The current status of NRQCD descriptions of J / and system - PowerPoint PPT Presentation

The current status of NRQCD descriptions of J /ψ and Υ system Jian-Xiong Wang Institute of High Energy, Chinese Academy of Science, Beijing HaPhy2012-11: APCTP-KIAS miniworkshop for Physics on Heavy Quarkonia November 23 (Fri), 2012, KIAS, Seoul, Korea 1 / 45

Introduction 1 J/psi production at the B factories 2 double charmonium production Inclusive J /ψ production J /ψ production at the Tevatron and LHC 3 QCD Correction to color-singlet J /ψ production QCD Correction to color-octet J /ψ production Other improtant Progress the other 4 c → J /ψ fragmentation function J /ψ production in Z decay J /ψ production from Υ Decay The α s v 2 correction or higher-order correction 5 Summary 6 2 / 45

Introduction Perturbative and non-perturbative QCD, hadronization, factorization Color-singlet and Color-octet mechanism was proposed based on NRQCD for heavy quarkonium Why so serious to on the test: Clear signal to detect J /ψ , very limited number of nonperturbative parameters, double perturbative expansions on α s and v (the vilocity of heavy quark in quarkonium) are better since b and c-quark is heavy. J /ψ production at the B factories J /ψ photoproduction at HERA J /ψ production and polarization at the Tevatron and LHC LO theoretical predication were given before more than 15 years NLO theoretical predications were given within last 5 years. The QCD NLO calculations can adequately describe the experimental data? There are still many difficulties. 3 / 45

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e + e − → J /ψ + η c Experimantal Data σ [ J /ψ + η c ] × B η c [ ≥ 2] = (25 . 6 ± 2 . 8 ± 3 . 4) fb BELLE: BARAR : σ [ J /ψ + η c ] × B η c [ ≥ 2] = (17 . 6 ± 2 . 8 +1 . 5 − 2 . 1 ) fb [ ? , ? , ? ] LO NRQCD Predictions 2 . 3 ∼ 5 . 5 fb [ ? , ? , ? ] 5 / 45

e + e − → J /ψ + η c Experimantal Data σ [ J /ψ + η c ] × B η c [ ≥ 2] = (25 . 6 ± 2 . 8 ± 3 . 4) fb BELLE: BARAR : σ [ J /ψ + η c ] × B η c [ ≥ 2] = (17 . 6 ± 2 . 8 +1 . 5 − 2 . 1 ) fb [ ? , ? , ? ] LO NRQCD Predictions 2 . 3 ∼ 5 . 5 fb [ ? , ? , ? ] NLO QCD corrections K ≡ σ NLO /σ LO ∼ 2 First given in PRL96, (2006) Y. J. Zhang, Y. J. Gao and K. T. Chao Confirmed by the analytic result in PRD77, (2008), B. Gong and J. X. Wang Relativistic corrections K ∼ 2 PRD67, (2007) E. Braaten and J. Lee AIP Conf. Proc. (2007), G.T. Bodwin, D. Kang, T. Kim, J. Lee and C. Yu PRD75, (2007), Z. G. He, Y. Fan and K. T. Chao PRD77,(2008),G.T. Bodwin, J. Lee and C. Yu 5 / 45

e + e − → J /ψ + J /ψ Problem LO NRQCD prediction indicates that the cross section of this process is large than that of J /ψ + η c production by a factor of 1.8, but no evidence for this process was found at the B factories. PRL90, (2003) G. T. Bodwin, E. Braaten and J. Lee PRD70, (2004), K. Abe, et al 6 / 45

e + e − → J /ψ + J /ψ Problem LO NRQCD prediction indicates that the cross section of this process is large than that of J /ψ + η c production by a factor of 1.8, but no evidence for this process was found at the B factories. PRL90, (2003) G. T. Bodwin, E. Braaten and J. Lee PRD70, (2004), K. Abe, et al NLO QCD corrections Greatly decreased, with a K factor ranging from − 0 . 31 ∼ 0 . 25 depending on the renormalization scale. Might explain the situation. PRL100, (2008) B. Gong and J. X. Wang 6 / 45

LO NRQCD Predictions: e + e − → J /ψ + c ¯ c 0 . 07 ∼ 0 . 20pb e + e − → J /ψ + gg 0 . 15 ∼ 0 . 3pb J , 1 S 8 e + e − → J /ψ ( 3 P 8 0 ) + g 0 . 3 ∼ 0 . 8pb PRL76,(1996), E. Braaten and Y. C. Chen, PLB577,(2003), K.Y. Liu, Z.G. He and K.T. chao, .... Experimental Data: σ [ e + e − → J /ψ + X ] = (2 . 54 ± 0 . 21 ± 0 . 21) pb BARAR σ [ e + e − → J /ψ + X ] = (1 . 9 ± 0 . 20) pb CLEO σ [ e + e − → J /ψ + X ] = (1 . 45 ± 0 . 10 ± 0 . 13) pb BELLE σ [ e + e − → J /ψ + c ¯ c + X ] = (0 . 87 +0 . 21 − 0 . 19 ± 0 . 17) pb [ ? , ? , ? , ? , ? ] New BELLE Data σ [ e + e − → J /ψ + X ] = (1 . 17 ± 0 . 02 ± 0 . 07) pb σ [ e + e − → J /ψ + c ¯ (0 . 74 ± 0 . 08 +0 . 09 c ] = − 0 . 08 ) pb σ [ e + e − → J /ψ + X non − c ¯ c ] = (0 . 43 ± 0 . 09 ± 0 . 09) pb [ ? ] 7 / 45

