Part I Generalities on gluon TMDs J.P. Lansberg (IPNO) Gluon TMD - - PowerPoint PPT Presentation

Gluon TMD studies using quarkonia: pinning

down the linearly-polarised gluons with di-J⑦ψ production

J.P. Lansberg IPN Orsay – Paris-Sud U./Paris Saclay U. –CNRS/IN2P3 REF 2017 workshop November 13 – 16, Madrid, Spain

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 1 / 20

Part I Generalities on gluon TMDs

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 2 / 20

Gluon TMDs in unpolarised protons

❼ ➁ ✁ ❙ ❼ ➁ ❼ ➁ ❼ ➁

❼ ✔ ➁ ❵ ❙

❼ ➁❯

✆

❼ ➁❯➐

• ✆❙ ❡❯
• ➐

❯ ❯➐

❼ ➁ ✏ ➐ ❼ ➁ ✏ ➀ ✔ ➅

Ù ❼

➁→ ✔

Ù

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 3 / 20

Gluon TMDs in unpolarised protons

Gauge-invariant definition:

Φµν

g ❼x, kT, ζ, µ➁ ✁ ❙

d❼ξP➁ d2ξT ❼xPn➁2❼2π➁3 ei❼xP✔kT➁ξ❵P❙Fnν❼0➁❯0,ξ✆Fnµ❼ξ➁❯➐

ξ,0✆❙P❡❯ ξP➐0

❯ and ❯➐ are process dependent gauge links

❼ ➁ ✏ ➐ ❼ ➁ ✏ ➀ ✔ ➅

Ù ❼

➁→ ✔

Ù

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 3 / 20

Gluon TMDs in unpolarised protons

Gauge-invariant definition:

Φµν

g ❼x, kT, ζ, µ➁ ✁ ❙

d❼ξP➁ d2ξT ❼xPn➁2❼2π➁3 ei❼xP✔kT➁ξ❵P❙Fnν❼0➁❯0,ξ✆Fnµ❼ξ➁❯➐

ξ,0✆❙P❡❯ ξP➐0

❯ and ❯➐ are process dependent gauge links Parametrisation:

• P. J. Mulders, J. Rodrigues, PRD 63 (2001) 094021; D. Boer et al. JHEP 1610 (2016) 013

Φµν

g ❼x, kT, ζ, µ➁ ✏ 1

2x➐gµν

T f g

1 ❼x, kT, µ➁ ✏ ➀kµ

T kν T

M2

p

✔ gµν

T

k2

T

2M2

p

➅ hÙ g

1 ❼x, kT, µ➁→ ✔ suppr.

Ù

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 3 / 20

Gluon TMDs in unpolarised protons

Gauge-invariant definition:

Φµν

g ❼x, kT, ζ, µ➁ ✁ ❙

d❼ξP➁ d2ξT ❼xPn➁2❼2π➁3 ei❼xP✔kT➁ξ❵P❙Fnν❼0➁❯0,ξ✆Fnµ❼ξ➁❯➐

ξ,0✆❙P❡❯ ξP➐0

❯ and ❯➐ are process dependent gauge links Parametrisation:

• P. J. Mulders, J. Rodrigues, PRD 63 (2001) 094021; D. Boer et al. JHEP 1610 (2016) 013

Φµν

g ❼x, kT, ζ, µ➁ ✏ 1

2x➐gµν

T f g

1 ❼x, kT, µ➁ ✏ ➀kµ

T kν T

M2

p

✔ gµν

T

k2

T

2M2

p

➅ hÙ g

1 ❼x, kT, µ➁→ ✔ suppr.

f g

1 : TMD distribution of unpolarised gluons

hÙ g

1 : TMD distribution of linearly polarised gluons

[Helicity-flip distribution]

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 3 / 20

gg fusion in arbitrary unpolarised process [colourless final state] dσ gg ➀

➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P ▼ ▼❻ ➃ ❈ ✆ ✟ ✔ ➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P ▼ ▼❻

✏ ✏ ➃ ❈

✕

Ù Ù ✆

✟ ➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P ▼ ▼❻

✏

➃ ❈ ✕

Ù ✆ ✔ ➌ ✏ ➑

✟ ❼ ➁ ✔ ➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P ▼

✏ ▼❻ ✏

➃ ❈ ✕

Ù Ù ✆

✟ ❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 4 / 20

gg fusion in arbitrary unpolarised process [colourless final state] dσ gg ➀

F1

➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P

λa,λb

ˆ ▼λa,λb ˆ ▼❻

λa,λb➃ ❈f g 1 f g 1 ✆

✟ helicity non-flip, azimuthally independent ✔ ➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P ▼ ▼❻

✏ ✏ ➃ ❈

✕

Ù Ù ✆

✟ ➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P ▼ ▼❻

✏

➃ ❈ ✕

Ù ✆ ✔ ➌ ✏ ➑

✟ ❼ ➁ ✔ ➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P ▼

✏ ▼❻ ✏

➃ ❈ ✕

Ù Ù ✆

✟ ❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 4 / 20

gg fusion in arbitrary unpolarised process [colourless final state] dσ gg ➀

F1

➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P

λa,λb

ˆ ▼λa,λb ˆ ▼❻

λa,λb➃ ❈f g 1 f g 1 ✆

✟ helicity non-flip, azimuthally independent ✔

F2

➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P

λ

ˆ ▼λ,λ ˆ ▼❻

✏λ,✏λ➃ ❈w0 ✕ hÙg 1 hÙg 1 ✆

✟ double helicity flip, azimuthally independent ➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P ▼ ▼❻

✏

➃ ❈ ✕

Ù ✆ ✔ ➌ ✏ ➑

✟ ❼ ➁ ✔ ➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P ▼

✏ ▼❻ ✏

➃ ❈ ✕

Ù Ù ✆

✟ ❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 4 / 20

gg fusion in arbitrary unpolarised process [colourless final state] dσ gg ➀

F1

➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P

λa,λb

ˆ ▼λa,λb ˆ ▼❻

λa,λb➃ ❈f g 1 f g 1 ✆

✟ helicity non-flip, azimuthally independent ✔

F2

➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P

λ

ˆ ▼λ,λ ˆ ▼❻

✏λ,✏λ➃ ❈w0 ✕ hÙg 1 hÙg 1 ✆

✟ double helicity flip, azimuthally independent +

F3

➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P

λa,λb

ˆ ▼λa,λb ˆ ▼❻

✏λa,λb➃ ❈w2 ✕ f g 1 hÙg 1 ✆ ✔ ➌a ✏ b➑

✟ single helicity flip, cos❼2ϕ➁-modulation ✔ ➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P ▼

✏ ▼❻ ✏

➃ ❈ ✕

Ù Ù ✆

✟ ❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 4 / 20

gg fusion in arbitrary unpolarised process [colourless final state] dσ gg ➀

F1

➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P

λa,λb

ˆ ▼λa,λb ˆ ▼❻

λa,λb➃ ❈f g 1 f g 1 ✆

✟ helicity non-flip, azimuthally independent ✔

F2

➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P

λ

ˆ ▼λ,λ ˆ ▼❻

✏λ,✏λ➃ ❈w0 ✕ hÙg 1 hÙg 1 ✆

✟ double helicity flip, azimuthally independent +

F3

➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P

λa,λb

ˆ ▼λa,λb ˆ ▼❻

✏λa,λb➃ ❈w2 ✕ f g 1 hÙg 1 ✆ ✔ ➌a ✏ b➑

✟ single helicity flip, cos❼2ϕ➁-modulation ✔

F4

➩➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➲➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➵➭ ❾ P

λ

ˆ ▼λ,✏λ ˆ ▼❻

✏λ,λ➃ ❈w4 ✕ hÙg 1 hÙg 1 ✆

✟ double helicity flip, cos❼4ϕ➁-modulation

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 4 / 20

Part II Quarkonium production and TMD factorisation applicability/breaking

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 5 / 20

Approaches to Quarkonium Production

See EPJC (2016) 76:107 for a recent review

❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 6 / 20

Approaches to Quarkonium Production

See EPJC (2016) 76:107 for a recent review

No consensus on the mechanisnm at work in quarkonium production

❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 6 / 20

Approaches to Quarkonium Production

See EPJC (2016) 76:107 for a recent review

No consensus on the mechanisnm at work in quarkonium production Yet, nearly all approaches assume a factorisation between the production of the heavy-quark pair, Q ¯ Q, and its hadronisation into a meson

❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 6 / 20

Approaches to Quarkonium Production

See EPJC (2016) 76:107 for a recent review

No consensus on the mechanisnm at work in quarkonium production Yet, nearly all approaches assume a factorisation between the production of the heavy-quark pair, Q ¯ Q, and its hadronisation into a meson Different approaches differ essentially in the treatment of the hadronisation

❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 6 / 20

Approaches to Quarkonium Production

See EPJC (2016) 76:107 for a recent review

No consensus on the mechanisnm at work in quarkonium production Yet, nearly all approaches assume a factorisation between the production of the heavy-quark pair, Q ¯ Q, and its hadronisation into a meson Different approaches differ essentially in the treatment of the hadronisation 3 fashionable models:

❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 6 / 20

Approaches to Quarkonium Production

See EPJC (2016) 76:107 for a recent review

No consensus on the mechanisnm at work in quarkonium production Yet, nearly all approaches assume a factorisation between the production of the heavy-quark pair, Q ¯ Q, and its hadronisation into a meson Different approaches differ essentially in the treatment of the hadronisation 3 fashionable models:

1

Colour Evaporation Model: application of quark-hadron duality;

• nly the invariant mass matters; bleaching via (numerous) sof gluons ?

❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 6 / 20

Approaches to Quarkonium Production

See EPJC (2016) 76:107 for a recent review

No consensus on the mechanisnm at work in quarkonium production Yet, nearly all approaches assume a factorisation between the production of the heavy-quark pair, Q ¯ Q, and its hadronisation into a meson Different approaches differ essentially in the treatment of the hadronisation 3 fashionable models:

1

Colour Evaporation Model: application of quark-hadron duality;

• nly the invariant mass matters; bleaching via (numerous) sof gluons ?

2

Colour Singlet Model: hadronisation w/o gluon emission; each emission costs αs❼mQ➁ and occurs at short distances; bleaching at the pair-production time

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 6 / 20

Approaches to Quarkonium Production

See EPJC (2016) 76:107 for a recent review

No consensus on the mechanisnm at work in quarkonium production Yet, nearly all approaches assume a factorisation between the production of the heavy-quark pair, Q ¯ Q, and its hadronisation into a meson Different approaches differ essentially in the treatment of the hadronisation 3 fashionable models:

1

Colour Evaporation Model: application of quark-hadron duality;

• nly the invariant mass matters; bleaching via (numerous) sof gluons ?

2

Colour Singlet Model: hadronisation w/o gluon emission; each emission costs αs❼mQ➁ and occurs at short distances; bleaching at the pair-production time

3

Colour Octet Mechanism (encapsulated in NRQCD): higher Fock states of the mesons taken into account; Q ¯ Q can be produced in octet states with different quantum # as the meson; bleaching with semi-sof gluons ?

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 6 / 20

Quarkonium production and TMD factorisation applicability/breaking

Ù Ù Ù

◗ ✔ ◗ ✔ ◗ ✔

❺

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 7 / 20

Quarkonium production and TMD factorisation applicability/breaking

hÙg

1

receives contributions from Initial-State Interactions (ISI) and Final-State Interactions (FSI)

Ù Ù

◗ ✔ ◗ ✔ ◗ ✔

❺

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 7 / 20

Quarkonium production and TMD factorisation applicability/breaking

hÙg

1

receives contributions from Initial-State Interactions (ISI) and Final-State Interactions (FSI) Tese can make hÙg

1

process dependent and even break factorisation Different independent hÙg

1

functions correspond to specific colour

• structures. Depending on the process, one extracts different combinations

Buffing, Mukherjee, Mulders, PRD 88 (2013) 054027); See also the nice overview by D. Boer : Few Body Syst. 58 (2017) 32

◗ ✔ ◗ ✔ ◗ ✔

❺

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 7 / 20

Quarkonium production and TMD factorisation applicability/breaking

hÙg

1

receives contributions from Initial-State Interactions (ISI) and Final-State Interactions (FSI) Tese can make hÙg

1

process dependent and even break factorisation Different independent hÙg

1

functions correspond to specific colour

• structures. Depending on the process, one extracts different combinations

Buffing, Mukherjee, Mulders, PRD 88 (2013) 054027); See also the nice overview by D. Boer : Few Body Syst. 58 (2017) 32

Quarkonium production in pp collisions might face factorisation breaking effects if the bleaching of the heavy-quark pair occurs over long times (COM-NRQCD and CEM approaches) as opposed to Colour-Singlet contributions ◗ ✔ ◗ ✔ ◗ ✔

❺

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 7 / 20

Quarkonium production and TMD factorisation applicability/breaking

hÙg

1

receives contributions from Initial-State Interactions (ISI) and Final-State Interactions (FSI) Tese can make hÙg

1

process dependent and even break factorisation Different independent hÙg

1

functions correspond to specific colour

• structures. Depending on the process, one extracts different combinations

Buffing, Mukherjee, Mulders, PRD 88 (2013) 054027); See also the nice overview by D. Boer : Few Body Syst. 58 (2017) 32

Quarkonium production in pp collisions might face factorisation breaking effects if the bleaching of the heavy-quark pair occurs over long times (COM-NRQCD and CEM approaches) as opposed to Colour-Singlet contributions CS vs. CO contributions should be analysed case by case [reactions and kinematics] ◗ ✔ ◗ ✔ ◗ ✔

❺

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 7 / 20

Quarkonium production and TMD factorisation applicability/breaking

hÙg

1

receives contributions from Initial-State Interactions (ISI) and Final-State Interactions (FSI) Tese can make hÙg

1

process dependent and even break factorisation Different independent hÙg

1

functions correspond to specific colour

• structures. Depending on the process, one extracts different combinations

Buffing, Mukherjee, Mulders, PRD 88 (2013) 054027); See also the nice overview by D. Boer : Few Body Syst. 58 (2017) 32

Quarkonium production in pp collisions might face factorisation breaking effects if the bleaching of the heavy-quark pair occurs over long times (COM-NRQCD and CEM approaches) as opposed to Colour-Singlet contributions CS vs. CO contributions should be analysed case by case [reactions and kinematics] However, if TMD factorisation holds for H0+jet as conjectured by

• D. Boer-C. Pisano, there should be no issue for ◗ ✔ γ, ◗ ✔ Z or ◗ ✔ γ❺
• D. Boer, C. Pisano PRD 91 (2015) 074024

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 7 / 20

Part III Quarkonia and gluon TMDs at hadron colliders

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 8 / 20

2 2 vs 2 1 processes

• ✟
• P
• Ñ

Ñ ❙Ñ ❙ P ✟ ❼ ✔ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 9 / 20

2 2 vs 2 1 processes

2 1 process :

Hard scale can only be the particle mass : Q2 ✟ M2 does not help to study TMD evolution Resulting particle has to be at small qT (qT P M) likely difficult to measure at colliders, in particular for mesons (less for H, W, Z)

• Ñ

Ñ ❙Ñ ❙ P ✟ ❼ ✔ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 9 / 20

2 2 vs 2 1 processes

2 1 process :

Hard scale can only be the particle mass : Q2 ✟ M2 does not help to study TMD evolution Resulting particle has to be at small qT (qT P M) likely difficult to measure at colliders, in particular for mesons (less for H, W, Z)

Back-to-back (low qT) 2 2 process :

Produced particles can each have a large Ñ pT adding up to make a small Ñ qT for the

• pair. One can impose ❙Ñ

pT❙ large enough for the particle to be detectable Tis renders the TMD “region” (qT P Q) virtually as wide as we wish Hard scale Q2 ✟ ❼p1 ✔ p2➁2 can be tuned to study the QCD evolution of the TMDs Drawback : yield can be populated by Double Parton Scatterings (DPS)

J.P.L., H.S. Shao JHEP 1610 (2016) 153, NPB 900 (2015) 273, PLB 751 (2015) 479 J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 9 / 20

Low PT quarkonia and TMDs

Ù ❼ ➁ ➀ ✏ ❼

➁

❼ ➁ ➀ ✔ ❼

➁

• ❈

Ù Ù ✆

❈ ✆

✟

◗ ❆

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 10 / 20

Low PT quarkonia and TMDs

Polarized gluon studies with charmonium and bottomonium at LHCb and AFTER

Danie ¨l Boer* Theory Group, KVI, University of Groningen, Zernikelaan 25, NL-9747 AA Groningen, The Netherlands Cristian Pisano† Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, C.P. 170, I-09042 Monserrato (CA), Italy PHYSICAL REVIEW D 86, 094007 (2012)

Ù ❼ ➁ ➀ ✏ ❼

➁

❼ ➁ ➀ ✔ ❼

➁

• ❈

Ù Ù ✆

❈ ✆

✟

◗ ❆

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 10 / 20

Low PT quarkonia and TMDs

Polarized gluon studies with charmonium and bottomonium at LHCb and AFTER

Danie ¨l Boer* Theory Group, KVI, University of Groningen, Zernikelaan 25, NL-9747 AA Groningen, The Netherlands Cristian Pisano† Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, C.P. 170, I-09042 Monserrato (CA), Italy PHYSICAL REVIEW D 86, 094007 (2012)

Low PT C-even quarkonium production is a good probe of hÙg

1

In general, heavy-flavor prod. selects out gg channels

❼ ➁ ➀ ✏ ❼

➁

❼ ➁ ➀ ✔ ❼

➁

• ❈

Ù Ù ✆

❈ ✆

✟

◗ ❆

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 10 / 20

Low PT quarkonia and TMDs

Polarized gluon studies with charmonium and bottomonium at LHCb and AFTER

Danie ¨l Boer* Theory Group, KVI, University of Groningen, Zernikelaan 25, NL-9747 AA Groningen, The Netherlands Cristian Pisano† Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, C.P. 170, I-09042 Monserrato (CA), Italy PHYSICAL REVIEW D 86, 094007 (2012)

Low PT C-even quarkonium production is a good probe of hÙg

1

In general, heavy-flavor prod. selects out gg channels Affect the low PT spectra:

1 σ dσ❼ηQ➁ dq2

T

➀ 1 ✏ R❼q2

T➁ & 1 σ dσ❼χQ,0➁ dq2

T

➀ 1 ✔ R❼q2

T➁

(R

❈whh

0 hÙg 1 hÙg 1 ✆

❈f g

1 f g 1 ✆

) ✟

◗ ❆

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 1 1.5 2 2.5 3

qT σ-1dσ / d (GeV-2)

