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IntroductionDIPSY
HEJˇ
DIPSY and HEJnew hadron-level generators forminimum bias and jet production
Leif Lönnblad
CERN-TH andDepartment of Astronomyand Theoretical Physics
Lund University
CERN 2011.05.10
DIPSY & HEJ 1 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
Introduction
◮ DIPSY: arXiv:1103.4321 [hep-ph]◮ Dipoles in Impact-Parameter Space and rapiditY◮ Based on LL BFKL (Mueller dipoles)◮ Adds non-leading effects◮ Now also exclusive hadronic final states
◮ HEJ: arXiv:1104.1316 [hep-ph]◮ High Energy Jets◮ Based on (N)LL BFKL◮ Takes full kinematics into account◮ Now also exclusive hadronic final states
DIPSY & HEJ 2 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
The virtual cascadeThe interaction
ˇThe Swing
DIPSY (with Christoffer Flensburg and Gösta Gustafson)
DIPSY & HEJ 3 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
The virtual cascadeThe interaction
ˇThe Swing
The virtual cascade
Q
Q
1
0
1
0
r01
2
r12
r02
1
0
2
3
y
x
◮ Muellers formulation of BFKL
◮dPdy = α
2πd2r2
r201
r202r2
12
◮ Dipoles in impact parameter space, evolved in rapidity◮ Builds up virtual Fock-states of the proton
DIPSY & HEJ 4 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
The virtual cascadeThe interaction
ˇThe Swing
Non-leading effects
◮ Running αs
◮ Introduce k⊥ ∼ 1/r to get energy–momentumconservation.
◮ Non-perturbative regularization with small gluon mass(confinement effects)
DIPSY & HEJ 5 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
The virtual cascadeThe interaction
ˇThe Swing
The interaction
◮ Dipole–dipole interaction:
F =∑
ij fij fij = α2s
2 ln2(
rii′ rjj′
rij′ rji′
)
◮ Unitarize to get saturation effects (pomeron loops):F → 1 − e−F
◮ Without energy conservation we get exponential growth ofsmall dipoles which do not interact
◮ Non-perturbative regularization with small gluon mass◮ Rederive Mueller’s expression above in transverse
momentum space for final states.
DIPSY & HEJ 6 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The interactionThe Swing
ˇReal gluons
The Swing
◮ Thu unitarized interaction probability gives pomeron loopsonly 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
DIPSY & HEJ 7 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The interactionThe Swing
ˇReal gluons
We now have a model for inclusive and semi-exclusiveobservables, which includes explicit modeling of fluctuations inthe initial state
◮ pp and ep-DIS total cross section OK◮ pp and ep-DIS (quasi) elastic cross section OK
including t-dependence◮ pp and ep-DIS diffraction OK◮ Double parton scattering at the LHC — interesting
predictions
But we want fully exclusive hadronic final states
DIPSY & HEJ 8 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
Real gluons
We have generated the gluonic Fock-states of the collidingprotons.
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 childrenwhich collides) with gluons from the proton with large p− will beable to come on-shell. All others must be reabsorbed.
DIPSY & HEJ 9 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
But... energy–momentum conservation effects were taken intoaccount assuming all gluons were real. When some arereabsorbed the kinematics will change.
Also some sequences of emissions in the evolution willcorrespond to local hard scatterings in some frame, and thesewill not get the proper ∼ 1/q4
⊥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 hencealso in rapidity).
These are the ones we know gives the non-vanishingcontributions to the cross section.
DIPSY & HEJ 10 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
◮ Choose which dipoles interact: 1 − e−Fij
◮ Take away non-interacting gluons◮ Take away kinematically impossible interactions/gluons◮ Take away wrongly distributed sub-scatterings◮ Take away non-ordered gluons
DIPSY & HEJ 11 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
Final state radiation and hadronization
The primary gluons are now sent to ARIADNE for final-stateshowering.
This is a unitary procedure and only emissions which areunordered in q+ and q− w.r.t. the primary gluons are allowed.
Then we send everything to PYTHIA8 for hadronization.
DIPSY & HEJ 12 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
Frame-independence
We have quite a lot of parameters:
◮ Rmax: Non-perturbative regularization◮ Rp: Proton size (≈ Rmax)◮ wp: Fluctuations in the initial proton size (small)◮ ΛQCD: in the running αs
◮ 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 guidancecan be found in perturbative QCD, especially for the selection ofthe real gluons.
Most of these can be fixed by requiring frame-independence.
