II. Institut für Theoretische Physik, Universität Hamburg · Institut für Theoretische Physik,...

Heavy-quarkonium theory in the LHC era

Bernd Kniehl

II. Institut für Theoretische Physik, Universität Hamburg

Heavy Flavor and Electromagentic Probes in Heavy Ion CollisionsSeptember 29 – October 1, 2014, INT Seattle

In collaboration with Mathias ButenschönPRL 104 (2010) 072001PRL 106 (2011) 022003

PRD 84 (2011) 051501 (Rapid Communications)PRL 107 (2011) 232001PRL 108 (2012) 172002

MPLA 28 (2013) 1350027 (Brief Reviews)

Introduction Technology Global fit Further tests Polarization Summary

CERN Courier, Volume 52, Issues 1 and 2

Heavy-quarkonium theory in the LHC era Bernd Kniehl


Outline

1 Introduction: CEM, CSM, NRQCD factorization

2 NLO NRQCD: General concept, singularities

3 Global fit: Unpolarized J/ψ yield

4 Further tests: ATLAS, FTPS, ZEUS

5 Polarization: HERA, Tevatron, LHC

6 Summary: NRQCD at the crossroads



Introduction: CEM, CSM, NRQCD factorization

Color evaporation model [Fritzsch 77; Halzen 77; Glück Owens Reya 78]

σJ/ψ ≈ 19

ρJ/ψ

∫ 2mD

2mcdscc

dσcc

dscc

1/9: statistical probability that 3×3 cc pair is asymtotically in color-single state

ρJ/ψ : fraction of charmonia that materialize as J/ψ

Based local parton-hadron duality

Assumes soft-gluon exchange with underlying event

2S+1L[c]J quantum numbers do not enter

Useful qualitative picture, rather than rigorous theory

]c [GeV/T

p0 5 10 15 20

)]c [n

b/(G

eV/

Tpd

)ψ/

J(σd

-110

1

10

210

310

410

510

< 4.5)yLHCb (2.0 <

< 4.5)yPrompt NLO CEM (2.0 <

=7 TeVs

[Schuler Vogt 96; Vogt 99; Frawley Ullrich Vogt 08]Heavy-quarkonium theory in the LHC era Bernd Kniehl


Color-singlet model vs. NRQCD factorization

Color-singlet model [Berger Jones 81; Baier Rückl 81]

cc pair in physical color-singlet state, e.g. cc[3S[1]1 ] for J/ψ.

Nonperturbative information in J/ψ wave function at origin.

Leftover IR divergences for P-wave quarkonia inconsistent!

Predicted cross section factor 101–102 below Tevatron data.

NRQCD factorization [Bodwin Braaten Lepage 95]

Rigorous effective field theory

Based on factorization of soft and hard scales(Scale hierarchy: Mv2∼<ΛQCD ≪ Mv ≪ M)

Theoretically consistent: no leftover singularities.

NNLO proof of factorization [Nayak Qiu Sterman 05]

Can explain hadroproduction at Tevatron.



NRQCD factorization in a nutshell

Factorization theorem σJ/ψ =∑n

σcc[n] · 〈OJ/ψ [n]〉

n: every possible Fock state, including color-octet states.

σcc[n]: production rate of cc[n], calculated in perturbative QCD.

〈OJ/ψ [n]〉: long-distance matrix elements (LDMEs),nonperturbative, extracted from experiment, universal?

Scaling rules [Lepage Magnea2 Nakhleh Hornbostel 92]LDMEs scale with relative velocity v (v2 ≈ 0.2).

scaling v3 (CS state) v7 (CO states) v11

n 3S[1]1

1S[8]0 , 3S[8]

1 , 3P [8]0/1/2 . . .

Double expansion in v and αs.

Leading term in v (n = 3S[1]1 ) corresponds to color-singlet model.



NLO NRQCD calculations

Petrelli Cacciari Greco Maltoni Mangano 98:Photo- and hadroproduction (only 2 → 1 processes)

Klasen BK Mihaila Steinhauser 05:Two-photon scattering (w/o resolved photons)

Butenschön BK 09:Photoproduction (w/o resolved photons)

Zhang Ma Wang Chao 10:e+e− annihilation

Ma Wang Chao 10, Butenschön BK 10:Hadroprduction

Butenschön BK 11:γp and γγ (resolved photons) global fit of CO LDMEs

Butenschön BK 11:Polarization in photoproduction

Butenschön BK 12, Chao Ma K. Wang Y.-J. Zhang 12, Gong, Wan,J.-X. Wang, H.-F. Zhang 12, Shao, Ma, K. Wang, Chao 14:Polarization in hadroprduction



Sample diagrams for J/ψ photoproduction in NRQCD

(a)

γ

g

c

c

g

c

c

(b)

γ

g

c

c

g

c

c

c

g

c

(c)

γ

g

c

c

g

g

c

g

(d)

γ

q

c

c

q

c

g

(e)

γ

q

c

c

q

g

q

q

g

q

(f)

γ

q

c

c

q

g

qg

q



Color and spin projection

Amplitudes for c c[n] production by projector application:

Acc[1S[8]

0 ]= Tr [C8Π0 Acc ] |q=0

Acc[3S[1/8]

1 ]= εα Tr

[

C1/8Πα Acc

]

|q=0

Acc[3P[8]

J ]= εαβ

ddqβ

Tr [C8Πα Acc ] |q=0

Acc : amputated pQCD amplitude for open cc production.

q: relative momentum between c and c.

