Quarkonium and Exotics Production

Bernd Kniehl

II. Institut für Theoretische Physik, Universität Hamburg

INT Program INT-18-1b: Multi-Scale Problems Using Effective

Field Theories

May 31, 2018

In collaboration with Mathias Butenschön and Zhiguo HePRL 104 (2010) 072001PRL 106 (2011) 022003

PRD 84 (2011) 051501 (Rapid Communications)

PRL 107 (2011) 232001

PRL 108 (2012) 172002

PRD 88 (2013) 011501 (Rapid Communications)

MPLA 28 (2013) 1350027 (Brief Reviews)PRL 114 (2015) 092004

PRL 115 (2015) 022002

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

CERN Courier, Volume 52, Issues 1 and 2

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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 ηc yield: LHC

7 Nature of X(3872): Tevatron, LHC

8 Summary: NRQCD at the crossroads

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Introduction: CEM, CSM, NRQCD factorization

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

σJ/ψ ≈1

9ρJ/ψ

∫ 2mD

2mc

dscc

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]

Jquantum numbers do not enter

Useful qualitative picture, rather than rigorous theory

s

]c [GeV/T

p0 5 10 15 20

)]c

[nb/(

GeV

/T

pd

)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] [Cheung Vogt 17]

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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!

NLO cross section factor 101–102 below Tevatron data.

However NNLO∗ [Lansberg 11] promising.

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.

Proof of factorization [Nayak Qiu Sterman 05; Nayak 15].

Can explain unpolarized yield at Tevatron and elsewhere.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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]

11S

[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.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Color and spin projection

Amplitudes for cc[n] production by projector application:

Acc[1S

[8]

0]= Tr [C8Π0 Acc ] |q=0

Acc[3S

[1/8]

1]= ǫαTr

[

C1/8ΠαAcc

]

|q=0

Acc[3P

[8]

J]= ǫαβ

ddqβ

Tr [C8ΠαAcc ] |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

ǫ: polarization vectors and tensors

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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 +

Bǫ +C

But: I(0) = Bǫ +C

=⇒ No Coulomb singularities in dimensional regularization!

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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.:

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Structure of Soft Singularities

Soft limits of the real corrections:

P/2+q→P/2−q→

→k4

Realk4→0−−−−→k4 soft

P/2+q→P/2−q→Born × E(q)

Asoft(q) = ABorn(q) ·E(q)

S and P states: Soft #1 + Soft #2 + Soft #3 terms:

Asoft,s = Asoft(0) = ABorn,s ·E(0)

Asoft,p = A ′soft

(0) = ABorn,p ·E(0) + ABorn,s ·E′(0)

|Asoft,s|2 = |ABorn,s|2 ·E(0)2

|Asoft,p|2 = |ABorn,p|2 ·E(0)2 + 2 Re A ∗Born,sABorn,p ·E(0)E′(0)

+ |ABorn,s |2 ·E′(0)2

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Radiative Corrections to Long Distance MEs

In NRQCD: Long distance MEs = cc scattering amplitudes:

〈OJ/ψ[n]〉 =

c c

c c

O[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

(

1

ǫUV

− 1

ǫIR

)

·

c c

c c

3P0

+3P1 +3P2

UV singularity cancelled by renormalization of 4-fermion operat.

IR singularity cancels soft #3 terms of P states!

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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; 578

pp 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

√

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Comparison with world data

p2T [GeV

2]

dσ(

ee

→J/ψ

ee

+X

)/d

p2 T

[pb

/Ge

V2]

|y| < 2

W < 35 GeV

θel < 32 mrad

√s– = 197 GeV

DELPHI data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

10

1 2 3 4 5 6 7 8 9 10

p2T [GeV

2]

dσ(

ep

→J/ψ

+X

)/d

p2 T

[nb

/Ge

V2]

60 GeV < W < 240 GeV

0.3 < z < 0.9

Q2 < 1 GeV

2

√s– = 314 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA1

10-5

10-4

10-3

10-2

10-1

1

1 10

W [GeV]

dσ(

ep

→J/ψ

+X

)/d

W [n

b/G

eV

]

