1. Evidence for π+π- Rescattering in p+p Collisions at √sNN = 200 GeV
P. Fachini, R. Longacre, Z. Xu and H. Zhang
Brookhaven National Laboratory
Outline:
Motivation
Measurements
Discussion
Conclusions
Data Set:
p+p, d+Au, and Au+Au @ √sNN = 200 GeV
Patricia Fachini

2. Motivation  Measurements
Patricia Fachini

3. ρ0 Mass in p+p
Minimum bias p+p
0.6 ≤ pT < 0.8 GeV/c
STAR
40 MeV shift position ρ0 peak measured by STAR in minimum bias p+p
Patricia Fachini

4. ρ0 Mass in p+p and Au+Au
ρ0 mass pT dependent and lower than previous pp measurement in both p+p and peripheral Au+Au collisions
ρ0 mass high multiplicity p+p lower than minimum bias p+p  multiplicity dependent
Systematic errors  common and correlated between p+p and peripheral Au+Au
10% of minimum bias p+p for |η|< 0.5
STAR
|y|< 0.5
Patricia Fachini

5. ρ0 Mass in d+Au
STAR
Preliminary
|y|< 0.5 T
50 MeV shift position ρ0 peak measured by STAR in minimum bias d+Au
Patricia Fachini

6. K* Mass in p+p and Au+Au
Central
Au+Au
STAR
STAR
Central
Au+Au
PDG value pp pp
PDG value
|y|< 0.5
10 MeV shift on the position of the K*0 peak at low pT in minimum bias p+p
Systematic and statistical errors added in quadrature
Patricia Fachini

7. K* and Δ++ Mass in d+Au 50 MeV shift on the position of the Δ++ peak
STAR
STAR
Preliminary
Preliminary T
|y|< 0.5 T
50 MeV shift on the position of the Δ++ peak
10 MeV shift on the position of the K*0 peak at low pT in minimum bias d+Au
Patricia Fachini

8. Phase Space -  M2 + pT2 M e T Phase Space =  M2 + pT2 π+ ρ0 π-
M = Invariant Mass; pT = transverse momentum; T = Inverse Slope
p+p  particle composition reasonably reproduced by statistical model  T = 160 MeV  also d+Au
F. Becattini, Nucl. Phys. A 702, 336 (2002); Z. Phys. C 69, 485 (1996); F. Becattini and U. Heinz, Z. Phys. C 76, 269 (1997)
Au+Au  between chemical and kinetic freeze-out  resonances formed until particles too far apart  resonances emitted T = 120 MeV
E.V. Shuryak and G.E. Brown, Nucl. Phys. A 717 (2003) 322
Γ(M) = Γρ
M2 – 4mπ2
Mρ2 – 4mπ2 3 2 Mρ M
BW(M) =
Γ(M)
(M2 – Mρ2)2 + Mρ2 Γ(M)2
P. Braun-Munzinger et.al., CERES Int. Note, March 2000, unpublished; E.V. Shuryak and G.E. Brown, Nucl. Phys. A 717 (2003) 322; P.K. Kolb and M. Prakash, nucl-th/ ; H.W. Barz et al., Phys. Lett. B 265, 219 (1991); R. Rapp, hep-ph/
Patricia Fachini

9. What about other measurements?
Patricia Fachini

10. NOTE: Previous experiments interested in K*
No detailed mass measurements
Mass integrated in pT, xF, xp
Previous experiments agree PDG value
STAR measurement  K*0 mass shifted 10 MeV minimum bias p+p pT < 1 GeV/c
Not a surprise that a mass shift was not measured before! ρ0
No detailed mass measurements
Mass integrated in pT, xF, xp
STAR measurement  ρ0 mass shifted 40 MeV in minimum bias p+p
Considerably large mass shift
Mass shift observed before!
Previous ρ0 mass measurements  NA27, OPAL, DELPHI, and ALEPH
NOTE: Previous experiments interested in
cross-sections and NOT in mass!
Patricia Fachini

