FFiinnaall ssoouurrccee eecccceennttrriicciittyy mmeeaassuurreedd bbyy HHBBTT iinntteerrffeerroommeettrryy wwiitthh tthhee eevveenntt sshhaappee

Transcription

1 FFiinnaall ssoouurrccee eecccceennttrriicciittyy mmeeaassuurreedd bbyy HHBBTT iinntteerrffeerroommeettrryy wwiitthh tthhee eevveenntt sshhaappee sseelleeccttiioonn

2 CCoonntteennttss

3 EEvveenntt sshhaappee eennggiinneeeerriinngg Q,x = w i cos( ) Q,x = w Q,y = w i cos( ) i sin( ) Q,y = wq i sin( ) Q q= Q = Q,x + = tan ( Q Q,y /p M,y ) = tan ( Q,y Q,x ) Q,x Q,x + Q,y /p M Ψ J.Schukraft et al., arxiv: number of events F number of events ε F ) B * (a) v5 B J.Jia et al., arxiv: Centrality -5% no cuts (c).64 q upper 5% 3,a 4 q lower 5% F q v 3 (e).354 Centrality -5% no cuts q upper 5%,a q lower 5%,a FIG. 3. (color online) Actual (true) v and v 3 distributions in the event samples selected by di erent cuts on the corresponding q n -vector magnitude indicated in the plot compared to that extracted from the BG fits to q n,b distribution shown 3,a B F B

4 HHaannbbuurryy BBrroowwnn aanndd TTwwiissss iinntteerrffeerroommeettrryy R" (HBT"radius)" HBT$effect Coulomb$repulsion$$ +$contamina6on R s# p detector" p detector" q = q = p p p p C = P (p,p ) P (p )P (p ) + (q) =+exp( R q ) C = N real(q) N mixed (q) beam R l# R o# ~ kt = (~p T + ~p T ) ~q o k ~ k T, ~q s? ~ k T C =C core + C halo =[ ( + G)F coul +[ G =exp( R sq s R oq o R l q l R osq s q o )

5 PPHHEENNIIXX eexxppeerriimmeenntt Beam line )> - Ψ r <cos(n[ Ψ n BBC R X N P EMCal PC DC R X N P BBC Resolution of Event planes Event Plane Resolution n=, North+South n=, North or South n=3, North+South n=3, North or South Centrality [% Mass(square Particle Identification by PbSc-EMC K "######### K + π "######### π Momentum( (charge 4 3

6 HHooww ttoo aappppllyy tthhee EESSEE f BesselGaus = x I ( x x )exp( (x + x ) )

7 CChhaarrggeedd hhaaddrroonn vv wwiitthh EESSEE

8 HHBBTT rraaddiiii ww..rr..tt Ψ wwiitthh EESSEE ~ kt = (~p T + ~p T ) ~q o k ~ k T, ~q s? ~ k T R s# beam R l# R o# observer R µ = R µ, +R µ, cos( )

9 FFrreeeezzee--oouutt eecccceennttrriicciittyy vvss NNppaarrtt wwiitthh EESSEE ε ε εinit R s, / R s, R o, / R o, ε final R side modulation R out modulation ε final

10 EEvveenntt ttwwiisstt sseelleeccttiioonn wwiitthh HHBBTT wwiitthh AAMMPPTT mmooddeell

11 TTwwiisstteedd ssoouurrccee?? arxiv: N B part 6= N F part Ψ B " B n 6= " F n Ψ F B part,n 6= F part,n z"direc(on

12 F.4 3 EEvveenntt ttwwiisstt sseelleeccttiioonn B.4 F initial twist F B (Ψ (Φ * *F -Φ -Ψ * ) *B ) (e).354 qf - F B (Ψ -Ψ ) (Ψ F -Ψ B ) C( φ). S cut (a) q bin = q..3 F 4, top % of Ψ.5-4 F B FIG. 4: Correlation of ϵ B vs. ϵ F (a), Φ FB vs. ϵ (b), ϵ F vs. q F (c), ϵ F vs. q B (d), Φ FB vs. Ψ FB bin =, top % of Ψ vs. Φ FB (f) for AMPT Pb+Pb events with b = 8fm.The bars around the circles in panel-(b) indicates the RMS width of Φ FB at given ϵ value, and the four regions delineated by the boxes in panel-(f) indicate the cuts for the four event classes defined in Table I. Thenumbersinsomepanelsindi-. cates the correlation coefficients of the distributions. φ 5-5 η C( φ).5 (b).5. F η [-6,-5 q.5 3 η [5,6 η [-4,-3 η [-,- - F B 4 φ η [3,4 η [, FIG. 8: The D correlation function (left), D correlation function in di erent s n rot n for n = 5 (right), for events selected in the fourth q S cut bin with largest valu (e), and ϵ F S cut ϵ F (a) q Δφ-Δη. final twist - B F.5 (f) -.5 C( φ) (Φ * -Φ * ) 5 η 3 C( φ) J.Jia et al., arxiv:4.668 ) B -Φ 3* F 3(Φ 3* - (e).5 AMPT Pb+Pb.76TeV C(, ) / + v a nv b n cos(n n (b) vs. 3 Φ FB 3(Ψ 3 -Ψ 3 ) rot n ) FIG. 5: Correlation of ϵ B 3 vs. q3 F (c), ϵ F 3 vs. q3 B (d), η [-6,-5 η [5,6 3 (f) for AMPT η [-4,-3 η [3,4 bars around the circles in η [-,- η [, of 3 Φ FB 3 at given ϵ 3 va by the boxes in panel-(f) classes defined in Table I cates the correlation coeffi

