a monte carlo for jet quenching: medium studies in alicegruppo3.ca.infn.it/cnfa08/cunqueiro.pdf ·...

1

A Monte Carlo for jet quenching: mediumstudies in ALICE

Leticia Cunqueiro

Laboratori Nazionali di Frascati

Leticia Cunqueiro Palau, 29-9-2008

2

Outline

At LHC a full unbiased jet reconstruction will be possible thanks to:

• The high rate of high energy jets (Ejet > 100 GeV) disentangled from the

background.

• New algorithms and background subtraction techniques.

• Detector properties.

New Accessible: Fragmentation functions, jet shapes, jet multiplicities, intrajet particle

correlations...that will allow for a much better characterization of the medium.

but to go beyond limited single inclusive measurements a Monte Carlo is needed.

We present Q-PYTHIA, a Monte Carlo for the Jet Quenching based on the ideas

described in [Armesto,Cunqueiro,Salgado,Xiang, JHEP 0802:048,2008]


3

Our framework: Medium-induced gluon radiation

Medium-Induced Radiation: In a QCD medium (QGP) a hard parton looses virtuality

by the induced emission of soft gluons. Their emission and their further (strong)

interactions with the medium are the dominant energy loss for high energy projectiles.

Y cuanto hemos podidio comprobar va desde

hasta

The hard parton looses virtuality from the initial scale t to the final hadronization one

t0 ' Λ2QCD. Hadronization happens outside the medium (for pT ≥ 7 GeV/c at RHIC)

The QCD vacuum radiation pattern is changed:

• energy loss of the leading parton( ∆E ' αSqL2)

• angular broadening of the jet cone (∆k2T >' qL)

• an increase and a softening of the shower multiplicity.


4

Medium-induced gluon radiation

The single inclusive distribution of medium induced gluons with energy

ω and kt from a parent parton of energy E was derived by Wiedemann (2000).

ωdI

dωdkT

=αSCR

(2π)2ω22Re

Z ∞

0

dyl

Z ∞

yl

dyl

Zdue

−ikTue−1

2

R∞yl

dζn(ζ)σ(u)×

∂

∂y

∂

∂u

Z u=r(yl)

y=0=r(yl)

Drei

R ylyl

dζω2 (r2−n(ζ)σ(r)

iω )

All the medium information is encoded in the product n(ζ)σ(r)

• n(ζ)=density of scattering centers.

• σ(r)=strength of the interaction.

BDMPS approximation (Brownian motion): n(ζ)σ(r) = 12q(ζ)r2

q(ζ) −→ < q2T > /λ .

(Transport coefficient, encodes information about the elementary interaction)

In this case→ numerically tractable expression for the spectra is obtained.


5

Medium Induced Gluon Radiation

-210 -110 1 10 210

0

0.5

1

1.5

2

2.5

3

3.5

4

]2κdω/[dmeddIω

2κ

-2=10cω/ω-1=10cω/ω

=1cω/ω=10cω/ω

ωTk

θ

p

Like in QED, the emission of a gluon has a phase

φ =k2T ∆z

2ω .

To strip the gluon out φ ∼ 1 → lcoh ∼ 2ω/k2t

D = average distance between the scattering

centers= L/N .

If lcoh < D → incoherent B-H limit.

If lcoh ≥ D → there is suppression of the radiation

due to LPM coherence.

Suppression happens at low k2t and/or great ω.

(κ2 =k2t

qL and ωc = 12qL2)


6

Medium-modified splitting functions

In vacuum: dIvac

dzdk2T

=αsP (z)vac

z−→12πk2

T

, P (z)vacz−→1 '

2CR1−z , z = 1− x

The ansatz is an extension of the former eq. to medium:

dI

dzdk2T

med=

αsP (z)medz−→1

2πk2T

, P (z)medz−→1 = 2πzt

qL F ( ωωc

, κ2) [Salgado-Polosa]

dIvac

dzdk2T

TOT= dIvac

dzdk2T

MEDIUM+ dIvac

dzdk2T

V ACUM

And the total splitting is taken to be the sum of vacuum + medium:

P TOTAL = P V ACUUM(z) + P MEDIUM(z, t, q, L)

Other approaches: [Borghini-Wiedemann] medium multiplicative factor, [Guo-Wang-

Majumder] higher twist corrections in DIS → P (z) = P (z) + δP (z).


