166
M. M. Aggarwal
where X n =
cos(nφ i ), Y n =
sin(nφ i ), and φ i is the azimuthal angle of the ith
particle in an event and summation runs over all particles used to determine the event
plane. The event plane determined is not isotropic due to detector non-uniformity.
To obtain uniform event plane angle distributions following corrections are applied
as discussed in [26]:
• Recenter the distributions of X n and Y n by subtracting the X n and Y n values
averaged over all events, i.e.,
X
n = X n − −X n
Y
n = Y n − −Y n
(13.4)
• After re-centering, correction for twist of the vector is applied as
X
n =
(X
n − λ
s −
2n Y
n )
(1 − λ
s +
2n λ
s −
2n )
Y
n =
(Y
n − λ
s +
2n X
n )
(1 − λ
s +
2n λ
s −
2n )
(13.5)
where
λ
s ±
2n = =S 2n /A
±
2n
A
±
2n = 1 ± ±C 2n
C 2n =
cos(2nφ)
S 2n =
sin(2nφ)
(13.6)
here average is taken over all particles in an event and over all events in a sample.
• Finally re-scale the vector as
X
n = X
/A
+
2n
Y
n = Y
/A
−
2n
(13.7)
One gets 2nd order event plane as
E P
2
= tan
−1
Y
2
X
2
/2
(13.8)
The v
obs
2 can be obtained using (13.2) as