〈 pT

2 〉 = 1 GeV2

qT

2

(GeV)

h1

⊥ g =

0) ( χ0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 1 1.5 2 2.5 3

qT σ-1dσ / d (GeV-2)

〈 pT

2 〉 = 1 GeV2

qT

2

(GeV)

h1

⊥ g =

0) ( χ2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 1 1.5 2 2.5 3

qT σ-1dσ / d (GeV-2)

〈 pT

2 〉 = 1 GeV2

qT

2

(GeV)

h1

⊥ g =

0) ( ηQ

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 10 / 20

Low PT quarkonia and TMDs

Polarized gluon studies with charmonium and bottomonium at LHCb and AFTER

Danie ¨l Boer* Theory Group, KVI, University of Groningen, Zernikelaan 25, NL-9747 AA Groningen, The Netherlands Cristian Pisano† Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, C.P. 170, I-09042 Monserrato (CA), Italy PHYSICAL REVIEW D 86, 094007 (2012)

Low PT C-even quarkonium production is a good probe of hÙg

1

In general, heavy-flavor prod. selects out gg channels Affect the low PT spectra:

1 σ dσ❼ηQ➁ dq2

T

➀ 1 ✏ R❼q2

T➁ & 1 σ dσ❼χQ,0➁ dq2

T

➀ 1 ✔ R❼q2

T➁

(R

❈whh

0 hÙg 1 hÙg 1 ✆

❈f g

1 f g 1 ✆

) Cannot tune Q: Q ✟ m◗

❆

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 1 1.5 2 2.5 3

qT σ-1dσ / d (GeV-2)

〈 pT

2 〉 = 1 GeV2

qT

2

(GeV)

h1

⊥ g =

0) ( χ0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 1 1.5 2 2.5 3

qT σ-1dσ / d (GeV-2)

〈 pT

2 〉 = 1 GeV2

qT

2

(GeV)

h1

⊥ g =

0) ( χ2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 1 1.5 2 2.5 3

qT σ-1dσ / d (GeV-2)

〈 pT

2 〉 = 1 GeV2

qT

2

(GeV)

h1

⊥ g =

0) ( ηQ

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 10 / 20

Low PT quarkonia and TMDs

Polarized gluon studies with charmonium and bottomonium at LHCb and AFTER

Danie ¨l Boer* Theory Group, KVI, University of Groningen, Zernikelaan 25, NL-9747 AA Groningen, The Netherlands Cristian Pisano† Istituto Nazionale di Fisica Nucleare, Sezione di Cagliari, C.P. 170, I-09042 Monserrato (CA), Italy PHYSICAL REVIEW D 86, 094007 (2012)

Low PT C-even quarkonium production is a good probe of hÙg

1

In general, heavy-flavor prod. selects out gg channels Affect the low PT spectra:

1 σ dσ❼ηQ➁ dq2

T

➀ 1 ✏ R❼q2

T➁ & 1 σ dσ❼χQ,0➁ dq2

T

➀ 1 ✔ R❼q2

T➁

(R

❈whh

0 hÙg 1 hÙg 1 ✆

❈f g

1 f g 1 ✆

) Cannot tune Q: Q ✟ m◗ Low PT: Experimentally very difficult

First ηc production study at collider ever, only released in 2014 for Pηc

T ❆ 6 GeV LHCb, EPJC75 (2015) 311

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 1 1.5 2 2.5 3

qT σ-1dσ / d (GeV-2)

〈 pT

2 〉 = 1 GeV2

qT

2

(GeV)

h1

⊥ g =

0) ( χ0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 1 1.5 2 2.5 3

qT σ-1dσ / d (GeV-2)

〈 pT

2 〉 = 1 GeV2

qT

2

(GeV)

h1

⊥ g =

0) ( χ2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.5 1 1.5 2 2.5 3

qT σ-1dσ / d (GeV-2)

〈 pT

2 〉 = 1 GeV2

qT

2

(GeV)

h1

⊥ g =

0) ( ηQ

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 10 / 20

Low PT quarkonia and TMDs II

ηc production at one-loop : factorisation holds ✏

• J.P. Lansberg (IPNO)

Gluon TMD studies using quarkonia November 16, 2017 11 / 20

Low PT quarkonia and TMDs II

ηc production at one-loop : factorisation holds χc0,2 factorisation issue ? ✏ Colour Octet - Colour Singlet mixing

Low qT χc data exist: empirical check of TMD factorisation possible

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 11 / 20

First phenomenological study of ηc production with TMDs

M.G. Echevarria, T. Kasemets, JPL, C. Pisano, A. Signori - in preparation

✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 12 / 20

First phenomenological study of ηc production with TMDs

M.G. Echevarria, T. Kasemets, JPL, C. Pisano, A. Signori - in preparation

Hard coefficient at one loop

• J. Kuhn, E. Mirkes, PRD 48 (1993) 17; A. Petrelli et al.NPB 514 (1998) 245; J.P. Ma, J.X. Wang, S. Zhao PRD 88 (2013) 014027

✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 12 / 20

First phenomenological study of ηc production with TMDs

M.G. Echevarria, T. Kasemets, JPL, C. Pisano, A. Signori - in preparation

Hard coefficient at one loop

• J. Kuhn, E. Mirkes, PRD 48 (1993) 17; A. Petrelli et al.NPB 514 (1998) 245; J.P. Ma, J.X. Wang, S. Zhao PRD 88 (2013) 014027

Evolution taken in account at NNLL ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 12 / 20

First phenomenological study of ηc production with TMDs

M.G. Echevarria, T. Kasemets, JPL, C. Pisano, A. Signori - in preparation

Hard coefficient at one loop

• J. Kuhn, E. Mirkes, PRD 48 (1993) 17; A. Petrelli et al.NPB 514 (1998) 245; J.P. Ma, J.X. Wang, S. Zhao PRD 88 (2013) 014027

Evolution taken in account at NNLL Considers both the TMD and FO contributions to extend the qT range up to the LHCb data ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 12 / 20

First phenomenological study of ηc production with TMDs

M.G. Echevarria, T. Kasemets, JPL, C. Pisano, A. Signori - in preparation

Hard coefficient at one loop

• J. Kuhn, E. Mirkes, PRD 48 (1993) 17; A. Petrelli et al.NPB 514 (1998) 245; J.P. Ma, J.X. Wang, S. Zhao PRD 88 (2013) 014027

Evolution taken in account at NNLL Considers both the TMD and FO contributions to extend the qT range up to the LHCb data Matching: inverse variance weighted average vs. ”improved W ✔ Y”

For iW+Y see J.C. Collins et al. PRD94 (2016) 034014 J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 12 / 20

First phenomenological study of ηc production with TMDs

M.G. Echevarria, T. Kasemets, JPL, C. Pisano, A. Signori - in preparation

Hard coefficient at one loop

• J. Kuhn, E. Mirkes, PRD 48 (1993) 17; A. Petrelli et al.NPB 514 (1998) 245; J.P. Ma, J.X. Wang, S. Zhao PRD 88 (2013) 014027

Evolution taken in account at NNLL Considers both the TMD and FO contributions to extend the qT range up to the LHCb data Matching: inverse variance weighted average vs. ”improved W ✔ Y”

For iW+Y see J.C. Collins et al. PRD94 (2016) 034014 J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 12 / 20

Processes proposed to study the gluon TMD at hh colliders

➐ ➐

❼ ⑦ ➁ ✔

• ✔

➐ ➐

✔ ❼ ⑦ ➁ ✔ ⑦ ❻

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 13 / 20

Processes proposed to study the gluon TMD at hh colliders

➐gg➐ γγ : J.W Qiu, M. Schlegel, W. Vogelsang, PRL 107, 062001 (2011)

gg ❼J⑦ψ, Υ➁ ✔ γ : W. den Dunnen, JPL, C. Pisano, M. Schlegel, PRL 112, 212001 (2014) gg ηc ✔ ηc : G.P. Zhang, PRD 90 (2014) 9 094011

➐gg➐ H0 ✔ jet : D. Boer, C. Pisano, PRD 91 (2015) 074024

gg ❼J⑦ψ, Υ➁ ✔ Z⑦γ❻ : JPL , C. Pisano, M. Schlegel, NPB 920 (2017) 192

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 13 / 20

Processes proposed to study the gluon TMD at hh colliders

➐gg➐ γγ : J.W Qiu, M. Schlegel, W. Vogelsang, PRL 107, 062001 (2011)

gg ❼J⑦ψ, Υ➁ ✔ γ : W. den Dunnen, JPL, C. Pisano, M. Schlegel, PRL 112, 212001 (2014) gg ηc ✔ ηc : G.P. Zhang, PRD 90 (2014) 9 094011

➐gg➐ H0 ✔ jet : D. Boer, C. Pisano, PRD 91 (2015) 074024

gg ❼J⑦ψ, Υ➁ ✔ Z⑦γ❻ : JPL , C. Pisano, M. Schlegel, NPB 920 (2017) 192

None are measured so far ...

