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

SLIDE 1

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

SLIDE 2

1

Introduction

2

J/psi production at the B factories double charmonium production Inclusive J/ψ production

3

J/ψ production at the Tevatron and LHC QCD Correction to color-singlet J/ψ production QCD Correction to color-octet J/ψ production Other improtant Progress

4

the other c → J/ψ fragmentation function J/ψ production in Z decay J/ψ production from Υ Decay

5

The αsv 2 correction or higher-order correction

6

Summary

2 / 45

SLIDE 3

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 αs 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

SLIDE 4

4 / 45

SLIDE 5

e+e− → J/ψ + ηc

Experimantal Data

BELLE: σ[J/ψ + ηc] × Bηc [≥ 2] = (25.6 ± 2.8 ± 3.4) fb BARAR: σ[J/ψ + ηc] × Bηc [≥ 2] = (17.6 ± 2.8+1.5

−2.1) fb [?, ?, ?]

LO NRQCD Predictions

2.3 ∼ 5.5 fb

[?, ?, ?] 5 / 45

SLIDE 6

e+e− → J/ψ + ηc

Experimantal Data

BELLE: σ[J/ψ + ηc] × Bηc [≥ 2] = (25.6 ± 2.8 ± 3.4) fb BARAR: σ[J/ψ + ηc] × Bηc [≥ 2] = (17.6 ± 2.8+1.5

−2.1) fb [?, ?, ?]

LO NRQCD Predictions

2.3 ∼ 5.5 fb

[?, ?, ?]

NLO QCD corrections

K ≡ σNLO/σLO ∼ 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

SLIDE 7

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 + ηc 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

SLIDE 8

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 + ηc 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

SLIDE 9

LO NRQCD Predictions:

e+e− → J/ψ + c¯ c 0.07 ∼ 0.20pb e+e− → J/ψ + gg 0.15 ∼ 0.3pb e+e− → J/ψ(3P8

J ,1 S8 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:

BARAR σ[e+e− → J/ψ + X] = (2.54 ± 0.21 ± 0.21) pb CLEO σ[e+e− → J/ψ + X] = (1.9 ± 0.20) pb BELLE σ[e+e− → J/ψ + X] = (1.45 ± 0.10 ± 0.13) pb 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¯ c] = (0.74 ± 0.08+0.09

−0.08) pb

σ[e+e− → J/ψ + Xnon−c¯

c]

= (0.43 ± 0.09 ± 0.09) pb

[?] 7 / 45

SLIDE 10

Cross section at NLO for e+e− → J/ψ + gg σ(1) = σ(0)

1 + αs(µ)

π

a(ˆ

s) + β0 ln µ 2mc

mc(GeV)

αs(µ) σ(0)(pb) a(ˆ s) σ(1)(pb) σ(1)/σ(0) 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

SLIDE 11

e+e− → J/ψ + c¯ c

(a) (b)

(a1) (a2) (a3) (a4) (b1) (b2) (b3) (b4) (b5) (b6) (c1) (c2)

σ(1) = σ(0)

1 + αs(µ)

π

a(ˆ

s) + β0 ln µ 2mc

mc(GeV)

αs(µ) σ(0)(pb) a(ˆ s) σ(1)(pb) σ(1)/σ(0) 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 mc with the renormalization scale µ = 2mc 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

SLIDE 12

More about the scale and comparision with data

Use Brodsky, Lepage and Mackenzie (BLM) scale setting [?] σ(1) = σ(0)(µ∗)[1 + αs(µ∗) π b(ˆ s)]. mc(GeV) αs(µ∗) σ(0)(pb) b(ˆ s) σ(1)(pb) σ(1)/σ(0) 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 mc. The renormalization scale µ = µ∗ ∼ mc. 10 / 45

SLIDE 13

Momentum distribution of inclusive J/ψ production with µ = µ∗ and mc = 1.4 GeV is taken for the J/ψcc channel. The contribution from the feed-down of ψ′ has been added to all curves by multiplying a factor of 1.29. 11 / 45

SLIDE 14

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

SLIDE 15

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

SLIDE 16

Constraint for color-octect matrix element of c¯ c(1S8

0, 3P8 J)

σ[e+e− → J/ψ + Xnon−c¯

c]