C1/8: color projectors

Π0/1: spin projectors

ε: polarization vectors and tensors



Main Difference to Previous Calculations

Virtual corrections: Two different approaches:First loop integration, then projectors: (Previous publications)– Loop integrals Coulomb divergent.

First projectors, then loop integration: (Our method)+ No Coulomb singularities.+ One scale less in loop integration.– Loop integrals not standard form.

Where do Coulomb divergences come from?

Projectors: Relative momentum q → 0.

Scalar diagrams with gluon between external c and c, e.g.:

I(q) ≡

P/2+q→

P/2−q→

c

c

limq→0

I(q) = Aq2 +

Bε +C

But: I(0) = Bε +C

=⇒ No Coulomb singularities in dimensional regularization!



Cancellation of divergences

UV divergences: Cancellation within virtual corrections:

Loop integrals

Charm mass renormalization

Strong coupling constant renormalization

Wave function renormalization of external particles

IR divergences: Cancellation between:

Virtual corrections (loop integrals + wave function renormal.)

Soft and collinear parts of real corrections

Universal part absorbed into proton and photon PDFs

Radiative corrections to long distance matrix elements



Overview of IR singularity structure

Absorption in PDFs

Collinear divergences Soft terms #1 Soft terms #2 Soft terms #3

NLO corr. MEsVirtual corrections

overlap

S states

P states

Real corr.:



Radiative Corrections to Long Distance MEs

In NRQCD: Long distance MEs = cc scattering amplitudes:

〈OJ/ψ [n]〉 =

c c

c cO[n]

O[n] = 4-fermion operators(n = 3S[1]

1 , 1S[8]0 , 3S[8]

1 , 3P [8]0/1/2, . . .)

Corrections to 〈OJ/ψ [3S[1/8]1 ]〉 with NRQCD Feynman rules:

c c

c c

3S1

+similar

diagrams∝

4αs

3πm2c

(

1εUV

− 1εIR

)

·

c c

c c3P0

+3P1 +3P2

UV singularity cancelled by renormalization of 4-fermion operat.

IR singularity cancels soft #3 terms of p states!



Global fit at NLO in NRQCD

Fit CO LDMEs to all available world data on J/ψ inclusive production:type

√s collider collaboration reference

pp 200 GeV RHIC PHENIX PRD82(2010)012001pp 1.8 TeV Tevatron I CDF PRL97(1997)572; 578pp 1.96 TeV Tevatron II CDF PRD71(2005)032001pp 7 TeV LHC ALICE NPB(PS)214(2011)56

ATLAS PoS(ICHEP 2010)013CMS EPJC71(2011)1575LHCb EPJC71(2011)1645

γp 300 GeV HERA I H1, ZEUS EPJ25(2002)25; 27(2003)173γp 319 GeV HERA II H1 EPJ68(2010)401γγ 197 GeV LEP II DELPHI PLB565(2003)76e+e− 10.6 GeV KEKB Belle PRD79(2009)071101

Fit values for CO LDMEs:10−2 GeV3+2L feed-down included feed-down subtracted

〈O[1S[8]0 ]〉 4.97±0.44 3.04±0.35

〈O[3S[8]1 ]〉 0.224±0.059 0.168±0.046

〈O[3P [8]0 ]〉 −1.61±0.20 −0.908±0.161

χ2/d.o.f. 857/194 = 4.42 725/194 = 3.74

Note: CO LDMEs ∝ v4 ×〈O[3S[1]1 ]〉 NRQCD velocity scaling rules

√



Comparison with world data

p2T [GeV2]

dσ(e

e→J/

ψ e

e+X

)/dp

2 T [

pb/G

eV2 ]

|y| < 2W < 35 GeVθel < 32 mrad√s

– = 197 GeV

DELPHI dataCS, LOCS, NLOCS+CO, LOCS+CO, NLO

10-3

10-2

10-1

1

10

1 2 3 4 5 6 7 8 9 10

p2T [GeV2]

dσ(e

p→J/

ψ+

X)/

dp2 T [

nb/G

eV2 ]

60 GeV < W < 240 GeV0.3 < z < 0.9Q2 < 1 GeV2

√s– = 314 GeV

CS, LOCS, NLOCS+CO, LOCS+CO, NLO

H1 data: HERA1

10-5

10-4

10-3

10-2

10-1

1

1 10W [GeV]

dσ(e

p→J/

ψ+

X)/

dW [n

b/G

eV]

√s– = 314 GeV, Q2 < 1 GeV2

0.3 < z < 0.9p2

T > 1 GeV2


H1 data: HERA1

10-3

10-2

60 80 100 120 140 160 180 200 220 240

z

dσ(e

p→J/

ψ+

X)/

dz [

nb]

60 GeV < W < 240 GeVp2

T > 1 GeV2Q2 < 1 GeV2

√s– = 314 GeV


H1 data: HERA1

1

10

10 2

0.3 0.4 0.5 0.6 0.7 0.8 0.9

p2T [GeV2]

dσ(e

p→J/

ψ+

X)/

dp2 T [

nb/G

eV2 ]

60 GeV < W < 240 GeV0.3 < z < 0.9

Q2 < 2.5 GeV2

√s– = 319 GeV


H1 data: HERA2

10-6

10-5

10-4

10-3

10-2

10-1

1

1 10 102

W [GeV]

dσ(e

p→J/

ψ+

X)/

dW [n

b/G

eV]

√s– = 319 GeV, Q2 < 2.5 GeV2

0.3 < z < 0.9p2

T > 1 GeV2


H1 data: HERA2

10-3

10-2

60 80 100 120 140 160 180 200 220 240

z

dσ(e

p→J/

ψ+

X)/

dz [

nb]