√s– = 314 GeV, Q

2 < 1 GeV

2

0.3 < z < 0.9

p2T > 1 GeV

2

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA1

10-3

10-2

60 80 100 120 140 160 180 200 220 240

z

dσ(

ep

→J/ψ

+X

)/d

z

[nb

]

60 GeV < W < 240 GeV

p2T > 1 GeV

2

Q2 < 1 GeV

2

√s– = 314 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA1

1

10

102

0.3 0.4 0.5 0.6 0.7 0.8 0.9

p2T [GeV

2]

dσ(

ep

→J/ψ

+X

)/d

p2 T

[nb

/Ge

V2]

60 GeV < W < 240 GeV

0.3 < z < 0.9

Q2 < 2.5 GeV

2

√s– = 319 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA2

10-6

10-5

10-4

10-3

10-2

10-1

1

1 10 102

W [GeV]

dσ(

ep

→J/ψ

+X

)/d

W [n

b/G

eV

]

√s– = 319 GeV, Q

2 < 2.5 GeV

2

0.3 < z < 0.9

p2T > 1 GeV

2

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA2

10-3

10-2

60 80 100 120 140 160 180 200 220 240

z

dσ(

ep

→J/ψ

+X

)/d

z

[nb

]

60 GeV < W < 240 GeV

p2T > 1 GeV

2

Q2 < 2.5 GeV

2

√s– = 319 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA2

1

10

102

0.3 0.4 0.5 0.6 0.7 0.8 0.9

σ(e

+e

- →J/ψ

+X

) [p

b]

√s– = 10.6 GeV

CS, LO: σ = 0

CS, NLO: σ = (0.24+0.20-0.09 ) pb

CS+CO, LO: σ = 0.23 pb

CS+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 [GeV

2]

dσ(

ep

→J/ψ

+X

)/d

p2 T

[nb

/Ge

V2]

50 GeV < W < 180 GeV

0.4 < z < 0.9

Q2 < 1 GeV

2

√s– = 300 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

ZEUS data

10-4

10-3

10-2

10-1

1

5 10 15 20 25 30

W [GeV]

dσ(

ep

→J/ψ

+X

)/d

W [n

b/G

eV

]

√s– = 300 GeV, Q

2 < 1 GeV

2

0.4 < z < 0.9

p2T > 1 GeV

2

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

ZEUS data

10-3

10-2

60 80 100 120 140 160 180

z

dσ(

ep

→J/ψ

+X

)/d

z

[nb

]

50 GeV < W < 180 GeV

p2T > 1 GeV

2

Q2 < 1 GeV

2

√s– = 300 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

ZEUS data

10-1

1

10

102

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

ee

) [n

b/G

eV

]

√s– = 200 GeV

|y| < 0.35

PHENIX data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10

10

102

3 4 5 6 7 8 9 10

-1

1

pT [GeV]

dσ/

dp

T(p

p–→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 1.8 TeV

|y| < 0.6

CDF data: Run 1

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

102

6 8 10 12 14 16 18 20

1

10

pT [GeV]

dσ/

dp

T(p

p–→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 1.96 TeV

|y| < 0.6

CDF data: Run 2

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

102

4 6 8 10 12 14 16 18 20

10

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

2.5 < y < 4

ALICE data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-2

10-1

1

102

103

3 4 5 6 7 8 9 10

10

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

|y| < 0.75

ATLAS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

10

102

103

4 6 8 10 12 14 16 18 20

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

0.75 < |y| < 1.5

ATLAS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

10

102

103

4 6 8 10 12 14 16 18 20

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

1.5 < |y| < 2.25

ATLAS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

10

102

103

4 6 8 10 12 14 16 18 20

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

|y| < 1.2

CMS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

103

4 6 8 10 12 14 16 18 20

10

102

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

1.2 < |y| < 1.6

CMS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

102

103

4 6 8 10 12 14 16 18 20

10

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

1.6 < |y| < 2.4

CMS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

10

103

4 6 8 10 12 14 16 18 20

102

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

2 < y < 2.5

LHCb data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

102

4 6 8 10 12 14

10

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

2.5 < y < 3

LHCb data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

102

4 6 8 10 12 14

10

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

3 < y < 3.5

LHCb data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

102

4 6 8 10 12 14

10

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

3.5 < y < 4

LHCb data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

102

4 6 8 10 12 14

10

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb

/Ge

V]