= (0.43 ± 0.09 ± 0.09) pb σ[e+e− → J/ψ + Xnon−c¯

c]color−singleTh

> (0.43) pb σ[e+e− → J/ψ + Xnon−c¯

c]color−octetTh

> (0.6) pb From the contribution of e+e− → J/ψ(1S8

0,3 P8 J ) + g at NLO PRD81, (2010) Y. J. Zhang, Y. Q. Ma, K. Wang and K. T. Chao

14 / 45

SLIDE 17

Introduction: NRQCD Formalism

The cross section of h hadroproduction is σ[pp → hx] = dx1dx2G i

pG j pˆ

σ[ij → (c¯ c)nx]Oh

n,

(1) where p is either a proton or anti-proton, the indices i, j run over all the partonic species and n represents the c¯ c intermediate states (3S1

1,3S8 1,1S8 0, 3P8 J ) for J/ψ and ψ′, and (3P1 J , 3S8 1) for χcJ.

double expansions in αs 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

SLIDE 18

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(1S8

0, 3S8 1) production and polariozation

QCD Correction to color-octet J/ψ(1S8

0, 3S8 1,3 P8 J ) production

QCD Correction to color-octet J/ψ(1S8

0, 3S8 1,3 P8 J ) polarization

QCD Correction to χcJ(3S8

1,3 P1 J ) production

Untill now, there are: pt distributioin of J/ψ yield for prompt J/ψ hadroproduction at QCD NLO pt distributioin of J/ψ polarization for direct J/ψ hadroproduction at QCD NLO feeddown of χcJ 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: pt 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

SLIDE 19

Polarization of Heavy Quarkonium The polarisation is defined from the dilepton decay of inclusively produced vector mesons and the general observable distribution is W (cos ϑ, ϕ) ∝ 1 (3 + λϑ) (1 + λ cos2 ϑ + λϕ sin2 ϑ cos 2ϕ + λϑϕ sin 2ϑ cos ϕ) ,

where ϑ and ϕ are the (polar and azimuthal) angles of the positive lepton with, respectively, the polarisation axis z and the production plane xz (with the colliding particles and the decaying meson in it).

The polarization factor λ is λ = σT − 2σL σT + 2σL (2) where λ = +1 completely transverse polarization λ = 0 unpolarization λ = −1 completely longitudinal polarization

In the helicity frame the polar axis coincides with the flight direction of the meson in the centre-of-mass frame of the colliding hadrons. In the Collins-Soper (CS) frame, the polar axis reflects, the direction of the relative velocity of the colliding partons.a 17 / 45

SLIDE 20

QCD Correction to color-singlet J/ψ production

Pt distribution of J/ψ production at QCD NLO was calculated in PRL98,252002 (2007),

J. Campbell, F. Maltoni F. Tramontano

Some technique problems must be solved to calculate J/ψ polarization Pt distribution of J/ψ polarization at QCD NLO was calculated in

PRL100,232001 (2008), B. Gong and J. X. Wang

18 / 45

SLIDE 21

QCD Correction to color-singlet Υ production

Υ polarization drastically changes from transverse polarization dominant at LO into longitudinal polarization dominant at NLO Pt distribution of Υ polarization at QCD NLO was calculated with detail in

PRD78 074011 (2008), B. Gong and J. X. Wang Partly NNLO calculation for Υ production calculated by PRL101, 152001(2008), P. Artoisenet, John M. Campbell, J.P. Lansberg, F. Maltoni, F. Tramontano

19 / 45

SLIDE 22

20 / 45

SLIDE 23

QCD Correction to J/ψ(3S1

1 , 1S8 0 , 3S8 1 ) production

To fit the Tevatron Pt distribution give more Oψ

8 (1

S0) = 0.075 GeV3 and less Oψ

8 (3

S1) = 0.0021 GeV3 than they are at LO fitting The experimental data with pt < 6 GeV have to abandon PLB673:197,2009, Erratum-ibid.693:612,2010 , B. Gong X. Q. Li and J. X. Wang Correction to J/ψ(3S1

1 , 1S8 0 , 3S8 1 , 3P8 J ) production was done without calculation of polarization, by

PRL 106, 042002,2011, Yan-Qing Ma, Kai Wang, Kuang-Ta Chao PRL 106, 022003,2011, Mathias Butenschoen, Bernd A. Kniehl 21 / 45