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 13 / 20

Part IV Te case

• f quarkonium pair production in more details

µ ν

P2

PQ,2 x1P1 + k1T x2P2 + k2T

P1 Φµν

g (x1, k1T )

Φρσ

g (x2, k2T )

ρ σ

PQ,1

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 14 / 20

J⑦ψ ✔ J⑦ψ at low Pψψ

T

⑦ ➸

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 15 / 20

J⑦ψ ✔ J⑦ψ at low Pψψ

T

J⑦ψ are relatively easy to detect. Already studied by LHCb, CMS & ATLAS at the LHC and D0 at the Tevatron

LHCb PLB 707 (2012) 52; JHEP 1706 (2017) 047; CMS JHEP 1409 (2014) 094; ATLAS EPJC 77 (2017) 76; D0 PRD 90 (2014) 111101

➸

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 15 / 20

J⑦ψ ✔ J⑦ψ at low Pψψ

T

J⑦ψ are relatively easy to detect. Already studied by LHCb, CMS & ATLAS at the LHC and D0 at the Tevatron

LHCb PLB 707 (2012) 52; JHEP 1706 (2017) 047; CMS JHEP 1409 (2014) 094; ATLAS EPJC 77 (2017) 76; D0 PRD 90 (2014) 111101

Negligible q¯ q contributions even at AFTER@LHC (➸s 115 GeV) energies

J.P.L., H.S. Shao NPB 900 (2015) 273 J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 15 / 20

J⑦ψ ✔ J⑦ψ at low Pψψ

T

J⑦ψ are relatively easy to detect. Already studied by LHCb, CMS & ATLAS at the LHC and D0 at the Tevatron

LHCb PLB 707 (2012) 52; JHEP 1706 (2017) 047; CMS JHEP 1409 (2014) 094; ATLAS EPJC 77 (2017) 76; D0 PRD 90 (2014) 111101

Negligible q¯ q contributions even at AFTER@LHC (➸s 115 GeV) energies

J.P.L., H.S. Shao NPB 900 (2015) 273

Negligible CO contributions, in particular at low Pψψ

T

[black/dashed curves vs. blue]

JPL, H.S. Shao PLB 751 (2015) 479

No final state gluon needed for the Born contribution: pure colourless final state

JPL, H.S. Shao PRL 111, 122001 (2013) 10 20 30 40 107 106 105 104 103 102 101 1

PT

ΨΨ GeV

dΣdPT

ΨΨ nbGeV

1S0 81S0 8 max 3S1 83S1 8 max

NLO SPS LO SPSsmearing CMS Accep. 7 TeVLHC

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 15 / 20

J⑦ψ ✔ J⑦ψ at low Pψψ

T

J⑦ψ are relatively easy to detect. Already studied by LHCb, CMS & ATLAS at the LHC and D0 at the Tevatron

LHCb PLB 707 (2012) 52; JHEP 1706 (2017) 047; CMS JHEP 1409 (2014) 094; ATLAS EPJC 77 (2017) 76; D0 PRD 90 (2014) 111101

Negligible q¯ q contributions even at AFTER@LHC (➸s 115 GeV) energies

J.P.L., H.S. Shao NPB 900 (2015) 273

Negligible CO contributions, in particular at low Pψψ

T

[black/dashed curves vs. blue]

JPL, H.S. Shao PLB 751 (2015) 479

No final state gluon needed for the Born contribution: pure colourless final state

JPL, H.S. Shao PRL 111, 122001 (2013)

At low Pψψ

T , small DPS effects, but DPS required by the CMS & ATLAS data at large ∆y

10 20 30 40 107 106 105 104 103 102 101 1

PT

ΨΨ GeV

dΣdPT

ΨΨ nbGeV

1S0 81S0 8 max 3S1 83S1 8 max

NLO SPS LO SPSsmearing CMS Accep. 7 TeVLHC ) ψ ,J/ ψ y(J/ ∆ 0.5 1 1.5 2 2.5 3 3.5 4 y [pb/0.3] ∆ /d σ d

2 −

10

1 −

10 1 10

2.1% ± = 9.2%

DPS

f Data DPS Estimate . DPS Pred NLO* SPS+DPS Pred. ATLAS

• 1

= 8 TeV, 11.4 fb s

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 15 / 20

What’s special about double vector onium production ?

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

❇

◗ ✔ ◗ ◗ ❼ ➁

• ◆

◗◗ ◗

✂

• ◗

❼ ➁

◗◗

✏

◗

❼ ➁

◗◗

• ◗◗

✟ ⑦

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 16 / 20

What’s special about double vector onium production ?

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

In general, the hard scattering coefficients are bounded :

F2,3,4 ❇ F1

◗ ✔ ◗ ◗ ❼ ➁

• ◆

◗◗ ◗

✂

• ◗

❼ ➁

◗◗

✏

◗

❼ ➁

◗◗

• ◗◗

✟ ⑦

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 16 / 20

What’s special about double vector onium production ?

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

In general, the hard scattering coefficients are bounded :

F2,3,4 ❇ F1

gg ◗ ✔ ◗ in the limit where Mψψ ◗ Mψ and cos❼θCS➁ 0 : F1 256◆ M4

◗◗M2 ◗

✂ F4, F2 F1 81M4

◗ cos❼θCS➁2

2M4

◗◗

, F3 F1 ✏24M2

◗ cos❼θCS➁2

M2

◗◗

• ◗◗

✟ ⑦

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 16 / 20

What’s special about double vector onium production ?

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

In general, the hard scattering coefficients are bounded :

F2,3,4 ❇ F1

gg ◗ ✔ ◗ in the limit where Mψψ ◗ Mψ and cos❼θCS➁ 0 : F1 256◆ M4

◗◗M2 ◗

✂ F4, F2 F1 81M4

◗ cos❼θCS➁2

2M4

◗◗

, F3 F1 ✏24M2

◗ cos❼θCS➁2

M2

◗◗

F4 F1 at large M◗◗

✟ di-J⑦ψ (or di-Υ) maximise the observability of cos4ϕ modulations in a kinematical region where data are already taken !

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 16 / 20

TMD modelling : f g

1 and the relevance of the LHCb data

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

Ñ ❼ Ñ ➁

❼ ➁ ❵ ❡

✏Ñ ❵ ❡

❼ ➁

❵ ❡ ❈ ✆ ⑦ ✟ ❼ ➁ P ✟ ❈ ✆

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 17 / 20

TMD modelling : f g

1 and the relevance of the LHCb data

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

f g

1 modelled as a Gaussian in Ñ

kT : f g

1 ❼x,Ñ

k2

T➁ g❼x➁ π❵k2

T❡e ✏Ñ k2 T ❵k2 T❡

where g❼x➁ is the usual collinear PDF

First experimental determination [with a pure colorless final state] of ❵k2

T❡

by fitting ❈f g

1 f g 1 ✆ over the normalised LHCb dσ⑦dPψψT spectrum at 13 TeV

✟ ❼ ➁ P ✟ ❈ ✆

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 17 / 20

TMD modelling : f g

1 and the relevance of the LHCb data

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

f g

1 modelled as a Gaussian in Ñ

kT : f g

1 ❼x,Ñ

k2

T➁ g❼x➁ π❵k2

T❡e ✏Ñ k2 T ❵k2 T❡

where g❼x➁ is the usual collinear PDF

First experimental determination [with a pure colorless final state] of ❵k2

T❡

by fitting ❈f g

1 f g 1 ✆ over the normalised LHCb dσ⑦dPψψT spectrum at 13 TeV

dσ/dPψψT / ∫0

<Mψψ> /2 dσ/dPψψT [GeV-1]

PψψT [GeV] Gaussian f1

g, <kT 2> fit

• ver [0 ;<Mψψ>/2]

LHCb data 0.1 0.2 0.3 0.4 2 4 6 8 10 12 14 <kT

2> = 4.9 ± 0.8 GeV2

<Mψψ> = 8 GeV

✟ ❼ ➁ P ✟ ❈ ✆

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 17 / 20

TMD modelling : f g

1 and the relevance of the LHCb data

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

f g

1 modelled as a Gaussian in Ñ

kT : f g

1 ❼x,Ñ

k2

T➁ g❼x➁ π❵k2

T❡e ✏Ñ k2 T ❵k2 T❡

where g❼x➁ is the usual collinear PDF

First experimental determination [with a pure colorless final state] of ❵k2

T❡

by fitting ❈f g

1 f g 1 ✆ over the normalised LHCb dσ⑦dPψψT spectrum at 13 TeV

dσ/dPψψT / ∫0

<Mψψ> /2 dσ/dPψψT [GeV-1]

PψψT [GeV] Gaussian f1

g, <kT 2> fit

• ver [0 ;<Mψψ>/2]