7

Medium effects at the level of the Sudakovs

10 210 310 4100

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1 and t2 GeV4=102=E

maxProbability of no emission between t

)2t (GeV

lines/markers: with/without large x correct.

upper/lower curves: quarks/gluons

L=2 fm vacuum

/fm2=0.5 GeVq

/fm2=5 GeVq

Sudakov Form Factor: ∆a(t, ta0) = e

−P

a−cc′R tta0

dt′t′

R 1−zmin(t′)zmin(t′)

dzαS(t′,z)

2π Pca(z)

It gives the probability for a parton not to radiate while evolving from t0 to another scale

t.

When our total vacuum+medium splitting functions are supplemented the radiation

probability is very much enhanced.Leticia Cunqueiro Palau, 29-9-2008

8

Medium Modified Fragmentation Functions

z-310 -210 -110 1

)2

(z,Q

gD

-910

-810

-710

-610

-510

-410

-310

-210

-110

110

210

310

410

510

610

=100 GeVjetE

/fm2=50 GeVq

/fm2=10 GeVq

/fm2=0 GeVq

z-310 -210 -110 1

)2

(z,Q

sM

/V

0

0.5

1

1.5

2

2.5

Solid/dashed=L=2,6 fm, Q = Ejet. Suppression (enhancement) of high (small) z par-

tons. These effects are enhanced with the medium lenght.

∂D(x, t)

∂t=

1

t

Z 1

x

dz

z

αS

2π(P (z) + ∆P (z, t, q, L))D(

x

z, t)

The medium accelerates the evolution.


9

Monte Carlo implementation

A Monte Carlo is a desireable tool: allows us to go beyond single inclusive production

and access more exclusive and differential observables → discriminate between energy

loss models.

Be aware that a probabilistic description of radiation in medium is not theoretically

proved: phenomenological assumptions are required.

Our approach: Q-PYTHIA (soon publicly avaliable)

1.Take final state showering routine PYSHOW in PYTHIA and correct vacuum split-

tings:

Ptot(z) = Pvac(z) → Ptot(z) = Pvac(z) + ∆P (z, t, q, L, E)

2.Consider the formation time of the radiated gluons to implement lenght evolution.

The interplay between gluon coherence and medium length is explored for the first time.


10


A Monte Carlo is a desireable tool: allows us to go beyond single inclusive production

and access more exclusive and differential observables → discriminate between energy

loss models.

Be aware that a probabilistic description of radiation in medium is not theoretically

proved: phenomenological assumptions are required.

Other recent MC related approaches:

1. JEWEL [Zapp et al]: multiplicative increase of the soft splittings.

2. PYQUEN [I.P.Lokhtin]: radiation superimposed on other effects like collisional energy loss.

3. coucou[T.Renk]: enlargement of the QCD evolution by giving virtuality to the partons.


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A branching algorithm must solve this problem:

given a parton with coordinates (t1,z1), which are (t2,z2) at the next branching? Two

steps:

1. Sudakov Form Factor: ∆(t1) = e−

Pa−cc′

R t1t0

$dzαS(t′,z)

2π Pca(z)

gives the probability for a parton not to branch while evolving from an initial scale t0

to another scale t1.

∆(t2)

∆(t1) stands for the probability of evolving from t1 to t2 without branching.

Thus t2 can be generated by solving the equation (R is a random number)

∆(t2)

∆(t1) = R

2. And z2 can be diced down by solving the equation:

R z2zmin

dzαS2π P (z) = R

R zmaxzmin

dzαS2π P (z).


12

Monte Carlo implementation in medium

A branching algorithm must solve this problem:

given a parton with coordinates (t1,z1), which are (t2,z2) at the next branching? Two

steps:

1. Sudakov Form Factor: ∆(t1) gives the probability for a parton evolving from an initial

scale t0 to another scale t1.

∆(t2)

∆(t1) stands for the probability of evolving from t1 to t2 without branching.

