SLAC2014.03.05 LeifLönnblad TheDIPSYmodelfornucleonandnucleicollsions

(1)

Introduction The DIPSY model Comparison with data ˇ

The DIPSY model for nucleon and nuclei collsions

Leif Lönnblad

Department of Astronomy and Theoretical Physics

Lund University

SLAC 2014.03.05

(2)

Outline

◮ Our modified Mueller dipole model

◮ Modeling exclusive final states

◮ Nucleon vs. nuclei collisions.

(3)

Muellers Dipole formulation The interaction ˇThe Swing

DIPSY

(with E. Avsar, C. Bierlich, C. Flensburg, G. Gustafson)

(4)

The virtual cascade

Q

Q¯ 1

0

1

0 r₀₁

2 r₁₂

r₀₂

1

0 2 3

y

x

◮ Muellers formulation of BFKL

◮ dP

dy = _2π^α^¯ d²r2 r₀₁² r₀₂²r₁₂²

◮ Dipoles in impact parameter space, evolved in rapidity

◮ Builds up virtual Fock-states of the proton

(5)

Non-leading effects

◮ Runningα_s

◮ Introduce k_⊥∼ 1/r to get energy–momentum conservation.

(Ordering in p+and p₋gives a dynamic cutoff)

◮ Non-perturbative regularization with small gluon mass (confinement effects)

(6)

The interaction

◮ Dipole–dipole interaction:

F =P

ijfij f_(12)(34) ∝ αs²ln²

r₁₃r₂₄ r₁₄r₂₃

◮ Unitarize to get saturation effects (pomeron loops):

F → 1 − e^−F

◮ Without energy conservation we get exponential growth of small dipoles which do not interact

◮ Non-perturbative regularization with small gluon mass

◮ Rederive Mueller’s expression above in transverse momentum space for final states.

(7)

ˆ The interaction The Swing ˇReal gluons

The Swing

◮ The unitarized interaction probability gives pomeron loops only in the interaction frame.

◮ To be Lorentz invariant we want them also in the evolution

◮ Accomplished by the Swing (colour reconnection)

◮ Two dipoles with the same colour may reconnect.

◮ Does not reduce the number of dipoles, but smaller dipoles are favoured, and these have weaker interactions.

◮ In the end we get saturation in both evolution and interaction

(8)

Get into the swing

1(g) ^✲ 2(¯g)

Swing probability∝ ^r_r¹²²2^r³⁴² 14r₃₂²

(9)

Get into the swing

1(g) ^✲ 2(¯g)

4(¯g) ^✛ 3(g)

(10)

Get into the swing

1(g) 2(¯g)

4(¯g) 3(g)

❇❇▼❇ ✓

✓✓

✴

(11)

Get into the swing

1(g) ^✲ 2(¯g)

4(¯g) ^✛ 3(g)

(12)

We now have a model for inclusive and semi-exclusive

observables, which includes explicit modeling of fluctuations in the initial state

◮ pp and ep-DIS total cross sectionOK

◮ pp and ep-DIS (quasi) elastic cross sectionOK including t-dependence

◮ pp and ep-DIS diffractionOK

◮ Double parton scattering at the LHC — interesting predictions

(σ_effdepends more on jet p_⊥than on x and rapidity, arXiv:1103.4320 [hep-ph])

Going further to produce fully exclusive final states is quite complicated.

(13)

ˆ The Swing Real gluons Final-state Shower

Real gluons

We have generated the gluonic Fock-states of the colliding protons.

Most of the gluons in this state are simply virtual fluctuations, which will not make it to the final state.

In the momentum picture all gluons in the proton with large p₊ will be off-shell with a negative p₋component.

Only those gluons which actually collides (or have children which collides) with gluons from the proton with large p₋will be able to come on-shell. All others must be reabsorbed.

(14)

Virtual vs Real gluons

Once the interactions are in place, it is easy to see the interacting gluon chains.

Emissions not on interacting chainsare emitted as final state radiation by ARIADNE,removed in DIPSYto not double count.

(15)

Virtual vs Real gluons

(16)

Virtual vs Real gluons

(17)

But...energy–momentum conservation effects were taken into account assuming all gluons were real. When some are reabsorbed the kinematics will change.