LHCb data 0.1 0.2 0.3 0.4 2 4 6 8 10 12 14 <kT

2> = 4.9 ± 0.8 GeV2

<Mψψ> = 8 GeV

Integration over ϕ ✟ cos❼nϕ➁-terms cancel out F2 P F1 ✟ only ❈f g

1 f g 1 ✆

contributes to the cross-section No evolution so far Room lef for DPS

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 17 / 20

Modelling hÙg

1

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 18 / 20

Modelling hÙg

1 1

◮ ”Gaussian” h⊥g 1 (x,

k2

T) ⇒ Model 1

Boer, de Dunnen, Pisano, Schlegel, Vogelsang, PRL 108 (2012) 032002

Florent Scarpa Gluon TMDs & J/ψ-pair production 10 / 13

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 18 / 20

Modelling hÙg

1 1

◮ ”Gaussian” h⊥g 1 (x,

k2

T) ⇒ Model 1

Boer, de Dunnen, Pisano, Schlegel, Vogelsang, PRL 108 (2012) 032002

◮ Positivity bound : h⊥g 1 (x,

k2

T) ≤ 2M2 p

• k2

T

f g

1 (x,

k2

T) = maximal value

(bound saturated) ⇒ Model 2 supported by low-x computations

Florent Scarpa Gluon TMDs & J/ψ-pair production 10 / 13

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 18 / 20

Modelling hÙg

1 1

◮ ”Gaussian” h⊥g 1 (x,

k2

T) ⇒ Model 1

Boer, de Dunnen, Pisano, Schlegel, Vogelsang, PRL 108 (2012) 032002

◮ Positivity bound : h⊥g 1 (x,

k2

T) ≤ 2M2 p

• k2

T

f g

1 (x,

k2

T) = maximal value

(bound saturated) ⇒ Model 2 supported by low-x computations

• 0.2

0.2 0.4 0.6 0.8 1 5 10 15 20 C[w TMD1 TMD2] / C[f1

g f1 g]

PψψT [GeV] <kT

2> = 4.9 GeV2 w2 h1

⊥g h1 ⊥g : Model 1

Model 2 − w3 f1

g h1 ⊥g : Model 1

Model 2 w4 h1

⊥g h1 ⊥g : Model 1

Model 2

Florent Scarpa Gluon TMDs & J/ψ-pair production 10 / 13

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 18 / 20

Expected azimuthal asymmetries

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684 J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 19 / 20

Expected azimuthal asymmetries

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

cos nφCS = 2π dφCS cos nφCS dσ 2π dφCS dσ n = 0, 2, 4 (7) = relative amplitude of the azimuthal modulations

Florent Scarpa Gluon TMDs & J/ψ-pair production 11 / 13

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 19 / 20

Expected azimuthal asymmetries

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

cos nφCS = 2π dφCS cos nφCS dσ 2π dφCS dσ n = 0, 2, 4 (7) = relative amplitude of the azimuthal modulations

• 8
• 6
• 4
• 2

2 4 6 8 10 <cos 2φCS> [in %] PψψT [GeV] <kT

2> = 4.9 GeV2

|cos θCS| < 0.25 Mψψ = 8 GeV Mψψ = 12 GeV Mψψ = 21 GeV Model 1 Model 2 10 20 30 40 50 60 2 4 6 8 10 <cos 4φCS> [in /%] PψψT [GeV] <kT

2> = 4.9 GeV2

|cos θCS| < 0.25 Mψψ = 8 GeV Mψψ = 12 GeV Mψψ = 21 GeV Model 1 Model 2 ◮ cos 4φ-modulations up to 50% !

Florent Scarpa Gluon TMDs & J/ψ-pair production 11 / 13

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 19 / 20

Expected azimuthal asymmetries

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

• 35
• 30
• 25
• 20
• 15
• 10
• 5

2 4 6 8 10 <cos 2φCS> [in %] PψψT [GeV] <kT

2> = 4.9 GeV2

0.25 < |cos θCS| < 0.5 Mψψ = 8 GeV Mψψ = 12 GeV Mψψ = 21 GeV Model 1 Model 2

• 25
• 20
• 15
• 10
• 5

5 2 4 6 8 10 <cos 4φCS> [in /%] PψψT [GeV] <kT

2> = 4.9 GeV2

0.25 < |cos θCS| < 0.5 Mψψ = 8 GeV Mψψ = 12 GeV Mψψ = 21 GeV Model 1 Model 2

Florent Scarpa Gluon TMDs & J/ψ-pair production 12 / 13

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 19 / 20

Expected azimuthal asymmetries

JPL, C. Pisano, F. Scarpa, M. Schlegel, arXiv:1710.01684

• 35
• 30
• 25
• 20
• 15
• 10
• 5

2 4 6 8 10 <cos 2φCS> [in %] PψψT [GeV] <kT

2> = 4.9 GeV2

0.25 < |cos θCS| < 0.5 Mψψ = 8 GeV Mψψ = 12 GeV Mψψ = 21 GeV Model 1 Model 2

• 25
• 20
• 15
• 10
• 5

5 2 4 6 8 10 <cos 4φCS> [in /%] PψψT [GeV] <kT

2> = 4.9 GeV2

0.25 < |cos θCS| < 0.5 Mψψ = 8 GeV Mψψ = 12 GeV Mψψ = 21 GeV Model 1 Model 2 ◮ cos 2φCS reaches 30% ⇒ important to determine the sign of h⊥g 1 ◮ cos 4φCS changes sign ⇒ one must be careful when integrating

• ver the phase space

Florent Scarpa Gluon TMDs & J/ψ-pair production 12 / 13

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 19 / 20

Conclusions and Outlooks

Unpolarised TMD studies in the gluon sector are very promising ⑦ ⑦ ✔ ✔ ❼ ➁

Ù ❼

➁

• ⑦

◗ ◗ ✔ ◗ ✔ ◗ ⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 20 / 20

Conclusions and Outlooks

Unpolarised TMD studies in the gluon sector are very promising With lepton beams, only possible at an EIC ⑦ ⑦ ✔ ✔ ❼ ➁

Ù ❼

➁

• ⑦

◗ ◗ ✔ ◗ ✔ ◗ ⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 20 / 20

Conclusions and Outlooks

Unpolarised TMD studies in the gluon sector are very promising With lepton beams, only possible at an EIC If we don’t want to wait for 10 years, LHC can help, right now ! ⑦ ⑦ ✔ ✔ ❼ ➁

Ù ❼

➁

• ⑦

◗ ◗ ✔ ◗ ✔ ◗ ⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 20 / 20

Conclusions and Outlooks

Unpolarised TMD studies in the gluon sector are very promising With lepton beams, only possible at an EIC If we don’t want to wait for 10 years, LHC can help, right now ! Low PT ηc production [below Mηc⑦2] is highly challenging, however NLO-NNLL pheno study available soon ⑦ ✔ ✔ ❼ ➁

Ù ❼

➁

• ⑦

◗ ◗ ✔ ◗ ✔ ◗ ⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 20 / 20

Conclusions and Outlooks

Unpolarised TMD studies in the gluon sector are very promising With lepton beams, only possible at an EIC If we don’t want to wait for 10 years, LHC can help, right now ! Low PT ηc production [below Mηc⑦2] is highly challenging, however NLO-NNLL pheno study available soon Back-to-back J⑦ψ ✔ γ or Υ ✔ γ is certainly at reach

[events already on tapes]

f g

1 ❼x,kT, µ➁ and hÙg 1 ❼x,kT, µ➁ can be determined separately

Q can even be tuned gluon TMD evolution Back-to-back J⑦ψ pair already measured ◗ ◗ ✔ ◗ ✔ ◗ ⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 20 / 20

Conclusions and Outlooks

Unpolarised TMD studies in the gluon sector are very promising With lepton beams, only possible at an EIC If we don’t want to wait for 10 years, LHC can help, right now ! Low PT ηc production [below Mηc⑦2] is highly challenging, however NLO-NNLL pheno study available soon Back-to-back J⑦ψ ✔ γ or Υ ✔ γ is certainly at reach

[events already on tapes]

f g

1 ❼x,kT, µ➁ and hÙg 1 ❼x,kT, µ➁ can be determined separately

Q can even be tuned gluon TMD evolution Back-to-back J⑦ψ pair already measured Back-to-back vector onium pair: largest possible cos4ϕ modulations ! ◗ ◗ ✔ ◗ ✔ ◗ ⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 20 / 20

Conclusions and Outlooks

Unpolarised TMD studies in the gluon sector are very promising With lepton beams, only possible at an EIC If we don’t want to wait for 10 years, LHC can help, right now ! Low PT ηc production [below Mηc⑦2] is highly challenging, however NLO-NNLL pheno study available soon Back-to-back J⑦ψ ✔ γ or Υ ✔ γ is certainly at reach

[events already on tapes]

f g

1 ❼x,kT, µ➁ and hÙg 1 ❼x,kT, µ➁ can be determined separately

Q can even be tuned gluon TMD evolution Back-to-back J⑦ψ pair already measured Back-to-back vector onium pair: largest possible cos4ϕ modulations ! Gluon Sivers effect uncovered by COMPASS; not small

COMPASS arXiv:1701.02453 See also D. Boer, C. Lorc´ e, C. Pisano, J. Zhou, Adv.High Energy Phys. 2015 (2015) 371396

◗ ◗ ✔ ◗ ✔ ◗ ⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 20 / 20

Conclusions and Outlooks

Unpolarised TMD studies in the gluon sector are very promising With lepton beams, only possible at an EIC If we don’t want to wait for 10 years, LHC can help, right now ! Low PT ηc production [below Mηc⑦2] is highly challenging, however NLO-NNLL pheno study available soon Back-to-back J⑦ψ ✔ γ or Υ ✔ γ is certainly at reach

[events already on tapes]

f g

1 ❼x,kT, µ➁ and hÙg 1 ❼x,kT, µ➁ can be determined separately

Q can even be tuned gluon TMD evolution Back-to-back J⑦ψ pair already measured Back-to-back vector onium pair: largest possible cos4ϕ modulations ! Gluon Sivers effect uncovered by COMPASS; not small