60 GeV < W < 240 GeVp2

T > 1 GeV2Q2 < 2.5 GeV2√s

– = 319 GeV


H1 data: HERA2

1

10

10 2

0.3 0.4 0.5 0.6 0.7 0.8 0.9

σ(e+

e- →J/

ψ+

X)

[pb]

√s– = 10.6 GeV

CS, LO: σ = 0CS, NLO: σ = (0.24+0.20

-0.09 ) pbCS+CO, LO: σ = 0.23 pbCS+CO, NLO: σ = (0.70+0.35

-0.17 ) pb

BELLE data: σ = (0.43±0.13) pb(J/ψ+cc

– contribution subtracted)

0

0.5

1

1.5

2

2.5

p2T [GeV2]

dσ(e

p→J/

ψ+

X)/

dp2 T [

nb/G

eV2 ]

50 GeV < W < 180 GeV0.4 < z < 0.9Q2 < 1 GeV2

√s– = 300 GeV


ZEUS data10

-4

10-3

10-2

10-1

1

5 10 15 20 25 30

W [GeV]

dσ(e

p→J/

ψ+

X)/

dW [n

b/G

eV]

√s– = 300 GeV, Q2 < 1 GeV2

0.4 < z < 0.9p2

T > 1 GeV2


ZEUS data

10-3

10-2

60 80 100 120 140 160 180

z

dσ(e

p→J/

ψ+

X)/

dz [

nb]

50 GeV < W < 180 GeVp2

T > 1 GeV2Q2 < 1 GeV2

√s– = 300 GeV


ZEUS data

10-1

1

10

10 2

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→ee

) [n

b/G

eV]

√s– = 200 GeV

|y| < 0.35

PHENIX data


10-4

10-3

10-2

10

10

10 2

3 4 5 6 7 8 9 10

-1

1

pT [GeV]

dσ/d

p T(p

p–→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/

GeV

]

√s– = 1.8 TeV

|y| < 0.6

CDF data: Run 1


10-4

10-3

10-2

10-1

10 2

6 8 10 12 14 16 18 20

1

10

pT [GeV]

dσ/d

p T(p

p–→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/

GeV

]

√s– = 1.96 TeV

|y| < 0.6

CDF data: Run 2


10-4

10-3

10-2

10-1

1

10 2

4 6 8 10 12 14 16 18 20

10

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

2.5 < y < 4

ALICE data


10-2

10-1

1

10 2

10 3

3 4 5 6 7 8 9 10

10

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

|y| < 0.75

ATLAS data


10-3

10-2

10-1

1

10

10 2

10 3

4 6 8 10 12 14 16 18 20pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

0.75 < |y| < 1.5

ATLAS data


10-3

10-2

10-1

1

10

10 2

10 3

4 6 8 10 12 14 16 18 20pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

1.5 < |y| < 2.25

ATLAS data


10-3

10-2

10-1

1

10

10 2

10 3

4 6 8 10 12 14 16 18 20pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

|y| < 1.2

CMS data


10-3

10-2

10-1

1

10 3

4 6 8 10 12 14 16 18 20

10

10 2

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

1.2 < |y| < 1.6

CMS data


10-4

10-3

10-2

10-1

1

10 2

10 3

4 6 8 10 12 14 16 18 20

10

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

1.6 < |y| < 2.4

CMS data


10-4

10-3

10-2

10-1

1

10

10 3

4 6 8 10 12 14 16 18 20

10 2

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

2 < y < 2.5

LHCb data


10-3

10-2

10-1

1

10 2

4 6 8 10 12 14

10

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

2.5 < y < 3

LHCb data


10-3

10-2

10-1

1

10 2

4 6 8 10 12 14

10

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

3 < y < 3.5

LHCb data


10-4

10-3

10-2

10-1

1

10 2

4 6 8 10 12 14

10

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

3.5 < y < 4

LHCb data


10-4

10-3

10-2

10-1

1

10 2

4 6 8 10 12 14

10

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

4 < y < 4.5

LHCb data


10-4

10-3

10-2

10-1

1

10 2

4 6 8 10 12 14

10



Comparison with RHIC and Tevatron

RHIC Tevatron II Decomposition ofPHENIX CDF NLO NRQCD

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→ee

) [n

b/G

eV]

√s– = 200 GeV

|y| < 0.35

PHENIX data


10-4

10-3

10-2

10

10

10 2

3 4 5 6 7 8 9 10

-1

1

pT [GeV]

dσ/d

p T(p

p–→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/

GeV

]

√s– = 1.96 TeV

|y| < 0.6

CDF data: Run 2


10-4

10-3

10-2

10-1

1

10

10 2

4 6 8 10 12 14 16 18 20pT [GeV]

dσ/d

p T(p

p–→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/

GeV

]

√s– = 1.96 TeV

|y| < 0.6

CDF data3S[1]

1 , NLO1S[8]

0 , NLO3S[8]

1 , NLO3P[8]

J , NLO-3P[8]

J , NLOTotal, NLO

10-4

10-3

10-2

10-1

1

10

10 2

4 6 8 10 12 14 16 18 20

Data well described by CS+CO at NLO.

CS orders of magnitudes below data.

Sizeable NLO corrections, especially in the 3P [8]J channels.



