Fluctuation and Flow Probes of Early-Time Correlations

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1 Flucuaio ad Flow Probes of Early-Time Correlaios WPCF 0 Frakfur am Mai, Seember 0 George Moschelli Frakfur Isiue for Adaced Sudies & Sea Gai Waye Sae Uiersiy

2 Moiaio Two Paricle Correlaios: d d d Pair Disribuio airs = sigles + correlaios Borghii, Dih, Olliraul Ca correlaios disiguish lumy s. smooh iiial codiios? ucl-h/ ucl-h/05.8 Sources of Correlaio: Sace Momeum Geomery (global, log rage) Same source (local, log rage) Oher + o-floiw Momeum coseraio (log rage) Jes (shor rage) Resoace decays (shor rage)

3 Correlaios ad Flucuaios correlaios = airs - sigles r,, r, d d Var ( ) Ifluece of lums : r (, ) 0 Muliliciy Flucuaios: o-zero alues idicae o-poissoia behaior R Var ( ) Ideede of geomery. Ideede of flow. GM, Gai ucl-h/07.337

4 Traserse Momeum Flucuaios coariace: Flucuaios Correlaios Ideede of geomery ad aisoroic flow, bu o aerage exasio. STAR ucl-ex/05003; Gai ucl-h/ j i j i, d d r Ifluece of lums : Correlaios, r (, ), modified by raserse exasio based o origi..

wae exasio: ormalized Bolzma disribuio f x, e u T Eccericiy e

5 Momeum Correlaio Fucio Local equilibrium hydro eoluio + Cooer-Frye freeze ou r, cx, x f x, f x, freezeou surface Blas wae exasio: ormalized Bolzma disribuio f x, e u T Eccericiy e characerizes elliic geomery. ad T Aerage alues from secra e x e xxˆ yyˆ y

6 Flux Tubes ad Correlaios Saial correlaios: c x, x x x x x Desiy lums emerge from flux ubes. Correlaed aros from same flux ube Flux ube size << R A r Aerage all flux ube disribuios c R Area RA FT R x x r R, R FT r R r r r r r, d d cx x dx dx R,

7 Flux Tubes i Glasma Correlaios of FT Flux Tubes : Flucuaios i ube umber R Var ( ) FT Gluo Raidiy Desiy Kharzee & ardi d dy gluos ube FT FT α s Q s Log rage Glasma flucuaios: Deeds oly o he sauraio scale, Q s. Dumiru, Gelis, McLerra & Veugoala; Gai, McLerra & GM R d dy s Q s

8 Muliliciy Flucuaios i Glasma Glasma redicio: R d dy k s Q s Dumiru, Gelis, McLerra & Veugoala; Gai, McLerra & GM Fix k usig ridge aalysis i 00 GeV Au+Au egaie biomial disribuio R k BD Gelis, Lai & McLerra GM, Gai ucl-h/07.337

9 Flucuaios i Glasma Momeum flucuaios Local momeum excess aeraged oer saial geomeries. Blas wae f (,x) Same scale facor Glasma eergy deedece r, dd Gai, GM. ucl-h/ R d dy s Q s

10 Aisoroic Flow Iiial Sae Cofiguraio Fourier Flow Coefficie: cos RP Fial Sae Momeum Two-aricle coefficie: o reacio lae eeded cos i j i j a y x

11 Aisoroic Flow Iiial Sae Cofiguraio Fial Sae Momeum x Fourier Flow Coefficie: cos Two-aricle coefficie: o reacio lae eeded d RP, cos dd

12 Cumula Exasio Pair Disribuio:, r, Borghii, Dih, Olliraul Two-aricle coefficie: Correlaed Par: < > = reacio lae correlaios = oher correlaios {} < > Borghii, Dih, Olliraul; Voloshi, Poskazer, Tag, Wag r, cos dd facorizaio is a sigaure of flow if = 0

13 Correlaio Mechaism Iiial Sae Cofiguraio Fial Sae Momeum r, x, x Fial sae momea are correlaed o iiial osiio. Reacio lae Commo origi eglec shor rage correlaios, Ifluece of lums : Arbirary ee shaes. Traserse exasio modifies correlaios based o origi..

14 Flow ad flucuaios: Elliic Flow Geomery model iu Dashed lie: Blas Wae {} eglec o-flow Calculaed flucuaios r, cos dd Eergy deedece from R GM, Gai ucl-h/05.8

15 Flow ad flucuaios: Geomery model iu Dashed lie: Blas Wae {} eglec o-flow Calculaed flucuaios r, cos dd Eergy deedece from R

16 Elliic Flow Flucuaios Coefficie of ariaio: Voloshi, Poskazer, Tag, Wag Cauio: is echically o he ariace

17 Flow Flucuaios ad 3 Flow Flucuaios: r, cos dd STAR 3 {} = 0 Eergy deedece from R Parameerized ALICE 3 {} A more realisic FT is eeded. 3 coribuios wihou riagular flow

18 Summary: Muliliciy flucuaios R. oly deeds o he exisece of desiy lums. Momeum flucuaios < T T > - from desiy lums ad aerage raserse exasio bu o aisoroic flow. Flow flucuaios - from desiy lums, geomery, ad aisoroic flow. The ridge he same as flow flucuaios. All deed o he umber ad size of desiy lums sysem, eergy, ad ceraliy deedecies. Correlaios Flow Flucuaios Look a hem ogeher!

20 Log Rage Correlaios Measuremes wih raidiy gas do o exlai {} ad {} differeces Jes, resoace decays, ad oher shor rage effecs should be remoed Log rage correlaios sugges iiial sae effecs. Collisio eergy deedece of he ridge should mimic A. Biladzic hesis

21 The Sof Ridge d d r ref dy cos dy ref Flow subraced ridge d dy ref cos Oly cos ad cos erms subraced These erms also coai flucuaios Glasma eergy deedece R scale facor se i Au-Au 00 GeV Blas wae f (,x) Differece i eriheral STAR ALICE

22 Four-Paricle Coefficies 3 cos ,,,,,, r r r 3 cos Voloshi, Poskazer, Tag, Wag Borghii, Dih, ad Olliraul Four-aricle coefficie: Four-Paricle Disribuio: kee oly wo-aricle correlaios

23 {} correcios Four-aricle coefficie: cos 3 Re Will cacel wih {} erms Re Correcios of order ~.% r, Re cos RP dd

24 R K flux ubes, assume K aries ee-by-ee K K K K K K K K K For K sources ha flucuae er ee R K K K K K Flucuaios er source Flucuaios i he umber of sources

Ee aerages rerese boh ee shae ad ee lae flucuaios.

25 Source Disribuios Aerage all flux ube disribuios FT The ee lae is correlaed wih real reacio lae. The 3 ee lae is arbirary. Ee aerages rerese boh ee shae ad ee lae flucuaios. Blas wae: Currely caures 3 ee lae flucuaios bu o riagular flow. Geomery: robabiliy disribuio of R FT R Area R flux ubes ~ uclear hickess A

Let s express the absorption of radiation by dipoles as a dipole correlation function.

Let s express the absorption of radiation by dipoles as a dipole correlation function. MIT Deparme of Chemisry 5.74, Sprig 004: Iroducory Quaum Mechaics II Isrucor: Prof. Adrei Tokmakoff p. 81 Time-Correlaio Fucio Descripio of Absorpio Lieshape Le s express he absorpio of radiaio by dipoles