√s– = 7 TeV

4 < y < 4.5

LHCb data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

102

4 6 8 10 12 14

10

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Comparison with RHIC and Tevatron

RHIC Tevatron II Decomposition of

PHENIX CDF NLO NRQCD

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

ee)

[nb/G

eV

]

√s– = 200 GeV

|y| < 0.35

PHENIX data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10

10

102

3 4 5 6 7 8 9 10

-1

1

pT [GeV]

dσ/

dp

T(p

p–→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 1.96 TeV

|y| < 0.6

CDF data: Run 2

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

10

102

4 6 8 10 12 14 16 18 20

pT [GeV]

dσ/

dp

T(p

p–→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 1.96 TeV

|y| < 0.6

CDF data3S

[1]1 , NLO

1S

[8]0 , 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

102

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]

Jchannels.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Comparison with ATLAS and CMS at LHC

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

|y| < 0.75

ATLAS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

10

102

103

4 6 8 10 12 14 16 18 20

pT [GeV]d

σ/dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

0.75 < |y| < 1.5

ATLAS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

10

102

103

4 6 8 10 12 14 16 18 20

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

1.5 < |y| < 2.25

ATLAS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

10

102

103

4 6 8 10 12 14 16 18 20

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

|y| < 1.2

CMS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

10

102

103

4 6 8 10 12 14 16 18 20

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

1.2 < |y| < 1.6

CMS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

10

102

103

4 6 8 10 12 14 16 18 20

pT [GeV]d

σ/dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

1.6 < |y| < 2.4

CMS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

10

102

103

4 6 8 10 12 14 16 18 20

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Comparison with ALICE and LHBb at LHC

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

2.5 < y < 4

ALICE data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-2

10-1

1

102

103

3 4 5 6 7 8 9 10

10

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

2 < y < 2.5

LHCb data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

10

102

4 6 8 10 12 14

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

2.5 < y < 3

LHCb data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

10

102

4 6 8 10 12 14

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

3 < y < 3.5

LHCb data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

10

102

4 6 8 10 12 14

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

3.5 < y < 4

LHCb data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

10

102

4 6 8 10 12 14

pT [GeV]d

σ/dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

4 < y < 4.5

LHCb data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-4

10-3

10-2

10-1

1

10

102

4 6 8 10 12 14

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Comparison with ZEUS at HERA I

p2T [GeV

2]

dσ(

ep

→J/ψ

+X

)/dp

2 T

[nb/G

eV

2]

50 GeV < W < 180 GeV

0.4 < z < 0.9

Q2 < 1 GeV

2

√s– = 300 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

ZEUS data

10-4

10-3

10-2

10-1

1

5 10 15 20 25 30

z

dσ(

ep

→J/ψ

+X

)/dz

[nb

]50 GeV < W < 180 GeV

p2T > 1 GeV

2

Q2 < 1 GeV

2

√s– = 300 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

ZEUS data

10-1

1

10

102

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

z

dσ(

ep

→J/ψ

+X

)/dz

[nb

]

50 GeV < W < 180 GeV

p2T > 1 GeV

2

Q2 < 1 GeV

2

√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

102

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]

0vs. 3P

[8]

J{ regular z→ 1 behavior.

Data well described by CS+CO at NLO.