COMPASS arXiv:1701.02453 See also D. Boer, C. Lorc´ e, C. Pisano, J. Zhou, Adv.High Energy Phys. 2015 (2015) 371396

Low PT ◗, ◗ ✔ γ, ◗ ✔ ◗ STSA precision studies are possible with A Fixed-Target Experiment at the LHC: AFTER@LHC

• D. Kikola et al. Few Body Syst. 58 (2017) 139

⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 20 / 20

Conclusions and Outlooks

Unpolarised TMD studies in the gluon sector are very promising With lepton beams, only possible at an EIC If we don’t want to wait for 10 years, LHC can help, right now ! Low PT ηc production [below Mηc⑦2] is highly challenging, however NLO-NNLL pheno study available soon Back-to-back J⑦ψ ✔ γ or Υ ✔ γ is certainly at reach

[events already on tapes]

f g

1 ❼x,kT, µ➁ and hÙg 1 ❼x,kT, µ➁ can be determined separately

Q can even be tuned gluon TMD evolution Back-to-back J⑦ψ pair already measured Back-to-back vector onium pair: largest possible cos4ϕ modulations ! Gluon Sivers effect uncovered by COMPASS; not small

COMPASS arXiv:1701.02453 See also D. Boer, C. Lorc´ e, C. Pisano, J. Zhou, Adv.High Energy Phys. 2015 (2015) 371396

Low PT ◗, ◗ ✔ γ, ◗ ✔ ◗ STSA precision studies are possible with A Fixed-Target Experiment at the LHC: AFTER@LHC

• D. Kikola et al. Few Body Syst. 58 (2017) 139

J⑦ψ ✔ γ STSA study might also be possible with STAR in very favourable conditions

JPL, C. Pisano, M. Schlegel, in progress J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 20 / 20

Part V Backup

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 21 / 20

◗ ✔ γ at low Pψ✏γ

T

• W. den Dunnen, JPL, C. Pisano, M. Schlegel, PRL 112, 212001 (2014)

Q γ

Unique candidate to pin down the gluon TMDs

✏ ✏

▲ ✟

✏

❙❼ ➁ ❾ ➃

✏

❘ ❼ ➁

❙❼ ➁

❈ ✆ ❘ ❈ ✆ Ù

❙❼ ➁

❈

Ù ✔

✏ ✆ ❘ ❈ ✆

❙❼ ➁

❈

Ù Ù ✆

❘ ❈ ✆

❙❼ ➁ ❙❼ ➁ ① ✟

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 22 / 20

◗ ✔ γ at low Pψ✏γ

T

• W. den Dunnen, JPL, C. Pisano, M. Schlegel, PRL 112, 212001 (2014)

Q γ

Unique candidate to pin down the gluon TMDs Hard scale Mψ✏γ (or Qψ✏γ) can be tuned ▲ ✟

✏

❙❼ ➁ ❾ ➃

✏

❘ ❼ ➁

❙❼ ➁

❈ ✆ ❘ ❈ ✆ Ù

❙❼ ➁

❈

Ù ✔

✏ ✆ ❘ ❈ ✆

❙❼ ➁

❈

Ù Ù ✆

❘ ❈ ✆

❙❼ ➁ ❙❼ ➁ ① ✟

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 22 / 20

◗ ✔ γ at low Pψ✏γ

T

• W. den Dunnen, JPL, C. Pisano, M. Schlegel, PRL 112, 212001 (2014)

Q γ

Unique candidate to pin down the gluon TMDs Hard scale Mψ✏γ (or Qψ✏γ) can be tuned gluon sensitive process [even at large xF (AFTER@LHC)] ▲ ✟

✏

❙❼ ➁ ❾ ➃

✏

❘ ❼ ➁

❙❼ ➁

❈ ✆ ❘ ❈ ✆ Ù

❙❼ ➁

❈

Ù ✔

✏ ✆ ❘ ❈ ✆

❙❼ ➁

❈

Ù Ù ✆

❘ ❈ ✆

❙❼ ➁ ❙❼ ➁ ① ✟

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 22 / 20

◗ ✔ γ at low Pψ✏γ

T

• W. den Dunnen, JPL, C. Pisano, M. Schlegel, PRL 112, 212001 (2014)

Q γ

Unique candidate to pin down the gluon TMDs Hard scale Mψ✏γ (or Qψ✏γ) can be tuned gluon sensitive process [even at large xF (AFTER@LHC)] With the ▲ ✟ 20 f✏1 of pp data on tape, one expects up to 2000 events ❙❼ ➁ ❾ ➃

✏

❘ ❼ ➁

❙❼ ➁

❈ ✆ ❘ ❈ ✆ Ù

❙❼ ➁

❈

Ù ✔

✏ ✆ ❘ ❈ ✆

❙❼ ➁

❈

Ù Ù ✆

❘ ❈ ✆

❙❼ ➁ ❙❼ ➁ ① ✟

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 22 / 20

◗ ✔ γ at low Pψ✏γ

T

• W. den Dunnen, JPL, C. Pisano, M. Schlegel, PRL 112, 212001 (2014)

Q γ

Unique candidate to pin down the gluon TMDs Hard scale Mψ✏γ (or Qψ✏γ) can be tuned gluon sensitive process [even at large xF (AFTER@LHC)] With the ▲ ✟ 20 f✏1 of pp data on tape, one expects up to 2000 events We define: ❙❼n➁

qT ❾ dσ dQdYd cos θCS➃ ✏1

❘ dϕCSπ cos❼nϕCS➁

dσ dQdYd2qTdΩ

❙❼ ➁

❈ ✆ ❘ ❈ ✆ Ù

❙❼ ➁

❈

Ù ✔

✏ ✆ ❘ ❈ ✆

❙❼ ➁

❈

Ù Ù ✆

❘ ❈ ✆

❙❼ ➁ ❙❼ ➁ ① ✟

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 22 / 20

◗ ✔ γ at low Pψ✏γ

T

• W. den Dunnen, JPL, C. Pisano, M. Schlegel, PRL 112, 212001 (2014)

Q γ

Unique candidate to pin down the gluon TMDs Hard scale Mψ✏γ (or Qψ✏γ) can be tuned gluon sensitive process [even at large xF (AFTER@LHC)] With the ▲ ✟ 20 f✏1 of pp data on tape, one expects up to 2000 events We define: ❙❼n➁

qT ❾ dσ dQdYd cos θCS➃ ✏1

❘ dϕCSπ cos❼nϕCS➁

dσ dQdYd2qTdΩ

❙❼0➁

qT ❈f g

1 f g 1 ✆

❘dq2

T ❈f g 1 f g 1 ✆: does not involve hÙg

1

[not always the case] ❙❼2➁

qT F3 ❈wfh

2 f g 1 hÙg 1 ✔x1✏x2✆

2F1❘dq2

T ❈f g 1 f g 1 ✆

❙❼4➁

qT F4 ❈whh

4 hÙg 1 hÙg 1 ✆

2F1❘dq2

T ❈f g 1 f g 1 ✆

❙❼2➁

qT ,❙❼4➁ qT ① 0 ✟ nonzero gluon polarisation in unpolarised protons !

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 22 / 20

Results with UGDs as Ans¨ atze for TMDs

• W. den Dunnen, JPL, C. Pisano, M. Schlegel, PRL 112, 212001 (2014)

2 4 6 8 10 qT GeV 0.005 0.010 0.020 0.050 0.100 SqT

0GeV2

Set B KMR CGC Gaussian

❙❼0➁

qT : f g 1 ❼x,kT➁ from the qT-dependence of the yield.

❙❼ ➁ ❘ ❙❼ ➁

❖❼ ✏ ➁

❙❼ ➁ ❙❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 23 / 20

Results with UGDs as Ans¨ atze for TMDs

• W. den Dunnen, JPL, C. Pisano, M. Schlegel, PRL 112, 212001 (2014)

2 4 6 8 10 qT GeV 0.005 0.010 0.020 0.050 0.100 SqT

0GeV2

Set B KMR CGC Gaussian 2 4 6 8 10 qT GeV 0.0010 0.0008 0.0006 0.0004 0.0002 SqT

2GeV2

Set B max KMR max CGC Gaussian max 2 4 6 8 10 qT GeV 0.0001 0.0002 0.0003 0.0004 SqT

4GeV2

Set B max KMR max CGC Gaussian max

❙❼0➁

qT : f g 1 ❼x,kT➁ from the qT-dependence of the yield.

❙❼4➁

qT : ❘ dqT❙❼4➁ qT should be measurable

[❖❼1 ✏ 2%➁: ok with 2000 events]

❙❼ ➁ ❙❼ ➁

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 23 / 20

Results with UGDs as Ans¨ atze for TMDs

• W. den Dunnen, JPL, C. Pisano, M. Schlegel, PRL 112, 212001 (2014)

2 4 6 8 10 qT GeV 0.005 0.010 0.020 0.050 0.100 SqT

0GeV2

Set B KMR CGC Gaussian 2 4 6 8 10 qT GeV 0.0010 0.0008 0.0006 0.0004 0.0002 SqT

2GeV2

Set B max KMR max CGC Gaussian max 2 4 6 8 10 qT GeV 0.0001 0.0002 0.0003 0.0004 SqT

4GeV2

Set B max KMR max CGC Gaussian max

❙❼0➁

qT : f g 1 ❼x,kT➁ from the qT-dependence of the yield.

