The final state swing Leif Lnnblad Department of Astronomy and - - PowerPoint PPT Presentation

Introduction Parton and dipole showers Colour reconnectionsˇ

The final state swing

Leif Lönnblad

Department of Astronomy and Theoretical Physics Lund University

Lund 2019-02-27

Swing 1 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Outline

◮ Parton showers,“Pre-confinement” and the size of NC ◮ Colour reconnections ◮ The dipole swing in the shower ◮ Outlook (pA & AA)

Swing 2 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

The importance of colour connections

◮ All hadrons are colour singlets. ◮ Any realistic hadronisation model must ensure this. ◮ Exact treatment of colour structures in LHC events is

impossible(?)

◮ All partons shower approaches use the NC → ∞

approximation which gives a unique colour strucure.

Swing 3 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Parton and dipole showers

γ⋆ ¯ q q

◮ Parton splitting ◮ Dipole splitting ◮ Pre-confinement: partons close

in phase space are likely to be colour-connected. Nature likes short strings.

◮ NC → ∞ gives a unique colour

flow.

◮ But NC = 3.

Swing 4 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Parton and dipole showers

γ⋆ ¯ q q

◮ Parton splitting ◮ Dipole splitting ◮ Pre-confinement: partons close

in phase space are likely to be colour-connected. Nature likes short strings.

◮ NC → ∞ gives a unique colour

flow.

◮ But NC = 3.

Swing 4 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Parton and dipole showers

γ⋆ ¯ q q

◮ Parton splitting ◮ Dipole splitting ◮ Pre-confinement: partons close

in phase space are likely to be colour-connected. Nature likes short strings.

◮ NC → ∞ gives a unique colour

flow.

◮ But NC = 3.

Swing 4 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Parton and dipole showers

γ⋆ ¯ q q

◮ Parton splitting ◮ Dipole splitting ◮ Pre-confinement: partons close

in phase space are likely to be colour-connected. Nature likes short strings.

◮ NC → ∞ gives a unique colour

flow.

◮ But NC = 3.

Swing 4 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Parton and dipole showers

γ⋆ ¯ q q

◮ Parton splitting ◮ Dipole splitting ◮ Pre-confinement: partons close

in phase space are likely to be colour-connected. Nature likes short strings.

◮ NC → ∞ gives a unique colour

flow.

◮ But NC = 3.

Swing 4 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Parton and dipole showers

γ⋆ ¯ q q

◮ Parton splitting ◮ Dipole splitting ◮ Pre-confinement: partons close

in phase space are likely to be colour-connected. Nature likes short strings.

◮ NC → ∞ gives a unique colour

flow.

◮ But NC = 3.

Swing 4 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Parton and dipole showers

γ⋆ ¯ q q

◮ Parton splitting ◮ Dipole splitting ◮ Pre-confinement: partons close

in phase space are likely to be colour-connected. Nature likes short strings.

◮ NC → ∞ gives a unique colour

flow.

◮ But NC = 3.

Swing 4 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Parton and dipole showers

γ⋆ ¯ q q

◮ Parton splitting ◮ Dipole splitting ◮ Pre-confinement: partons close

in phase space are likely to be colour-connected. Nature likes short strings.

◮ NC → ∞ gives a unique colour

flow.

◮ But NC = 3.

Swing 4 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Parton and dipole showers

γ⋆ ¯ q q

◮ Parton splitting ◮ Dipole splitting ◮ Pre-confinement: partons close

in phase space are likely to be colour-connected. Nature likes short strings.

◮ NC → ∞ gives a unique colour

flow.

◮ But NC = 3.

Swing 4 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Parton and dipole showers

γ⋆ ¯ q q

◮ Parton splitting ◮ Dipole splitting ◮ Pre-confinement: partons close

in phase space are likely to be colour-connected. Nature likes short strings.

◮ NC → ∞ gives a unique colour

flow.

◮ But NC = 3.