11. ρ0-meson Measured in pp  NA27
M. Aguilar-Benitez, Z. Phys. C 50, 405 (1991)
√s = 27.5 GeV
The ρ0 mass obtained by fitting same event distribution of π+π- to
BG + PS x BW = BG + BGxBW = BG(1 + BW)
BW = Breit-Wigner
BG = Background
PS = Phase Space
π+π-
pT > 0
xF > 0
PS = BG
xF =
pLongitudinal
pTotal
Signal
Signal π+π- distribution after background subtraction
Background
 exponential
function
Signal
Same event distribution π+π-
Patricia Fachini

12. ρ0-meson Measured in pp  NA27
M. Aguilar-Benitez, Z. Phys. C 50, 405 (1991)
CERN  √s = 27.5 GeV
ρ0 mass = ± 2.6 MeV/c2  only p+p measurement used in average by PDG
PDG average “other reactions” hadroproduced  ρ0 mass = ± 0.9 MeV/c2
PDG average e+e- (exclusive)  ρ mass = ± 0.5 MeV/c2
 The position of the ρ0 peak is clearly below reported value
762.6 MeV/c2
775.9 MeV/c2
“scanned version”
Patricia Fachini

13. ρ0-meson Measured in pp  NA27
M. Aguilar-Benitez, Z. Phys. C 50, 405 (1991)
BW(M) =
Γ(M)
(M2 – Mρ2)2 + Mρ2 Γ(M)2
Γ(M) = Γρ
M2 – 4mπ2
Mρ2 – 4mπ2 3 2 Mρ M
Fitting to a p-wave BW function  M = ± 2.0 MeV
Patricia Fachini

14. ρ0-meson Measured in e+e-  LEP
P. D. Acton et al., Z. Phys. C 56 (1992) 521; G. Abbiendi et al., Eur. Phys. J. C 5 (1998) 411; P. Abreu et al., Phys. Lett. B 298 (1993) 236; D. Buskulic et al., Z. Phys. C 69 (1996) 379; G. D. Lafferty, Z. Phys. C 60 (1993) 659, private communication
√s = 90 GeV
OPAL  ρ0 mass shifted by ~70 MeV/c2 at low xp and no shift at high xp (xp ~1)
OPAL  -10 to -30 MeV/c2 shift in the position of the maximum of the resonance ρ±  consistent with ρ0 measurement
DELPHI  0.1 < xp < 0.4  ρ0 peak fit to (BWxBG) + BG  ρ0 mass = 757 ± 2 MeV/c2  five standard deviations below PDG value
ALEPH  same ρ0 mass shift observed by OPAL
­ Jetset 7.3
+ ALEPH Data
xp =
E(meson)
E(beam) ρ0
­ Jetset 7.2
● OPAL Data ρ0
Patricia Fachini

15. Mass Shift in p+p collisions
Patricia Fachini

16. Discussing Phase Space
Patricia Fachini

17. What is the meaning of Phase Space in Au+Au?
Hadrons scattering  forming resonances  modifying mass distributions
Check  Transport Model Calculations  UrQMD ρ0 π- π+
π spectra 
Γ = 150 MeV
Patricia Fachini

18. Transport Model - UrQMD
M. Bleicher, SQM2003
Au+Au
Au+Au
b ≤ 3 fm
b ≤ 3 fm 0 ρ0
√sNN = 200 GeV
1.2 ≤ pT < 1.4 GeV/c
|y| ≤ 0.5
0.2 ≤ pT < 0.4 GeV/c
|y| ≤ 0.5
BW × PS
M = 769 MeV/c2
UrQMD  Only imaginary part  No medium modification
Central Au+Au  ρ0 mass shifted ~30 MeV at low pT
ρ0 shape reproduced by p-wave Breit-Wigner × Phase Space
Mρ= MeV for 0.2 ≤ pT < 0.4 GeV/c
Mρ = MeV for 1.2 ≤ pT < 1.4 GeV/c
Mρ = 769 MeV/c2 input
Г = 150 MeV
Patricia Fachini

