1. Study of vector meson modification in nuclear matter at KEK-PS
Kyoto Univ., KEKA, RIKENB, CNS Univ. of TokyoC, ICEPP Univ. of TokyoD,
Tohoku Univ.E
F.Sakuma, J.ChibaA, H.En’yoB, Y.Fukao, H.Funahashi, H.HamagakiC, M.IeiriA, M.IshinoD, H.KandaE, M.Kitaguchi, S.MiharaD, K.Miwa, T.Miyashita, T.Murakami, R.MutoB, M.Nakura, M.NarukiB, K.OzawaC, O.SasakiA, M.SekimotoA, T.TabaruB, K.H.TanakaA, M.Togawa, S.Yamada, S.YokkaichiB, Y.Yoshimura
Physics motivation
E325 Experiment
Results of data analysis
r/w  e+e- spectra
f  e+e- spectra
f  K+K- spectra
nuclear mass-number dependences of fe+e- & fK+K-
Summary

2. chiral symmetry restoration chiral symmetry braking
Physics Motivation
Quark Mass
chiral symmetry restoration
effective mass
in QCD vacuum
　mu≒md≒300MeV/c2
ms≒500MeV/c2
bare mass
mu≒md≒5MeV/c2
ms≒150MeV/c2
chiral symmetry braking
How we can detect such a quark mass change?
at very high temperature or density, the chiral symmetry is expected to restore
W.Weise
NPA553,59 (1993)
even at normal nuclear density, the chiral symmetry is expected to restore partially

3. Vector Meson Modification
dropping mass
Brown & Rho (’91)
m*/m=0.8 (r=r0)
Hatsuda & Lee (’92)
m*/m=1-0.16r/r0 for r/w
m*/m=1-0.03r/r0 for f
Muroya, Nakamura & Nonaka (’03)
Lattice Calc.
width broadening
Klingl, Kaiser & Weise (’97&98)
1GeV> for r, 45MeV for f (r=r0)
Oset & Ramos (’01)
22MeV for f (r=r0)
Cabrera & Vicente (’03)
33MeV for f (r=r0)

4. Vector Meson, r/w/f r/w meson f meson mass decreases 16%  130MeV/c2
large production cross-section
cannot distinguish r & w
f meson
mass decreases
2~4%  20-40MeV/c2
small production cross-section
narrow decay width (G=4.3MeV/c2),
no other resonance nearby
　⇒sensitive to the mass
spectrum change
T.Hatsuda, S.H.Lee,
Phys. Rev. C46(1992)R34.

5. Expected Invariant Mass Spectra in e+e-
small FSI in e+e- decay channel
double peak (or tail-like) structure
+
m*/m=1-0.16r/r0
second peak is made by inside-nucleus decay w f
m*/m=1-0.02r/r0 p e
r/w/f
outside decay
inside decay r
bglab~1
depends on the nuclear size & meson velocity
enhanced for larger nuclei & slower meson

6. Vector Meson Measurements
Hot / Cold
(’93)
e+e-
anomaly at lower region of r in A+A,
not in p+A
(’04)
rp+p-
mass shift in p+p & A+A peripheral
(’05)
wp0g(ggg)
anomaly in g+Nb, not in g+p
(’06)
rm+m-
width broadening, no mass shift in In+In
CERES
TAPS

7. to decay inside a nucleus
KEK-PS E325 Experiment
History of E325
’93 proposed
’96 construction start
NIM, A457, 581 (2001).
NIM, A516, 390 (2004).
’97 first K+K- data
’98 first e+e- data
PRL, 86, 5019 (2001).
’99~’02
x100 statistics in e+e-
PRL, 96, (2006).
nucl-ex/
nucl-ex/
x10 statistics in K+K-
nucl-ex/
’02 completed
Measurements
Invariant Mass of e+e-, K+K-
in 12GeV p+Ar,w,f+X reactions
slowly moving vector mesons (plab~2GeV/c)
large probability
to decay inside a nucleus
Beam
Primary proton beam
(~109/spill/1.8s)
Target
Very thin targets
e.g. 0.4% radiation length &
0.2% interaction length for C-target

8. Forward LG Calorimeter
Detector Setup
M.Sekimoto et al., NIM, A516, 390 (2004).
Hodoscope
Aerogel Cherenkov
Forward TOF
Start Timing Counter
Forward LG Calorimeter
Rear LG Calorimeter
Side LG Calorimeter
Barrel Drift Chamber
Cylindrical DC
Vertex DC B
0.81Tm
Front Gas Cherenkov
Rear Gas Cherenkov 1m
12GeV proton beam

9. Observed Invariant Mass SpectraCu
w(783)
w(783)
counts/10MeV/c2
counts/10MeV/c2
e+e-
f(1020)
f(1020) C Cu
f(1020)
f(1020)
counts/4MeV/c2
counts/4MeV/c2
K+K-
K+K-
threshold

