Applications of the light-conedistribution amplitudes for quakonia中科学院研究生院Graduate University of the CASDeshan YangBasedonYuJia&DSYNPB814,217(2009):inpreparation2010.4.18南昌大学第八届全国高能物理大会
Applications of the light-cone distribution amplitudes for quakonia 2010.4.18 南昌大学 第八届全国高能物理大会 1 Based on Yu Jia & DSY, NPB814, 217 (2009); in preparation Graduate University of the CAS Deshan Yang
Outline1. Introduction & Motivation2. Example 1 - e*e--→nby3.Example2-h-→Yy4. Summary22010.4.18南昌大学第八届全国高能物理大会
Outline 2010.4.18 南昌大学 第八届全国高能物理大会 2 1. Introduction & Motivation 2. Example 1 – 3. Example 2 – 4. Summary 𝑒 +𝑒 − → 𝜂𝑏𝛾
Exclusive OCD ProcessesHistory: iny(q)r(p)-→元(p')1979-81,Brodskyetal(元(p)|TLjm(x) jem(O)|0)ET =iF(")p° pqwhen,Qe forrq'fz>asan be factorizedF(Q") = (" dx,(x, μ,)T(x,O’; μr)Where the light-cone distribution amplitude (LCDA)can bedefinedas(元(p)(x)y"[x, 0],q(O)|0) = -if, p" " duep*,(u, μr)The same LCDA can appearin the factorization formulaeinotherexclusiveprocesses,suchaspion electro-magneticform-factorand B exclusivehadronicdecays.32010.4.18南昌大学第八届全国高能物理大会
Exclusive QCD Processes 2010.4.18 南昌大学 第八届全国高能物理大会 3 History: in 1979-81, Brodsky et al when , the form-factor can be factorized Where the light-cone distribution amplitude (LCDA) can be defined as The same LCDA can appear in the factorization formulae in other exclusive processes, such as pion electro-magnetic form-factor and B exclusive hadronic decays. 0 2 . . ( ) [ ( ) (0)] 0 ( ) v em em F T p T j x j iF Q p q = 1 2 2 0 ( ) ( , ) ( , ; ) F Q dx x T x Q = F F 2 2 2 Q q = − QCD 1 0 5 0 ( ) ( ) [ ,0] (0)] 0 ( , ) iup x F p q x x q if p due u = − * 0 ( ) ( ) ( ) q p p →
The LCDA for quarkoniumDefinition: 1981, Chernyak & Zhintnisky(H[00('。)](p')(x)"s[x, 0(0)]0) = -if p"" [dueup*(u, μ,)> Could be used in procleesses HM> Different from the LCDAs of light mesons,it can be calculated perturbatively.> The RGE running is governed by theBrodsky-Lepage equation金0as(CFVo(a, ) s(y, μ),dy2元1o2010.4.18南昌大学第八届全国高能物理大会
The LCDA for quarkonium 2010.4.18 南昌大学 第八届全国高能物理大会 4 1 1 0 5 0 [ ( )]( ) ( ) [ ,0] (0)] 0 ( , ) iup x H QQ S p Q x x Q if p due u H H F = − Definition: 1981, Chernyak & Zhintnisky ➢ Could be used in procecesses ➢ Different from the LCDAs of light mesons, it can be calculated perturbatively. ➢ The RGE running is governed by the Brodsky-Lepage equation * → → H B HM
Charmonium production at B factories> Exlusive quarknium production at B-factorife : le+e~- /Wnl× Bl22]=(25.6±2.8±3.4)bBaBar: o[e+e- → J /Wnc] × Bnc[≥ 2] = (17.6 ± 2.8±2:5)fbAbe et al (Belle Collaboration), PRL 2002Aubert et al (BaBar Collaboration),PRD2005;> Suprises for theoristsfS- → J /ncl ~ (2.3 - 5.5)fboletLONRQCD:BraatenandLee,PRD2003:PRD2005;Liu,HeandChao,PLB2003Hagiwara,KouandQiao,PLB2003;52010.4.18南昌大学第八届全国高能物理大会
Charmonium production at B factories 2010.4.18 南昌大学 第八届全国高能物理大会 5 ➢ Exlusive quarknium production at Bfactories Abe et al (Belle Collaboration), PRL 2002; Aubert et al (BaBar Collaboration), PRD 2005; ➢ Suprises for theorists LONRQCD: Braaten and Lee, PRD 2003; PRD 2005; Liu, He and Chao, PLB 2003; Hagiwara, Kou and Qiao, PLB 2003; Belle : 𝜎[𝑒 +𝑒 − → 𝐽Τ𝛹𝜂𝑐 ] × 𝐵 𝜂𝑐[≥ 2] = (25.6 ± 2.8 ± 3.4)fb BaBar: 𝜎[𝑒 +𝑒 − → 𝐽Τ𝛹𝜂𝑐 ] × 𝐵 𝜂𝑐[≥ 2] = (17.6 ± 2.8±2.1 1.5 )fb 𝜎[𝑒 +𝑒 − → 𝐽Τ𝛹𝜂𝑐 ] ≈ (2.3 − 5.5)fb