Battlefield for NRQCD guys> NLO OCD Corrections: K~ 2Zhang, Gao, Chao, PRL 2006;Gong, Wang, PRD 2008; Relativistic Corrections: K~ 2Bodwin, Kang, Kim, Lee, Yu, AIP ConfProceeding 2007;He, Fan, Chao, PRD 2007:Triumph? Confusions? Questions?Perturbation stabilityNon-relativistic vs. Relativistic62010.4.18南昌大学第八届全国高能物理大会
Battlefield for NRQCD guys ➢ NLO QCD Corrections: K~ 2 Zhang, Gao, Chao, PRL 2006; Gong, Wang, PRD 2008; ➢ Relativistic Corrections: K~ 2 Bodwin, Kang, Kim, Lee, Yu, AIP Conf. Proceeding 2007; He, Fan, Chao, PRD 2007; ➢ Triumph? Confusions? Questions? ◆ Perturbation stability ◆ Non-relativistic vs. Relativistic 2010.4.18 南昌大学 第八届全国高能物理大会 6
Salute to those guysGong,QWG2008Non-pert. quantities!TLO128Ra-aeR(0)R0)F0-4)g (0)27m2Killrenormalization scale dependenceNLOKi(S)as(n)2mg(0))BoInONLO79:6822193342/±160434K.G)3(2+D)22N24(-4)(-2)80 diagrams in total+1943642165302±64832332-4+h32(32(342-4)+K(S/m2)=aNLO/OLO19+130)4=(8-70)36-4)425+1（-130+19元+8-) ±-3284-1103-6393±696+1722:(8-70)+ 4,451(73-8)32(-4)N(-4):4(2+1)2-4)2010.4.18南昌大学第八届全国高能物理大会
Salute to those guys 2010.4.18 南昌大学 第八届全国高能物理大会 7 Non-pert. quantities! Kill renormalization scale dependence 𝐾(𝑠Τ𝑚𝑐 2 ) = 𝜎 Τ NLO 𝜎LO Gong, QWG2008
NROCD factorizationFor single quarkonium productionM[H) ~ Cn(Q,m)(HOn/0),2On RQCD operator with definite velocity power countingmulti-scale problem: Q>>mstability of the perturbation: large log(Q/m)may need the resummation.82010.4.18南昌大学第八届全国高能物理大会
NRQCD factorization For single quarkonium production ➢ : NRQCD operator with definite velocity power counting ➢ multi-scale problem: Q>>m ➢ stability of the perturbation: large log(Q/m) may need the resummation. 2010.4.18 南昌大学 第八届全国高能物理大会 8
Light-cone frameworkMt i2b65; R 20 4Rods a260reypkFrc(J/b(p)ne(h)Jj)=iQeerae(p)pakgF()Ama(ete"- J/0n)=4ra202/F(o)PLCDA: Non-pert. quantities!64Sragb dida((F(8)=Lead to end-point singularity!-+m/e(=)()[(1-)(1-32)3121(1-2)2+()(D(+),J/Fit to the expr.!o(ete→ J/bnc)7.37fb.2for a=o(ete-- J/bne)20.1fb.fora=1.5~o(ete-- J/bnc)31.7fb.fora=1.75292010.4.18南昌大学第八届全国高能物理大会
Light-cone framework Ma and Si, PRD 2004;Bonder and Chernyak, PLB 2005;Braguta, arXiv:0811.2640[hep-ph] From Ma and Si, PRD 2004; 2010.4.18 南昌大学 第八届全国高能物理大会 9 Fit to the expr.! LCDA: Non-pert. quantities! Lead to end-point singularity!