19. What is the meaning of Phase Space in p+p?
Particles born at hadronization according to phase space
No final state interaction expected
Particle spectra
No need to be thermodynamically equilibrated
Multiparticle production saturates available phase space
Valid for p+p and e+e-
MT scaling
~ e
- pT T
Patricia Fachini

20. ρ0 Spectra in p+p at sNN = 200 GeV
π- Minimum bias p+p
Tslope = 160 MeV
ρ0 Minimum bias p+p
Tslope ~ 180 MeV
ρ0 High Multiplicity p+p
ρ0 Tslope multiplicity independent!
STAR
|y|< 0.5
Patricia Fachini

21. ρ0 Mass in p+p at sNN = 200 GeV
10% of minimum bias p+p for |η|<0.5
STAR
|y|< 0.5
ρ0 mass pT dependent!
ρ0 mass multiplicity dependent!
Patricia Fachini

22. Show that ρ0 mass multiplicity dependent  Evidence for π+π- Rescattering
Patricia Fachini

23. Quantum Mechanics A resonance at rest is described by
The probability amplitude
(x,t) e e
-iE0t ħ -t 2ζ 
E0 is energy at rest ζ
is the lifetime
(E,x) ∫ (e )* (x,t) dt ~  
-iEt ħ
Patricia Fachini

24. Quantum Mechanics ~ (E,x) (x) E-E0 1 i - ħ 2ζ P(E) | |2 ∫ |(x)|2 dx
E-E0 ħ i 1 2ζ
P(E) | |2 ∫ |(x)|2 dx 
E-E0 ħ i 1 2ζ
P(E) 
(E-E0)2 + Γ2 4
Γ/2
Γ = ħ/ζ
P(E) = Breit-Wigner distribution
Patricia Fachini

25. Adding Phase Space String fragmentation Multiplicity independent Data:
Multiplicity dependent!  Inconsistency!
P(E) 
(E-E0)2 + Γ2 4
Γ/2
x PS 
P(E) 
BW(Γ) x PS ρ0 π- π+
Necessary!
Patricia Fachini

26. String Fragmentation s u d s u ρ d u s π π π ρ
Patricia Fachini

27. Phase Shift Analysis
R. Longacre, nucl-exp/ ρ0 π- π+ D
Minimum bias p+p
0.6 ≤ pT < 0.8 GeV/c
STAR
Interference  Partial-wave analysis + π+π- scattering
Mρ = MeV/c Г = 150 MeV/c2
Distance of interaction in π+π- scattering  1/3 fm π- π+ A ρ0
Interference π- π+ A
T = 180 MeV
Patricia Fachini

28. Phase Shift Analysis |T|2 = |D|2 + |α sin(δ1) + PS’ cos(δ1)|2 PS’
|D|2 is the direct production ρ0
δ1 is the p-wave phase shift
|A|2 is the PS overlap of di-pions in l=1 partial waves
2q(q/q0)2
E(q/q0)2
(1-(q/q0)2)
PS’ =
α = ( ) r2
r02
r is the radius
r0 = 1.0 fm
q0 = 200 MeV/c
Patricia Fachini

29. π+ π- Rescattering Good Agreement with Data! Minimum bias p+p
0.6 ≤ pT < 0.8 GeV/c
Minimum bias p+p
0.6 ≤ pT < 0.8 GeV/c
STAR
Good Agreement with Data!
Patricia Fachini

30. Conclusions
Measurement mass and width wide resonances  exclusive reactions ONLY!  e+e-  π+π-
ρ0 and K*0  mass shift observed in p+p, d+Au, and Au+Au collisions at RHIC by STAR  even after phase space correction
ρ0 mass shift observed by previous experiments  NA27, OPAL, DELPHI, and ALEPH  even after phase space correction
Phase space  does NOT reproduce mass shift measured
ρ0 mass shift multiplicity dependent  Evidence for π+π- Rescattering in p+p collisions
Phase shift plus rescattering reproduces well STAR data
Patricia Fachini