1. HADES XXIII collaboration meeting
Reaction plane reconstruction with FW
in Au+Au beam test run
Alexander Sadovsky
Institute for Nuclear Research RAS,
Moscow
Introduction
Guideline from simulation
What do we learn from test beam data
Backup slides
HADES XXIII collaboration meeting
October , 2011
GSI, Darmstadt

2. Flow analysis and azimuthal angular distributions
K+ in by (KaoS)
Azimuthal angular distribution
of K+ for peripheral, semi-central and central events in collisions of by KaoS collaboration. PRL.81(1998)
In the frames of Fourier decomposition of obtained azimuthal distributions:
which allows determination of directed (a1) and elliptic (a2) flows one may draw conclusions about the in-plane and out-of plane emission of K+, in medium potential...
peripheral
semi-central
central
𝑑𝑁 𝑑φ =𝐶 1+2 𝑎 1 cos φ +2 𝑎 2 cos 2φ 𝑎 1 cos φ +2 𝑎 2 cos 2φ
φ= φ 𝑖 − ψ 𝑅 2

3. Reconstruction of reaction plane
(transverse momentum method)
𝑄 = 𝑖=1 𝑁𝑠𝑝 𝑤 𝑖 𝑝 𝑖 𝑡
Transverse momentum
space
Pti
where:
Q – reaction plane vector;
Nsp – number of spectators detected;
wi – weight factor:
wi>0 flying forward,
wi<0 flying backward;
pit – transverse momentum vector.
See e.g. [PL.157B,146,1985].
Projectile
spectators
Secondaries
reaction
plane
Target
spectators 3

4. Reconstruction of reaction plane
(modified transverse momentum method)
Hits in cells
𝑄 = 𝑖=1 𝑁𝑠𝑝 𝑤 𝑖 𝑟 𝑖 ∣ 𝑟 𝑖 ∣
Forward Wall
(or HCAL)
where:
Q – reaction plane vector estimate;
Nsp – number of fragments;
wi – weight factor:
wi>0 if flying forward,
wi<0 if flying backward,
absolute value is set to
mass (m) or charge (Z)
of the spectator;
ri – position vector of cell with a hit-i.
Transverse momentum
space
Pti
(projectile
spectators)
Projectile spectators
Secondaries
reaction
plane
Target spectators 4

5. HADES Forward Wall, installed: March 2007
Fully operational: summer 2010, 2011
Distance to target 8 m
140 small 4x4cm
64 middle 8x8cm
84 large 16x16cm
cells 5

6. Simulation (Au@1.25AGeV)+Au
SHIELD + hGeant
FW is 8m from target, spectators selected by time-of-flight.
Higher values of |Q| lead to better
reaction plane determination:
0<|Q|<4 : poor RP angle resolution
4<|Q|<14 : higher resolution
By selecting |Q|>4 we also suppress peripheral events
drp=(ϕrec-ϕgen) Q
Impact parameter b [fm] 6

7. Method to determine resolution of reaction plane angle (RPA) suitable for real data
QRPA
QARPA
QBRPA
Hits in each event are randomly divided into two equal subgroups:
A and B and RPA determination is done separately for cells A and B.
Difference between the reaction plane reconstruction in two subgroups determines the reaction plane resolution of the whole event. 7

8. Method to determine resolution of reaction plane angle (RPA) suitable for real data
But first we apply it for simulation
Hits of an event are randomly divided into two equal groups:
A and B determining the reaction plane in each group separately.
Reaction plane angle determination based
on whole hits in FW of the event and in two subgroups A and B show flat distribution.
Difference between the reaction plane reconstruction in two subgroups determines the
reaction plane resolution of the whole event.
dN/dΦRPA
for
whole event
(group A + B)
dN/dΦRPA: group A
dN/dΦRPA: group B 8

