# Presentation: 082544

## Sotiria Batsouli 
Columbia University
For the PHENIX Collaboration

Quark Matter 2002

- Columbia University
- For the PHENIX Collaboration
- Quark Matter 2002

**Electron Inversion into Charm D Meson**

## Electron spectra at PHENIX

- <date/time>

-                     spectra  at midrapidity for
- Au-Au collisions, at        =130GeV
**(Phys.Rev.Lett.88:192303,2002)**
- Sources:
- 1.  Dalitz decays
- 2.  Di-electron decays
- 3.  Photon conversions
- 4.  Kaon decays
- 5.    c  D eX
- 6.    b  B  eX
- 7.  Thermal dileptons
- 1-4 background subtracted
- Decays of D mesons dominant remaining
- contribution to the e-spectra

## The extraction of the D meson spectrum from the electron spectrum
study of the strongly interacting initial system.

Heavy Quark energy loss dE/dx in medium

  1.  Radiative  + elastic dE/dx  of fast parton in
     medium with longitudinal expansion and partial
     thermalization independent of quark mass 
      suppression of large pt charm mesons  
     (Z. W. Lin et al. Phys.Rev.C 57:899,1992.
      Z. W. Lin et al. Nucl.Phys.B 544:339,1999 )

2. Gluon radiation from a fast parton  is suppressed at angles < Mq/Eq (“dead cone”  effect)  the suppression of heavy hadron pt distribution is smaller for heavy than light hadrons  D/ enhancement (depending on density of color charges in medium) 
      (D. Kharzeev et al. Phys.Lett.B 519:1999,2001)

- study of the strongly interacting initial system.
- Heavy Quark energy loss dE/dx in medium
-   1.  Radiative  + elastic dE/dx  of fast parton in
-      medium with longitudinal expansion and partial
-      thermalization independent of quark mass
-       suppression of large pt charm mesons
-      (Z. W. Lin et al. **Phys.Rev.C 57:899,1992.**
**      **Z. W. Lin et al. **Nucl.****Phys.B 544:339,1999** )
- 2. Gluon radiation from a fast parton  is suppressed at angles < Mq/Eq (“*dead cone*”  effect)  the suppression of heavy hadron pt distribution is smaller for heavy than light hadrons  D/ enhancement (depending on density of color charges in medium)
-       (D. Kharzeev et al. **Phys.Lett.B 519:1999,2001)**

- Electron Inversion into Charm D Meson

-                                           Pt                              GeV

## D formation time

- However what if the c-quark is not fast enough to escape the medium before it
- fragments into D meson...
- Fusion:                        and          pairs fragment into D mesons
- Peterson fragmentation function:
-                                                         gives
- D with
-  comes from a c-quark with

## 
Q.M. time        to build up a hadronic wave function and 
    distance        traveled by c before it fragments into a D

                                                                         for 

The expanding fireball has a transverse size:

                                        t the proper time of expanding system

It could be that                                   inside the fireball?

- Q.M. time        to build up a hadronic wave function and
-     distance        traveled by c before it fragments into a D
-                                                                          for
- The expanding fireball has a transverse size:
-                                         t the proper time of expanding system
- It could be that                                   inside the fireball?

- D formation time

-    R (compton wavelength)

## Low and medium pt (0-4 GeV) D may be formed inside fireball and  
     rescattering with surrounding particles may lead to collective  behavior.
     Interactions with other hadrons are relatively weak (D)~10 mb 
      (Ziwei Lin, C. M. Ko, Bin Zhang, Phys. Rev. C 61, 024904 (2000).
      Ziwei Lin, C. M. Ko, Bin Zhang, preprint [nucl-th/9905007] )
     However there is an abundance of  (for T~170MeV
or
     Charm quarks undergo significant scattering in partonic medium and
      participate in hydrodynamic type expansion then either fragment into D 
      mesons or coalesce with commoving spectators of low relative momentum to form D mesons.    

Thermalization, hydrodynamic flow of D?

