Canonical description of charm and bottom

Transcription

1 Canoncal descrpton of charm and bottom producton n e + e, pa, π A, pp and pp collsons Krzysztof Redlch Statstcal Model and exact charge conservaton laws: e Its phenomenologcal consequences + e n HIC SM applcaton to partcle productons n e + e annhlaton lght flavors producton heavy flavors producton Relatve producton yelds of charm and bottom hadrons n pa, π A, pp and pp collsons and SM results In collaboraton wth: A. Andronc, F. Beutler, P. Braun-Munznger &J. Stachel Phys. Lett. B 675 (2009) J. Phys. G 36 (2009) arxv: [hep-ph] Phys. Lett. B n prnt See also: P. Braun-Munznger et. al. n Quark Gluon Plasma 3 F. Beutler, dploma theses arxv: [nucl-th] 1

2 Statstcal operator and mass spectrum resonance domnance µ ur 2V GC µ p 2 l n Z ( T, µ ) = τ ( p, µ,, ) 3 B µ S µ Q e 2 τ ( m, ur ( 2π ) µ ) + approxmate by expermentally known mass spectrum uurur Q µ VT T 2 2π hadrons ur s B W ln Z( T, µ ) d e ds s K2( ) F ( m, s) T < N > V n T µ Γ T µ = + Only 2-parameters needed to fx all partcle yeld ratos 2 β th th Re s. [ (, B ) K n (, B )] K µ p µ Bret-Wgner res. partcle yeld thermal densty BR thermal densty of resonances

3 LGT phase boundary and chemcal freezeout

4 φ S φ S e He = H [ S, H ] = 0 conservaton on the average exact conservaton Z GC ( T, µ, V) = Tr [ e β ( H µ SS) ] Z C ( T, V) = Tr [ e β H ] S S = + G C S µ S / T Z e Z A A = S A = A C S Consder thermal system wth Total Strangenes S =0 S 2π 1 S GC S ZS ( T, V ) = dϕe Z ( T, ϕ ) 2π T 0 S= -1 S=1 S ϕ µ V V A C h part n C S γ s S n GC I I S 0 ( γ 2 V n n ) GC GC s C s= 1 s=+ 1 ( γ 2 V n n ) GC GC s C s= 1 s=+ 1 suppresson factor 1 GC < N > A part < > C 2 N A part suppresson ncreases wth S and wth decreasng collson energy 4

5 ) Strong, quadratc dependance of S =1 partcles wth A part at SIS ) strange ant-partcle/partcle ratos ndependent of + π + N K + Y π A e + C < K > + ( m µ B ) / T < > J. Cleymans, H. Oeschler & K.R. part A e A part e 2 mk / T ( my µ B )/ T part KaoS (GSI-SIS) 5

6 ) Scalng propertes of partcle producton yelds J. Cleymans, H. Oeschler & K.R. Excellent descrpton of kaon producton from SIS to AGS subthreshold + + π + N K + Λ [ K ] = [ Λ] [ π ] [ K ] π + Λ K + N = κ [ N] [ Λ] Scalng: [ K ] [ ] = κ π + [ K ] [ N] + + smlar scalng for [ Ξ ]/[ K ] = κ [ K ]/[ N] : A. Andronc, P. Braun-Munznger & K.R. 6

7 Strangeness enhancement from p-be to central Pb-Pb collsons at snn = 17.3 GeV Canoncal model wth exact strangeness conservaton at fxed T 168 MeV and µ B beng centralty dependent provde good descrpton of NA57 data f the correlaton volume scales as: α V = ( A / 2) wth α 1/ 3 part 7

8 Partcles exctaton functons n HG model Braun-Munznger, Cleymans, Oeschler &K.R. Andronc, Braun-Munznger &Stachel (09) Nu Xu & K.R. H.Oeschler et al. 8

9 + Hadron producton n e e annhlaton Jet structure of hadrons producton Flavor content of the jets: up type quarks = ( u, c) down type quarks = ( d, s, b) Can we quantfy lght and heavy flavor partcles wthn Statstcal Model?? 9

10 Canoncal model for partcle producton yelds n e + e The partton functons wth exact, N=Baryon, S=Strangeness, Q=Electrc, C=Charm, B=Bottom quantum numbers under quantum statstc constructed from: L. Turko, Phys. Lett. (1981) GC Z ( T, V, βµ ϕ ) 1 ur d V Z T V d e d p e 2π ur uur 5 3 1,,,, (, ) exp ln(1 E uur uur ϕ X β x ϕ ± N S Q C B = ϕ ) 5 0 ± 3 (2 π ) (2 π ) K k The ntegral s not convenent for numercal analyss as the ntegrand s a strongly oscllatng functon The partton functon and partcle multplcty can be expressed as mult-sum and products of dfferent Bessel functons Because of the hgh precson of the LEP measurements, a hgh mass cut M 3GeV and quantum statstc are requred 10

11 Quantum statstc and Mass cut effects on partcle yelds Quantum statstc 1 x = k = 1 ln(1 ) k x k! M M = 1.7GeV = 3.0GeV k Strong, 8-15 % devaton of baryon yelds f cuttng the mass spectrum at M 1.7GeV Quantum statstc needed for Pons and Kaons 11

12 Most hadronc events n hgh energy e+e Each jet represents an ndependent freball collsons are two-jet events Problem: Open Charm an Bottom shows dramatc devatons from data ur 2-jets wth Q = 0 mod el < N B > / data mod el < N ± > / data D Subtract the contrbutons from charm an bottom to lghter partcles e.g. C,B contrbutons to 2-jets wth ur Q = 0 sub. decays of C and B π K *0 11.7%, K 30.0% + + (892) 16.5%, φ(102 0) 68. 0% 12