10. Result of r/we+e-
M.Naruki et al., PRL, 96, (2006).

11. e+e- Invariant Mass Spectra
counts/10MeV/c2
from 2002 run data
(~70% of total data)
C & Cu targets
acceptance uncorrected
M<0.2GeV/c2 is suppressed
by the detector acceptance C
w(783)
f(1020)
 fit the spectra with known sources

12. Fitting with known sources
resonance
r/w/fe+e-, wp0e+e-, hge+e-
relativistic Breit-Wigner shape (with internal radiative corrections)
nuclear cascade code JAM gives momentum distributions
experimental effects are estimated through the Geant4 simulation
(multiple scattering, energy loss, external bremsstrahlung,
chamber resolution,
detector acceptance, etc.)
background
combinatorial background obtained
by the event mixing method
fit parameter
relative abundance of these
components is determined
by the fitting
estimated spectrum using GEANT4
fe+e-
experimental effects +
internal radiative correction
relativistic
Breit-Wigner

13. Fitting Results C Cu
c2/dof=159/140
c2/dof=150/140
the excess over the known hadronic sources on the low mass side of w peak has been observed.
the region GeV/c2 is excluded from the fit, because the fit including this region results in failure at 99.9% C.L..

14. Fitting Results (BG subtracted) r/w ratios are consistent with zero !
events[/10MeV/c2]
events[/10MeV/c2] C Cu
r/w ratios are consistent with zero !
r/w = 0.0±0.03(stat.)±0.09(sys.)
0.0±0.04(stat.)±0.21(sys.)
r/w=1.0±0.2 in former experiment (p+p, 1974)
 the origin of the excess is modified r mesons

15. Toy Model Calculation pole mass: m*/m = 1-kr/r0 (Hatsuda-Lee formula)
generated at surface of incident
hemisphere of target nucleus
aw~2/3 [nucl-ex/ ]
decay inside a nucleus:
nuclear density distribution : Woods-Saxon
mass spectrum: relativistic Breit-Wigner Shape
no width modification p
r/w e Cu C
r=4.1fm
r=2.3fm C Cu r
52%
66% w 5%
10%

16. Fitting Results by the Toy Model
m*/m = r/r0
r/w = 0.7±0.1
r/w = 0.9±0.2 Cu C
the excesses for C and Cu are well reproduced by the model including the mass modification.

17. Result of fe+e-
R.Muto et al., nucl-ex/

18. fe+e- Invariant Mass Spectra
from 2001 & 2002 run data
C & Cu targets
acceptance uncorrected
fit with
simulated mass shape of f
(evaluated as same as r/w)
polynomial curve background
f(1020)
 examine the mass shape as a function of bg (=p/m)
(anomaly could be enhanced for slowly moving mesons)

19. Fitting Results Rejected at 99% confidence level bg<1.25 (Slow)
1.75<bg (Fast)
Small Nucleus
Large Nucleus
Rejected at 99% confidence level

20. A significant enhancement is seen in the Cu data, in bg<1.25
Amount of Excess
A significant enhancement is seen in the Cu data, in bg<1.25
 the excess is attributed to the f mesons
which decay inside a nucleus and are modified
To evaluate the amount the excess Nexcess, fit again excluding the excess region (0.95~1.01GeV/c2) and integrate the excess area.
excluded from
the fitting

21. to increase the decay probability in a nucleus
Toy Model Calculation
Toy model like r/w case, except for
pole mass: m*/m = 1-k1r/r0 (Hatsuda-Lee formula)
width broadening: G*/G = 1+k2r/r0
(no theoretical basis)
e+e- branching ratio is not changed
G*e+e-/G*tot=Ge+e-/Gtot
uniformly generated in target nucleus
af~1 [nucl-ex/ ]
decay inside a nucleus (for bg<1.25):
to increase the decay probability in a nucleus f p C Cu f 3% 6%

22. Fitting Results by the Toy Model
m*/m = r/r0, G*/G = r/r0
bg<1.25 (Slow)
1.25<bg<1.75
1.75<bg (Fast)
Small Nucleus
Large Nucleus
well reproduce the data, even slow/Cu

23. Result of fK+K-
F.Sakuma et al., nucl-ex/

24. C fK+K- Invariant Mass Spectra f(1020) from 2001 run data
C & Cu targets
acceptance uncorrected
fit with
simulated mass shape of f
(evaluated as same as r/w)
combinatorial background obtained
by the event mixing method
counts/4MeV/c2
f(1020)
 examine the mass shape as a function of bg

25. Mass-spectrum changes are NOT statistically significant
Fitting Results
bg<1.7 (Slow)
1.7<bg<2.2
2.2<bg (Fast)
Small Nucleus
Large Nucleus
Mass-spectrum changes are NOT statistically significant
However, impossible to compare fe+e- with fK+K-, directly