Comparison with ATLAS and CMS at LHC

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

|y| < 0.75

ATLAS data


10-3

10-2

10-1

1

10

10 2

10 3

4 6 8 10 12 14 16 18 20pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

0.75 < |y| < 1.5

ATLAS data


10-3

10-2

10-1

1

10

10 2

10 3

4 6 8 10 12 14 16 18 20pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

1.5 < |y| < 2.25

ATLAS data


10-3

10-2

10-1

1

10

10 2

10 3

4 6 8 10 12 14 16 18 20

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

|y| < 1.2

CMS data


10-3

10-2

10-1

1

10

10 2

10 3

4 6 8 10 12 14 16 18 20pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

1.2 < |y| < 1.6

CMS data


10-4

10-3

10-2

10-1

1

10

10 2

10 3

4 6 8 10 12 14 16 18 20pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

1.6 < |y| < 2.4

CMS data


10-4

10-3

10-2

10-1

1

10

10 2

10 3

4 6 8 10 12 14 16 18 20



Comparison with ALICE and LHBb at LHC

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

2.5 < y < 4

ALICE data


10-2

10-1

1

10 2

10 3

3 4 5 6 7 8 9 10

10

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

2 < y < 2.5

LHCb data


10-3

10-2

10-1

1

10

10 2

4 6 8 10 12 14pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

2.5 < y < 3

LHCb data


10-3

10-2

10-1

1

10

10 2

4 6 8 10 12 14

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

3 < y < 3.5

LHCb data


10-4

10-3

10-2

10-1

1

10

10 2

4 6 8 10 12 14pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

3.5 < y < 4

LHCb data


10-4

10-3

10-2

10-1

1

10

10 2

4 6 8 10 12 14pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

4 < y < 4.5

LHCb data


10-4

10-3

10-2

10-1

1

10

10 2

4 6 8 10 12 14



Comparison with ZEUS at HERA I

p2T [GeV2]

dσ(e

p→J/

ψ+

X)/

dp2 T [

nb/G

eV2 ]

50 GeV < W < 180 GeV0.4 < z < 0.9Q2 < 1 GeV2

√s– = 300 GeV


ZEUS data10

-4

10-3

10-2

10-1

1

5 10 15 20 25 30

z

dσ(e

p→J/

ψ+

X)/

dz [

nb]

50 GeV < W < 180 GeVp2

T > 1 GeV2Q2 < 1 GeV2

√s– = 300 GeV


ZEUS data

10-1

1

10

10 2

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

z

dσ(e

p→J/

ψ+

X)/

dz [

nb]

50 GeV < W < 180 GeVp2

T > 1 GeV2Q2 < 1 GeV2

√s– = 300 GeV

ZEUS data

3S[1]1 , NLO

1S[8]0 , NLO

3S[8]1 , NLO

-3P[8]J , NLO

Total, NLO

10-1

1

10

10 2

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

W = γp CM energy.

z = fraction of γ energy going to J/ψ in p rest frame.

Compensation of 1S[8]0 vs. 3P [8]

J regular z → 1 behavior.

Data well described by CS+CO at NLO.

CS factor of 3–5 below the data.



Comparison with H1 at HERA I and II

p2T [GeV2]

dσ(e

p→J/

ψ+

X)/

dp2 T [

nb/G

eV2 ]

60 GeV < W < 240 GeV0.3 < z < 0.9Q2 < 1 GeV2

√s– = 314 GeV


H1 data: HERA1

10-5

10-4

10-3

10-2

10-1

1

1 10W [GeV]

dσ(e

p→J/

ψ+

X)/

dW [n

b/G

eV]

√s– = 314 GeV, Q2 < 1 GeV2

0.3 < z < 0.9p2

T > 1 GeV2


H1 data: HERA1

10-3

10-2

60 80 100 120 140 160 180 200 220 240

z

dσ(e

p→J/

ψ+

X)/

dz [

nb]

60 GeV < W < 240 GeVp2

T > 1 GeV2Q2 < 1 GeV2

√s– = 314 GeV


H1 data: HERA1

1

10

10 2

0.3 0.4 0.5 0.6 0.7 0.8 0.9

p2T [GeV2]

dσ(e

p→J/

ψ+

X)/

dp2 T [

nb/G

eV2 ]

60 GeV < W < 240 GeV0.3 < z < 0.9

Q2 < 2.5 GeV2

√s– = 319 GeV


H1 data: HERA2

10-6

10-5

10-4

10-3

10-2

10-1

1

1 10 102

W [GeV]

dσ(e

p→J/

ψ+

X)/

dW [n

b/G

eV]

√s– = 319 GeV, Q2 < 2.5 GeV2

0.3 < z < 0.9p2

T > 1 GeV2


H1 data: HERA2

10-3

10-2

60 80 100 120 140 160 180 200 220 240

zdσ

(ep→

J/ψ

+X

)/dz

[nb

]

60 GeV < W < 240 GeVp2

T > 1 GeV2Q2 < 2.5 GeV2√s

– = 319 GeV


H1 data: HERA2

1

10

10 2

0.3 0.4 0.5 0.6 0.7 0.8 0.9



Comparison with DELPHI at LEP II

e+e− → e+e−J/ψ X at LEP2

10-2

10-1

1

10

0 1 2 3 4 5 6 7 8 9 10pT

2 (GeV2)

dσ/d

p T2 (p

b/G

eV2 )

←

←←←

←

NRQCD

3PJ [8]

3PJ [1]

1S0 [8]

3S1 [8]

DELPHI prelim.