Swing 4 Leif Lönnblad Lund University

Introduction Parton and dipole showers Colour reconnectionsˇ

Parton and dipole showers

γ⋆ ¯ q q

◮ Parton splitting ◮ Dipole splitting ◮ Pre-confinement: partons close

in phase space are likely to be colour-connected. Nature likes short strings.

◮ NC → ∞ gives a unique colour

flow.

◮ But NC = 3.

Swing 4 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

Colour reconnections

Colour reconnections is a way to include effects of NC < ∞. The guiding principles are:

◮ Probability to reconnect ∼ 1/N2 C ◮ Nature likes short strings ◮ There are no colour-singlet gluons.

[Sjöstrand, Khoze, Gustafson, Zerwas, Lönnblad, Edin, Ingelman, Rathsman, Gieseke, Kirchgaeßer, . . . ] Swing 5 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

Short strings?

We typically measure the string lengths in terms of the λ-measure For a string consisting of n dipoles between a quark and an anti-quark connected with n − 1 gluons: (q0 − g1 − g2 − · · · − gn−1 − ¯ qn) λ =

n−1

• i=0

log

• 1 +

m2

i,i+1

m2

• Swing

6 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

Short strings?

We typically measure the string lengths in terms of the λ-measure For a string consisting of n dipoles between a quark and an anti-quark connected with n − 1 gluons: (q0 − g1 − g2 − · · · − gn−1 − ¯ qn) λ =

n−1

• i=0

log

• 1 +

m2

i,i+1

m2

• ∼

n−1

• i=0

log

• m2

i,i+1

m2

• Swing

6 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

Simple reconnections

q1 ¯ q2 ¯ q4 q3 Reconnect?

◮ with probability 1/N2 C ◮ only if m14m23 < m12m34

Swing 7 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

Simple reconnections

q1 ¯ q2 ¯ q4 q3 Reconnect?

◮ with probability 1/N2 C ◮ only if m14m23 < m12m34

Swing 7 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

Simple reconnections

q1 ¯ q2 ¯ q4 q3 Reconnect?

◮ with probability 1/N2 C ◮ only if m14m23 < m12m34

Swing 7 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

Junctions

q1 ¯ q2 ¯ q4 q3 Reconnect?

◮ with probability 1/NC ◮ only if λ-measure is reduced

Swing 8 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

Junctions

q1 ¯ q2 ¯ q4 q3 Reconnect?

◮ with probability 1/NC ◮ only if λ-measure is reduced

Swing 8 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

Junctions

q1 ¯ q2 ¯ q4 q3 Reconnect?

◮ with probability 1/NC ◮ only if λ-measure is reduced

Swing 8 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

Junctions

q1 ¯ q2 ¯ q4 q3 Reconnect?

◮ with probability 1/NC ◮ only if λ-measure is reduced

Swing 8 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

More Junctions

q1 ¯ q2 ¯ q4 q3 ¯ q6 q5 Reconnect?

◮ with probability 1/N3 C ◮ only if λ-measure is reduced ◮ (acessible with two subsequent reconnections)

Swing 9 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

More Junctions

q1 ¯ q2 ¯ q4 q3 ¯ q6 q5 Reconnect?

◮ with probability 1/N3 C ◮ only if λ-measure is reduced ◮ (acessible with two subsequent reconnections)

Swing 9 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

More Junctions

q1 ¯ q2 ¯ q4 q3 ¯ q6 q5 Reconnect?

◮ with probability 1/N3 C ◮ only if λ-measure is reduced ◮ (acessible with two subsequent reconnections)

Swing 9 Leif Lönnblad Lund University

Parton and dipole showersˆ Colour reconnections The dipole swingˇ

More Junctions

q1 ¯ q2 ¯ q4 q3 ¯ q6 q5 Reconnect?