13 HHBBTT ssttuuddyy iinn AAMMPPTT HBT "3.5<η<3.5 Δη=step "6"5"4"3""3456 twistcut areferenceangleofhbt C =+exp( R sq s R oq o R l q l R osq o q s R olq o q l R slq s q l ) η

14 HHBBTT rraaddiiii ww..rr..tt bbaacckkwwaarrdd Ψ R s 9 R o 7 6 B F (Ψ -Ψ )>.6 bbaacckkwwaarrdd Ψ B 8 Ψ F 7 3 φ [rad < η<-.5.5<η< < η<-.5.5<η<.5 3 φ [rad z"direc(on ffoorrwwaarrdd AMPT Pb+Pb.76TeV ππ-hbt.<k < GeV/c, EP: -6<η<-4 T R µ = R µ, +R µ, cos( + ) -3.5< η<-.5.5<η< < η<-.5.5<η<.5 -.5< η<.5.5<η<.5

15 HHBBTT rraaddiiii ww..rr..tt ffoorrwwaarrdd Ψ R s 9 R o 7 6 B F (Ψ -Ψ )>.6 bbaacckkwwaarrdd Ψ B 8 Ψ F 7 3 φ [rad < η<-.5.5<η< < η<-.5.5<η<.5 3 φ [rad z"direc(on ffoorrwwaarrdd R µ = R µ, +R µ, cos( + ) R µ = R µ, +R µ, cos( + ) R µ =R µ, sin( + ) AMPT Pb+Pb.76TeV ππ-hbt.<k < GeV/c, EP: 4<η<6 T -3.5< η<-.5.5<η< < η<-.5.5<η<.5 -.5< η<.5.5<η<.5

16 η--ddeeppeennddeennccee ooff pphhaassee sshhiifftt R µ = R µ, +R µ, cos( + ) R os =R os, sin( + ) [rad α side.6.4. [rad α out.6.4. [rad α os.6.4. AMPT Pb+Pb.76TeV η -.4 Ψ BB η -.4 Ψ FF -.6 B w.r.t Ψ F w.r.t Ψ η

17 SSuummmmaarryy ε

18 TThhaannkk yyoouu ffoorr yyoouurr aatttteennttiioonn

19 Rside : width 5 pair and ΨEP, SSppaaccee--mmoommeennttuumm ccoorrrreellaattiioonn Rout : depth cos((' + emission duration )) Emission points of pions in the Blast-wave model (PRC7, 4497) HBT radii = length of homogeneity known)) as kt dependence of HBT radii by radial flow out-of-plane PHYSICAL REVIEW C 7, 4497 (4) mass and cles with s that are t 4 in, observer in-plane po Because on points us of the e average mit. This described e particle βx.974 ew 4: 4 βx.97 vi cos((' and s, kaons omentum. rameters " T = GeV. =. GeV. e: Rx = Ry nd order Event plane FIG. 37. Distribution of the emission points in the transverse Azimuthal plane plane, for different particle species emitted at the same velocity, 9 'y = and 'x =.97 on the left-hand side and 'x =.974 on the

20 HHBBTT rraaddiiii ww..rr..tt Ψ wwiitthh EESSEE ((RRll aanndd RRooss))

21 EEvveenntt--bbyy--eevveenntt vvnn aatt AATTLLAASS p >.5 GeV, h <.5 T ATLAS Pb+Pb s NN =.76 TeV - = 7 µb L int p >.5 GeV, h <.5 T ATLAS Pb+Pb s NN =.76 TeV - = 7 µb L int p >.5 GeV, h <.5 T ATLAS Pb+Pb s NN =.76 TeV - = 7 µb L int dn ) p(v - - centrality: -% 5-% -5% 3-35% 4-45% 6-65%.. v ) 3 p(v - centrality: -% 5-% -5% 3-35% 4-45%.5. v 3 ) p(v 4 centrality: -% 5-% -5% 3-35% 4-45% Figure. TheprobabilitydensitydistributionsoftheEbyEv n in several centrality intervals fo n =(leftpanel),n =3(middlepanel)andn =4(rightpanel). Theerrorbarsarestatistica uncertainties, and the shaded bands are uncertainties on the v n -shape. The solid curves are distri butions calculated from the measured v n according to eq. (.6). The solid curve is shown only fo % centrality interval for v,butforallcentralityintervalsincaseofv 3 and v 4. v 4.5 from ref. [3. However, the uncertainties from ref. [3 for the v n -scale (table ) and v n -shape, are well within the total systematic uncertainties derived from the data analysis