Cross section at NLO for e + e − → J /ψ + gg � µ � 1 + α s ( µ ) � ��� σ (1) = σ (0) a (ˆ s ) + β 0 ln π 2 m c σ (0) (pb) σ (1) (pb) σ (1) /σ (0) m c (GeV) α s ( µ ) a (ˆ s ) 1.4 0.267 0.341 2.35 0.409 1.20 1.5 0.259 0.308 2.57 0.373 1.21 1.6 0.252 0.279 2.89 0.344 1.23 Consistent results from two group: PRL102, (2009) Y. Q. Ma, Y. J. Zhang and K. T. Chao PRL102, (2009) B. Gong and J. X. Wang Relativistic Correction enchance results about a factor 1.3 from two group: PRD81, (2010) Z. G. He, Y. Fan and K. T. Chao PRD82, (2010). Y. Jia 8 / 45

e + e − → J /ψ + c ¯ c ( a 1 ) ( a 2 ) ( a 3 ) ( a 4 ) ( b 1 ) ( b 2 ) ( b 3 ) ( b 4 ) ( b 5 ) ( b 6 ) ( c 1 ) ( c 2 ) ( a ) ( b ) � µ � 1 + α s ( µ ) � ��� σ (1) = σ (0) a (ˆ s ) + β 0 ln π 2 m c σ (0) (pb) σ (1) (pb) σ (1) /σ (0) m c (GeV) α s ( µ ) a (ˆ s ) 1.4 0.267 0.224 8.19 0.380 1.70 1.5 0.259 0.171 8.94 0.298 1.74 1.6 0.252 0.129 9.74 0.230 1.78 Cross sections with different charm quark mass m c with the renormalization scale µ = 2 m c and √ s = 10 . 6 GeV . The former result given by PRL98, (2007) Y. J. Zhang and K. T. Chao confirmed by PRD80, (2009) B. Gong and J. X. Wang 9 / 45

More about the scale and comparision with data Use Brodsky, Lepage and Mackenzie (BLM) scale setting [ ? ] σ (1) = σ (0) ( µ ∗ )[1 + α s ( µ ∗ ) b (ˆ s )] . π σ (0) (pb) σ (1) (pb) σ (1) /σ (0) m c (GeV) α s ( µ ∗ ) b (ˆ s ) µ ∗ (GeV) 1.4 0.348 0.381 3.77 0.540 1.42 1.65 1.5 0.339 0.293 4.31 0.429 1.47 1.72 1.6 0.332 0.222 4.90 0.337 1.52 1.79 Cross sections with different charm quark mass m c . The renormalization scale µ = µ ∗ ∼ m c . 10 / 45

Momentum distribution of inclusive J /ψ production with µ = µ ∗ and m c = 1 . 4 GeV is taken for the J /ψ cc channel. The contribution from the feed-down of ψ ′ has been added to all curves by multiplying a factor of 1.29. 11 / 45

Momentum and angular distributions of inclusive J /ψ production. The contribution from the feed-down of ψ ′ has been added to all curves by multiplying a factor of 1.29. 12 / 45

Polarization parameter α and angular distribution parameter A of J /ψ as functions of p . 13 / 45

c ( 1 S 8 0 , 3 P 8 Constraint for color-octect matrix element of c ¯ J ) σ [ e + e − → J /ψ + X non − c ¯ c ] = (0 . 43 ± 0 . 09 ± 0 . 09) pb σ [ e + e − → J /ψ + X non − c ¯ c ] color − singleTh > (0 . 43) pb σ [ e + e − → J /ψ + X non − c ¯ c ] color − octetTh > (0 . 6) pb From the contribution of e + e − → J /ψ ( 1 S 8 0 , 3 P 8 J ) + g at NLO PRD81, (2010) Y. J. Zhang, Y. Q. Ma, K. Wang and K. T. Chao 14 / 45

Introduction: NRQCD Formalism The cross section of h hadroproduction is � � d x 1 d x 2 G i p G j c ) n x ] �O h σ [ pp → hx ] = p ˆ σ [ ij → ( c ¯ n � , (1) where p is either a proton or anti-proton, the indices i , j run over all the c intermediate states ( 3 S 1 1 , 3 S 8 1 , 1 S 8 partonic species and n represents the c ¯ 0 , 3 P 8 J ) for J /ψ and ψ ′ , and ( 3 P 1 J , 3 S 8 1 ) for χ cJ . double expansions in α s and the heavy-quark velocity v . predication can be sysmatically improved with these two perturbative expansions. limited number of universal long-distance matrix elements to be extracted from experiment. 15 / 45

Introduction In last five years, there were a few very important progresses in the next-to-leading Order (NLO) QCD correction calculation: QCD Correction to color-singlet J /ψ production QCD Correction to color-singlet J /ψ polarization QCD Correction to color-octet J /ψ ( 1 S 8 0 , 3 S 8 1 ) production and polariozation 1 , 3 P 8 QCD Correction to color-octet J /ψ ( 1 S 8 0 , 3 S 8 J ) production 1 , 3 P 8 QCD Correction to color-octet J /ψ ( 1 S 8 0 , 3 S 8 J ) polarization 1 , 3 P 1 QCD Correction to χ cJ ( 3 S 8 J ) production Untill now, there are: p t distributioin of J /ψ yield for prompt J /ψ hadroproduction at QCD NLO p t distributioin of J /ψ polarization for direct J /ψ hadroproduction at QCD NLO feeddown of χ cJ about 20 − 30% to prompt J /ψ production and very improtant. prompt: included the J /ψ feeddown from excited charmonium state than direct production We need: p t distributioin of J /ψ polarization for prompt J /ψ hadroproduction at QCD NLO We have finished this work and presented in a recent paper ArXiv:1205.6682, Bin Gong, Lu-Ping Wan, Jian-Xiong Wang and Hong-Fei Zhang 16 / 45