◮ with probability 1/N3 C ◮ only if λ-measure is reduced ◮ (acessible with two subsequent reconnections)

Swing 9 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

Perturbative effects

We expect effects of NC = 3 < ∞ also on the perturbative level. We want a full-colour parton shower, but this probably requires an amplitude-level parton shower scheme, which can become very messy. Instead modify what we have: the dipole shower. Amend it with dipole reconnections between each emission. Let’s put some swing into the the dipole shower!

Swing 10 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

The Dipole Swing

γ⋆ ¯ q q

◮ Assign a colour index (1-9) to

each dipole

◮ Dipoles connected with a gluon

must have ci = cj

◮ New colour index between the

emitted gluon and the emitter

◮ Only dipoles with the same index

may swing

◮ Let’s Swing

Swing 11 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

The Dipole Swing

γ⋆ ¯ q q c2 c1 c3

◮ Assign a colour index (1-9) to

each dipole

◮ Dipoles connected with a gluon

must have ci = cj

◮ New colour index between the

emitted gluon and the emitter

◮ Only dipoles with the same index

may swing

◮ Let’s Swing

Swing 11 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

The Dipole Swing

γ⋆ ¯ q q c2 c1 c3

◮ Assign a colour index (1-9) to

each dipole

◮ Dipoles connected with a gluon

must have ci = cj

◮ New colour index between the

emitted gluon and the emitter

◮ Only dipoles with the same index

may swing

◮ Let’s Swing

Swing 11 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

The Dipole Swing

γ⋆ ¯ q q c2 c1 c3

◮ Assign a colour index (1-9) to

each dipole

◮ Dipoles connected with a gluon

must have ci = cj

◮ New colour index between the

emitted gluon and the emitter

◮ Only dipoles with the same index

may swing

◮ Let’s Swing

Swing 11 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

The Dipole Swing

γ⋆ ¯ q q c2 c1 c2

◮ Assign a colour index (1-9) to

each dipole

◮ Dipoles connected with a gluon

must have ci = cj

◮ New colour index between the

emitted gluon and the emitter

◮ Only dipoles with the same index

may swing

◮ Let’s Swing

Swing 11 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

The Dipole Swing

γ⋆ ¯ q q c2 c1 c2

◮ Assign a colour index (1-9) to

each dipole

◮ Dipoles connected with a gluon

must have ci = cj

◮ New colour index between the

emitted gluon and the emitter

◮ Only dipoles with the same index

may swing

◮ Let’s Swing

Swing 11 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

The Dipole Swing

γ⋆ ¯ q q c2 c1 c2

◮ Assign a colour index (1-9) to

each dipole

◮ Dipoles connected with a gluon

must have ci = cj

◮ New colour index between the

emitted gluon and the emitter

◮ Only dipoles with the same index

may swing

◮ Let’s Swing both ways

Swing 11 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

The dipole emissions are limited by the dipole mass (cf. angular

• rdering)

The dipole shower is ordered in transverse momentum, k⊥ The distribution of the next emission is given by dP dk2

⊥

= αS k2

⊥

• i
• dz Pi(z) × ∆(k2

⊥max, k2 ⊥)

where ∆ is the no-emission probability (Sudakov form factor)

Swing 12 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

The dipole emissions are limited by the dipole mass (cf. angular

• rdering)

The dipole shower is ordered in transverse momentum, k⊥ The distribution of the next emission is given by dP dk2

⊥

= αS k2

⊥

• i
• dz Pi(z) × ∆(k2

⊥max, k2 ⊥)

where ∆ is the no-emission probability (Sudakov form factor) Add the probability that a dipole may swing dPswing dk2

⊥

= λm2

12m2 34

m2

14m2 32

× ∆swing(k2

⊥max, k2 ⊥)

where λ is a strength parameter

Swing 12 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

q1 ¯ q2 ¯ q4 q3

◮ Pswing = λ m2

12m2 34

m2

14m2 32

◮ For large λ the effect saturates ◮ The weighted average of the radiation from the two dipole

pair configuration emulates quadrupole radiation.