26. Kinematical Distributions of observed f
the detector acceptance is different between e+e- and K+K-
very limited statistics for fK+K- in bg<1.25 where the modification is observed in fe+e-
the histograms for fK+K- are scaled by a factor ~3

27. Result of nuclear mass-number dependences of fe+e- & fK+K-
F.Sakuma et al., nucl-ex/

28. Vector Meson, f simple example small decay Q value (QK+K-=32MeV/c2)
mass decreases
2~4%  20-40MeV/c2
narrow decay width (G=4.3MeV/c2)
　⇒ sensitive to the mass spectrum
change
small decay Q value
(QK+K-=32MeV/c2)
⇒ the branching ratio is
sensitive to f or K modification
f mass
K+K-
threshold
simple example
f mass decreases
 GfK+K- becomes small
K mass decreases
 GfK+K- becomes large
r0:normal nuclear density
f : T.Hatsuda, S.H.Lee,
Phys. Rev. C46(1992)R34.
K : H.Fujii, T.Tatsumi,
PTPS 120(1995)289.

29. GfK+K-/Gfe+e- and Nuclear Mass-Number Dependence a
GfK+K-/Gfe+e- increases in a nucleus
 NfK+K- /Nfe+e- becomes large
The lager modification is expected in the larger nucleus
(A1>A2)
afK+K- becomes larger than afe+e-
The difference of a is expected to be enhanced in slowly moving f mesons

30. - Results of Nuclear Mass-Number Dependence a Da=bg
rapidity pT
ae+e- with corrected for the K+K- acceptance =
Da= -
K+K-
e+e- bg
possible modification of the decay widths is discussed
averaged
(0.13+/-0.12)
afK+K- and afe+e- are consistent

31. Discussion on GfK+K- and Gfe+e-
The values of expected Da are obtained by the MC.
f mesons are uniformly produced in a nucleus and decayed according to the values of kK and ke.
The measured Da provides constraints on kK and ke.

32. Discussion on GfK+K- and Gfe+e-
The constraint on kK is obtained from the K+K- spectra.
In the K+K- spectra, we fit again excluding the region 0.987(=2mk) ~ 1.01GeV/c2.
We obtain a surplus over the f peak and BG.
From the MC, we estimate the ratio of the number of f mesons decayed inside to outside Nin/Nout (inside = the half-density radius of the Woods-Saxon dist.).
When the surpluses are assumed as the f-meson decayed inside a nucleus, we obtain the constraint on kK by comparing Nsurplus/Nf with Nin/Nout. Cu Cu
excluded from
the fitting
~ Nsurplus/Nf MC
Nin/Nout
surplus
data kK
Nsurplus/Nf = / / (C)
0.076+/ / (Cu)
kK=2.1+/-1.2+/-2.0 (C&Cu)

33. Discussion on GfK+K- and Gfe+e-
Limits on the in-medium decay widths are obtained.
We renormalize the PDF eliminating an unphysical region corresponding to G*/G<0, and obtain the 90% confidence limits.
the first experimental limits assigned to the in-medium broadening of the partial decay widths

34. Summary
KEK PS-E325 measured e+e- and K+K- invariant mass distributions in 12GeV p+A reactions.
The significant excesses at the low-mass side of we+e- and fe+e- peak have been observed.
These excesses are well reproduced by the toy model
calculations which take Hatsuda-Lee prediction into
account.
Mass spectrum changes are not statistically significant in the K+K- invariant mass distributions.
Our statistics in the K+K- decay mode are very limited in
the bg region in which we see the excess in the e+e- mode.
The observed nuclear mass-number dependences of fe+e- and fK+K- are consistent.
We have obtained limits on the in-medium decay width
broadenings for both the fe+e- and fK+K- decay
channels.

35. Backup

36. mass of r/w meson decreases by 9% at normal nuclear density.
Contours for r/w and k
C and Cu data are
simultaneously fitted.
free parameters
production ratio r/w
shift parameter k
Best-Fit values are
k = 0.092±0.002
r/w = 0.7±0.1 (C)
0.9±0.2 (Cu)
mass of r/w meson decreases by 9% at normal nuclear density.

37. Contours for k1 and k2 of fe+e-
Pole Mass Shift
M*/M = 1–k1r/r0
Width Broadening
G*/G = 1+k2r/r0
C and Cu data are
simultaneously fitted.
free parameters
parameter k1 & k2
Best-Fit values are
k1 = ± 0.007
k2 = 2.6 ±1.3

38. Acceptance Correction for abg bg
extrapolate afe+e- for the kaon acceptance
assumption : afe+e- is linearly dependent on the y-pT plane in our detector acceptance
values of mean & RMS for each bin
divide e+e- data into 3x3 bins in the y-pT plane
fit the data with the linear function bg
slice