Teaney Yan correlation

Teaney Yan correlation
堀泰斗
東大CNS
V3を含むcorrelation
V3のfluctuation
 ALICEのtrack数なら
e-b-e v3 も測れるか？
Mixed harmonics correlation
<V23V32cos(6(Y2-Y3))>/V23V32
Teaney Yan CorrelationのIntro
Initial fluctuationの議論で予想されるcorrelation。
V1 はe1 ~ <r3cosf> 由来のh-even V1 。
簡単にいうと次の式であらわされるcorrelation。
3p correlationのうえ、少なくともO(v1v2v3)なので、
統計的に難しいが、
測定量 V123 = << cos( fa - 3fb + 2fg ) >>
= << cos( (fa – Y1) -3(fb - Y3) + 2(fg - YPP) + (Y1- 3Y3 +2YPP) )>>
~ (V1(pT or h) V2V3 )/(e1e2e3) x <<e1e2e3 cos (Y1- 3Y3 +2YPP) >>
V1 の
STAR(QM poster by Jim Thomas)、ALICE(not yet preliminary)ではsignalらしいものが見えている
V1がすべてh-odd V1 だったら
V123 = << cos( fa - 3fb + 2fg ) >>
= << cos( (fa – Y1) -3(fb - Y3) + 2(fg - YPP) + (Y1- 3Y3 +2YPP) )>>
= << cos (fa- Y1) >> x << cos 3(fb- Y3) >> x << cos 2(fg -YPP) >>
x << cos (Y1- 3Y3 + 2YPP) >>
= V1V2V3 x <<cos (YPP + p/2 - 3Y3 + 2YPP) >> ~ 0 (h-odd なY1 はYPPとfully correlate)
ではALICEでは、 h-even な V1 と Y1
h-odd な V1 と Y1
はどれくらいの大きさをもつのか？ (ilyaというひとのQM talk)
この二つはSame order で 10-3 くらい。 POI (fa) の h の範囲を変えた測定が必要！！
Dipole direction with respect to direction of PP is uniform, but
Position A (dipole = in-plane) triangle direction = dipole
Position B (dipole=out-plane) triangle direction = opposite of dipole
Measured V1 vector = (h-even V1 vector) + (h-odd V1 vector)
h-odd V1 Vector
Position B
h-even V1 Vector
PP
spectator
h-odd V1 Vector
Position A
h-even V1 Vector
PP
spectator
How to reduce non-flow contribution?
Teaney Yan correlation に対して non-flow contribution の寄与がどのくらいあるか。
1) Large eta gap (1 nest loop)
use forward detector for fg in <<cos(fa - 3fb + 2fg)>>
2) 4p correlation (1 nest loop)  large eta gap + multi-correlation
V1311 = <<cos( fa - 3fb + fg + fd )>>
= <<cos( (fa – Y1) -3(fb - Y3) + (fg - Y1`) + (fd – Y1`) + (Y1- 3Y3 +2Y1`) )>>
use forward detector for fg and fd, then Y1` is h-odd and fully correlated to YPP
= V1V2V1` V1` x <<cos(Y1- 3Y3 + 2YPP)>>
3) 6p correlation (5 nest loop  QC method must be used)
V123123 = <<cos( fa - 3fb + 2fg + fd - 3fs + 2fz )>>
= <<cos( (fa – Y1) -3(fb - Y3) + 2(fg - YPP) + (fd – Y1) -3(fs - Y3) + 2(fz - YPP)
+ 2(Y1- 3Y3 +2YPP) )>>
= V1V2V3 V1V2V3 x <<cos 2(Y1- 3Y3 + 2YPP)>>
= V1V2V3 V1V2V3 x ( 2 <<cos(Y1- 3Y3 + 2YPP)>> 2 - 1 )
Results of quick analysis(far from preliminary)
3p correlation with QC method
If use FMD for fg
< exp ( fa - 3fb + 2fg ) > = < exp ( fa - 3fb ) > x < exp ( 2fg ) >FMD
= (pnQ3n* - q2n*)/(mpM - mq) x Q2nFMD /MFMD
Calculation of 6p correlation
Use FMD A side track for fg and FMD C side track for fz
Use central track for fa , fb , fd , fs  3 next loop
V123123 = <<cos( fa - 3fb + 2fg + fd - 3fs + 2fz )>>
= Q2nFMD C /MFMD C x Q2nFMD A /MFMD A
x ( p1n2 (Q3n*)2 - p1n2 Q6n* - q2n (Q3n*)2 - 4q2n*p1nQ3n*
- 2(q2n*)2 + 4q2n*p2n* + 4q5n*p1n + 4q1n*Q3n* - 5q4n* )
/ ( mp2M2 – 2mpM2 - 4mpmqM + 4mpmq + 4mqM +mpM -5mq )
V1を含むcorrelation
<V12V2cos(2(Y1-Y2))>/V12V2
<V13V31cos(3(Y1-Y3))>/V13V3

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