SLIDE 24

QCD Correction to prompt J/ψ(1S8

0, 3S8 1, 3P8 J ) production

PRL 106, 042002,2011, Yan-Qing Ma, Kai Wang, Kuang-Ta Chao 22 / 45

SLIDE 25

QCD Correction to J/ψ(3S1

1, 1S8 0, 3S8 1, 3P8 J ) production

pT [GeV] (a) dσ/dpT(pp

–→J/ψ+X) × B(J/ψ→µµ) [nb/GeV]

√s

– = 1.96 TeV

|y| < 0.6 CDF data CS, LO CS, NLO CS+CO, LO CS+CO, NLO 10

4

10

3

10

2

10

1

1 10 10 2 4 6 8 10 12 14 16 18 20 0.5 1 1.5 2 2.5 3 4 6 8 10 12 14 16 18 20 10 20 30 40 50 60 4 6 8 10 12 14 16 18 20 pT [GeV] (b) pT [GeV] CDF Data / CSM CDF Data / NRQCD pT [GeV] (c) dσ/dpT(pp

–→J/ψ+X) × B(J/ψ→µµ) [nb/GeV]

√s

– = 1.96 TeV

|y| < 0.6 CDF data

3S[1] 1

, NLO

1S[8]

, NLO

3S[8] 1

, NLO

3P[8] J

, NLO

3P[8]

J

, NLO Total, NLO 10

4

10

3

10

2

10

1

1 10 10 2 4 6 8 10 12 14 16 18 20 pT [GeV] (b) dσ/dpT(pp→J/ψ+X) × B(J/ψ→µµ) [nb/GeV] √s

– = 7 TeV

1.6 < |y| < 2.4 CMS data CS, LO CS, NLO CS+CO, LO CS+CO, NLO 10

3

10

2

10

1

1 10 10 2 10 3 4 6 8 10 12 14 16 18 20

PRL 106, 022003,2011, Mathias Butenschoen, Bernd A. Kniehl 23 / 45

SLIDE 26

QCD Correction to polarization of J/ψ(1S8

0, 3S8 1, 3P8 J ) direct production

PRL 108, 248004,2012 Kuang-Ta Chao, Yan-Qing Ma, Hua-Sheng Shao, Kai Wang, Yu-Jie Zhang 24 / 45

SLIDE 27

QCD Correction to polarization of J/ψ(3S1

1, 1S8 0, 3S8 1, 3P8 J ) direct production

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 3 4 5 6 7 8 9 10

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 3 4 5 6 7 8 9 10 pT [GeV] (c) pT [GeV] λφ(pT) λθ(pT) ALICE data CS, LO CS, NLO CS+CO, LO CS+CO, NLO Collins-Soper frame 2.5 < y < 4 √s

– = 7 TeV

pp → J/ψ + X

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 3 4 5 6 7 8 9 10

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 3 4 5 6 7 8 9 10 pT [GeV] (b) pT [GeV] λφ(pT) λθ(pT) ALICE data CS, LO CS, NLO CS+CO, LO CS+CO, NLO Helicity frame 2.5 < y < 4 √s

– = 7 TeV

pp → J/ψ + X

1
0.8
0.6
0.4
0.2

0.2 0.4 0.6 0.8 1 5 10 15 20 25 30

0.2
0.15
0.1
0.05

0.05 0.1 0.15 0.2 5 10 15 20 25 30 pT [GeV] (a) pT [GeV] λφ(pT) λθ(pT) CDF data: Run I / II / CS, LO CS, NLO CS+CO, LO CS+CO, NLO Helicity frame |y| < 0.6 √s

– = 1.96 TeV

pp

– → J/ψ + X

PRL 108, 172002,2012, Mathias Butenschoen, Bernd A. Kniehl 25 / 45

SLIDE 28

Relativistic Correction to color-octet J/ψ(3S1

1, 1S8 0, 3S8 1, 3P8 J ) production

10 20 30 40 50

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 3s11 1s08 3s18 3pj8 LHC @ 7TeV y p T (GeV) R 10 20 30 40 50

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 3s11 1s08 3s18 3pj8 LHC @ 7TeV y p T (GeV) R 5 10 15 20 25 30 35 40 45 50

