B U → γ = → ( ) 2 i f i f g m − m i f 1 6 ( 1 )( 1 ) 1 x + − ε − x ( 0 ) + A Σ → pU = b + s 9 2 1 2 3 2 R R x − c R 190 1 Δ m MeV s R contains c R s x = ≈ ≈ 570 3 Δ ω MeV ε – additional SU(3) breaking (as in magnetic moments) Data on B.R. & asymmetries b R ≈ +5.3 ×10 − 7 b = 4d/F π + parity conserving WRHD amplitudes s R ≈ − 0.75 × 10 − 7 c = 6(f+d)/F π Corections f R , d R B.R. ( Ξ − → Σ − γ ) small c R ≈ 0 to f S ,d S P. Ż . - BEACH 2006 - Lancaster, UK 10

Results 20% errors at amplitude level Branching ratios Sensitive to Asymmetries SU(3) breaking in par.cons. data this data this amplitudes approach approach Σ + → p γ Σ + → p γ 1.23±0.05 0.72 − 0.76±0.08 − 0.67 uncertain Λ→ n γ 1.75±0.15 0.77 Λ→ n γ − 0.93 Ξ 0 → Λγ 1.16±0.08 1.02 reliable Ξ 0 → Λγ − 0.78±0.19 − 0.97 Ξ 0 → Σ 0 γ Ξ 0 → Σ 0 γ 3.33±0.10 4.42 − 0.63±0.09 − 0.92 Ξ − → Σ − γ 0.127±0.023 0.16 Ξ − → Σ − γ + 1.0±1.3 +0.80 SU(3) SU(3) broken x=0, ε =1 x=1/3, ε =2/3 Resolution of Σ + → p γ 0 0.196 PUZZLE #2 Coefficients at b R Λ→ n γ 0.192 0.048 (relative size of Ξ 0 → Λγ − 0.192 − 0.128 two-quark contribution) Ξ 0 → Σ 0 γ − 0.333 − 0.5 P. Ż . - BEACH 2006 - Lancaster, UK 11

Resolution of puzzle #2 (S:P in NLHD) Commutator (in units of 10 − 7 ) f S = f P b S = b P contribution in p.v. − 5 ≈ − 11.1 d S = d P c S = c P only: 12 ≈ 13.4 With x =1/3 (in units of 10 − 7 ) With non-soft pion b S = b P +b R /(1+x) − 5 ≈ − 6.6 contribution c S ≈ c P 12 ≈ 13.4 If x: ≈ 0 Differences between S and P waves mainly d P /d S ≈ 2 from two-quark contributions f P /d P ≈ − 1.8 f S /d S ≈ − 2.6 P. Ż . - BEACH 2006 - Lancaster, UK 12

Conclusions: simultaneous description of WRHD and NLHD in Commutator SU(3)-breaking + non-soft-pion VMD model correction All WRHD described Simultaneous resolution In particular: large negative Σ of the dominant part + → p γ asymmetry through SU(3) breaking of the S:P problem in NLHD Questions: relation to nuclear parity-violation (Desplanques, Donoghue, Holstein paper) P. Ż . - BEACH 2006 - Lancaster, UK 13