jets in phenix
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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
07/23/2004 Jiangyong Jia 3
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
07/23/2004 Jiangyong Jia 4
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
07/23/2004 Jiangyong Jia 5
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
07/23/2004 Jiangyong Jia 6
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)
07/23/2004 Jiangyong Jia 7
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)
07/23/2004 Jiangyong Jia 8
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
07/23/2004 Jiangyong Jia 9
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.
07/23/2004 Jiangyong Jia 10
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
07/23/2004 Jiangyong Jia 11
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().
07/23/2004 Jiangyong Jia 12
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
07/23/2004 Jiangyong Jia 13
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
07/23/2004 Jiangyong Jia 14
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.
07/23/2004 Jiangyong Jia 15
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
07/23/2004 Jiangyong Jia 16
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.
07/23/2004 Jiangyong Jia 17
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
07/23/2004 Jiangyong Jia 18
Corrected CY compared with true CY
Near side
Far side
07/23/2004 Jiangyong Jia 19
The ratio between true and corrected
The agreement is good. This implies that our correction and
extrapolation is valid.
07/23/2004 Jiangyong Jia 20
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
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