jets in phenix

1

Jets in PHENIXJiangyong Jia, Columbia Univerisity

How to measure jet properties using two particle correlation

method (In PHENIX)?

Discuss formula for jT, kT Discuss formula for the conditional yield

Hot Quark Matter, Taos Valley, NM

07/23/2004 Jiangyong Jia 2

Hard-scattering and Jet fragmentation Partons scatters with large Q2 – hard-scattering Outgoing partons fragment into sprays of hadrons –Jets Properties that we want to measure

The spread of the hadrons around the jet axis and relative orientation of the two jets – jT, kT.

The multiplicity of hadrons – fragmentation function Dqh(z)

Leading hadron

Q2


jT and kT jT = Momentum perpendicular to jet axis: jT= pT sin

<jT> is related to the non-perturbative QCD. Typical value is 500 MeV/c, very weakly depends on pT and

s.

jet

Jets are not exactly back-to-back in transverse direction kT = Intrinsic + radiative transverse momentum of the

initial partons.

, 1 , 2 ,1 ,2T jet T jet T Tp p k k


Projected to azimuth plane

Same jet correlation

Assuming tq and aq are statistical independent 2 2 2 2 2sin = sin cos sin cos ta tq aq ta tq aq aq tq Cross terms = 0

,

,,

,

,,

, ,

, ,

sin( ) =

sin( ) =

sin( ) ,

y

y

T asso

aq j assoT asso

T trig

tq j trigT trig

out N T assoat h

T asso T trig

jx

p

jx

p

p pdefine x

p p

2 2 2 2 2 2, , ,sin 1 2

yout N T asso ta T h j trigp p j x x

Simple relations derived for trigger and associated particles

tq trigger-partonaq associated-partonta trigger-associated ta tq aq


Far side jet correlation ,qq is the angle between the jets.

Assuming tq , aq and qq are statistical independent2 2 2 2 2 2 2

2 2 2 2 2 2

sin = sin cos cos sin cos cos

sin cos cos sin sin sin

ta tq aq qq aq tq qq

qq aq tq aq tq qq

Cross terms = 0

ta tq aq qq

,1 ,2 ,

, , , ,

2 2sin( ) ,

y y y yT T T T trig T trig

qq k trigT jet T jet T trig T jet

k k k k z px z

p p p p

At small angle, qq is

,1 ,2BBBBBBBBBBBBBBBBBBBBBBBBBBBBT Tk k 2

2 2 2 2 2 2 2 4, , , , ,1 2 2

yout F out F k T trig h h j trig j trig j trigp p x k z x x x x xSo we have

Projected to azimuth plane


jT, kT RMS values

1D RMS value:

2

,

2 21,1 2

y

out N

TD

h j trig

pj

x x

2,1 y D yV V

2 2 2, ,

2 2 2 2 41, , ,

12

2

y

out F out N k

T trigD

h h j trig j trig j trig

p p xk z

x x x x x

Pout is directly related to the angular width:

(for Gauss statistics)

Comparing with Jan’s formula

2 2 2

1

22 sin (1 )sin

2

T NTy trig F hD

h

pk z x

x

21 1

y

T NT

Dh

pj

x

(QM2004)


Comparison using Pythia simulation Trigger pt>5 GeV/c, change associated pT

2yj

2

y Trigk z

Jan’s formulaThis formula

“Seagull” effect at low pT. Some of the pt dependence is due to zTrig bias

(mean z ~ 0.7)


kT Broadening in dAu Presence of cold medium can broaden the jet kT

2 2Intrisic Radiation C

2pA old l

2 nuc k kk k

2 2Intrisic Radiation C

2pA old l

2 nuc k kk k

p+p p+A

dAu

C~ 0.2-0.4

Small additional kT:

Typical additional broadening is0.8-1.6 (GeV/c)2 in central collisions

This was thought to be the origin of Cronin enhancement

1(GeV/c)20.9(GeV/c)2 7(GeV/c)2

W.Volgelsang, hep-ph/0312320For STAR pp


hep-ph/0310274I.Vitev

Is kT in dAu sensitive to broadening? Seems radiation contribution dominate over the broadening

10% difference between dAu and pp for 4.5 GeV trigger

Radiation contribution is even stronger at higher pT

-h correlation

Pythia the sensitivity on broadening decreases as pT increases.