DIPSY & HEJ 13 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
Comparison with datab b b b b b b b b b b b b b b b b b
bbbbb b
bb
b
b
b
× × × × × × × × × × × × × × × × × × × × × × × × × × ××
×ATLAS datab
DIPSY
Pythia8
Pythia8(ND)
DIPSY(asym)×
10−6
10−5
10−4
10−3
10−2
10−1
Charged multiplicity ≥ 6 at 900 GeV, track p⊥ > 500 MeV
1/
σd
σ/
dN
ch
× × × × × × × × × × × × × × × × × × × × ×× ×
10 15 20 25 30 35 40 45
0.6
0.8
1
1.2
1.4
Nch
MC
/d
ata
More plots on http://home.thep.lu.se/∼leif/DIPSY.html
DIPSY & HEJ 14 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
b b b b b b b b b b b b b b b b b b b b b b b b b b bb
b
b
b
b
b
b
××××××××××××××××××××××××××× ××
××
×
×
×
ATLAS datab
DIPSY
Pythia8
Pythia8(ND)
DIPSY(asym)×
10−6
10−5
10−4
10−3
10−2
10−1
Charged multiplicity ≥ 6 at 7 TeV, track p⊥ > 500 MeV
1/
σd
σ/
dN
ch
×××××××
×××××××××××××××××××× × × ×
×
×
20 40 60 80 100 120
0.6
0.8
1
1.2
1.4
Nch
MC
/d
ata
DIPSY & HEJ 15 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
bb
bb b b b b b b b b b b b b b b b b b
bbbb
bb
b
bb
bb
b
b
b
b
× × × × × ××××××××××××××××××× × × × × × × × ××
××
×
ATLAS datab
DIPSY
Pythia8
Pythia8(ND)
DIPSY(asym)×
10−9
10−8
10−7
10−6
10−5
10−4
10−3
10−2
10−1
1
Charged particle p⊥ at 7 TeV, track p⊥ > 500 MeV, for Nch ≥ 6
1/
Nev
1/
2π
p⊥
dσ
/d
ηd
p⊥
× × × ××
×××××××××××××
××××
×××
×
1 10 1
0.6
0.8
1
1.2
1.4
p⊥ [GeV]
MC
/d
ata
DIPSY & HEJ 16 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
b b b b b b bb b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
b b b bbb
××××××××××××××××××××××××××××××××××××××××××××××××××
ATLAS datab
DIPSY
Pythia8
Pythia8(ND)
DIPSY(asym)×
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5Charged particle η at 900 GeV, track p⊥ > 500 MeV, for Nch ≥ 6
1/
Nev
dN
ch/
dη
××××××××××××××××××××××××××××××××××××××××××××××××××
-2 -1 0 1 2
0.6
0.8
1
1.2
1.4
η
MC
/d
ata
DIPSY & HEJ 17 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
bb b b
b b bb b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b b
b b bb b b
b
××××××××××××××××××××××××××××××××××××××××××××××××××
ATLAS datab
DIPSY
Pythia8
Pythia8(ND)
DIPSY(asym)×
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5Charged particle η at 7 TeV, track p⊥ > 500 MeV, for Nch ≥ 6
1/
Nev
dN
ch/
dη
××××××××××××××××××××××××××××××××××××××××××××××××××
-2 -1 0 1 2
0.6
0.8
1
1.2
1.4
η
MC
/d
ata
DIPSY & HEJ 18 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
Valence configuration
In general the description of data is worse than for PYTHIA8(Tune 4c), but better than most other generators(c.f. mcplots.cern.ch).
One main problem is the naive valence configuration used: wemay get very high energy gluons interacting and giving too hardjets in the forward region. (We’re working on it).
DIPSY & HEJ 19 Leif Lönnblad CERN/Lund University
IntroductionDIPSY
HEJˇ
ˆ The SwingReal gluonsComparison with data
Heavy Ions
DIPSY can also be used for heavy-ion collisions.
This give us a model of possible fluctuations and correlations inthe initial state gluon distribution necessary to understandpossible hydrodynamical and other collective effects in the finalstate.
(DIPSY is a bit too slow right now, ∼ 30min for an LHC event)
DIPSY & HEJ 20 Leif Lönnblad CERN/Lund University
DIPSYˆHEJ
Summary
Matching to a collinear showerJet shapes
ˇFuture Developments
HEJ - High Energy Jets(with Jeppe Andersen and Jennifer Smillie)
From Minimum Bias to Jet production. . .
HEJ is basically a Matrix Element generator (à la MadEvent)with a perturbative approximation of jet production to any orderof αs.
The predictions are exact in the limit of large invariant massbetween all partons (BFKL). And is matched to MadGraph forlow parton multiplicities.