9. Simulation (Au@1.25AGeV)+Au SHIELD + hGeant
Simulation w/o trigger conditions:
Event selection: for 4<|Q|<14
reaction plane angle resolution for all hits in FW from each event:
RMS=60o
Gaussian fit sigma=48o (in central part)
Gaussian fit sigma=37o {5<b<10 & Q>6}
/ K.Lapidus HADES coll.meeting /
NB: the estimate is done comparing
with reaction plane from SHIELD.
Estimate of reaction plane resolution
based on two subgroups (A and B) of
hits in each event:
RMS=81.34o /√2 = 58o
i.e. in a good agreement with the one
obtained with knowledge of reaction plane angle from simulation.
NB: this estimate is also applicable to exp. data.
* Known only in simulation
drp=ϕrec- ϕgen 9

10. (Au@1.24AGeV)+Au HADES 2011 test beam
(spectators selection by FW information)
Time-of-flight needed by spectators to travel from target to FW cell
is selected
Time [ns]
FW cell #
All charges accepted, but
pedestals are taken away
dE/dx [arb.u]
FW cell # 10

11. (Au@1.24AGeV)+Au HADES 2011 test beam (events selection: target)
Data selection:
several files from day 227, 229, 230
Target selection:
{(x2+y2)½<3.33mm} && z-unrestricted
3<vertex.Chi2<60
vertexClus.getSumOfWeights>6
Target Y [mm]
Target X [mm]
be *
be *
be *
Target Z [mm]
Target Z [mm]
Target Z [mm] 11

12. (Au@1.25AGeV)+Au HADES 2011 test beam
FW azimuthal anisotropy (day 229 be *)
𝑄 = 𝑖=1 𝑁𝑠𝑝 𝑟 𝑖 ∣ 𝑟 𝑖 ∣
All sp. charges are treated as
Z=1 (wi=1)
(H-L)/(H+L) = 20% =
( )/( )
y [mm]
x [mm]
Reconstructed phiRP [o]
Adjusting for
beam shift
x = x - (0mm)
y = y - (0mm);
Rmin = 220mm
(to gain isotropy)
(H-L)/(H+L) = 13% =
( )/( )
y [mm]
x [mm]
Reconstructed phiRP [o] 12

13. (Au@1.25AGeV)+Au HADES 2011 test beam RPA distribution (Rmin=220mm)
Experiment:
RMS(A^B)=74o
RMS(RPA)~52o
4<|Q|<9
Simulation:
RMS(A^B)=83o
RMS(RPA)=59o (63o)*
Preferable directions
(systematics)
Data files:
be *
Moderate
4<|Q|<9 values
closest to flat RPA
distribution
12-20%
diff
Experiment:
RMS(A^B)=69o
RMS(RPA)~49o
4<|Q|<14
Simulation:
RMS(A^B)=80o
RMS(RPA)~57o (61o)*
Range of |Q|-values
suggested by the simulation 4<|Q|<14
still too anisotropic w.r. RPA reconstructed
16-22%
diff
No selection on
|Q|-values
NB:
partially
explained by
the azimuthal
anisotropy in
phiRP of 13%
obvious correlation
to +/- 120o
|Q|>14
( excluded ) 13

14. FW ϕ(cell) distributions for different Rmin cut
(beginning of beam time, day 227: be *)
Rmin>40mm
Rmin>120mm
Rmin>220mm
ϕcell [o]
ϕcell [o]
ϕcell [o] 14

15. RPA, ϕ(A^B) distributions for different Rmin cut
(beginning of beam time, day 227: be *)
Rmin>40mm
Rmin>120mm
Rmin>220mm
Moderate transverse momentum transfer selected 4<|Q|<14
exp:
RMS(ϕ(A^B)) = 68o
sim:
RMS(ϕ(A^B)) = 81o
sim/exp=1.19
exp:
RMS(ϕ(A^B)) = 68o
sim:
RMS(ϕ(A^B)) = 81o
sim/exp=1.19
exp:
RMS(ϕ(A^B)) = 67o
sim:
RMS(ϕ(A^B)) = 80o
sim/exp=1.19 15