Fragmentation function Conditional yield

1( ) h

jet

dND z

N dz

Direct jet reconstruction. e+e-

= z E trigx z

,,

,

cos( ),

T trigT asso

E trigT trig jet

ppx z

p p

=>

CCOR,s = 63 GeV

Two particle correlation methods are used to extract FF. Jet direction and momentum approximated by the trigger define

1)( () tri

hE

trigg

E

dNCY x

N dxz D z 0.7z


Two particle azimuth correlation method

0 / ( , )realdN d d jet

In ideal acceptance, real pair distribution is

/ ( , )mixdN d d Acc

Pair acceptance function can be determined from event mixing technique

00 ( , )

1 /

/

real real

mixTrig

dN dN d d

N d d dN d djet

Real/mix gives the acceptance corrected CY (modulo constant background ).

/ ( , )( )( , )real jdN d d Acc et

Real distribution is modulated by pair acceptance function Acc().


Pair acceptance function ACC in PHENIX

Single particle acceptance

Triangle results from convoluting two flat distribution

Pair acceptance in

Pair acceptance in

effi is 100% at , Average is 25%

Shape from overlapping four triangles: west1-west2, east1-east2, west1-east2, east1-west2


Normalization for 2D and 1D CY 2D CY

00

2 1.

/

0 7 /

1 1 /mix

mix

real realasso

dN d dTrig Trig asso

d d dN d d

dN N dN d d

N d d N N

Acceptance+ efficiency Mix normalized to pair phase spaceUnderling triggers

Detected triggers

1D CY can be obtained by integrating out .

2 /

0 00

/

1 1 / /mix

mix

real mix real mix

dN dTrig Trig

d dN d

dN dN dN d dN d

N d d N

sin ( )

0.7 ( ) /

realgle

mix mix

R k

k K

Pair cuts and two track resolution

Single particle efficiency in full azimuth and 1 unit

Fraction of jet yield falls in acceptanceCan be calculated analytically assuming Gauss shape

( ) ( )

( )

d jet AccR

d jet


Test the correction with Pythia simulation

Generate 1 M triggered events and 1 M minimum bias events. Mixed distribution is obtained by mixing trigger with minbias event. Requiring trigger always has ||<0.35.

If we don’t constrain associated particle, we would get full yield.

Compare three correlations. No cut on associated particle full jet yield (near side)

Near side jet has a gauss shape in — the integral of the gauss. Cut | |<0.7 on associated particle full yield in ||

<0.7(away side) Far side jet has a very broad shape in

PHENIX acceptance cut measured yield in near and away side.


CY, with no constrain on associated particle

Trigger pt > 5 GeV/c, associated 1<pT <1.5 GeV/c Trigger ||<0.35, associated no eta cut. This gives the true conditional yield for the near side :0.717

FG

MIX

True conditional yield


CY, with associated particle in ||<0.7 Trigger pt > 5 GeV/c, 1<pTasso <1.5 GeV/c Trigger ||<0.35, and associated particle: ||<0.7 This gives the true conditional yield with in ||<0.7 for the far

side: 0.92

FG

MIX

True conditional yield

Because the away side correlation is very wide in . We just want the yield in ||<0.7, which is the range sampled by PHENIX.


Conditional yield in PHENIX acceptance Trigger pt > 5 GeV/c, 1<pTasso <1.5 GeV/c Trigger ||<0.35, and associated ||<0.35. Azimuth acceptance cut on both particles.. This gives the Measured conditional yield for same side and way

side 0.279(near), 0.233(far).

FG

MIX

Raw conditional yield


Corrected CY compared with true CY

Near side

Far side


The ratio between true and corrected

The agreement is good. This implies that our correction and

extrapolation is valid.


Summary

Discuss the general formula for and

Some difference from previously used formula, especially for kTz and low associated pT region.

The sensitivity on kT dies out as the trigger pT increases.

Discuss the how to extract the conditional yield using two particle correlation method and event mixing. The correction factor is derived for limited detector acceptance(can be trivially generalized to other detectors).

Verified with Pythia simulation

2yj 2

y Trigk z

jets in phenix

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