Also some sequences of emissions in the evolution will

correspond to local hard scatterings in some frame, and these will not get the proper∼ 1/q_⊥⁴ behavior.

In the end we want to just have primary (a.k.a. backbone) gluons left, which are ordered in both q+ and q₋(and hence also in rapidity).

These are the ones we know will completely dominate the cross section.

(18)

◮ Choose which dipoles interact: 1− e^−F^ij

◮ Take away non-interacting gluons

◮ Take away kinematically impossible interactions/gluons

◮ Take away wrongly distributed sub-scatterings

◮ Take away non-ordered gluons

(19)

Final state radiation and hadronization

The primary gluons are now sent to ARIADNEfor final-state showering.

This is a unitary procedure and only emissions which are unorderedin q+and q₋w.r.t. the primary gluons are allowed.

Then we send everything to PYTHIA8 for hadronization.

(20)

Frame-independence

We have quite a lot of parameters:

◮ Rmax: Non-perturbative regularization

◮ Rp: Proton size (≈ R^max)

◮ wp: Fluctuations in the initial proton size (small)

◮ Λ_QCD: in the runningα_s

◮ λr: Swing parameter (saturated)

Most of these can be fit to the total and elastic cross sections.

But there are also a lot of choices made for which no guidance can be found in perturbative QCD, especially for the selection of the real gluons.

Most of these can be fixed by requiring frame-independence.

(21)

The DIPSY modelˆ Comparison with data

Heavy Ions ˇ

Inclusive observables Minimum bias observables

Inclusive cross sections.

(22)

Heavy Ions ˇ

1e-05 0.0001 0.001 0.01 0.1 1 10 100 1000 10000

0 0.5 1 1.5 2

-t (GeV²)

630GeV (x10) 546GeV (x100)

1.8TeV 14TeV (x0.1)

UA4 Tevatron MC LHC

(23)

Heavy Ions ˇ

Minimum-Bias Observables

bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

ATLAS data

b

DIPSY Pythia8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Charged particle η at 900 GeV, track p⊥>500 MeV, for Nch≥6

1/NevdNch/dη

-2 -1 0 1 2

0.6 0.8 1 1.2 1.4

η

MC/data bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb

ATLAS data

b

DIPSY Pythia8

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Charged particle η at 7 TeV, track p⊥>500 MeV, for Nch≥6

1/NevdNch/dη

-2 -1 0 1 2

0.6 0.8 1 1.2 1.4

η

MC/data

(24)

Heavy Ions ˇ

b bb b bb b b bb b b bb b b bb b b bb b b bbb b b b b b b b

ATLAS data

b

DIPSY Pythia8

10⁻⁶ 10⁻⁵ 10⁻⁴ 10⁻³ 10−2 10−1

Charged multiplicity≥6 at 7 TeV, track p_⊥>_{500 MeV}

1/σdσ/dNch

20 40 60 80 100 120

0.6 0.8 1 1.2 1.4

Nch

MC/data bbbbbbbbbbbbbbbbbbbbb bbbbb b b b b b b b b

ATLAS data

b

DIPSY Pythia8

0 0.2 0.4 0.6 0.8 1 1.2

Transverse ∑ p_⊥density vs. p^trk1_⊥ ,√_s

=⁷TeV

hd2∑p⊥/dηdφi[GeV]

2 4 6 8 10 12 14 16 18 20

0.6 0.8 1 1.2 1.4

p_⊥(leading track) [GeV]

MC/data

(25)

Heavy Ions ˇ

More final-state observables can be found on

http://home.thep.lu.se/∼leif/DIPSY.html

In general the description of data is worse than for e.g. PYTHIA8 (Tune 4c), but better than many other generators/tunes

(c.f. mcplots.cern.ch).

One main problem is the naive valence configuration used: we may get very high energy gluons interacting and giving too hard jets in the forward region.

Other issues:

◮ Frame dependence

◮ Final state swing

◮ Hadronization of dense string configurations

(26)

Heavy Ions ˇ

The DIPSY model in unique in its treatment of correlations and fluctuations in the colliding protons, and even if it does not describe final states as well as PYTHIA8 it is still interesting.

Especially for understanding multiple interactions and minimum bias.

And the extention to also model heavy-ion collisions is“trivial”

(27)

Comparison with dataˆ Heavy Ions

Summary

Inclusive observables Final states?

