zebo tang, lecture for zhangbu's class 1 9/21/2009 唐泽波...

Zebo Tang, Lecture for Zhangbu's class 19/21/2009

唐泽波中国科学技术大学近代物理系

Resonance K* reconstruction and its role in heavy-ion collisions

相对论重离子碰撞中矢量介子 K*的重建及其应用

• Why do we need resonance

• How to reconstruct it

• What can it tell us


QGP evolution

Colliding

Chemical Freeze-Out

Kinetic Freeze-OutWhat we can measure

• How to study the property of the hot dense medium and its evolution?

• What kind of probe we can use?

A time scale compatible to the lifetime of the medium is needed


Property of K*

=4 fm/c


Re-Scattering vs. Re-Generation

hadronizationbegins

Chemicalfreeze-out

Thermalfreeze-out

tColliding

K*K

K K*

K

Measured

K

K*

K

K K*

Lost

Resonances produced at chemical freeze-out stageDaughter particle’s re-scattering effect destroys part of resonance signalRe-generation effect compensates on resonance yield


Jet Quenching

hadrons

hadronsleadingparticle suppressed

leading particle suppressed

q

q

hadrons

q

q

hadrons

leading particle

130 GeV nucl-ex/0206011

ddpdT

ddpNdpR

TNN

AA

TAA

TAA /

/)(

2

2

Au+Au

p+p

9

The high pT suppression behavioris different for KS

0 and

Is this a mass effect or dependingon particle species (meson vs.baryon) ?

Hydrodynamic Model

Quark Recombination Model

K* and : mesons but their massesClose to

K* at high pT ( > 2 GeV/c ) are the same as individual hadrons

K* RAA can distinguish this difference


A typical Au+Au event at 200 GeV

Primary vertex

K

K*

K

K*

~1000 tracks/particles produced within STAR acceptance in a central Au+Au event

K* dN/dy ~ 10 in central Au+Au collisions at 200 GeV


K* reconstruction

• What we can detect is final stable particles• How to identify K*?• What properties does K* have?

)()(22

* ppEEKKM K


Pion and Kaon Identification

|N|<2 and |NK|<2


Kaon Pion paring

How to find the K- pair from the same parent?No way! What should we do?Pair every pion with every kaon in the same event

Nothing! Why?


Random Combinatorial BG Reconstruction

Like-sign technique Mixed-event technique Rotate technique


Like-sign

K+

K*

+

uncorrelated

uncorrelated


Rotate

K+

K*-’

Remove correlation


Mixed-event

K+

K*

uncorrelated

-’’


Invariant Mass Distribution


Combinatorial BG subtracted


BG reconstruction method comparison

Advantage Disadvantage

Like-sign Same event, no event structure difference

Limited statistics

Rotate Same as above Same as above, create wired structure due to jet-like correlation etc.

Mixed-event Enhance statistics Event structure difference

Mixed-eventRotate

Same as above Same as above, create wired structure due to jet-like correlation etc.


Source of residual background

Elliptic flow

Particle mis-identification

D0K etc.

K*

K

K*

K

X

Y

K*K*

K

X

Y


K* signal


K* raw pT spectra

Branching ratio corrected


Efficiency×acceptance determination

1. Generate K*, flat y, , pT distribution

2. Decay in GEANT, simulate STAR sub-detectors’ responses

3. Embed into a real event

4. Reconstruct embedded event

5. Associate MC tracks with reconstructed tracks

6. Run through embedded events, applied all of the cuts and get the counts of reconstructed K*, compare to MC K* counts


Efficiency×acceptance vs. pT

• Increase as increasing pT

• Decrease as increasing multiplicity


K* pT spectra

Exponential function:

Extract integrated yield dN/dyand inverse slope T

Extrapolate to unmeasured pT range


dN/dy

• Increase with increasing energy• No system size dependence


<pT>

Higher in central collisionsRe-scattering effect

Close to proton, higher than Pion and KaonMass instead of particle type


K*/K- Ratio

• K* and K- have same quark content• Ratio in Au+Au collisions smaller than that in p+p collisions

(res-cattering dominant over regeneration)• Decrease as increasing system size (increasing fireball

lifetime)