-      rescattering with surrounding particles may lead to collective  behavior.
-      Interactions with other hadrons are relatively weak (D)~10 mb
-       (Ziwei Lin, C. M. Ko, Bin Zhang, Phys. Rev. C 61, 024904 (2000).
-       Ziwei Lin, C. M. Ko, Bin Zhang, preprint [nucl-th/9905007] )
-      However there is an abundance of  (for T~170MeV
- or
-      Charm quarks undergo significant scattering in partonic medium and
-       participate in hydrodynamic type expansion then either fragment into D
-       mesons or coalesce with commoving spectators of low relative momentum to form D mesons.
******Thermalization, hydrodynamic flow of D?**

- D thermalization ?

## Hydrodynamic model

- Thermal model with longitudinal and transverse flow
- (U. Heinz et al., Phys. Rev. C 48, 2462 (1993).
- Transverse velocity distribution:
-                                                           the max surface velocity, n=1
-                                                  R the max radius of expanding source
- Each fluid element is locally thermalized and boosted with angle :
- Instantaneous freeze-out in radial direction leads to model independence of freeze out hypersurface (points of last interaction). Only as normalization factor.
- Examine only the dynamics of the collision zone at freeze-out (shape of spectra). D is not assumed to have reached chemical equilibrium .
-                              enters also as a normalization factor

## 
Resulting spectrum is a superposition of the individual thermal components

Azimuthal symmetry - 
Integrate over fireball rapidity - 
PHOBOS: charged particle  flat over 2 units of   and integrand  
for       >2 (PHOBOS Collaboration, Phys.Rev.Lett.87:102303,2001. )
T the freeze-out temperature

- Resulting spectrum is a superposition of the individual thermal components
- Azimuthal symmetry -
- Integrate over fireball rapidity -
- PHOBOS: charged particle  flat over 2 units of   and integrand
- for       >2 (PHOBOS Collaboration, Phys.Rev.Lett.87:102303,2001. )
- T the freeze-out temperature

- Hydrodynamic model

## PHENIX Collaboration, Single Inclusive Hadron Spectra from           =130 GeV Au+Au Collisions at RHIC, in preparation.     
                                                          All particles decouple                    
                                                          kinematically at same freeze-out 
                                                          T on the freeze-out hypersurface  
                                                          + Heinz hydrodynamic model
                                                                 Simultaneous fit to the pt                                    
                                                           spectra of 
                                                           to extract T  and  

Min.               for dof=40 

-                                                           All particles decouple
-                                                           kinematically at same freeze-out
-                                                           T on the freeze-out hypersurface
-                                                           + Heinz hydrodynamic model
-                                                                  Simultaneous fit to the pt
-                                                            spectra of
-                                                            to extract T  and
- Min.               for dof=40

- Hydro-model application to PHENIX data

## Hydro-model for D meson

-     shape of D from
- Hydro-model
- normalized so that the
- e spectrum (---) best
-  matches the data

## Hydro-model for D meson

-      min       flow parameters
-                          contours

- Not very sensitive to values of T and
- due to statistics

## Electron Inversion into Charm D Meson (1)

- PYTHIA 6.152 as decay generator
- Average Branching Ratio for all the D states
-                         that contribute to the e spectrum estimated 11% from PDG (different from PYTHIA 9.7%)
- For each D meson        bin  electron       spectrum  (per D invariant multiplicity) for

## Assume functional form for D        spectrum
      1.  Power Law Parameterization

     2.  Gauss Parameterization (Hydrodynamic model inspired)  

Iterate over set of free parameters, perform 
De mapping and obtain the parameters 
corresponding to best fit to the electron data.

- Assume functional form for D        spectrum
-       1.  Power Law Parameterization
-      2.  Gauss Parameterization (Hydrodynamic model inspired)
- Iterate over set of free parameters, perform
- De mapping and obtain the parameters
- corresponding to best fit to the electron data.