22 OOsscciillllaattiioonn aammpplliittuuddeess aass aa ffuunnccttiioonn ooff NNppaarrtt wwiitthh EESSEE

23 HHBBTT rraaddiiii ww..rr..tt Ψ BB R s 4 R o B F (Ψ -Ψ )>.6 R l φ [rad 4 3 φ [rad 5 3 φ [rad R os R ol R sl AMPT Pb+Pb.76TeV ππ-hbt.<k < GeV/c, EP: -6<η<-4 T - 3 φ [rad - 3 φ [rad < η<-.5.5<η< < η<-.5.5<η<.5 -.5< η<.5.5<η<.5 -.5<η<.5 3 φ [rad

24 HHBBTT rraaddiiii ww..rr..tt Ψ BB((FF)) ((η<<)) R side φ [rad R out φ [rad R long 5 AMPT Pb+Pb.76TeV φ [rad R os 4 R os = R ol R sl B w.r.t Ψ (-6<η<-4) -3.5< η< <η< < η< <η< φ [rad φ [rad - - F - w.r.t Ψ (4<η<6) -3.5< η< <η< < η< <η< φ [rad R µ = R µ, +R µ, cos( + ) R os =R os, sin( + )

25 HHBBTT rraaddiiii ww..rr..tt Ψ BB((FF)) ((η>>)) R side φ [rad R out φ [rad R long 5 AMPT Pb+Pb.76TeV φ [rad R os 4 R os = R ol R sl B w.r.t Ψ (-6<η<-4) -.5< η<.5.5<η<.5.5< η<.5.5<η< φ [rad φ [rad - - F w.r.t Ψ (4<η<6) -.5< η<.5.5<η<.5.5< η<.5.5<η< φ [rad

26 HBT Interferometry 956, H. Brown and R. Twiss, measured angular diameter of Sirius _ 96, Goldhaber et al., correlation among identical pions in p+p By quantum interference between two identical particles wave function for bosons(fermions) : = p [ (x,p ) (x,p ) ± (x,p ) (x,p ) C = P (p,p ) P (p )P (p ) + (q) =+exp( R q ) R (HBT radius) p detector /R spatial distribution ρ (r) exp( r R ) p detector q=p -p [GeV/c

27 Correlation Function Experimental Correlation Function C is defined as: " R(q): Real pairs at the same event. " M(q): Mixed pairs selected from different events. Event mixing was performed using events with similar z-vertex, centrality, E.P. relative momentum dist. C = R(q) M(q) R(q) M(q) q = p p 4 " Real pairs include HBT effects, Coulomb interaction and detector inefficient effect. Mixed pairs doesn t include HBT and Coulomb effects... HBT effect C =R/M Coulomb repulsion q inv qinv[gev/c

28 3D-HBT Analysis Core-Halo picture with Out-Side-Long frame " Longitudinal center of mass system (p z =p z ) " taking into account long lived decay particles R s ~ kt = (~p T + ~p T ) ~q o k ~ k T, ~q s? ~ k T C =C core + C halo =[ ( + G)F coul +[ beam R o R l G =exp( R sq s R oq o R l q l R osq s q o ) F coul : Coulomb correction factor λ : fraction of pairs in the core Detector

29 Correction of Event Plane Resolution Smearing effect by finite resolution of the event plane Reaction Plane Event Plane Reaction Plane true size measured size Correction for q-distribution " PRC.66, 4493() # model-independent correction " Checked by MC-simulation Smeared Corrected Rs Δφ [rad Ro A crr (q, j) =A uncrr (q, j) n,m [A c cos(n j )+A s sin(n j ) n / n,m = sin(n /)hcos(n( m real))i Δφ [rad event plane resolution w.r.t RP w.r.t RP Uncorrected w.r.t EP Uncorrected w.r.t EP Corrected w.r.t EP

30 (fm ) (fm ) Azimuthal sensitive HBT w.r.t nd -order event plane R out-of-plane central STAR, PRL93, 3-5% -% 4-8% 5 ) (fm R o 3 5 Rs in-plane R in-plane Reaction plane nd -order event plane(v plane) ) (fm R l peripheral 3.5<k T <.6 GeV/c - Ros PRC7, 4497 (4), Blast-wave model R s,n = R s,n (Δφ)cos(nΔφ) ε final = R s, R s, π/ π π/ Φ (radians) R s, is sensitive to final eccentricity " Oscillation indicates elliptical shape extended to out-of-plane direction. π Results of HBT w.r.t nd - and 3 rd -order event planes are presented today

31 Event Plane Determination < η <.8 4 scintillator segments φ i Ψ 3 <cos(n[ Ψ n - Ψ r )> Resolution of Event planes Event Plane Resolution n=, North+South n=, North or South n=3, North+South n=3, North or South beam axis Determined by anisotropic flow itself using Reaction Plane Detector n = n tan wi cos(n i ) w i sin(n i ) Ψ Ψ Centrality [% EP resolutions <cos[n(ψ n -Ψ real )> " Res{Ψ } ~.75, Res{Ψ 3 } ~.34