CS factor of 3–5 below the data.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Comparison with H1 at HERA I and II

p2T [GeV

2]

dσ(

ep

→J/ψ

+X

)/dp

2 T

[nb/G

eV

2]

60 GeV < W < 240 GeV

0.3 < z < 0.9

Q2 < 1 GeV

2

√s– = 314 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA1

10-5

10-4

10-3

10-2

10-1

1

1 10

W [GeV]d

σ(ep

→J/ψ

+X

)/dW

[nb/G

eV

]

√s– = 314 GeV, Q

2 < 1 GeV

2

0.3 < z < 0.9

p2T > 1 GeV

2

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA1

10-3

10-2

60 80 100 120 140 160 180 200 220 240

z

dσ(

ep

→J/ψ

+X

)/dz

[nb

]

60 GeV < W < 240 GeV

p2T > 1 GeV

2

Q2 < 1 GeV

2

√s– = 314 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA1

1

10

102

0.3 0.4 0.5 0.6 0.7 0.8 0.9

p2T [GeV

2]

dσ(

ep

→J/ψ

+X

)/dp

2 T

[nb/G

eV

2]

60 GeV < W < 240 GeV

0.3 < z < 0.9

Q2 < 2.5 GeV

2

√s– = 319 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA2

10-6

10-5

10-4

10-3

10-2

10-1

1

1 10 102

W [GeV]

dσ(

ep

→J/ψ

+X

)/dW

[nb/G

eV

]

√s– = 319 GeV, Q

2 < 2.5 GeV

2

0.3 < z < 0.9

p2T > 1 GeV

2

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA2

10-3

10-2

60 80 100 120 140 160 180 200 220 240

zd

σ(ep

→J/ψ

+X

)/dz

[nb

]

60 GeV < W < 240 GeV

p2T > 1 GeV

2

Q2 < 2.5 GeV

2

√s– = 319 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

H1 data: HERA2

1

10

102

0.3 0.4 0.5 0.6 0.7 0.8 0.9

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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 10p

T2 (GeV

2)

dσ/

dp

T2 (

pb

/GeV

2)

←

←←←

←

NRQCD

3P

J [8]

3P

J [1]

1S

0 [8]

3S

1 [8]

DELPHI prelim.

√ S = 197 GeV

−2 < yJ/ψ < 2

CSM

MRST98 fit

NRQCD

CTEQ5 fit

p2T [GeV

2]

dσ(

ee

→J/ψ

ee+

X)/

dp

2 T

[pb/G

eV

2]

|y| < 2

W < 35 GeV

θel < 32 mrad

√s– = 197 GeV

DELPHI data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-3

10-2

10-1

1

10

1 2 3 4 5 6 7 8 9 10

p2T [GeV

2]

dσ(

ee

→J/ψ

ee+

X)/

dp

2 T

[pb/G

eV

2]

√s– = 197 GeV

θel < 32 mrad

W < 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 of

Steinhauser 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.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Comparison with Belle at KEKB

σ(e

+e

- →J/ψ

+X

) [p

b]

√s– = 10.6 GeV

CS, LO: σ = 0

CS, NLO: σ = (0.24+0.20-0.09 ) pb

CS+CO, LO: σ = 0.23 pb

CS+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.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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

pT [GeV]

dσ/

dp

T(p

p→

J/ψ

+X

) ×

B(J

/ψ→

µµ)

[nb/G

eV

]

√s– = 7 TeV

|y| < 0.75

ATLAS data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

10-5

10-4

10-3

10-2

10-1

1

102

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].

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Comparison with Fermilab Tagged-Photon

Spectrometer data (excluded from fit) [PRL52(1984)795]

1

10

102

0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

z

dσ(

γp→

J/ψ

+X

)/d

z

[nb

]

Eγ = 105 GeV

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

FTPS data

10-4

10-3

10-2

10-1

1

10

10 102

Eγ [GeV]

σ(γp

→J/ψ

+X

) [n

b]

0.4 < z < 0.9

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

FTPS data

Inelastic scattering of 105 GeV photons on hydrogen target.