√ S = 197 GeV

−2 < yJ/ψ < 2

CSM

MRST98 fit

NRQCD

CTEQ5 fit

p2T [GeV2]

dσ(e

e→J/

ψ e

e+X

)/dp

2 T [

pb/G

eV2 ]

|y| < 2W < 35 GeVθel < 32 mrad√s

– = 197 GeV

DELPHI dataCS, LOCS, NLOCS+CO, LOCS+CO, NLO

10-3

10-2

10-1

1

10

1 2 3 4 5 6 7 8 9 10p2

T [GeV2]

dσ(e

e→J/

ψ e

e+X

)/dp

2 T [

pb/G

eV2 ]

√s– = 197 GeV

θel < 32 mradW < 35 GeV

|y| < 2

DELPHI data

10-3

10-2

10-1

1

10

1 2 3 4 5 6 7 8 9 10

[Klasen BK Mihaila NLO NRQCD Decomposition ofSteinhauser 02] NLO NRQCD

Agreement with NRQCD at NLO worse than in 2002 at LO.

Just 16 DELPHI events with pT > 1 GeV.

No results from ALEPH, L3, OPAL.

Data exhausted by single-resolved contribution.



Comparison with Belle at KEKB

σ(e+

e- →J/

ψ+

X)

[pb]

√s– = 10.6 GeV

CS, LO: σ = 0CS, NLO: σ = (0.24+0.20

-0.09 ) pbCS+CO, LO: σ = 0.23 pbCS+CO, NLO: σ = (0.70+0.35

-0.17 ) pb

BELLE data: σ = (0.43±0.13) pb(J/ψ+cc

– contribution subtracted)

0

0.5

1

1.5

2

2.5

At NLO, both CSM and NRQCD agree with data.

# of charged tracks > 4, missing events not corrected for. Belle point likely higher.



Comparison with ATLAS (after fit) [NPB850(2011)387]

pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

√s– = 7 TeV

|y| < 0.75

ATLAS data


10-5

10-4

10-3

10-2

10-1

1

10 2

5 10 15 20 25 30 35 40

10

Resummation of large logs ln(p2T /M2) necessary at large pT .

New formalism to include non-leading powers in p2T /M2

[Kang Qiu Sterman 2012].



Comparison with Fermilab Tagged-PhotonSpectrometer data (excluded from fit) [PRL52(1984)795]

1

10

10 2

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

z

dσ(γ

p→J/

ψ+

X)/

dz [

nb]

Eγ = 105 GeV


FTPS data

10-4

10-3

10-2

10-1

1

10

10 102

Eγ [GeV]

σ(γp

→J/

ψ+

X)

[nb]

0.4 < z < 0.9


FTPS data

Inelastic scattering of 105 GeV photons on hydrogen target.

Data remarkably well described by CS+CO at NLO.



Comparison with ZEUS (after fit) [JHEP1302(2013)071]

10-3

10-2

10-1

1

10-3

10-2

10-1

1

dσ

(γ p

→ J

/ψ X

)/dp

t2 (n

b/G

eV2 )

0.1 < z < 0.3

ZEUS

0.3 < z < 0.45

0.45 < z < 0.6 0.6 < z < 0.75

pt2 (GeV2)

0.75 < z < 0.9

pt2 (GeV2)

ZEUS (prel.) 468 pb -1

NLO CS+CO

NLO CS

10

10-4

10-3

10-2

10-1

1

1 10

Notorious NRQCD overshoot at large z overcome.



Polarized J/ψ photo- and hadroproduction

Decay angular distribution:dΓ(J/ψ → l+l−)

d cosθ dφ∝ 1+λθ cos2 θ +λφ sin2 θ cos(2φ)+λθφsin(2θ)cosφ

Polarization observables in spin density matrix formalism:

λθ =dσ11 −dσ00

dσ11 +dσ00, λφ =

dσ1,−1

dσ11 +dσ00, λθφ =

√2Redσ10

dσ11 +dσ00

λ = 0,+1,−1: unpolarized, transversely and longitudinally porarized.Heavy-quarkonium theory in the LHC era Bernd Kniehl


Comparison with H1 and ZEUS

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

1 2 3 4 5 6 7 8 9 10

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

1 2 3 4 5 6 7 8 9 10pT [GeV](a)

pT [GeV]

ν(p T

)λ(

p T)

H1 data


Helicity frame

60 GeV < W < 240 GeV0.3 < z < 0.9

Q2 < 2.5 GeV2

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

1 2 3 4 5 6 7 8 9 10

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

1 2 3 4 5 6 7 8 9 10pT [GeV](b)

pT [GeV]

ν(p T

)λ(

p T)

H1 data


Collins-Soper frame

60 GeV < W < 240 GeV0.3 < z < 0.9

Q2 < 2.5 GeV2

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

1 2 3 4 5 6 7 8 9 10

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

1 2 3 4 5 6 7 8 9 10pT [GeV](c)

pT [GeV]

ν(p T

)λ(

p T)

ZEUS data (till z=1)


Target frame

50 GeV < W < 180 GeV0.4 < z < 0.95Q2 < 1 GeV2

No z cut on ZEUS data diffractive production included.

Perturbative stability in NRQCD higher than in CSM.

J/ψ preferrably unpolarized at large pT .



Comparison with H1 and ZEUS (cont.)

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.3 0.4 0.5 0.6 0.7 0.8 0.9

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.3 0.4 0.5 0.6 0.7 0.8 0.9z(d)

z

ν(z)

λ(z)

H1 data


Helicity frame

60 GeV < W < 240 GeVpT > 1 GeV

Q2 < 2.5 GeV2

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.3 0.4 0.5 0.6 0.7 0.8 0.9

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.3 0.4 0.5 0.6 0.7 0.8 0.9z(e)

zν(

z)λ(

z)

H1 data


Collins-Soper frame


Q2 < 2.5 GeV2

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.3 0.4 0.5 0.6 0.7 0.8 0.9

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

0.3 0.4 0.5 0.6 0.7 0.8 0.9z(f)

z

ν(z)

λ(z)

ZEUS data


Target frame


Q2 < 1 GeV2

Large scale uncertainties due to low cut pT > 1.