ˇRope fragmentation

Heavy Ions

◮ An ion starts asA nucleons(dipole triangles)distributed in transverse space.

◮ Wood-Saxon with hard core.

◮ Theswings, within andbetween nucleons, describe the saturationin the evolution.

◮ Get afull partonic picturewithboth momentum and transverse position.

◮ Dynamically describes all fluctuations and correlations.

◮ No new model dependence! (only nucleon distribution) Everything tuned from pp andγ^∗p.

◮ (DIPSY is a bit too slow right now,∼30 min for a

(38)

Summary

0.9 1.0 1.1

0 1 2 3 4 5

σinel(ND)/DIPSY

n-n collision energy (TeV)

p-Cu inelastic non-diffractive cross section DIPSY no swing

black disc grey disc grey(3) disc

(39)

Summary

The final states are extremely messy. We have to think very carefully of how to hadronize strings in this very colourful environment.

The transverse size of a (Lund) string is rather large.

What will happen if several strings overlap in impact-parameter space?

(40)

Summary

ˆ Final states?

Rope fragmentation

Strings → Ropes

Take the simplest case of two simple, un-correlated, completely overlapping strings, with opposite colour flow.

q ←− ¯q

¯

q^′ −→ q^′

◮ 1/9: A colour-singlet

◮ 8/9: A colour-octet

The string tension is proportional to the Casimir operator C₂⁽⁸⁾= ⁹₄C₂⁽³⁾.

(41)

Summary

ˆ Final states?

Rope fragmentation

A toy model for rope-fragmentation

The singlet case is dealt with by introducing a final-state swing.

The octet case is approximated by normal fragmentation of two strings but with increased string tension

κ_eff = C₂⁽⁸⁾ 2C₂⁽³⁾κ0

The higher string tension affects several fragmentation parameters in a non-trivial way, basically increasing the probability to create heavy quarks or di-quarks in string break-ups.

(42)

Summary

ˆ Final states?

Rope fragmentation

Preliminary results from toy model. pp data from CMS

K dn/dη Λ dn/dη Ξ dn/dη

b b b b b b b b b b

Data

b

String Rope

0 0.5 1 1.5 2

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

K⁰Srapidity distribution at√s = 7 TeV

K⁰_S|y|

(1/NNSD)dN/dy b b b b b b b b b b

Data

b

String Rope

0 0.5 1 1.5 2

0 0.05 0.1 0.15 0.2

Λrapidity distribution at√s = 7 TeV

Λ|y|

(1/NNSD)dN/dy b b b b b b b b b b

Data

b

String Rope

0 0.5 1 1.5 2

0 0.005 0.01 0.015 0.02 0.025

Ξ−rapidity distribution at√s = 7 TeV

Ξ−|y|

(1/NNSD)dN/dy

K dn/dp_⊥ Λ dn/dp_⊥ Ξ dn/dp_⊥

bbbbbbbbbbbbbbbbbbbb b b b b

Data

b

String Rope

0 2 4 6 8 10

10−4 10−3 10−2 10⁻¹ 1

K⁰_Stransverse momentum distribution at√s = 7 TeV

K⁰SpT[GeV/c]

(1/NNSD)dN/dpT(GeV/c)−1 bbbbbbbbbbbbbbbbbbbb b b b b

Data

b

String Rope

0 2 4 6 8 10

10⁻⁴ 10−3 10⁻² 10−1 1

Λtransverse momentum distribution at√s = 7 TeV

ΛpT[GeV/c]

(1/NNSD)dN/dpT(GeV/c)−1 bbbbbbbbbbbbbbbbbbbb b b

Data

b

String Rope

0 1 2 3 4 5 6

10⁻⁴ 10−3 10−2 10⁻¹

Ξ−transverse momentum distribution at√s = 7 TeV

Ξ−pT[GeV/c]

(1/NNSD)dN/dpT(GeV/c)−1

(43)

Summary

◮ With DIPSY we have a detailed partonic 3D-picture of the nucleon, including fluctuations and correlations.

◮ So far there are a lot of short comings:

◮ only gluons (small-x)

◮ only leading-log x (+ some NLL corrections)

◮ no ME-corrections (difficulties with hard jets)

◮ . . .

◮ but also possibilities (eg. Heavy Ion)

(44)

Summary