2. (2S) decays and 12%ruleM. Appelquist and H. D. Politzer, PRL34, 43 (1975)F= [M,/2/Φ(0)/2(3)=(2/9m）(2-9）3（号）3mgThe leptonic width via one photon into il is(4)F,=M/24(0)/2=（号）(号）3mgwhere ~rAlthough separately these calcula-This is the famoustionsare not trustworthy,the ratio(or notorious)1025(5)Th（2/9m）（m2_9)5/α"12% rule".is independentof wave-functioneffectsBy'-xBy'-e+e_ = 12%Qn=iBJ/-xBJ/μ-e+e-6
M. Appelquist and H. D. Politzer, PRL34, 43 (1975) 𝑄ℎ = 𝐵ψ′→𝑋 𝐵J/ψ→𝑋 = 𝐵ψ′→𝑒 +𝑒 − 𝐵J/ψ→𝑒+𝑒− = 12% This is the famous (or notorious) “12% rule”. 6
"12% rule"(2S) → pn_,pn+: 3-bodyπ*π-π°*KKT, YTTT? Multi-body. Radiative decay7
“12% rule” 𝜓(2𝑆) → 𝑝𝑛LJ𝜋 −,𝑝LJ𝑛𝜋+ 𝜋 +𝜋 −𝜋 0𝐾 +𝐾 − 𝛾𝐾𝐾LJ 𝜋, γηππ • 3-body • Multi-body • Radiative decay 7
PRD74.12004（2006)'→3-body150150(b)(a)E921±40914±42100100pnT15050中110.600.800.901.001.101.200.700.700.800.901.001.200.601.10recoilmassofp元(GeVic3)recoil massofp元+(GeV/c2)MainBG.forBBMf.s1.pn元-2.pn元-元083.元0
’→3-body 921±40 914±42 PRD74, 12004 (2006) 8
BESII:PRD71,072006 (2005)y'-→3-bodyBESII:PRD74,12004 (2006)ModeQh(%)B(2S)→x(10-4)BJ/±→x(10-3)t12.1 ± 1.6pn-2.45 ± 0.11 ± 0.212.02 ±0.17pn+2.52±0.12 ±0.221.93 ± 0.1713.1 ± 1.8ppr01.32 ± 0.10 ± 0.151.09 ± 0.0912.1 ± 1.90.58 ± 0.11 ± 0.072.09 ± 0.182.8 ±0.7ppn+ : PDG valueSuppressed!!B(pp°) : B(pnπ-) : B(p+) 1 : 2 : 29
Suppressed!! ’→3-body BESII: PRD71, 072006 (2005) BESII: PRD74, 12004 (2006) 9
Multi-body y' decays BESII, PRD73, 052004 (2006)b(2S)→K+K-π+π-° final state300T00人(a)40fo(1710)Tcontinum10(3)N10200302010000.000.150.300.450.000.150.300.450.851.11.351.6D.0winvariantmass(GeV/c)Yyinvariantmass(GeV/c)#invariantmass (GeV/c)K*K"invariantmass (GeV/c)120(892)+K*(a30p100(892)04080603020604020490201020.09g030.65031.450.851.051.251.450.50.70.91.31.50.50.70.91.11.50.851.051.251.113korktinvariantmass(GeV/c)k'n"orktinvariantmass (GeV/)ninvariantmass(GeV/c)ntortxinvariantmass(GeV/c)10
Multi-body ’ decays BESII, PRD73, 052004 (2006) 10