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 3s11 1s08 3s18 3pj8 LHC @ 14TeV y p T (GeV) R 5 10 15 20 25 30 35 40

2.0
1.5
1.0
0.5

0.0 0.5 1.0 1.5 3s11 1s08 3s18 3pj8 Tevatron @ 1.96TeV y p T (GeV) R

ArXiv:1203.0207, gng-Zhi Xu, Yi-Jie Li, Kui-Yong Liu, and Yu-Jie Zhang 26 / 45

SLIDE 29

QCD Correction to prompt J/ψ(3S1

1, 1S8 0, 3S8 1, 3P8 J ) production and polarization

In addtion to all the calculation for J/ψ, we need to calculate the polarization of χcJ(3P1

J ,3 S8 1). At LO, there are three partonic processes:

g(p1) + g(p2) → J/ψ

3

P(1)

J

(p3) + g(p4),

g(p1) + q(p2) → J/ψ

3

P(1)

J

(p3) + q(p4),

q(p1) + q(p2) → J/ψ

3

P(1)

J

(p3) + g(p4).

There are eight processes involved in the real corrections: gg → J/ψ

3

P(1)

J

gg,

gg → J/ψ

3

P(1)

J

qq,

gq → J/ψ

3

P(1)

J

gq,

qq → J/ψ

3

P(1)

J

gg,

qq → J/ψ

3

P(1)

J

qq,

qq → J/ψ

3

P(1)

J

q′q′,

qq → J/ψ

3

P(1)

J

qq,

qq′ → J/ψ

3

P(1)

J

qq′,

ArXiv:1205.6682, Bin Gong, Lu-Ping Wan, Jian-Xiong Wang and Hong-Fei Zhang 27 / 45

SLIDE 30

The present status and problem

It is well known that the uncertainties in pt distribution of charmonium hadroproduction yield from charm-quak mass mc, NRQCD scale µΛ, renormalization scale µr and factorization scale µf are large at small pt

range. And recent work on relativistic correction to J/ψ hadroproduction

shows that the correction is negtive and large at small pt range (pt < 10GeV .). For large pt range, the large logarithm term ln(pt/mc) will appear even with the default choice of all the scales µr = µf = pt, µΛ = mc and it may ruin the result without proper treatment of this term. In the other side, it very clearly show in the previous fitting and also this fitting that the experimental data for pt < 7 and pt > 15 can not be represeted very welll simultaneously.

28 / 45

SLIDE 31

QCD Correction to prompt J/ψ(3S1

1, 1S8 0, 3S8 1, 3P8 J ) production

Figure: pt distribution of prompt J/ψ and ψ′ hadroproduction. The CDF and LHCb data are taken in the fitting.

ArXiv:1205.6682, Bin Gong, Lu-Ping Wan, Jian-Xiong Wang and Hong-Fei Zhang 29 / 45

SLIDE 32

QCD Correction to ψ′(3S1

1, 1S8 0, 3S8 1, 3P8 J ) polarization

Figure: Polarization parameter λ of J/ψ′ in helicity(left) and CS(right) frames.

ArXiv:1205.6682, Bin Gong, Lu-Ping Wan, Jian-Xiong Wang and Hong-Fei Zhang 30 / 45

SLIDE 33

QCD Correction to χcJ(3P1

J , 3S8 1) → J/ψ polarization

Figure: Polarization parameter λ of J/ψ in helicity(left) and CS(right) frames.

ArXiv:1205.6682, Bin Gong, Lu-Ping Wan, Jian-Xiong Wang and Hong-Fei Zhang 31 / 45

SLIDE 34

QCD Correction to prompt J/ψ(3S1

1, 1S8 0, 3S8 1, 3P8 J ) polarization

Figure: Polarization parameter λ of prompt J/ψ hadroproduction in helicity(left) and CS(right) frames.

ArXiv:1205.6682, Bin Gong, Lu-Ping Wan, Jian-Xiong Wang and Hong-Fei Zhang 32 / 45

SLIDE 35

QCD Correction to color-octet Υ(3S1

1, 1S8 0, 3S8 1) production

PRD 83:114021,2011, B. Gong, J. X. Wang and H. F. Zhang

33 / 45

SLIDE 36

QCD Correction to color-octet Υ(3S1

1, 1S8 0, 3S8 1, 3P8 J ) production

ArXiv:1201.6012 Kai Wang, Yan-Qing Ma, Kuang-Ta Chao 34 / 45

SLIDE 37

A new factorization scheme for J/ψ hadronproduction

The main point is to extended the fragmentation factorization from: one-parton fragment into hadron to: two-parton fragment into hadron There will be more fragmentation function needed in this scheme.