Data remarkably well described by CS+CO at NLO.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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

)/d

pt2

(n

b/G

eV

2)

0.1 < z < 0.3

ZEUS

0.3 < z < 0.45

0.45 < z < 0.6 0.6 < z < 0.75

pt2 (GeV

2)

0.75 < z < 0.9

pt2 (GeV

2)

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.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Polarized J/ψ photo- and hadroproduction

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

d cosθdφ∝ 1+λθcos2θ+λφsin2θcos(2φ)+λθφ sin(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.Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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 10

pT [GeV](a)

pT [GeV]

ν(p

T)

λ(p

T)

H1 data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

Helicity frame

60 GeV < W < 240 GeV

0.3 < z < 0.9

Q2 < 2.5 GeV

2

-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 10

pT [GeV](b)

pT [GeV]

ν(p

T)

λ(p

T)

H1 data

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

Collins-Soper frame

60 GeV < W < 240 GeV

0.3 < z < 0.9

Q2 < 2.5 GeV

2

-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 10

pT [GeV](c)

pT [GeV]

ν(p

T)

λ(p

T)

ZEUS data (till z=1)

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

Target frame

50 GeV < W < 180 GeV

0.4 < z < 0.95

Q2 < 1 GeV

2

No z cut on ZEUS data{ diffractive production included.

Perturbative stability in NRQCD higher than in CSM.

J/ψ preferrably unpolarized at large pT .

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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

-0.050

0.050.1

0.150.2

5 10 15 20 25 30

pT [GeV](a)

pT [GeV]

λ φ(p

T)

λ θ(p

T)

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

-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 10

pT [GeV](b)

pT [GeV]

λ φ(p

T)

λ θ(p

T)

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

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 10

pT [GeV](c)

pT [GeV]

λ φ(p

T)

λ θ(p

T)

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

CDF I [PRL85(2000)2886] and II [PRL99(2007)132001] data

mutually inconsistent for pT < 12 GeV.

CDF J/ψ polarization anomaly persits at NLO.

4/8 ALICE [PRL108 (2012) 082001] points agree w/ NLO NRQCD

within errors, others < 2σ away.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Comparison with ALICE [PRL108 (2012) 082001] and LHCb

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

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

4 6 8 10 12 14

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

4 6 8 10 12 14

pT [GeV]

pT [GeV]

ν/2

= λ

φλ

= λ

θ

ALICE / LHCb 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

00.20.40.60.8

1

4 6 8 10 12 14

-1-0.8-0.6-0.4-0.2

00.20.40.60.8

1

4 6 8 10 12 14

pT [GeV]

pT [GeV]

ν/2

= λ

φλ

= λ

θ

ALICE / LHCb 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

ALICE and LHCb data mutually agree.

NLO NRQCD predictions systematically disagree w/ data.Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Comparison with CMS data on prompt J/ψ and ψ′

polarization [PLB727(2013)381]

-1

-0.5

0

0.5

1

10 15 20 25 30 35 40

-0.4

-0.2

0

0.2

0.4

10 15 20 25 30 35 40

-0.4

-0.2

0

0.2

0.4

10 15 20 25 30 35 40

pT [GeV]

pT [GeV]

pT [GeV]

λ θφ(p

T)

λ φ(p

T)

λ θ(p

T)

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

CMS data Helicity frame

|y| < 0.6

√s– = 7 TeV

pp → J/ψ + X

-1

-0.5

0

0.5

1

10 15 20 25 30 35 40

-0.4

-0.2

0

0.2

0.4

10 15 20 25 30 35 40

-0.4

-0.2

0

0.2

0.4

10 15 20 25 30 35 40

pT [GeV]

pT [GeV]

pT [GeV]

λ θφ(p

T)

λ φ(p

T)

λ θ(p

T)

CS, LO

CS, NLO

CS+CO, LO

CS+CO, NLO

CMS data Helicity frame

|y| < 0.6

√s– = 7 TeV

pp → ψ(2S) + X

NLO NRQCD predictions systematically disagree w/ data on λθ.Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Comparison with ALICE data on prompt J/ψpolarization [arXiv:1805.04374 [hep-ex]]