16. (one of “non-isotropic” days 229: be1122901465*)
Some guilty cells??
(one of “non-isotropic” days 229: be *)
Selecting events with Rmin=0
Dis: dN/d{#cell} for |Q|<7
– very isotropic part from of RPAs
Dun: dN/d{#cell} for |Q|>17
– most non-isotropic part of RPAs
Make normalized difference:
Dun*(Int{Dis}/Int{Dun}) - Dis
Dis
cell#
Dun
cell#
cell# 16

17. Conclusions and possible improvements
* Given anisotropy leads to systematic error in RPA determination
* Source of anisotropy shall be studied:
In simulation: shift of mean X, mean Y does not reproduce neither
half-moon shape, no the RPA phi-distribution.
* Depending on the source of the anisotropy one may try:
1. Increase minimal radius cut-off in analysis (~loosing resolution)
2. Move FW closer to target (~time of flight dectease)
3. Try to weight cell response to force isotropy

18. Summary
First test beam Aug'11 data of reaction were analyzed aiming determination of the reaction plane angle from FW.
Some non-trivial azimuthal anisotropy of beam profile on FW is seen. This leads to non-flat distribution of reconstructed reaction plane angle. A suppression of this anisotropy can be done to some extend by shifting the center of gravity of the beam spot on FW and by geometrical cutoff of the FW acceptance.
An estimate of reconstruction accuracy of RPA is by ~25% “better” in real data compared to the simulation, while remaining RPA anisotropy is seen on the level of ~15%.
More investigations needed.
Suggestion: move FW closer to target
Forward wall team:
INR Moscow:
O.Busygina, M.Golubeva, F.Guber, A.Ivashkin, A.Reshetin, A.Sadovsky, E.Usenko
NPI Řež:
A.Kugler, Yu.Sobolev, O.Svoboda, P.Tlusty, V.Wagner.

19. Backup slides

20. (Au@1.25AGeV)+Au HADES 2011 test beam
FW azimuthal anisotropy (day 227 be *) R R R
220mm 20

21. (Au@1.25AGeV)+Au HADES 2011 test beam
FW azimuthal anisotropy (day 229 be *) R R R
220mm 21

22. (Au@1.25AGeV)+Au HADES 2011 test beam
FW azimuthal anisotropy (day 230 be *) R R R
220mm 22

23. FW cell response after new time calibration
with walk correction
dN/dt[ns] 23

24. (Au@1.24AGeV)+Au HADES 2011 test beam
FW azimuthal anisotropy (day 229) no targ.cut
y [mm]
y [mm]
TOF multiplicity>20
(no improvement)
x [mm]
x [mm]
Reconstructed phiRP [o]
Adjusting for beam shift x=x-(-7.2mm) y=y-(-1mm); and Rmin = 138mm (to gain isotropy)
TOF multiplicity>20
(no improvement)
y [mm]
y [mm]
x [mm]
x [mm]
Reconstructed phiRP [o] 24

25. Simulation: FW fired cells distribution Au+Au@1.25AGeV
(selection of spectators in FW)
Selecting spectators
by peak at time-of-flight distrib. in FW cells
(left ): inside 2sigma
(right): outside2sigma
Spectators
Secondaries y y
100%
hits
x [cm]
x [cm]
16%
dN/dx
dN/dx
Time [ns]
Mean =18.1
Sigma=0.87
74%
x [cm]
Time [ns]
x [cm]

26. Reaction plane reconstr.: Au+Au@1.25GeV/u
no selection
0 < b < 5
no weight
Z weight
5 < b < 10
10 < b < 15
43°
⇉ K.Lapidus (HADES coll.meet 2010, GSI)

27. Reaction plane recons. : Au+Au@1.25GeV/u
Cut on Q value helps in suppression of tails and
improves the resolution
5 < b < 10
Q > 6
Q > 3
No cut
37o
Simulations with FW
located at 5-7m from target
⇉ K.Lapidus (HADES coll.meet. 2010, GSI)