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28.09.2013NTHEP, Crimea, September 23-29, 2013I1 Correlation Femtoscopy – status & prospects History QS correlations FSI correlations Correlation study of particle interaction Correlation asymmetries Summary In memory of V.L.Lyuboshitz (19.3.1937-4.5.2013) R. Lednický @ JINR Dubna & IP ASCR Prague

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2 History Fermi’34: e ± Nucleus Coulomb FSI in β-decay modifies the relative momentum (k) distribution → Fermi (correlation) function F(k,Z,R) is sensitive to Nucleus radius R if charge Z » 1 measurement of space-time characteristics R, c ~ fm Correlation femtoscopy : of particle production using particle correlations

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3 Fermi function(k,Z,R) in β-decay = | -k (r)| 2 ~ (kR) -(Z/137) 2 Z=83 (Bi) β-β- β+β+ R=8 4 2 fm k MeV/c

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4 2 x Goldhaber, Lee & Pais GGLP’60: enhanced + +, - - vs + - at small opening angles – interpreted as BE enhancement depending on fireball radius R 0 R 0 = 0.75 fm p p 2 + 2 - n 0

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5 Modern correlation femtoscopy formulated by Kopylov & Podgoretsky KP’71-75: settled basics of correlation femtoscopy in > 20 papers proposed CF= N corr /N uncorr & showed that sufficiently smooth momentum spectrum allows one to neglect space-time coherence at small q* (for non-interacting identical particles) mixing techniques to construct N uncorr clarified role of space-time characteristics in various models |∫ d 4 x 1 d 4 x 2 p 1 p 2 ( x 1,x 2 )... | 2 → ∫ d 4 x 1 d 4 x 2 p 1 p 2 ( x 1,x 2 )| 2...

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6 QS symmetrization of production amplitude momentum correlations of identical particles are sensitive to space-time structure of the source CF=1+(-1) S cos q x p 1 p 2 x1x1 x 2 q = p 1 - p 2 → {0,2k*} x = x 1 - x 2 → {t*,r*} nn t, t , nn s, s 2 1 0 |q| 1/R 0 total pair spin 2R 0 KP’71-75 exp(-ip 1 x 1 ) CF → | S -k* ( r* )| 2 = | [ e -ik*r* +(-1) S e ik*r* ]/√2 | 2 PRF

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7 Assumptions to derive KP formula CF - 1 cos q x - two-particle approximation (small freeze-out PS density f ) - smoothness approximation: R emitter R source | p| |q| peak - incoherent or independent emission ~ OK, 1 ? low p t fig. ~ OK in HIC, R source 2 0.1 fm 2 p t 2 -slope of direct particles 2 and 3 CF data ~ consistent with KP formulae: CF 3 (123) = 1+|F(12)| 2 +|F(23)| 2 +|F(31)| 2 +2Re[F(12)F(23)F(31)] CF 2 (12) = 1+|F(12)| 2, F(q)| = e iqx - neglect of FSI OK for photons, ~ OK for pions up to Coulomb repulsion

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8 Phase space density from CFs and spectra Bertsch’94 May be high phase space density at low p t ? ? Pion condensate or laser ? Multiboson effects on CFs spectra & multiplicities rises up to SPS Lisa..’05

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“General” parameterization at |q| 0 Particles on mass shell & azimuthal symmetry 5 variables: q = {q x, q y, q z } {q out, q side, q long }, pair velocity v = {v x,0,v z } R x 2 =½ ( x-v x t) 2 , R y 2 =½ ( y) 2 , R z 2 =½ ( z-v z t) 2 q 0 = qp/p 0 qv = q x v x + q z v z y side x out transverse pair velocity v t z long beam Podgoretsky’83, Bertsch, Pratt’95; so called out-side-long parameterization Interferometry or correlation radii: cos q x =1-½ (q x) 2 +.. exp(-R x 2 q x 2 -R y 2 q y 2 -R z 2 q z 2 -2R xz 2 q x q z ) Grassberger’77 RL’78 Csorgo, Pratt’91: LCMS v z = 0

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10 Examples of NA49 & STAR data 3-dim fit: CF=1+ exp(-R x 2 q x 2 –R y 2 q y 2 -R z 2 q z 2 -2R xz 2 q x q z ) zxy Correlation strength or chaoticity NA49 Interferometry or correlation radii KK STAR Coulomb corrected