10

5

10

4

10

3

10

2

10

1

1 10 √s=1.96 TeV |y|<0.6 dσ/dpT×B(ψ→µµ)

1
0.5

4 6 8 10 12 14 16 18 20 pT (GeV) α PRL 108 (2012) 102002, Zhong-Bo Kang, Jian-Wei Qiu and George Sterman 35 / 45

SLIDE 38

double-quarkonium production at the Large Hadron Collider

Testing Charmonium Production Mechamism via Polarized J/ψ Pair Production at the LHC J.Phys. G37 (2010) 075019, Cong-Feng Qiao, Li-Ping Sun, Peng Sun Inclusive double-quarkonium production at the Large Hadron Collider JHEP 1101 (2011) 070, P. Ko, Chaehyun Yu, Jungil Lee p + p → J/ψ + Υ + X as a clean probe to the quarkonium production mechanism Phys.Rev. D83 (2011) 054015, P. Ko, Chaehyun Yu, Jungil Lee J/ψ Pair Production at the Tevatron with √s = 1.96 TeV arXiv:1204.1700, Cong-Feng Qiao, Li-Ping Sun 36 / 45

SLIDE 39

The fragmentation function of c → J/ψ at QCD NLO

NLO Fragmentation function of c → J/ψ with µr = 2mc (The curves with lower peaks are LO ones). The limit without √s dependence is seen. ArXiv:1102.0118, B. Gong, R. Li and J. X. Wang 37 / 45

SLIDE 40

Experimental and Leading-order Theoretical Results.[Acciarri:1998] Br(Z → J/ψprompt + X) = (2.1+1.4

−1.2) × 10−4

Dominant process: Z → J/ψ + c¯ c + X, and the total decay width is presented as ΓNLO(µ) = ΓLO(µ)[1 + αs(µ) π (A + β0ln µ 2mQ + Bnf )]. (3) Brtotal = (7.3 ∼ 10) × 10−5 The result is presented in: PRD82, (2010), Li and J. X. Wang, The Experimental Data points from PRD 59, 054016 1999.

38 / 45

SLIDE 41

The situation for J/ψ production in Υ decay

LO NRQCD Predictions:

Br(Υ → J/ψ(3S8

1 ) + gg) = 6.2 × 10−4

,M. Napsuciale, Phys. Rev. D 57, 5711 (1998) Br(Υ → J/ψ + c¯ cg) = 5.9 × 10−4 ,S. Y. Li, Q. B. Xie and Q. Wang, Phys. Lett. B 482, 65 (2000) Br(Υ → J/ψ + gg) = order at × 10−4 ,????

Experimental Data for Br(Υ → J/ψ + X):

CLEO(11 ± 4 ± 2) × 10−4Phys. Lett. B 224, 445 ARGUS < 6.8 × 10−4Z. Phys. C55, 25(1992) CLEO(6.4 ± 0.4 ± 0.6) × 10−4Phys. Rev. D70, 072001(2004) The situation is quite strange ???? The correct leading order prediction is BDirect(Υ → J/ψ + c¯ cg) = 3.9 × 10−5.

Z. G. He and J. X. Wang, Phys.Rev.D81:054030,2010.

Part of NLO prediction from Υ → J/ψ + gg is BDirect(Υ → J/ψ + gg) = 3.1 × 10−5.

Z. G. He and J. X. Wang, Phys.Rev. D82 (2010) 094033.

The full QCD correction for the inclusive J/ψ production in Υ decay would be a very interesting and challenge work for explaining the experimental data.