Thus t2 can be generated by solving the equation (R is a random number)

∆(t2)

∆(t1) = R medium change P (z) → P (z) + ∆P

2. And z2 can be diced down by solving the equation:

R z2zmin

dzαS2π P (z) = R

R zmaxzmin

dzαS2π P (z).

In medium change P (z) → P (z) + ∆P


13

Implementing the longitudinal and energy evolution ofthe shower

1. In our DGLAP approach each kernel is evaluated at the same L and energy E: evolution

in virtulality but not an evolution in length nor in energy.

2. However, not every fragmenting gluon “feels” the same L as the shower developes. And

the energy is reduced at each branching.

3. Use this: each gluon travels a length before it becomes real (before it decoheres from

the hard parton wave function ):

The gluon phase: φ =k2T ∆z

2ω

To strip it out from the parton: φ ∼ 1 → lcoh = 2ω

k2T

P(L)

1cohl

2cohl

)1coh

P(L-l

)2coh-l1

cohP(L-l

4. First branching: P (L, E). Next branching: P (L− l1coh, zE) and so on.


14

Litmus check, intrajet distributions 0

0 1 2 3 4 5 6 7 8 9 10

0

0.5

1

1.5

2

2.5

3

3.5

=100 GeVjetEξd

partondN

/p)jet

=ln(Eξ0 5 10 15 20 25 30 35 40

−310

−210

−110

1

PYTHIAQ−PYTHIA

)−1 (GeVT

dp

partondN

(GeV)T

p0 0.5 1 1.5 2 2.5 3

0

2

4

6

8

10

12

14

16

18

20

θd

partondN

θCompare Q-PYTHIA with q = 0 and PYTHIA. Small differences mainly due to:

PYTHIA: P (z → 1), Q-PYTHIA: P (z).


15

Medium in Pythia, intrajet distributions I

0 1 2 3 4 5 6

0

0.5

1

1.5

2

2.5

3

3.5

4

=10 GeVjetE

ξd

partondN

/p)jet

=ln(Eξ0 1 2 3 4 5 6

−310

−210

−110

1

10

)−1 (GeVT

dp

partondN

(GeV)T

p0 0.5 1 1.5 2 2.5 3

0

1

2

3

4

5

6

7

=100 GeVjetE

θd

partondN

=acos(pz/p)θ

vacuum/fm2=1 GeVq

/fm2=10 GeVq

The spectra are softened. Suppression/enhancement of large/low z values. High pT

suppression. pT broadening? → not clear due to energy conservation in PYTHIA. Clear

angular broadening. (L = 2 fm)


16

Medium in Pythia, intrajet distributions II

0 1 2 3 4 5 6 7 8 9 10

0

1

2

3

4

5

6

7

8

9

10

ξd

partondN

/p)jet

=log(Eξ0 2 4 6 8 10 12 14

−210

−110

1

10

=100 GeVjetE

)−1 (GeVT

dp

partondN

(GeV)T

p0 0.5 1 1.5 2 2.5 3

0

5

10

15

20

25

30

=100 GeVjetE

θd

partondN

/p)z

=acos(pθ

vacuum

/fm2=5 GeVq

/fm2=50 GeVq

The same but for Ejet = 100 GeV (L = 2 fm).


17

Medium in Pythia, intrajet distributions III

0 1 2 3 4 5 6

0

1

2

3

4

5

6

7

8

9

10

=10 GeVjetEξd

hadrondN

/p)jet

=ln(Eξ0 1 2 3 4 5 6

−310

−210

−110

1

10

210

)−1 (GeVT

dp

hadrondN

(GeV)T

p0 0.5 1 1.5 2 2.5 3

1

2

3

4

5

6

7

8

9

10

=100 GeVjetE

θd

hadrondN

=acos(pz/p)θ

vacuum/fm2=1 GeVq

/fm2=10 GeVq

Hadronization sweeps out soft effects. (L = 2 fm)


18

Medium in Pythia, intrajet distributions IV

0 1 2 3 4 5 6 7 8 9 10

0

5

10

15

20

25

30

35

40

=100 GeVjetEξd

hadrondN

/p)jet

=log(Eξ0 2 4 6 8 10 12 14

−210

−110

1

10

210 )−1 (GeVT

dp

hadrondN

(GeV)T

p0 0.5 1 1.5 2 2.5 3

10

15

20

25

30

35

40

45

50

=100 GeVjetE

θd

hadrondN

/p)z

=acos(pθ

vacuum

/fm2=5 GeVq

/fm2=50 GeVq

The same but for Ejet = 100 GeV (L = 2 fm).