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11 Probing source shape and emission duration Static Gaussian model with space and time dispersions R 2, R || 2, 2 R x 2 = R 2 +v 2 2 R y 2 = R 2 R z 2 = R || 2 +v || 2 2 Emission duration 2 = (R x 2 - R y 2 )/v 2 (degree) R side 2 fm 2 If elliptic shape also in transverse plane R y R side oscillates with pair azimuth R side ( =90°) small R side =0°) large z A B Out-of reaction plane In reaction plane In-planeCircular Out-of plane KP (71-75) …

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Probing source dynamics - expansion Dispersion of emitter velocities & limited emission momenta (T) x-p correlation: interference dominated by pions from nearby emitters Interferometry radii decrease with pair velocity Interference probes only a part of the source Resonances GKP’71.. Strings Bowler’85.. Hydro P t =160 MeV/cP t =380 MeV/c R out R side R out R side Collective transverse flow F R side R/(1+m t F2 /T) ½ during proper freeze-out (evolution) time R long (T/m t ) ½ /coshy Pratt, Csörgö, Zimanyi’90 Makhlin-Sinyukov’87 } 1 in LCMS ….. Bertch, Gong, Tohyama’88 Hama, Padula’88 Mayer, Schnedermann, Heinz’92 Pratt’84,86 Kolehmainen, Gyulassy’86 Longitudinal boost invariant expansion

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pion Kaon Proton , , Flow & Radii in Blast Wave model ← Emission points at a given tr. velocity p x = 0.15 GeV/c0.3 GeV/c p x = 0.53 GeV/c1.07 GeV/c p x = 1.01 GeV/c2.02 GeV/c For a Gaussian density profile with a radius R G and linear flow velocity profile F (r) = 0 r/ R G : 0.73c0.91c R z 2 2 (T/m t ) R x 2 = x’ 2 -2v x x’t’ +v x 2 t’ 2 R z = evolution time R x = emission duration R y 2 = y’ 2 R y 2 = R G 2 / [1+ 0 2 m t /T] R x, R y 0 = tr. flow velocity p t –spectra T = temperature t’ 2 ( - ) 2 ( ) 2 BW: Retiere@LBL’05 x = R G x 0 /[ 0 2 +T/m t ] x( ) < x(K) < x(p)

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BW fit of Au-Au 200 GeV T=106 ± 1 MeV = 0.571 ± 0.004 c = 0.540 ± 0.004 c R InPlane = 11.1 ± 0.2 fm R OutOfPlane = 12.1 ± 0.2 fm Life time ( ) = 8.4 ± 0.2 fm/c Emission duration = 1.9 ± 0.2 fm/c 2 /dof = 120 / 86 Retiere@LBL’05 R β z ≈ z/τ β x ≈ β 0 (r/R)

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Femto-puzzle I Contradiction with transport and simple hydro calcul. - - small space-time scales - - their weak energy dep. - - R out /R side ~ 1 Basically solved due to the initial flow increasing with energy (likely related to the increase of the initial energy density and partonic energy fraction)

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16 Femtoscopy Puzzle I basically solved due to initial flow appearing in realistic IC

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Femtoscopic signature of QGP onset 3D 1-fluid Hydrodynamics Rischke & Gyulassy, NPA 608, 479 (1996) With 1 st order Phase transition Initial energy density 0 Long-standing signature of QGP onset: increase in , R OUT /R SIDE due to the Phase transition hoped-for “turn on” as QGP threshold in 0 is reached decreases with decreasing Latent heat & increasing tr. Flow (high 0 or initial tr. Flow)

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18 Cassing – Bratkovskaya: Parton-Hadron-String-Dynamics Perspectives at FAIR/NICA energies

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19 Femto-puzzle II No signal of a bump in R out near the QGP threshold (expected at AGS- SPS energies) !? likely solved due to a dramatic decrease of partonic phase with decreasing energy

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Femtoscopy of Pb+Pb at LHC ALICE arXiv:1012.4035 All radii increase with N ch from RHIC to LHC (not from SPS to RHIC)! Multiplicity scaling of the correlation volume universal freeze-out density Freeze-out time f from R long = f (T/m t ) 1/2 The LHC fireball: - hotter - lives longer & - expands to a larger size

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Ridge effect Dense matter (collective flows) also in pp collisions at LHC (for high N ch ) ? - p t increases with n ch and particle mass - BE CF vs n ch and p t points to expansion at high n ch - Ridge effect observed in angular correlations at high n ch R(k t ) at large N ch expansion CMS