13 Canoncal effects and charm/bottom mesons Charge of the system Q Q Q =± 1 γv z < N > = Charge of the partcle Z I m1 Qm1 x I Q (2γVx) ( 2γVx) d ur ur z d p β E b µ (2 π ) Q 3 = exp( ( ) 3 + Z z = Q =± 1 ± x = Z Z Total charge of the system Q = 0 Q = + 1 And small 2V x << 1 c < N > γv z γv Z Q= 0 Q =+ 1 1 Strong Suppresson of thermal partcle phase-space < N > Q=+ 1 Q = + 1 Vγ z Vγ Z + 1 Strong Enhancement of thermal partcle phase-space Charge Q=+1 redstrbuted between dfferent partcle speces 13

14 Charm and Bottom partcles at LEP at s = 91 GeV D ± Use the same thermal parameters as obtaned from the ft to the lght quark hadron multplctes Very good agreement wth χ 2 / dof = 34 /18 for all data and χ 2 / dof = 22 /16 when excludng Y and J / ψ Open charm and bottom well descrbed by thermalzaton of the freball wth overall Charm= ± 1 and Bottom= ± 1 ' J / ψ, ψ and χc are entrely comng from Bottom s decays and agree wth model Hdden charm, Y s of non-thermal orgn, thus t does not ft to model systematcs! 14

15 Statstcal Model and relatve charm and bottom producton n ha and hh collsons at dfferent s Remark: Fxed thermal parameters n ha and hh collsons wthn the Statstcal model Consder partcle ratos of open charm only Consder ratos of charmona or bottomona 15

16 Fxng thermal parameters n h-a and hh: J. Cleymans et al. p-p C-C S-S Pb-Pb I. Kraus et al. Temperature ndependent of system sze and centralty Strong varaton of baryon chemcal potental wth centralty and system sze for md-rapdty data 16

17 Centralty dependence of baryon chemcal potental T 168 MeV For NA57 the temperature s fxed to from central Pb-Pb collsons: ( the value consstent wth recent analyss of A. Andronc et al.) 17

18 Open charm producton ratos n p( )A collsons π Andronc, Beutler, Braun-Munznger, Stachel &K.R. The energy dependence of thermal parameters taken from systematc analyss of heavy on data on dfferent partcle yelds by: A.Andronc, P. Braun-Munznger & J. Stachel Phys. Lett. B Good agreement of Statstcal Model and data for the relatve producton cross secton of charged to neutral D-mesons: Partcularly wth data average by PDG Data average wth PDG recpe Data complaton by: 18

19 χ c The contrbutons to meson J / ψ A. Andronc, F. Beutler, P. Braun-Munznger, J. Stachel &K.R. NA50 The fracton of J / ψ from radatve decays of states: χ c and χ 1 c2 RHIC CDF s far above the statstcal model predctons Data complaton by HERA-B Coll.: Clear, non-thermal orgn of charmona ha pp n and collsons Data average Data average at lower energes: From: 19

20 ' ψ Producton cross secton of relatve to J / ψ A. Andronc, F. Beutler, P. Braun-Munznger, J. Stachel &K.R. NA50 The rato for the Tevatron energy was derved ' from the CDF data on J / ψ and ψ and s for pt > 1.25 GeV : ' We have extrapolated the ψ measurements from p 2 GeV down to 1.25 GeV t RHIC Data pa complaton by: CDF ' Strong suppresson of ψ / ( J / ψ ) rato n PbPb relatve to pa, pp and pp dfferent producton mechansm n elementary and heavy on collsons The nuclear modfcaton canceled ' out n the ψ / ( J / ψ ) rato as the pp value s the same as n the pa Good agreement of Statstcal Model and data n PbPb collsons 20

21 The relatve producton of charmona χ c to χ c 1 1 A. Andronc, F. Beutler, P. Braun-Munznger, J. Stachel &K.R. RHIC NA50 CDF χ to The relatve producton of c1 c2 s seen to be consstent wth Statstcal Thermal Model. However, due to smlar masses m 3510 MeV m 3556 MeV χ χc χc1 1 d χ 2 m K m T ( / ) s almost consstent wth the spn statstc rato, thus ths agreement s trval χ c1 c1 c1 J χc 2 χ 1 c1 J χc 2 χ 1 c χ = 1 c2 d m K2( m / T ) J d = χc χ 1 c1 J d χ 0.6 Data complaton by HERA-B Coll.: Data average 21

22 The relatve producton of bottomona A. Andronc, F. Beutler, P. Braun-Munznger, J. Stachel &K.R. The relatve producton of botomona s strongly nconsstent wth NA50 Statstcal Thermal Model results. Ther ratos descrbed by RHIC CDF Data are from E866 and CDF Coll. Y Y d = d Y J Y J 2 m K2 m Y Y T 2 my K2 my T ( / ) ( / ) wth T 170 MeV exceed the data by one and even two orders of magntude ndcatng: A non-thermal orgn of charmona and botomona producton n elementary and ha collsons. 22

23 Conclusons An excellent descrpton of open charm and bottom meson yelds n e + e annhlatons by the thermal model The above yelds are almost ndependent of the freball volume and/or any factor quantfyng devatons from chemcal equlbrum Hdden bottom n e + e annhlatons s not descrbed by the thermal model. Hdden charm s consstent wth the model results as t s almost entrely comng from the open bottom decays The relatve producton of D-mesons n hh and ha collsons s well descrbed by the model The charmona and bottomona ratos n hh and ha collsons are not consstent wth the model predctons ' Ths s n contradcton wth AA data at the SPS where the rato ψ / ( J / ψ ) s well quantfed by the model. The above ndcates a dfferent producton mechansm of hdden charm and bottom n hh, ha and AA collsons 23