❙❼4➁

qT : ❘ dqT❙❼4➁ qT should be measurable

[❖❼1 ✏ 2%➁: ok with 2000 events]

❙❼2➁

qT : slightly larger than ❙❼4➁ qT

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 23 / 20

J⑦ψ⑦Υ ✔ Z

Extending to J⑦ψ⑦Υ ✔ Z

Rates similar for Υ ✔ Z and J⑦ψ ✔ Z [Same for ◗ ✔ γ for Q à 20 GeV]

• B. Gong, J.P. Lansberg, C. Lorc´

e, J.X. Wang, JHEP 1303 (2013) 115

Q Z

◗ ✔ ⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 24 / 20

J⑦ψ⑦Υ ✔ Z

Extending to J⑦ψ⑦Υ ✔ Z

Rates similar for Υ ✔ Z and J⑦ψ ✔ Z [Same for ◗ ✔ γ for Q à 20 GeV]

• B. Gong, J.P. Lansberg, C. Lorc´

e, J.X. Wang, JHEP 1303 (2013) 115

Q Z

1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1 25 50 75 100 125 150

dσ/dPT x Br (fb/GeV)

PT

J/ψ (GeV) sqrt(s)=8 TeV µR=µF=mZ |yJ/ψ| < 2.4

NLO LO

1e-06 1e-05 0.0001 0.001 0.01 0.1 25 50 75 100 125 150

dσ/dPT x Br (fb/GeV)

Pϒ

T (GeV) sqrt(s)=8 TeV µR=µF=mZ |yϒ| < 2.4 NLO LO

◗ ✔ ⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 24 / 20

J⑦ψ⑦Υ ✔ Z

Extending to J⑦ψ⑦Υ ✔ Z

Rates similar for Υ ✔ Z and J⑦ψ ✔ Z [Same for ◗ ✔ γ for Q à 20 GeV]

• B. Gong, J.P. Lansberg, C. Lorc´

e, J.X. Wang, JHEP 1303 (2013) 115

Q Z

1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1 25 50 75 100 125 150

dσ/dPT x Br (fb/GeV)

PT

J/ψ (GeV) sqrt(s)=8 TeV µR=µF=mZ |yJ/ψ| < 2.4

NLO LO

1e-06 1e-05 0.0001 0.001 0.01 0.1 25 50 75 100 125 150

dσ/dPT x Br (fb/GeV)

Pϒ

T (GeV) sqrt(s)=8 TeV µR=µF=mZ |yϒ| < 2.4 NLO LO

Potential probe of gluon TMDs as well ◗ ✔ ⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 24 / 20

J⑦ψ⑦Υ ✔ Z

Extending to J⑦ψ⑦Υ ✔ Z

Rates similar for Υ ✔ Z and J⑦ψ ✔ Z [Same for ◗ ✔ γ for Q à 20 GeV]

• B. Gong, J.P. Lansberg, C. Lorc´

e, J.X. Wang, JHEP 1303 (2013) 115

Q Z

1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1 25 50 75 100 125 150

dσ/dPT x Br (fb/GeV)

PT

J/ψ (GeV) sqrt(s)=8 TeV µR=µF=mZ |yJ/ψ| < 2.4

NLO LO

1e-06 1e-05 0.0001 0.001 0.01 0.1 25 50 75 100 125 150

dσ/dPT x Br (fb/GeV)

Pϒ

T (GeV) sqrt(s)=8 TeV µR=µF=mZ |yϒ| < 2.4 NLO LO

Potential probe of gluon TMDs as well Rate clearly smaller than ◗ ✔ γ even at low PT; but much better detectability ⑦ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 24 / 20

J⑦ψ⑦Υ ✔ Z

Extending to J⑦ψ⑦Υ ✔ Z

Rates similar for Υ ✔ Z and J⑦ψ ✔ Z [Same for ◗ ✔ γ for Q à 20 GeV]

• B. Gong, J.P. Lansberg, C. Lorc´

e, J.X. Wang, JHEP 1303 (2013) 115

Q Z

1e-07 1e-06 1e-05 0.0001 0.001 0.01 0.1 1 25 50 75 100 125 150

dσ/dPT x Br (fb/GeV)

PT

J/ψ (GeV) sqrt(s)=8 TeV µR=µF=mZ |yJ/ψ| < 2.4

NLO LO

1e-06 1e-05 0.0001 0.001 0.01 0.1 25 50 75 100 125 150

dσ/dPT x Br (fb/GeV)

Pϒ

T (GeV) sqrt(s)=8 TeV µR=µF=mZ |yϒ| < 2.4 NLO LO

Potential probe of gluon TMDs as well Rate clearly smaller than ◗ ✔ γ even at low PT; but much better detectability First measurement of J⑦ψ ✔ Z by ATLAS; large DPS yield : unequal pT cuts ?

ATLAS EPJC 75 (2015) 229 ; J.P.L., H.S. Shao JHEP 1610 (2016) 153 J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 24 / 20

J⑦ψ⑦Υ ✔ Z

Υ ✔ Z & Υ ✔ γ❺ @➸s 14 TeV

JPL, C. Pisano, M. Schlegel, NPB 920 (2017) 192

• ❘ ❙❼ ➁ ✂

❘ ❙❼ ➁ ✂

• ❘ ❙❼ ➁ ✂

❘ ❙❼ ➁ ✂

• ❘ ❙❼ ➁ ✂

❘ ❙❼ ➁ ✂ ❙❼ ➁ ◗ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 25 / 20

J⑦ψ⑦Υ ✔ Z

Υ ✔ Z & Υ ✔ γ❺ @➸s 14 TeV

JPL, C. Pisano, M. Schlegel, NPB 920 (2017) 192

Q 120 GeV : Z on-shell [❘ ❙❼2➁ ✂ 0.007%; ❘ ❙❼4➁ ✂ 0.001%]

Set B KMR 10 20 30 40qT [GeV] 0.0005 0.0010 0.0015 0.0020 0.0025 S(0) [GeV-2] Set B + max KMR + max 10 20 30 40qT [GeV]

• 6.×10-8
• 4.×10-8
• 2.×10-8

S(2) [GeV-2] Set B + max KMR + max 10 20 30 40 qT [GeV] 2.×10-9 4.×10-9 6.×10-9 8.×10-9 1.×10-8 1.2×10-8 S(4) [GeV-2]

• ❘ ❙❼ ➁ ✂

❘ ❙❼ ➁ ✂

• ❘ ❙❼ ➁ ✂

❘ ❙❼ ➁ ✂ ❙❼ ➁ ◗ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 25 / 20

J⑦ψ⑦Υ ✔ Z

Υ ✔ Z & Υ ✔ γ❺ @➸s 14 TeV

JPL, C. Pisano, M. Schlegel, NPB 920 (2017) 192

Q 120 GeV : Z on-shell [❘ ❙❼2➁ ✂ 0.007%; ❘ ❙❼4➁ ✂ 0.001%]

Set B KMR 10 20 30 40qT [GeV] 0.0005 0.0010 0.0015 0.0020 0.0025 S(0) [GeV-2] Set B + max KMR + max 10 20 30 40qT [GeV]

• 6.×10-8
• 4.×10-8
• 2.×10-8

S(2) [GeV-2] Set B + max KMR + max 10 20 30 40 qT [GeV] 2.×10-9 4.×10-9 6.×10-9 8.×10-9 1.×10-8 1.2×10-8 S(4) [GeV-2]

Q 20 GeV & dilepton mass [5:7] GeV [❘ ❙❼2➁ ✂ 0.5%; ❘ ❙❼4➁ ✂ 0.05%]

Set B KMR 2 4 6 8 10qT [GeV] 0.005 0.010 0.015 0.020 0.025 S(0) [GeV-2]

Set B + max KMR + max 1 2 3 4 5 6 qT [GeV]

• 0.00008
• 0.00006
• 0.00004
• 0.00002

S(2) [GeV-2] Set B + max KMR + max 1 2 3 4 5 6 qT [GeV] 1.×10-6 2.×10-6 3.×10-6 4.×10-6 5.×10-6 S(4) [GeV-2]

• ❘ ❙❼ ➁ ✂

❘ ❙❼ ➁ ✂ ❙❼ ➁ ◗ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 25 / 20

J⑦ψ⑦Υ ✔ Z

Υ ✔ Z & Υ ✔ γ❺ @➸s 14 TeV

JPL, C. Pisano, M. Schlegel, NPB 920 (2017) 192

Q 120 GeV : Z on-shell [❘ ❙❼2➁ ✂ 0.007%; ❘ ❙❼4➁ ✂ 0.001%]

Set B KMR 10 20 30 40qT [GeV] 0.0005 0.0010 0.0015 0.0020 0.0025 S(0) [GeV-2] Set B + max KMR + max 10 20 30 40qT [GeV]

• 6.×10-8
• 4.×10-8
• 2.×10-8

S(2) [GeV-2] Set B + max KMR + max 10 20 30 40 qT [GeV] 2.×10-9 4.×10-9 6.×10-9 8.×10-9 1.×10-8 1.2×10-8 S(4) [GeV-2]

Q 20 GeV & dilepton mass [5:7] GeV [❘ ❙❼2➁ ✂ 0.5%; ❘ ❙❼4➁ ✂ 0.05%]

Set B KMR 2 4 6 8 10qT [GeV] 0.005 0.010 0.015 0.020 0.025 S(0) [GeV-2]

Set B + max KMR + max 1 2 3 4 5 6 qT [GeV]

• 0.00008
• 0.00006
• 0.00004
• 0.00002

S(2) [GeV-2] Set B + max KMR + max 1 2 3 4 5 6 qT [GeV] 1.×10-6 2.×10-6 3.×10-6 4.×10-6 5.×10-6 S(4) [GeV-2]

Q 40 GeV & dilepton mass [20:25] GeV [❘ ❙❼2➁ ✂ 0.15%; ❘ ❙❼4➁ ✂ 0.01%]

Set B KMR 5 10 15 20qT [GeV] 0.002 0.004 0.006 0.008 S(0) [GeV-2]

Set B + max KMR + max 2 4 6 8 10 12 qT [GeV]

• 7.×10-6
• 6.×10-6
• 5.×10-6
• 4.×10-6
• 3.×10-6
• 2.×10-6
• 1.×10-6

S(2) [GeV-2]

Set B + max KMR + max 2 4 6 8 10 12 qT [GeV] 1.×10-7 2.×10-7 3.×10-7 4.×10-7 5.×10-7 S(4) [GeV-2]

❙❼ ➁ ◗ ✔

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 25 / 20

J⑦ψ⑦Υ ✔ Z

Υ ✔ γ already measured ?