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22 Final State Interaction Similar to Coulomb distortion of -decay Fermi’34: e -ikr -k ( r ) [ e -ikr +f( k )e ikr / r ] eicAceicAc F=1+ _______ + … kr+kr kaka Coulomb s-wave strong FSI FSI f c A c (G 0 +iF 0 ) } } Bohr radius } Point-like Coulomb factor k=|q|/2 CF nn pp Coulomb only | 1+f/r| 2 FSI is sensitive to source size r and scattering amplitude f It complicates CF analysis but makes possible Femtoscopy with nonidentical particles K, p,.. & Study relative space-time asymmetries delays, flow Study “exotic” scattering , K, KK, , p , ,.. Coalescence deuterons,.. | -k (r)| 2 Migdal, Watson, Sakharov, … Koonin, GKW, LL,...

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Assumptions to derive “Fermi-like” formula CF = | -k* (r*)| 2 t FSI (s-wave) = µf 0 /k* |k * | = ½|q * | hundreds MeV/c - same as for KP formula in case of pure QS & - equal time approximation in PRF typical momentum transfer in production RL, Lyuboshitz’82 eq. time condition |t*| r* 2 OK (usually, to several % even for pions) fig. RL, Lyuboshitz..’98 same isomultiplet only: + 0 0, - p 0 n, K + K K 0 K 0,... & account for coupled channels within the - t FSI d dE > t prod

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24 Effect of nonequal times in pair cms RL, Lyuboshitz SJNP 35 (82) 770; RL nucl-th/0501065 Applicability condition of equal-time approximation: |t*| m 1,2 r* 2 r 0 =2 fm 0 =2 fm/c r 0 =2 fm v=0.1 OK for heavy particles & small k* OK within 5% even for pions if 0 ~r 0 or lower → |k*t*| m 1,2 r*

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Resonance contribution to CF vs r-k correl. b R peak (STAR) ----------- 0.025 R peak (NA49) ---------- 0.10 0.14 Smoothness assumption: W P (r,½(k-kn)) W P (r,-kn) W P (r,k) Exact W P (r,k) ~ exp[-r 2 /4r 0 2 + bkrcos ]; = angle between r and k CF suppressed by a factor W P (0,k) ~ exp[-b 2 r 0 2 k 2 ] To leave a room for a direct production b > 0.3 is required for π + - system; however, BW b ~ 0.2; likely eq.-time approx. not valid for π + - at k*~ 150 MeV/c * (k=146 MeV/c), r 0 =5 fm (k=126 MeV/c), r 0 =5 fm -----------

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FSI effect on CF of neutral kaons STAR data on CF(K s K s ) Goal: no Coulomb. But R may go up by ~1 fm if neglected FSI in = 1.09 0.22 R = 4.66 0.46 fm 5.86 0.67 fm KK (~50% K s K s ) f 0 (980) & a 0 (980) RL-Lyuboshitz’82 couplings from Martin or Achasov t Achasov’01,03 Martin’77 no FSI Lyuboshitz-Podgoretsky’79: K s K s from KK also show BE enhancement R ↓ M t Universal expansion !

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27 NA49 central Pb+Pb 158 AGeV vs RQMD: FSI theory OK Long tails in RQMD: r* = 21 fm for r* < 50 fm 29 fm for r* < 500 fm Fit CF=Norm [ Purity RQMD(r* Scale r*)+1-Purity] Scale=0.76Scale=0.92 Scale=0.83 RQMD overestimates r* by 10-20% at SPS cf ~ OK at AGS worse at RHIC p

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28 p CFs at AGS & SPS & STAR Fit using RL-Lyuboshitz’82 with consistent with estimated impurity R~ 3-4 fm consistent with the radius from pp CF & m t scaling Goal: No Coulomb suppression as in pp CF & Wang-Pratt’99 Stronger sensitivity to R =0.5 0.2 R=4.5 0.7 fm Scattering lengths, fm: 2.31 1.78 Effective radii, fm: 3.04 3.22 singlet triplet AGSSPS STAR R=3.1 0.3 0.2 fm

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Pair purity problem for CF(p )@STAR PairPurity ~ 15% Assuming no correlation for misidentified particles and particles from weak decays Fit using RL-Lyuboshitz’82 (for np) but, there can be residual correlations for particles from weak decays requiring knowledge of , p , , , p , , correlations

