Teaney Yan correlation

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1 Teaney Yan correlation
堀　泰斗 東大CNS

2 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

3 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) >>　　 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　の

4 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！！　

5 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

6 h-odd V1　Vector Position A h-even V1 Vector PP spectator

7 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 V = <<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) V = <<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)>> )

8 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 V = <<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 )

9 V1を含むcorrelation <V12V2cos(2(Y1-Y2))>/V12V2