/K* Ratio

• K* and have similar mass and same spin, different strangeness• K* re-scattering or strangeness enhancement or both


Nuclear Modification Factor

K* RAA @ pT<1.5 GeV/c Lower than other particles Rescattering EffectK* RAA @ pT>1.5 GeV/c Close to KS

0, different from

No strong mass dependence


Elliptic Flow v2: second Fourier coefficient

Elliptic Flow

x

z

y

Non-central Au+Au Collisions

Reaction plane r

])(cos21[2

1

1

2

3

3

n

rnTT

nvdydpp

Nd

pd

NdE

10

y

x

coordinate space py

px

Momentum space

Fourier expansion for particle azimuthaldistribution in momentum space:

Elliptic flow carries information at initialstage

Multiple interactions and pressure gradient lead to the final observable elliptic flow


v2 vs. pT

STAR

PHENIX

LOW INTERMEDIATE HIGH

Low pT : affected by hydrodynamic flow

Intermediate pT : may be related to quark matter anisotropy

High pT : space emission


K* v2 scaling

Coordinate phase space

K*

K

K*

K

X

Y

Momentum phase space

K*K*

K

pX

pY

Low pT:

Resonance daughter particles’ re-scattering and re-generation effects depend on the fire ball shape in the coordinate space

Resonance v2 compared to hadron v2 at low pT can tell the fireball shape in the coordinate space at late stage

Intermediate pT:

For directly produced K*, n =2For regenerated K*, n=4


Event Plane Reconstruction

iii

iii

w

w

)2cos(

)2sin(tan

2

1 12

iii

iiin nwnwQ )sin(,)cos(


Event Plane Distribution


Extract v2

In certain pT bin, get the same-event and mixed-event invariant mass distribution in several (-2) bins

Fit background subtracted invariant mass distribution, get K* yield N(-2,pT)

Fit N(-2,pT) with A*(1+2v2cos(2(-2))), get v2(pT)


v2 results

n=2.0±0.4, 2/ndf = 2/6


Spin alignment


Global polarization in non-central A+A collisions

11 10 1 1

01 00 0 1

11 10 1 1

mm

mn

density operator:

= m p m

spin density matrix:

jm jn

In non-central A+A collisions

large initial orbital angular momentum of partonic system

quarks and anti-quarks will be polarized opposite to reaction plane

For vector mesons, spin density matrix elementρ00 should be 1/3 in unpolarized case. The deviation of ρ00 from 1/3 manifests the global polarization of vector mesons.

1. Z.T.Liang and X.N.Wang, PRL 94 102301 (2005), PLB 629 (2005) 20-262. S.A.Voloshin, nuch-th/0410089


vs. hadronization mechanism00

Three different hadronization scenario :

1) recombine quark and anti-quark in QGP;

2) recombine in QGP with those from accompanying process;

3) fragmentation of a fast quark/anti-quark from the QGP.

q/q

Two kinds of quarks and anti-quarks:

1) quarks and anti-quarks in QGP ---- Polarized;

2) created in accompanying process ----- higher pT and unpolarized.

2( ) *( )

00 002

1 1 and < 1/3

3 3q q srec K rec

q q s

P P P

P P P

000 or 0, so 1/ 3q qP P

2 2 2( ) *( )

00 002 2 2

1 1 1, > 1/3

3 3 3q qfrag K frag s s s

q s s q s s s

P Pf n P

P n f P n f P


measurement

good Particle IDentification capability

large acceptance

uniform at both azimuth and polar directions

* * *2cos sin sin( )

K* is relatively short-lived (~4fm/c) vector meson.

In the rest frame of K*, K/π distribute as:

200 00

31 (3 1)cos *

4W

00

z*

*

2 *

2( / 2)

L

K

*

Event plane


Extract 00


00 vs pT

Consistent with 1/3, provide no evidence of global spin alignment


Summary

Resonance is a unique/important tool to probe the property of the hot dense medium and its evolution


Homework

已知 K*0K的分支比约 100% ， K*0K+-

的分支比是多少？

从 RAA和 v2的测量中我们可以看出在 STAR 中KS和的测量要比 K*要好得多，为什么？

zebo tang, lecture for zhangbu's class 1 9/21/2009 唐泽波...

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