◮ Prefers small mass dipoles giving less radiation

Swing 13 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

q1 ¯ q2 ¯ q4 q3

◮ Pswing = λ m2

14m2 32

m2

12m2 34

◮ For large λ the effect saturates ◮ The weighted average of the radiation from the two dipole

pair configuration emulates quadrupole radiation.

◮ Prefers small mass dipoles giving less radiation

Swing 13 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

q1 ¯ q2 ¯ q4 q3

◮ Pswing = λ m2

12m2 34

m2

14m2 32

◮ For large λ the effect saturates ◮ The weighted average of the radiation from the two dipole

pair configuration emulates quadrupole radiation.

◮ Prefers small mass dipoles giving less radiation

Swing 13 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

q1 ¯ q2 ¯ q4 q3

◮ Pswing = λ m2

12m2 34

m2

14m2 32

◮ For large λ the effect saturates ◮ The weighted average of the radiation from the two dipole

pair configuration emulates quadrupole radiation.

◮ Prefers small mass dipoles giving less radiation

Swing 13 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

q1 ¯ q2 ¯ q4 q3

◮ Pswing = λ m2

12m2 34

m2

14m2 32

◮ For large λ the effect saturates ◮ The weighted average of the radiation from the two dipole

pair configuration emulates quadrupole radiation.

◮ Prefers small mass dipoles giving less radiation

Swing 13 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

q1 ¯ q2 ¯ q4 q3

◮ Pswing = λ m2

14m2 32

m2

12m2 34

◮ For large λ the effect saturates ◮ The weighted average of the radiation from the two dipole

pair configuration emulates quadrupole radiation.

◮ Prefers small mass dipoles giving less radiation

Swing 13 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

q1 ¯ q2 ¯ q4 q3

◮ Pswing = λ m2

12m2 34

m2

14m2 32

◮ For large λ the effect saturates ◮ The weighted average of the radiation from the two dipole

pair configuration emulates quadrupole radiation.

◮ Prefers small mass dipoles giving less radiation

Swing 13 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

q1 ¯ q2 ¯ q4 q3

◮ Pswing = λ m2

14m2 32

m2

12m2 34

◮ For large λ the effect saturates ◮ The weighted average of the radiation from the two dipole

pair configuration emulates quadrupole radiation.

◮ Prefers small mass dipoles giving less radiation

Swing 13 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

Small effects in e+e− (after retuning)

b b b b b b b b b b b b b b b b b b b b

Data

b

No swing Swing 10−3 10−2 10−1 1 10 1 1 − Thrust N dσ/d(1 − T) 0.1 0.2 0.3 0.4 0.5 0.6 0.8 1 1.2 1.4 1 − T MC/Data Swing 14 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

Small effects in e+e− (after retuning)

b b b b b b b b b b b b b b b b b

Data

b

No swing Swing 10−3 10−2 10−1 1 10 1 10 2 Out-of-plane p⊥ in GeV w.r.t. sphericity axes N dσ/dpout

⊥

0.5 1 1.5 2 2.5 3 3.5 0.6 0.8 1 1.2 1.4 pout

⊥

/ GeV MC/Data Swing 14 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

Outlook

◮ Implemented in Ariadne (DIPSY) ◮ Will be implemented in Pythia8 (Angantyr) ◮ Need to include a space-time picture in pA & AA ◮ Will affect flow and jet shapes

Swing 15 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

Thanks!

Swing 16 Leif Lönnblad Lund University

Colour reconnectionsˆ The dipole swing

Colour Reconnections

◮ Sjöstrand et al., Phys.Rev. D36 (1987) 2019 ◮ Gustafson et al., Z.Phys. C64 (1994) 659-664 ◮ Sjöstrand et al., Phys.Rev.Lett. 72 (1994) 28-31 ◮ Edin et al., Phys.Lett. B366 (1996) 371-378 ◮ Lönnblad, Z.Phys. C70 (1996) 107-114 ◮ Gieseke et al., JHEP 1811 (2018) 149

Swing 17 Leif Lönnblad Lund University