Search for Higgs and Z Boson Decays to J=ψγ and ϒðnSÞγ with the ATLAS Detector

• G. Aad et al.*

(ATLAS Collaboration)

(Received 15 January 2015; published 26 March 2015) A search for the decays of the Higgs and Z bosons to J=ψγ and ϒðnSÞγ (n ¼ 1; 2; 3) is performed with pp collision data samples corresponding to integrated luminosities of up to 20.3 fb−1 collected at ffiffi ffi s p ¼ 8 TeV with the ATLAS detector at the CERN Large Hadron Collider. No significant excess of events is observed above expected backgrounds and 95% C.L. upper limits are placed on the branching fractions. In the J=ψγ final state the limits are 1.5 × 10−3 and 2.6 × 10−6 for the Higgs and Z boson decays, respectively, while in the ϒð1S; 2S; 3SÞγ final states the limits are ð1.3; 1.9; 1.3Þ × 10−3 and ð3.4; 6.5; 5.4Þ × 10−6, respectively.

PRL 114, 121801 (2015) P H Y S I C A L R E V I E W L E T T E R S

week ending 27 MARCH 2015

[GeV]

γ µ µ

m 40 80 120 160 200 Events / 4 GeV 10 20 30 40 50 60 70 80 ATLAS

=8 TeV s

• 1

Ldt = 20.3 fb

∫

Data S+B Fit Combinatoric (nS) ϒ Z FSR ]

• 3

H [B=10 ]

• 6

Z [B=10

[GeV]

γ µ µ T

p 50 100 150 200 Events / 4 GeV 10 20 30 40 50 ATLAS

=8 TeV s

• 1

Ldt = 20.3 fb

∫

Data S+B Fit Combinatoric (nS) ϒ Z FSR ]

• 3

H [B=10 ]

• 6

Z [B=10

[GeV]

µ µ

m 8 8.5 9 9.5 10 10.5 11 11.5 12 Events / 0.125 GeV 5 10 15 20 25 30 35 ATLAS

=8 TeV s

• 1

Ldt = 20.3 fb

∫

Data S+B Fit Combinatoric (nS) ϒ Z FSR ]

• 3

H [B=10 ]

• 6

Z [B=10

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 26 / 20

J⑦ψ⑦Υ ✔ Z

Same at AFTER@LHC

AFTER@LHC : a fixed-target experiment using the LHC beams

➺2 ✕ mN ✕ Ep

7TeV

• 115 GeV

❃ ✏ ✂ ✆ ✏ à ✔

• ❼

➁ ✟ ✏

✟ ⑦ ✕ ✟ ✏ ❆ ✏

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 27 / 20

J⑦ψ⑦Υ ✔ Z

Same at AFTER@LHC

AFTER@LHC : a fixed-target experiment using the LHC beams

➺2 ✕ mN ✕ Ep

7TeV

• 115 GeV

Experimental coverage of ALICE or LHCb is about ycms ❃ ✏3 ✂ 0✆ down to xF ✏1 for Q à 5 GeV ✔

• ❼

➁ ✟ ✏

✟ ⑦ ✕ ✟ ✏ ❆ ✏

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 27 / 20

J⑦ψ⑦Υ ✔ Z

Same at AFTER@LHC

AFTER@LHC : a fixed-target experiment using the LHC beams

➺2 ✕ mN ✕ Ep

7TeV

• 115 GeV

Experimental coverage of ALICE or LHCb is about ycms ❃ ✏3 ✂ 0✆ down to xF ✏1 for Q à 5 GeV For ψ ✔ γ, smaller yield (14 TeV 115 GeV) compensated by an access to lower PT

❼ ➁ ✟ ✏

✟ ⑦ ✕ ✟ ✏ ❆ ✏

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 27 / 20

J⑦ψ⑦Υ ✔ Z

Same at AFTER@LHC

AFTER@LHC : a fixed-target experiment using the LHC beams

➺2 ✕ mN ✕ Ep

7TeV

• 115 GeV

Experimental coverage of ALICE or LHCb is about ycms ❃ ✏3 ✂ 0✆ down to xF ✏1 for Q à 5 GeV For ψ ✔ γ, smaller yield (14 TeV 115 GeV) compensated by an access to lower PT

0.01 0.1 1 10 100 10 15 dσ/dQ/dY/d cosθCS x Br(Onium → µ µ) (fb/GeV)

QJ/ψ + γ (GeV)

Direct back-to-back J/ψ + γ at sqrt(s)=115 GeV

µR=µF=monium

T | mQ=monium/2

|Y | < 0.5; |cosθCS| <0.45

10 15

QJ/ψ + γ (GeV)

<O

1S[8] 0 (J/ψ)>=0.02 GeV3

<O

3S[8] 1 (J/ψ)>=0.002 GeV3

• 1.5<Y <-0.5; |cosθCS| <0.45

10 15

QJ/ψ + γ (GeV)

• 2.5 < Y < -1.5; |cosθCS| <0.45

gg: Color Singlet gg: Color Octet qq: Color Singlet qq: Color Octet

❼ ➁ ✟ ✏

✟ ⑦ ✕ ✟ ✏ ❆ ✏

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 27 / 20

J⑦ψ⑦Υ ✔ Z

Same at AFTER@LHC

AFTER@LHC : a fixed-target experiment using the LHC beams

➺2 ✕ mN ✕ Ep

7TeV

• 115 GeV

Experimental coverage of ALICE or LHCb is about ycms ❃ ✏3 ✂ 0✆ down to xF ✏1 for Q à 5 GeV For ψ ✔ γ, smaller yield (14 TeV 115 GeV) compensated by an access to lower PT

0.01 0.1 1 10 100 10 15 dσ/dQ/dY/d cosθCS x Br(Onium → µ µ) (fb/GeV)

QJ/ψ + γ (GeV)

Direct back-to-back J/ψ + γ at sqrt(s)=115 GeV

µR=µF=monium

T | mQ=monium/2

|Y | < 0.5; |cosθCS| <0.45

10 15

QJ/ψ + γ (GeV)

<O

1S[8] 0 (J/ψ)>=0.02 GeV3

<O

3S[8] 1 (J/ψ)>=0.002 GeV3

• 1.5<Y <-0.5; |cosθCS| <0.45

10 15

QJ/ψ + γ (GeV)

• 2.5 < Y < -1.5; |cosθCS| <0.45

gg: Color Singlet gg: Color Octet qq: Color Singlet qq: Color Octet

At Y❼cms➁ ✟ ✏2, x2 ✟ 10⑦115 ✕ e2 ✟ 0.65. Yet, g ✏ g ❆ q ✏ ¯ q !

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 27 / 20

J⑦ψ⑦Υ ✔ Z

S(0)

qT : Model predictions for Υ + γ production at √s = 14 TeV

Q = 20 GeV, Y = 0, θCS = π/2 Models for fg

1 : assumed to be the same as for Unintegrated Gluon Distributions

• Set B: B0 solution to CCFM equation with input based on HERA data

Jung et al., EPJC 70 (2010) 1237

• KMR: Formalism embodies both DGLAP and BFKL evolution equations

Kimber, Martin, Ryskin, PRD 63 (2010) 114027

• CGC: Color Glass Condensate Model

Dominguez, Qiu, Xiao, Yuan, PRD 85 (2012) 045003 Metz, Zhou, PRD 84 (2011) 051503

J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 28 / 20

J⑦ψ⑦Υ ✔ Z

S(2,4)

qT

: Model predictions for Υ + γ production at √s = 14 TeV

• Q = 20 GeV,

Y = 0, θCS = π/2

• h⊥g

1

: predictions only in the CGC: in the other models saturated to its upper bound

• S(2,4)

qT

smaller than S(0)

qT : can be integrated up to qT = 10 GeV

2.0% (KMR) < |

• dq2

T S(2)

qT |

< 2.9% (Gauss) 0.3% (CGC) <

• dq2

T S(4)

qT

< 1.2% (Gauss) Possible determination of the shape of fg

1 and verification of a non-zero h⊥g 1 J.P. Lansberg (IPNO) Gluon TMD studies using quarkonia November 16, 2017 29 / 20