DIPSY & HEJ 21 Leif Lönnblad CERN/Lund University
DIPSYˆHEJ
Summary
Matching to a collinear showerJet shapes
ˇFuture Developments
The typical process: f1f2 → f1g · · ·gf2
σresum,match2j =
∑
f1,f2
∞∑
n=2
n∏
i=1
(∫ pi⊥=∞
pi⊥=λ
d2p i⊥
(2π)3
∫
dyi
2
)
|Mf1f2→f1g···gf2HEJ ({pi})|
2
s2
×∑
m
Oemj({pi}) wm−jet
× xafA,f1(xa, Qa) x2fB,f2(xb, Qb) (2π)4 δ2
(
n∑
i=1
p i⊥
)
O2j({pi})
Resum to all-orders the leading logarithmic virtual correctionsto the t-channel poles.
DIPSY & HEJ 22 Leif Lönnblad CERN/Lund University
DIPSYˆHEJ
Summary
Matching to a collinear showerJet shapes
ˇFuture Developments
Matching to a collinear shower
As with all matrix element generators, we want to add partonshowers and hadronization to get fully simulated final states.And we must be careful not to double count!
How do we do that here, where HEJ already resums sometowers of logarithms?
◮ Parton Shower: soft and collinear resummation◮ HEJ: soft resummation (not exactly the same as in the PS).
DIPSY & HEJ 23 Leif Lönnblad CERN/Lund University
DIPSYˆHEJ
Summary
Matching to a collinear showerJet shapes
ˇFuture Developments
We will simply send the partonic state generated by HEJ toARIADNE and start the shower.
For each emission, we send back the state to HEJ and ask,Hej! How would you have done this emission?
The dipole splitting function in ARIADNE is an approximation tothe ratio of matrix elements
DAri(p2⊥, y) ≈
z16π2
|Mn+1|2
|Mn|2 .
From this we simply subtract the corresponding HEJ calculation
DHEJ(p2⊥, y) =
z16π2
∣
∣MHEJn+1
∣
∣
2
∣
∣MHEJn
∣
∣
2 .
DIPSY & HEJ 24 Leif Lönnblad CERN/Lund University
DIPSYˆHEJ
Summary
Matching to a collinear showerJet shapes
ˇFuture Developments
We veto the ARIADNE emission with probability DHEJ/DAri in away such that the collinear logarithms are still resumed in theSudakov form factors. (c.f. the Veto algorithm)
(wrt. beam) [GeV]k0 10 20 30 40 50 60
]-2
<Spl
it> [G
eV
-510
-410
-310
-210
-110
1
HEJ
Ariadne
r0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
]-2
<Spl
it> [G
eV
-410
-310
-210
HEJ
Ariadne
DIPSY & HEJ 25 Leif Lönnblad CERN/Lund University
DIPSYˆHEJ
Summary
Matching to a collinear showerJet shapes
ˇFuture Developments
Jet shapes
-5 -4 -3 -2 -1 0 1 2 3 4 5
-3-2
-10
12
30
1020304050607080
HEJ partons
Particles after showerRapidity
φ
(GeV)p
DIPSY & HEJ 26 Leif Lönnblad CERN/Lund University
DIPSYˆHEJ
Summary
Matching to a collinear showerJet shapes
ˇFuture Developments
r0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
to
t /
p(r
) =
pρ
-110
1
10
)=(1.64,2.02)φ(y,
)=(-3.535,1.817)φ(y,
DIPSY & HEJ 27 Leif Lönnblad CERN/Lund University
DIPSYˆHEJ
Summary
Matching to a collinear showerJet shapes
ˇFuture Developments
1
10
100
1000
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
ρ(r)
r
ATLAS jet profiles
160 < p⊥ < 210 (x35)
110 < p⊥ < 160 (x34)
80 < p⊥ < 110 (x33)
60 < p⊥ < 80 (x32)
40 < p⊥ < 60 (x31)
30 < p⊥ < 40
ATLASHEJ+Ariadne
Pythia P10Pythia P10 (no MI)
DIPSY & HEJ 28 Leif Lönnblad CERN/Lund University
DIPSYˆHEJ
Summary
ˆ Jet shapesFuture Developments
Future Developments
For very hard jets there is still a problem that the existence ofsoft gluons from HEJ close to the jet, prevents ARIADNE fromemitting enough collinear radiation, making the jets a bit toonarrow.
We’re working on that...
DIPSY & HEJ 29 Leif Lönnblad CERN/Lund University
DIPSYˆHEJ
Summary
Summary
◮ Two new BFKL-based hadron-level generators◮ DIPSY: Minimum Bias and Heavy Ions◮ HEJ: Jets
DIPSY & HEJ 30 Leif Lönnblad CERN/Lund University
DIPSYˆHEJ
Summary
DIPSY & HEJ 31 Leif Lönnblad CERN/Lund University