)c (GeV/T

p

0 2 4 6 8 10 12 14

ϕθλ

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

ϕλ

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

θλ

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Collins-Soper

-1 = 1.23 pbint

= 8 TeV, LsALICE pp

< 4y: 2.5 < ψInclusive J/

)c (GeV/T

p

0 2 4 6 8 10 12 140

Helicity

NLO CSM

NLO NRQCD

NLO NRQCD2

)c (GeV/T

p0 2 4 6 8 10 12 14

λ∼

-1

-0.5

0

0.5

1

1.5 ψ<4, inclusive J/y = 8 TeV, 2.5<sALICE pp

Helicity frame

Collins-Soper frame

NLO CSM

NLO NRQCD

NLO NRQCD predictions systematically disagree w/ data on λθand λφ.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

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 [GeV

2]

dσ(e

p→

J/ψ

+X)/

dp2 T

[nb/

Ge

V2]

60 GeV < W < 240 GeV

0.3 < z < 0.9

Q2 < 2.5 GeV

2

√s± = 319 GeV

CS+CO, NLO: Butenschön et al.

H1 data: HERA1

H1 data: HERA2

10-4

10-3

10-2

10-1

1

10

102

5 10 15 20 25 30 35 40

pT [GeV]

dσ/d

pT(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

CS+CO, NLO: Butenschön et al.

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

5 10 15 20 25 30

pT [GeV]

λ θ(p

T)

pp± → J/ψ + X, helicity frame

CDF data: √s± = 1.96 TeV, |y| < 0.6

CS+CO, NLO: Butenschön et al.

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.

BELLE data: √s± = 10.6 GeV

10-5

10-4

10-3

10-2

10-1

1

1 10 102

p2T [GeV

2]

dσ(e

p→

J/ψ

+X)/

dp2 T

[nb/

Ge

V2]

60 GeV < W < 240 GeV

0.3 < z < 0.9

Q2 < 2.5 GeV

2

√s± = 319 GeV

CS+CO, NLO: Gong et al.

H1 data: HERA1

H1 data: HERA2

10-4

10-3

10-2

10-1

1

10

102

5 10 15 20 25 30 35 40

pT [GeV]

dσ/d

pT(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

CS+CO, NLO: Gong et al.

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

5 10 15 20 25 30

pT [GeV]

λ θ(p

T)

pp± → J/ψ + X, helicity frame

CDF data: √s± = 1.96 TeV, |y| < 0.6

CS+CO, NLO: Gong et al.

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.

BELLE data: √s± = 10.6 GeV

10-5

10-4

10-3

10-2

10-1

1

1 10 102

p2T [GeV

2]

dσ(e

p→

J/ψ

+X)/

dp2 T

[nb/

Ge

V2]

60 GeV < W < 240 GeV

0.3 < z < 0.9

Q2 < 2.5 GeV

2

√s± = 319 GeV

CS+CO, NLO: Ma et al.

H1 data: HERA1

H1 data: HERA2

10-4

10-3

10-2

10-1

1

10

102

5 10 15 20 25 30 35 40

pT [GeV]

dσ/d

pT(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

CS+CO, NLO: Ma et al.

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

5 10 15 20 25 30

pT [GeV]

λ θ(p

T)

pp± → J/ψ + X, helicity frame

CDF data: √s± = 1.96 TeV, |y| < 0.6

CS+CO, NLO: Ma et al.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

LHCb data on ηc yield [EPJC75(2015)311]

10-2

10-1

1

10

102

103

104

4 6 8 10 12 14 16 18 20

pT [GeV]

dσ/d

pT(p

p→

η c+X

) [n

b/G

eV

]

√s± = 7 TeV

LDMEs: Butenschön et al.

ηc: 1S

[1]0

ηc: 3S

[8]1

ηc: 1S

[8]0

ηc: -1P[8]1

Total

10-2

10-1

1

10

102

103

104

4 6 8 10 12 14 16 18 20

pT [GeV]dσ

/dp

T(p

p→

η c+X

) [n

b/G

eV

]

√s± = 8 TeV

LDMEs: Butenschön et al.

ηc: 1S

[1]0

ηc: 3S

[8]1

ηc: 1S

[8]0

ηc: -1P[8]1

Total

7 TeV 8 TeV

M. Butenschoen, Z. He, BK, PRL114(2015)092004

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

What are the implications of X(3872) production cross

section measurements for its interpretation?