Overall χ2 w.r.t. default prediction more than halved by goingfrom CSM to NRQCD.



Comparison with CDF and ALICE

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

5 10 15 20 25 30

-0.2-0.15

-0.1-0.05

00.05

0.10.15

0.2

5 10 15 20 25 30pT [GeV](a)

pT [GeV]

λ φ(p T

)λ θ(

p T)

CDF data: Run I / II/


Helicity frame

|y| < 0.6√s

– = 1.96 TeV

pp– → J/ψ + X

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

3 4 5 6 7 8 9 10

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

3 4 5 6 7 8 9 10pT [GeV](b)

pT [GeV]

λ φ(p T

)λ θ(

p T)

ALICE data


Helicity frame

2.5 < y < 4√s

– = 7 TeV

pp → J/ψ + X

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

3 4 5 6 7 8 9 10

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

3 4 5 6 7 8 9 10pT [GeV](c)

pT [GeV]

λ φ(p T

)λ θ(

p T)

ALICE data


Collins-Soper frame

2.5 < y < 4√s

– = 7 TeV

pp → J/ψ + X

CDF I and II data mutually inconsistent for pT < 12 GeV.

CDF J/ψ polarization anomaly persits at NLO.

4/8 ALICE points agree w/ NLO NRQCD within errors, others< 2σ away.



Decomposition for ALICE

pT [GeV](a)

dσ00

/dp T

(pp→

J/ψ

+X

) [n

b/G

eV]

Helicity frame√s

– = 7 TeV

2.5 < y < 4

3S[1]1 , NLO

1S[8]0 , NLO

3S[8]1 , NLO

3P[8]J , NLO

Total, NLO

10-1

1

10

10 2

10 3

3 4 5 6 7 8 9 10pT [GeV](b)

dσ11

/dp T

(pp→

J/ψ

+X

) [n

b/G

eV]

Helicity frame√s

– = 7 TeV

2.5 < y < 4

3S[1]1 , NLO

1S[8]0 , NLO

3S[8]1 , NLO

3P[8]J , NLO

Total, NLO

10-1

1

10

10 2

10 3

3 4 5 6 7 8 9 10pT [GeV](c)

dσ1

-1/d

p T(p

p→J/

ψ+

X)

[nb/

GeV

]

Helicity frame√s

– = 7 TeV

2.5 < y < 4

3S[1]1 , NLO

3S[8]1 , NLO

3P[8]J , NLO

Total, NLO

10-3

10-2

10-1

1

10

10 2

3 4 5 6 7 8 9 10

pT [GeV](d)

dσ00

/dp T

(pp→

J/ψ

+X

) [n

b/G

eV]

Collins-Soper frame√s

– = 7 TeV

2.5 < y < 4

3S[1]1 , NLO

1S[8]0 , NLO

3S[8]1 , NLO

3P[8]J , NLO

Total, NLO

10-1

1

10

10 2

10 3

3 4 5 6 7 8 9 10pT [GeV](e)

dσ11

/dp T

(pp→

J/ψ

+X

) [n

b/G

eV]


– = 7 TeV

2.5 < y < 4

3S[1]1 , NLO

1S[8]0 , NLO

3S[8]1 , NLO

3P[8]J , NLO

Total, NLO

10-1

1

10

10 2

10 3

3 4 5 6 7 8 9 10pT [GeV](f)

dσ1

-1/d

p T(p

p→J/

ψ+

X)

[nb/

GeV

]


– = 7 TeV

2.5 < y < 4

3S[1]1 , NLO

3S[8]1 , NLO

3P[8]J , NLO

Total, NLO

10-1

1

10

10 2

3 4 5 6 7 8 9 10

dσunpol= dσ00 +2dσ11; dσ1,−1 auxiliary.

Previously unknown 3P [8]J NLO correction significant.



LHCb data on prompt J/ψ polarization [EPJC73(2013)2631]

]c) [GeV/ψ(J/T

p5 10 15

θλ

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

2.0 < y < 2.52.5 < y < 3.03.0 < y < 3.53.5 < y < 4.04.0 < y < 4.5

= 7 TeVsLHCb

]c) [GeV/ψ(J/T

p5 10 15

θλ

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

2.0< y < 2.52.5 < y < 3.03.0 < y < 3.53.5 < y < 4.04.0 < y < 4.5

= 7 TeVsLHCb

) [GeV/c]ψ(J/T

p5 10 15

θλ

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

LHCbALICE

2.5 < y < 4.0

= 7 TeVspp

) [GeV/c]ψ(J/T

p5 10 15

θλ

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

LHCbALICE

2.5 < y < 4.0

= 7 TeVspp

helicity frame Collins-Soper frame



Comparison with LHCb and CMS polarization data

) [GeV/c]ψ(J/T

p0 5 10 15

θλ

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.81

NLO NRQCD(1)NLO NRQCD(2)NLO NRQCD(3)NLO CS

2.5 < y < 4.0

= 7 TeVsLHCb

[GeV]Tp

10 15 20 25 30 35 40 45 50

-1.5

-1

-0.5

0

0.5

1

1.5

, total uncert. 68.3% CL-1CMS preliminary, L = 4.9 fb

NLO NRQCD, B. Kniehl et al, MPLA28 (2013) 1350027 and private comm.