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30 Correlation study of particle interaction - + & & p scattering lengths f 0 from NA49 and STAR NA49 CF( + ) vs RQMD with SI scale: f 0 sisca f 0 (= 0.232fm ) sisca = 0.6 0.1 compare ~0.8 from S PT & BNL data E765 K e Fits using RL-Lyuboshitz’82 NA49 CF( ) data prefer | f 0 ( )| f 0 (NN) ~ 20 fm STAR CF( p ) data point to Re f 0 ( p ) < Re f 0 ( pp ) 0 Im f 0 ( p ) ~ Im f 0 ( pp ) ~ 1 fm But R( p ) < R( p ) ? Residual correlations pp

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Correlation study of particle interaction - - scattering lengths f 0 from NA49 correlation data Fit using RL-Lyuboshitz (82) with fixed Pair Purity =0.16 from feed-down and PID Data prefer |f 0 | « f 0 (NN) ~ 20 fm - CF=1+ [ CF FSI + S S (-1) S exp(-r 0 2 Q 2 )] 0 = ¼(1-P 2 ) 1 = ¼(3+P 2 ) P=Polariz.=0 CF FSI = 2 0 [½|f 0 (k)/r 0 | 2 (1-d 0 0 /(2r 0 )) +2Re(f 0 (k)/(r 0 ))F 1 (r 0 Q) - 2Im(f 0 (k)/r 0 )F 2 (r 0 Q)] f S (k)=(1/f 0 S +½d 0 S k 2 - ik) -1 k=Q/2 F 1 (z)= 0 z dx exp(x 2 -z 2 )/z F 2 (z)=[1-exp(-z 2 )]/z

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CF=N{1+ [ CF FSI -½exp(-r 0 2 Q 2 )]} N r0r0 f00f00 d00d00 fm B

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33 Correlation asymmetries CF of identical particles sensitive to terms even in k*r* (e.g. through cos 2k*r* ) measures only dispersion of the components of relative separation r * = r 1 * - r 2 * in pair cms CF of nonidentical particles sensitive also to terms odd in k*r* measures also relative space-time asymmetries - shifts r * RL, Lyuboshitz, Erazmus, Nouais PLB 373 (1996) 30 Construct CF +x and CF -x with positive and negative k* -projection k* x on a given direction x and study CF-ratio CF +x /CF x

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34 Simplified idea of CF asymmetry (valid for Coulomb FSI) x x v v v1v1 v2v2 v1v1 v2v2 k*/ = v 1 -v 2 p p k* x > 0 v > v p k* x < 0 v < v p Assume emitted later than p or closer to the center p p Longer t int Stronger CF Shorter t int Weaker CF CF CF

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35 CF-asymmetry for charged particles Asymmetry arises mainly from Coulomb FSI CF A c ( ) |F(-i ,1,i )| 2 =(k*a) -1, =k*r*+k*r* F 1+ = 1+r*/a+k*r*/(k*a) r* |a| k* 1/r* Bohr radius } ±226 fm for ± p ±388 fm for + ± CF +x /CF x 1+2 x* /a k* 0 x* = x 1 *-x 2 * r x * Projection of the relative separation r* in pair cms on the direction x In LCMS ( v z =0) or x || v : x* = t ( x - v t t) CF asymmetry is determined by space and time asymmetries

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36 ad hoc time shift t = –10 fm/c CF + /CF Sensitivity test for ALICE a, fm 84 226 249 CF + /CF 1+2 x* /a k* 0 Here x* = - v t CF-asymmetry scales as - t /a Erazmus et al.’95 Delays of several fm/c can be easily detected

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37 Usually: x and t comparable RQMD Pb+Pb p +X central 158 AGeV : x = -5.2 fm t = 2.9 fm/c x* = -8.5 fm + p-asymmetry effect 2 x* /a -8% Shift x in out direction is due to collective transverse flow RL’99-01 x p > x K > x > 0 & higher thermal velocity of lighter particles rtrt y x FF tTtT tt FF = flow velocity tTtT = transverse thermal velocity tt = F + t T = observed transverse velocity x r x = r t cos = r t ( t 2 + F2 - t T2 )/(2 t F ) y r y = r t sin = 0 mass dependence z r z sinh = 0 in LCMS & Bjorken long. exp. out side measures edge effect at y CMS 0

