Hi Genya and all,
Last night I send you my T20, T21 and their kinematic coefficients.
Unfortunately, there were mistakes. I apologize but my wife was turning
red and fat from head to toe so I really could not concentrate. Some
obvious mistakes slipped through.
This morning I did hand calculations and compared to numbers I copied from
screen dump of my codes last night, here are the same tables with the
corrections:
Observed asymmetries:
para perp
Q N+ N- A*100 N+ N- A*100
1.95 2747 1669 -6.9+-1.1 3953 1362 11.4+-0.9
2.29 746 482 -9.1+-2.1 1200 358 15.4+-1.6
(-8.7+-3.4) (14.7+-1.2)
2.64 175 163 -22.5+-4.1 389 78 24.8+-2.6
(-19.8+-3.4) (23.0+-2.3)
your numbers are in the parenthesis. No change. No difference between you
and mine.
calculation of T20, T21 and the coefficients:
Q T20 T21 theta_q R20 R21 A_theory*100
para/perp para/perp para/perp
1.95 -0.601 -0.071 70.7 0.355/-0.450 -1.208/0.439 -13/22
2.29 -0.861 -0.127 67.2 0.445/-0.477 -1.177/0.296 -24/35
2.64 -1.115 -0.210 63.5 0.536/-0.494* -1.126/0.140 -37/49
hand calculation of the coefficients:
Q theta_q R20 R21
para/perp para/perp
1.95 70.7 0.362/-0.448 -1.211/0.447
2.29 67.2 0.452/-0.476 -1.180/0.305
2.64 63.5 0.543/-0.494 -1.127/0.149
the entry with a *, I made a typo in my email last night, I checked my
code dump again, code says 0.494 too. The A_theories I gave last night
were wrong. They were for 900MeV. hand calculation confirms code
calculation to 1 to 2%. The difference is even smaller consider that code
calculation is done compute the coefficients per event first then averaged.
calculation is done averaging the angle per event and then compute the
coefficients. averaging is not commutable with non-linear operations, but
with small bins, it s not that important.
Pzzs need to be updated accordingly, and I believe I did the errors in
Pzz wrong last night. Errors are under estimated and that explains why I
had so many more than 1 sigma inconsistancies.
Q Pzz*100
para perp
1.95 75+-12 73+-6
2.29 54+-12 62+-6
2.64 86+-16 72+-8
This looks better to me, numbers are withing reach of one each other.
Except for the 86+-16 which stands 1.14 sigma away from 54+-12. If I
average them weighted by the errors (this takes into account both the
statistics and the size of the asymmetry), I get:
Pzz*100 = 68.6.
In my email on 28th, I already reported that for runs(8648-9313) I find
0.67+-0.03 for Pzz, which is considerably higher than runs 8479-8598.
Things happened between these two bunch is the debug of TDC modules.
Again, I find consistancy with myself.
I would even suggest to leave the 3rd bin(your 2nd) out because of the
discrepancy in Pzz.
To quantify the "systematics" between you and me. With +-10% systematic,
added to the statistics quadratically, I have
Pzz = 0.67+-0.07.
your 0.8 is still out there a little bit. but +-10% is a bit conservative
on the systematics at these Q2. If take +-15% systematics, it would be:
Pzz = 0.67+-0.10.
Better, if you have 0.80+-0.03, our errors touch. But it highlights our
dooming situation in normalization.
Very sorry I could not show up at our meeting as I promised. But I do
consider my wife's situation more important.
Chi
P.S.
For everyone interested to check the above calculation the coefficients
read:
R20 = 1.5*cos(theta_d*)^2 - 0.5
R21 = -sqrt(1.5)*sin(2*theta_d*)*cos(phi_d*)
theta_d* and phi_d* are spin angle relative to 3-momentum transfer. To
lowest order, theta_d* = theta_q +- 30, phi_d* = 0. Phi_d* is little
tricky because it requires transformation into Madison frame. Aaron has
educated me about Madison convention times and again so I hope I did it
right. Basically X' always points to downstream direction (dot product of
X' and Z >0) So a spin angle as forward as 30 degree in LAB will always
have 0 in phi_d* unless Q2 is really big.
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