= 7 TeVspp

HX frame

|y| < 0.6

(2S)s

�h

prompt J/ψ polarization ψ′ polarizationLHCb, EPJC73(2013)2631 CMS, PLB727(2013)381

(1): Global NLO NRQCD fit to J/ψ yield [PRD84(2011)051501(R)]

New NLO NRQCD fit to ψ′ yield from HERA, Tevatron, and LHC



CMS data on J/ψ and ψ′ polarization [PLB727(2013)381]

-0.5

0

0.5

CMS HX frame

-0.5

0

0.5

-0.2

0

0.2

J/

-1 = 7 TeV L = 4.9 fbs pp

-0.2

0

0.2

(2S)

-0.2

0

0.2

20 30 40 50 60 70

[GeV]Tp

| < 0.6y|

| < 1.2y0.6 < |

| < 1.5y1.2 < |

-0.2

0

0.2

20 30 40 50

[GeV]Tp

NLO NRQCD [26], |y| < 2.4 NLO NRQCD [26], |y| < 2.4



Comparison with Gong et al. and Chao et al.

e+e− yield γp yield pp/pp yield CDF polariz.

BK, MBPRL108(2012)172002

0

0.5

1

1.5

2

2.5

3

3.5

σ(e+

e- →J/

ψ+

X)

[pb]

CS+CO, NLO: Butenschön et al.

BELLE data: √s– = 10.6 GeV

10-5

10-4

10-3

10-2

10-1

1

1 10 102

p2T [GeV2]

dσ(e

p→J/

ψ+

X)/

dp2 T [

nb/G

eV2 ]

60 GeV < W < 240 GeV0.3 < z < 0.9

Q2 < 2.5 GeV2

√s– = 319 GeV


H1 data: HERA1H1 data: HERA2

10-4

10-3

10-2

10-1

1

10

10 2

5 10 15 20 25 30 35 40pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]

ATLAS data: √s– = 7 TeV

|y| < 0.75

CDF data: √s– = 1.96 TeV

|y| < 0.6


-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

5 10 15 20 25 30pT [GeV]

λ θ(p T

)

pp– → J/ψ + X, helicity frame

CDF data: √s– = 1.96 TeV, |y| < 0.6


Gong et al.PRL110(2013)042002

0

0.5

1

1.5

2

2.5

3

3.5

σ(e+

e- →J/

ψ+

X)

[pb]

CS+CO, NLO: Gong et al.


10-5

10-4

10-3

10-2

10-1

1

1 10 102

p2T [GeV2]

dσ(e

p→J/

ψ+

X)/

dp2 T [

nb/G

eV2 ]

60 GeV < W < 240 GeV0.3 < z < 0.9

Q2 < 2.5 GeV2

√s– = 319 GeV



10-4

10-3

10-2

10-1

1

10

10 2

5 10 15 20 25 30 35 40pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]


|y| < 0.75


|y| < 0.6


-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

5 10 15 20 25 30pT [GeV]

λ θ(p T

)


CDF data: √s– = 1.96 TeV, |y| < 0.6


Chao et al.PRL108(2012)242004

0

0.5

1

1.5

2

2.5

3

3.5

σ(e+

e- →J/

ψ+

X)

[pb]

CS+CO, NLO: Ma et al.


10-5

10-4

10-3

10-2

10-1

1

1 10 102

p2T [GeV2]

dσ(e

p→J/

ψ+

X)/

dp2 T [

nb/G

eV2 ]

60 GeV < W < 240 GeV0.3 < z < 0.9

Q2 < 2.5 GeV2

√s– = 319 GeV



10-4

10-3

10-2

10-1

1

10

10 2

5 10 15 20 25 30 35 40pT [GeV]

dσ/d

p T(p

p→J/

ψ+

X)

× B

(J/ψ

→µµ

) [n

b/G

eV]


|y| < 0.75


|y| < 0.6


-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

5 10 15 20 25 30pT [GeV]

λ θ(p T

)


CDF data: √s– = 1.96 TeV, |y| < 0.6




Summary

NRQCD provides rigorous factorization theorem for productionand decay of heavy quarkonia; predicts:

existence of CO states;universality of LDMEs.

Previous LO tests not conclusive.

Here: first global analysis of unpolarized J/ψ world data at NLO.

Hadro- and photoproduction: striking evidence for NRQCD.

CSM greatly undershoots data, except for e+e− annihilation.

γγ scattering not conclusive yet.

Contributions from feed-down and B decays throughout smallagainst theoretical uncertainties subtracted in fit.

Hadroproduction data alone cannot reliably fix all 3 CO LDMEs.



Summary (cont.)

Case for NRQCD less strong in polarized J/ψ photoproductionat HERA.

NLO NRQCD predictions for polarized J/ψ hadroproductionbased on global analysis of J/ψ yield agrees with ALICE, butdisagrees with CDF, CMS, and LHCb.

NRQCD factorization remains among the hottest topics of QCD@ LHC.


Backup Slides


Comparison with Tevatron (cont.)

Relative importance of CO processes:

pT [GeV]

dσ/d

p T(p

p–→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/

GeV

]

√s– = 1.96 TeV

|y| < 0.6

CDF data3S[1]

1 , NLO1S[8]

0 , NLO3S[8]

1 , NLO3P[8]

J , NLO-3P[8]

J , NLOTotal, NLO

10-4

10-3

10-2

10-1

1

10

10 2

4 6 8 10 12 14 16 18 20

Short-distance σ(cc[3P [8]J ])< 0 for pT ' 7 GeV.

But: Short-distance cross sections and LDMEs unphysical(NRQCD scale and scheme dependence) No problem!