19

Different effects in the shower

0 1 2 3 4 5 60

1

2

3

4

5

6

7

8

9

10

ξd

partondN

/p)jet

=ln(Eξ0 2 4 6 8 10 12 14

-210

-110

1

10

210

=100 GeVjetE

)-1 (GeVT

dp

partondN

(GeV)T

p0 0.5 1 1.5 2 2.5 3

0

5

10

15

20

25

30

35

θd

partondN

=acos(pz/p)θ

No evolution in energy (QW-like), no evolution in length

Evolution in energy, not in length

Our default: Evolution in energy, evolution in length


20

Caveats/Open issues

1. Our implementation assumes that there is an ordering variable in the medium. Is this

probabilistic interpretation valid?

2. There is no energy and momentum exchange with the medium. In an energy conserving

Monte Carlo this is of great importance.

3. Elastic energy loss not included: our BDMPS based implementation considers static

scattering centers → the recoil is not taken into account.

4. How does the Medium Induced Gluon Radiation affect jet hadroquemistry?

The medium causes color rotations and changes the color flow. The effects should

be tested by using different hadronization models.

An enhanced splitting probability is enough to change jet composition:

baryon/meson ratio is modified if just the number of splittings is increased.

Recombination, elastic scattering putting/taking particles in/from the jet etc.

5. our to-do list: Study these effects in a realistic nuclear envionment with current

background subtraction and jet reconstruction techniques. In a realistic detector envi-

ronment


21

Comparison: QW vs our new approach

z-110 1

)2

(z,Q

ME

Dg

D

-710

-610

-510

-410

-310

-210

-110

1

10

2=2 GeV2Q2=300 GeV2Q

2=10000 GeV2Q

/fm, L=6 fm2=1GeVq=100 GeV jetEsoli/dashed=ours/QW

z-110 1

)2

(z,Q

VA

C

g)/

D2

(z,Q

ME

Dg

D

0

0.2

0.4

0.6

0.8

1

2=2 GeV2Q2=300 GeV2Q

2=10000 GeV2Q

/fm, L=6 fm2=1GeVq=100 GeV jetEsoli/dashed=ours/QW

For Q2 << E2jet QW overestimate suppression

At Q2 ' E2jet , it can be shown that this new method equals QW.

• good agreement in the relevant z range for inclusive particle production.


22

Nuclear Modification Factor

qt0 2 4 6 8 10 12 14 16 18 20 22

(qt,y=

0)AAR

0

0.2

0.4

0.6

0.8

1=200 GeVs

/fm2=0.33GeVq

/fm2=0.66GeVq

/fm2=1.GeVq

/fm2=1.33GeVq

/fm2=1.66GeVq/fm2=2.GeVq

/fm2=2.33GeVq

/fm2=2.66GeVq

/fm2=3.GeVq

L=6 fm

data0πdata points:PHENIX preliminary AuAu-

RAA = dσ(pdf + EKS + MMFF )/dσ(pdf + V ACFF ).

q ' 1 GeV2/fm at a fixed lenght of 6 fm. (the same as with the QW)

Tp

0 2 4 6 8 10 12 14 16 18 20 22

,y=0)

T(pAAR

0

0.2

0.4

0.6

0.8

1 /fm2=1 GeVq

/fm2=10 GeVq

solid/dashed=spherical/cylindrical geometry

Considering a path lenght distribution in a cylinder and in a sphere, the value of q grows

up to 10 GeV 2/fm.Leticia Cunqueiro Palau, 29-9-2008

23

Reconstruction example


24

RHIC experimental results collage

partN100 150 200 250 300 350

b

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

200 GeV Au+Au

= 0.2η∆b |

= 1.8η∆b |

I.Akiba [QM2005]

D.J.Tarnowsky [STAR]


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