39 / 45

SLIDE 42

The αs correction

QCD corrections to e+e−toJ/ψ(ψ(2S)) + χcJ(J = 0, 1, 2) at B Factories Belle BaBar LO result NLO result LO result σ × B>2(0)[?] σ × B>2[?] (µ = 2mc) (µ = 2mc ) (µ = √s/2) σ(J/ψ + χc0) 6.4 ± 1.7 ± 1.0 10.3 ± 2.5+1.4

−1.8

6.0 ± 0.9 9.5 ± 1.2 4.0 ± 0.8 σ(J/ψ + χc1)

1.02+0.08

−0.10

0.93+0.04

−0.07

0.68+0.09

−0.10

σ(J/ψ + χc2)

1.47+0.01

−0.05

1.15+0.05

−0.08

0.97+0.07

−0.08

σ(J/ψ + χc1) + σ(J/ψ + χc2) <5.3 at 90% C.L.

2.49+0.09

−0.16

2.08+0.08

−0.14

1.65+0.16

−0.19

σ(ψ(2S) + χc0) 12.5 ± 3.8 ± 3.1

2.6 ± 0.4

4.1 ± 0.5 1.7+0.4

−0.3

σ(ψ(2S) + χc1)

0.44+0.03

−0.05

0.40+0.01

−0.03

0.29 ± 0.04 σ(ψ(2S) + χc2)

0.63+0.01

−0.02

0.49+0.02

−0.03

0.42+0.02

−0.04

σ(ψ(2S) + χc1) + σ(ψ(2S) + χc2) <8.6 at 90% C.L.

1.06+0.05

−0.06

0.89+0.04

−0.06

0.71+0.06

−0.08

Phys.Rev. D84 (2011) 034022, Kai Wang, Yan-Qing Ma, Kuang-Ta Chao QCD corrections to J/ψ(ψ(2S)) + χcJ production at B Factories JHEP 1110 (2011) 141, Hai-Rong Dong, Feng Feng, Yu Jia 40 / 45

SLIDE 43

The αsv 2 correction

αsv2 correction to Hadronic and Electromagnetic Decays of 1S0 Heavy Quarkonium Phys.Rev. D83 (2011) 114038, Huai-Ke Guo, Yan-Qing Ma, Kuang-Ta Chao The αsv2 correction to pseudoscalar quarkonium decay to two photons JHEP 1106 (2011) 097, Yu Jia, Xiu-Ting Yang, Wen-Long Sang 41 / 45

SLIDE 44

The αsv 2 correction

The αsv2 correction to J/ψ → 3γ,Very huge αsv2 correction

1.0 1.5 2.0 2.5 3.0 20 15 10 5 5 10 Μ GeV BrJΨ3Γ 105 BESIII

ArXiv:1210.6337, Feng Feng, Yu Jia, Wen-Long Sang O(sv2) correction to e+e− → J/ψ + ηc at B factories

Table: Individual contributions to the predicted σ[e+e− → J/ψ + ηc ] at √s = 10.58 GeV, labeled by powers of αs and

v. The cross sections are in units of fb.

αs(µr ) σ(0) σ(1) σ(0)

2

σ(1)

2

αs(

√s 2 ) = 0.211

4.40 5.22 1.72 0.73 αs(2mc) = 0.267 7.00 7.34 2.73 0.24 Hai-Rong Dong, Feng Feng, Yu Jia, Phys.Rev. D85 (2012) 114018 42 / 45

SLIDE 45

Resummation of relativistic corrections to exclusive productions of charmonia in e+ e- collisions The two exclusive processes, e+e− → ηc + γ and e+e− → J/ψ + J/ψ, at the center-of-momentum energy √s = 10.58 GeV within the framework of the nonrelativistic QCD factorization approach. A class of relativistic corrections is resummed to all orders in the heavy-quark velocity v and the corrections are large negative. arXiv:1211.4111, Ying Fan, Jungil Lee, Chaehyun Yu 43 / 45

SLIDE 46

Summary

For B-factories: NRQCD at NLO of αs and v can well described J/ψ production data. strong constraint to the values of color-octect matrix element of c¯ c(1S8

0, 3P8 J) to almost zero. The dominant part c¯

c(3S8

1) for

hadronproduction is still there. The polarization problem for prompt J/psi hadroproduction is still there even when the QCD NLO fitting and prediction are archived. The more precision experimental measurements at LHC are needed to clarify the situation. The experimental measurements at BESIII on J/ψ polarization where J/ψ feeddown from χcJ or ψ(2s) will be very helpful to clarify the situation. More theoretical Progresses are needed on relativistic coorection, .... to solve the polarization pzzle.

44 / 45

SLIDE 47

Thank you!

45 / 45