M. Butenschoen, Z. He, BK, Phys. Rev. D88 (2013) 011501(R)Test hypothesis X(3872) ≡ χc1(2P) in prompt hardoproduction at NLO in NRQCD

dσ(pp→ χc1(2P)+X) =∑

i,j,n

∫

dxdy fi/A (x)fj/B (y)〈Oχc1(2P)[n]〉dσ(ij→ cc[n]+X)

Fix 〈Oχc1(2P)(3P[1]

1)〉= (2J+1)

3CA2π |R′2P

(0)|2 = 0.438 GeV5.

w/ LHCb w/o LHCb

〈Oχc1(2P)(3S[8]

1)〉 [GeV

3] (3.84+0.28−0.24

)×10−3 (4.30+0.30−0.26

)×10−3

χ2/d.o.f. 79.1/5 = 15.8 16.7/4 = 4.18

CMSTotal3S1@8D

3P1@1D

CDF

CMS

LHCb

10 15 20 25 3010-5

10-4

0.001

0.01

0.1

1

pt HGeVL

dΣ´

BR

dptHn

b�G

eVL

0.5

1.0

2.0

5.0

10.0

20.0

nb´BR

CMSTotal3S1@8D

3P1@1D

CDF

CMS

LHCb

10 15 20 25 3010-5

10-4

0.001

0.01

0.1

1

pt HGeVL

dΣ´

BR

dptHn

b�G

eVL

0.5

1.0

2.0

5.0

10.0

20.0

nb´BR

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Two-parameter fit

w/ LHCb w/o LHCb 1304.6710 [hep-ph]1

〈Oχc1(2P)(3P[1]

1)〉 [GeV

5] 0.10+0.050−0.050

0.19+0.092−0.094

0.17±0.7

〈Oχc1(2P)(3S[8]

1)〉 [GeV

3] (3.84+0.28−0.24

)×10−3 (4.30+0.30−0.26

)×10−3 (3.34±1.69)×10−3

χ2/d.o.f. 4.26/4 = 1.07 0.63/3 = 0.21 0.52/2 = 0.26

CMSTotal3S1@8D

3P1@1D

CDF

CMS

LHCb

10 15 20 25 3010-5

10-4

0.001

0.01

0.1

1

pt HGeVL

dΣ´

BR

dptHn

b�G

eVL

0.5

1.0

2.0

5.0

10.0

nb´BR

CMSTotal3S1@8D

3P1@1D

CDF

CMS

LHCb

10 15 20 25 3010-5

10-4

0.001

0.01

0.1

1

pt HGeVLdΣ´

BR

dptHn

b�G

eVL

0.5

1.0

2.0

5.0

10.0

nb´BR

1 C. Meng, H. Han, K.-T. Chao, Phys. Rev. D96 (2017) 074014

Fix |R′2P

(0)|2 = 0.075 GeV5 and fit 〈Oχc1(2P)(3S

[8]

1)〉 and overall factor

dσ(pp→X(3872)+X)dσ(pp→χc1(2P)+X)

to CMS pT distribution.

Quarkonium and Exotics Production Bernd Kniehl

Introduction Technology Global fit Further tests Polarization ηc yield X(3872) Summary

Summary

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

existence of CO states;

universality of LDMEs.

NLO NRQCD nicely describes world data on unpolarized J/ψyield.

NLO CSM greatly undershoots data, except for e+e−

annihilation.

γγ scattering not conclusive yet.

Hadroproduction data alone cannot reliably fix all 3 CO LDMEs.

NLO NRQCD predictions for polarized J/ψ hadroproductionbased on global analysis of J/ψ yield agrees with ALICE (low

pT ), but strongly disagrees with CDF, CMS, and LHCb.

NLO NRQCD predictions for ηc yield based on heavy-quark spinsymmetry systematically overshoot LHCb data.

NRQCD factorization remains among the hottest topics of QCD

@ LHC.

Quarkonium and Exotics Production Bernd Kniehl