Comparison with ZEUS at HERA I (cont.)

p2T [GeV2]

dσ(e

p→J/

ψ+

X)/

dp2 T [

nb/G

eV2 ]

50 GeV < W < 180 GeV0.4 < z < 0.9Q2 < 1 GeV2

√s– = 300 GeV

Direct, NLOResolved, NLOTotal, NLO

ZEUS data10

-4

10-3

10-2

10-1

1

5 10 15 20 25 30

W [GeV]

dσ(e

p→J/

ψ+

X)/

dW [n

b/G

eV]

√s– = 300 GeV, Q2 < 1 GeV2

0.4 < z < 0.9p2

T > 1 GeV2


ZEUS data10

-4

10-3

10-2

60 80 100 120 140 160 180

z

dσ(e

p→J/

ψ+

X)/

dz [

nb]

50 GeV < W < 180 GeVp2

T > 1 GeV2Q2 < 1 GeV2

√s– = 300 GeV


ZEUS data

10-1

1

10

10 2

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Data for 0.4 < z < 0.9 exhausted by direct photoproduction.

Resolved photoproduction only relevant for z∼<0.4.


Comparison with ZEUS at HERA I (cont.)

p2T [GeV2]

dσ(e

p→J/

ψ+

X)/

dp2 T [

nb/G

eV2 ]

50 GeV < W < 180 GeV0.4 < z < 0.9Q2 < 1 GeV2

√s– = 300 GeV

ZEUS data10

-4

10-3

10-2

10-1

1

5 10 15 20 25 30

W [GeV]

dσ(e

p→J/

ψ+

X)/

dW [n

b/G

eV]

√s– = 300 GeV, Q2 < 1 GeV2

0.4 < z < 0.9p2

T > 1 GeV2

ZEUS data3S[1]

1 , NLO1S[8]

0 , NLO3S[8]

1 , NLO-3P[8]

J , NLOTotal, NLO

10-3

10-2

10-1

60 80 100 120 140 160 180

z

dσ(e

p→J/

ψ+

X)/

dz [

nb]

50 GeV < W < 180 GeVp2

T > 1 GeV2Q2 < 1 GeV2

√s– = 300 GeV

ZEUS data

3S[1]1 , NLO

1S[8]0 , NLO

3S[8]1 , NLO

-3P[8]J , NLO

Total, NLO

10-1

1

10

10 2

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

〈O[3P [8]0 ]〉< 0 3P [8]

0 contribution negative.

Negative interference with 1S[8]0 contribution beneficial.

3S[8]1 contribution negligible here.


Dependence on low-pT cut: Global fit

Vary low-pT cut on pp and pp data:pT > 1 GeV pT > 2 GeV pT > 3 GeV pT > 5 GeV pT > 7 GeV

Data left 148 points 134 points 119 points 86 points 60 points

〈OJ/ψ [1S[8]0 ]〉 5.68±0.37 4.25±0.43 4.97±0.44 4.92±0.49 3.91±0.51

〈OJ/ψ [3S[8]1 ]〉 0.90±0.50 2.94±0.58 2.24±0.59 2.23±0.62 2.96±0.64

〈OJ/ψ [3P [8]0 ]〉 −2.23±0.17 −1.38±0.20 −1.61±0.20 −1.59±0.22 −1.16±0.23

Global fit insensitive to low-pT cut on pp and pp data as long as γp,γγ (74 points with pT > 1 GeV), and e+e− data (1 point) are retained.

Vary low-pT cut on γp and γγ data:pT > 1 GeV pT > 2 GeV pT > 3 GeV pT > 5 GeV pT > 7 GeV


〈OJ/ψ [1S[8]0 ]〉 4.97±0.44 5.10±0.92 4.05±1.17 5.44±1.27 9.56±1.59

〈OJ/ψ [3S[8]1 ]〉 2.24±0.59 2.11±1.22 3.52±1.56 1.73±1.68 −3.66±2.09

〈OJ/ψ [3P [8]0 ]〉 −1.61±0.20 −1.58±0.48 −0.97±0.63 −1.63±0.68 −3.73±0.83

Global fit insensitive to moderate low-pT cut on γp and γγ data aslong as pp and pp data (119 points with pT > 3 GeV), and e+e− data(1 point) are retained.


Dependence on low-pT cut: Fit to pp and pp data only

Vary low-pT cut:pT > 1 GeV pT > 2 GeV pT > 3 GeV pT > 5 GeV pT > 7 GeV


〈OJ/ψ [1S[8]0 ]〉 8.54±0.52 16.85±1.23 11.02±1.67 1.68±2.20 2.18±2.56

〈OJ/ψ [3S[8]1 ]〉 −2.66±0.69 −13.36±1.60 −5.56±2.19 8.75±2.98 10.34±3.55

〈OJ/ψ [3P [8]0 ]〉 −3.63±0.23 −7.70±0.61 −4.46±0.87 2.20±1.23 3.50±1.50

M0 2.25±0.12 3.51±0.19 3.29±0.20 5.50±0.29 8.24±0.58M1 6.37±0.19 5.80±0.19 5.54±0.20 3.27±0.29 1.63±0.43

Fit highly sensitive to low-pT cut.

Comparison with fit to unpolarized, direct CDF II data with pT > 7 GeVY.-Q. Ma, K. Wang, and K.-T. Chao, Phys. Rev. D 84, 114001 (2011):M0 = (8.54±1.02)×10−2 GeV3

M1 = (1.67±1.05)×10−3 GeV3


II. Institut für Theoretische Physik, Universität Hamburg · Institut für Theoretische Physik,...

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