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NA49 & STAR out-asymmetries Pb+Pb central 158 AGeV not corrected for ~ 25% impurity r* RQMD scaled by 0.8 Au+Au central s NN =130 GeV corrected for impurity Mirror symmetry (~ same mechanism for and mesons) RQMD, BW ~ OK points to strong transverse flow pp pp KK ( t yields ~ ¼ of CF asymmetry)

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39 Decreasing R(p t ): x-p correlation usually attributed to collective flow taken for granted femtoscopy the only way to confirm x-p correlations x 2 -p correlation:yes x -p correlation:yes Non-flow possibility hot core surrounded by cool shell important ingredient of Buda-Lund hydro picture Csörgő & Lörstad’96 x 2 -p correlation:yes x -p correlation:no x = R G x 0 /[ 0 2 +T/m t + T/T r ] radial gradient of T decreasing asymmetry ~1 ? problem

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40 Summary Assumptions behind femtoscopy theory in HIC seem OK at k 0. At k > ~ 100 MeV/c, the usual smoothness and equal-time approximations may not be valid. Wealth of data on correlations of various particle species ( ,K 0,p , , ) is available & gives unique space-time info on production characteristics including collective flows Rather direct evidence for strong transverse flow in HIC at SPS & RHIC comes from nonidentical particle correlations LHC femtoscopic data vs n ch and m t point to a universal fireball freeze- out density settled at RHIC energies and indicate collective expansion in high-multiplicity pp-collisions Absence of femtoscopic signals of QGP 1-st order PT (onset and CEP) at √s NN < 10 GeV is likely due to a dramatic decrease of partonic phase with decreasing energy dedicated high statistics, precise experiments (like planned at NICA and FAIR) are required Info on two-particle strong interaction: & & p scattering lengths from HIC at SPS and RHIC. Good perspective at RHIC & LHC (a problem of residual correlations is to be solved).

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AGS SPS RHIC: radii STAR Au+Au at 200 AGeV0-5% central Pb+Pb or Au+Au Clear centrality & m t dependence Weak energy dependence R ↑ with centrality & with m t only R long slightly ↑ with energy R side R/(1+m t F2 /T) ½ R long (T/m t ) ½ tr. collective flow velocity F Evolution (freeze-out) time

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42 hadronization initial state pre-equilibrium QGP and hydrodynamic expansion hadronic phase and freeze-out Expected evolution of HI collision vs RHIC data dN/dt 1 fm/c5 fm/c10 fm/c50 fm/c time Kinetic freeze out Chemical freeze out RHIC side & out radii: 2 fm/c R long & radii vs reaction plane: 10 fm/c Bass’02

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43 Even stronger effect of KK-bar FSI on K s K s correlations in pp-collisions at LHC ALICE: PLB 717 (2012) 151 e.g. for k t < 0.85 GeV/c, N ch =1-11 the neglect of FSI increases by ~100% and R inv by ~40% = 0.64 0.07 1.36 0.15 > 1 ! R inv = 0.96 0.04 1.35 0.07 fm

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44 Correlation study of particle interaction - + scattering length f 0 from NA49 CF Fit CF( + ) by RQMD with SI scale: f 0 sisca f 0 input f 0 input = 0.232 fm sisca = 0.6 0.1 Compare with ~0.8 from S PT & BNL E765 K e ++ CF=Norm [ Purity RQMD(r* Scale r*)+1-Purity]

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45 Large lifetimes evaporation or phase transition x || v | x| | t| CF-asymmetry yields time delay Ghisalberti’95 GANIL Pb+Nb p+d+X CF + (pd) CF (pd) CF + /CF < 1 Deuterons earlier than protons in agreement with coalescence e -t p / e -t n / e -t d /( /2) since t p t n t d Two-phase thermodynamic model CF + /CF < 1 123 1 2 3 Strangeness distillation : K earlier than K in baryon rich QGP Ardouin et al.’99

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46 Coalescence: deuterons.. E d d 3 N/d 3 p d = B 2 E p d 3 N/d 3 p p E n d 3 N/d 3 p n p p p n ½p d WF in continuous pn spectrum -k* (r*) WF in discrete pn spectrum b (r*) Coalescence factor: B 2 = (2 ) 3 (m p m n /m d ) -1 t | b (r*)| 2 ~ R -3 Triplet fraction = ¾ unpolarized Ns Usually: n p Much stronger energy dependence of B 2 ~ R -3 than expected from pion and proton interferometry radii B2B2 R(pp) ~ 4 fm from AGS to SPS Lyuboshitz (88)..

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