- Electron Inversion into Charm D Meson (1)

- 10% most central electron data

- Best inversion fit for the two models
- Resultant electron spectra
-          90% statistical confidence limits

- The Gaussian and Power Law parameterization
- match the data equally well

## Electron Inversion into Charm D Meson (1)

- Minimum bias 0-92% electron data

-  The ratio of central to minimum bias electron
-  data indicates that their shapes are quite
-  similar  disagreement could be obvious because
-  of better statistics

- Single electrons with energies greater than ~1.5GeV
- could be mainly from energetic heavy quarks that
- escape after energy loss
- Single electrons with smaller energies could be from
-  thermalized charm quarks and therefore exhibit a
- hydrodynamic type behavior

-  Gaussian parameterization does not
-  match Data as well as Power Law

- Power Law

- Hydro-type

- But
-  B meson contribution could be important for
-  high pt

## PYTHIA D rapidity distribution ~flat for 
5% change in the electron PHENIX acceptance
                           if       is forced to be flat in the    range [-1,1]

- PYTHIA D rapidity distribution ~flat for
- 5% change in the electron PHENIX acceptance
-                            if       is forced to be flat in the    range [-1,1]

***Dependence of the electron pt spectrum ******on input  D PYTHIA model?***

-       D0,            D+            Ds+

-  y>1 contribution mostly to electrons with
-    -outside the measured range

-   |      |>1,               1>|      |>0.8,          0.8>|     |>0.6,
- 0.6>|     |>0.4,         0.4>|    |>0.2,        0.2>|     |>0.0,

## UA1 – CDF method for inverting
single lepton, dilepton spectra into D and 
B mesons
 ( Albajar  et al., Phys. Lett. B 186, 237 (1987),
C. Albajar et al., ZPC 37, 487 (1987),
C. Albajar et al, Phys. Lett. B 213, 405 (1988),
C. Albajar et al., Phys. Lett. B 256, 121 (1991),
C. Albajar et al., ZPC 369, 46 (1996),
CDF, Phys. Rev. Lett. 71, 500 (1993),
CDF, Phys. Rev. Lett. 71, 2396 (1993).   )

- UA1 – CDF method for inverting
- single lepton, dilepton spectra into D and
- B mesons
-  ( Albajar  et al., Phys. Lett. B 186, 237 (1987),
- C. Albajar et al., ZPC 37, 487 (1987),
- C. Albajar et al, Phys. Lett. B 213, 405 (1988),
- C. Albajar et al., Phys. Lett. B 256, 121 (1991),
- C. Albajar et al., ZPC 369, 46 (1996),
- CDF, Phys. Rev. Lett. 71, 500 (1993),
- CDF, Phys. Rev. Lett. 71, 2396 (1993).   )

- Electron Inversion into Charm D Meson (2)

- Every electron pT point contains mostly information about the integrated D meson with
- pTD >pTe . For each electron pT   D pTmin where 90% of the contribution to electrons are
- above that value.
- Using a model   map from each electron point to an integrated dN/dy D meson point:

- electron level

-      e 0.4<pt<0.5
-      e 0.8<pt<0.9
-      e 1.4<pt<1.6

**D**

## Electron Inversion into Charm D Meson (2)

- 10% most central electron data

- Minimum bias 0-92% electron data

-        Upper points:    inverted (using method 2) dN/dy (pT>pT(min)) integrated D meson points.
-        Lower points:   PHENIX electron invariant multiplicity data
-        Inputs:       PYTHIA (black),     best fit power law (blue),     best fit Gaussian (red).
-        The calculted D meson and electron distributions are shown as curves.
- 10% most central data   all models agree within statistical errors with both the electrons and D mesons.
-  minimum bias data       PYTHIA and Gaussian distribution disagree with the data

- PYTHIA

- Power
-  Law

- Gauss

## B meson contribution to electron spectra

- Z. W. Lin et al. **Phys.Rev.C 57:899,1992** predict that with energy loss, the electron yield from
- charm decays is close to that from bottom at E>2GeV.

- Hydro:      B mesons scaled with respect to D mesons as their total cross sections
-                   the B contribution becomes important above 2 Gev
- PYTHIA:  B meson contribution becomes important at higher pt

-          total e
-          D  e
-          B  e
-          B De

- D mesons

- B mesons