KEK-PS E325実験におけるベクター中間子の質量に対する

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
Physics Motivation
Quark Mass
bare mass
mu≒md≒5MeV/c2
ms≒150MeV/c2
chiral symmetry
restoration
chiral symmetry
braking
effective mass
in QCD vacuum
mu≒md≒300MeV/c2
ms≒500MeV/c2
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
2
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)
3
Vector Meson, r/w/f
r/w 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.
4
Expected Invariant Mass Spectra in e+esmall FSI in e+e- decay channel
r+w
double peak (or tail-like) structure m*/m=1-0.16r/r0
second peak is made by
inside-nucleus decay
e
p
e
e
r/w/f
outside decay
p
w
f
m*/m=1-0.02r/r0
bglab~1
r
r/w/f e
inside decay
depends on the nuclear
size & meson velocity
enhanced for larger nuclei
& slower meson
5
Vector Meson Measurements
Hot / Cold
CERES@CERN-SPS (’93)
– e+ e– anomaly at lower region of r in A+A,
not in p+A
CERES
STAR@BNL-RHIC (’04)
– rp+p– mass shift in p+p & A+A peripheral
TAPS
CBELSA/TAPS@ELSA (’05)
– wp0g(ggg)
– anomaly in g+Nb, not in g+p
NA60@CERN-SPS (’06)
– rm+m– width broadening, no mass shift in In+In
6
KEK-PS E325 Experiment
Measurements
Invariant Mass of e+e-, K+Kin 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
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, 092301 (2006).
nucl-ex/0511019
nucl-ex/0603013
x10 statistics in K+K-
nucl-ex/0606029
Very thin targets
’02 completed
e.g. 0.4% radiation length &
0.2% interaction length for C-target
7
Detector Setup
M.Sekimoto et al., NIM, A516, 390 (2004).
Start Timing
Counter
Forward LG Calorimeter
Hodoscope
Aerogel Cherenkov
Rear LG Calorimeter
Forward TOF
Side LG Calorimeter
Barrel Drift Chamber
B
0.81Tm
Cylindrical DC
1m
Rear Gas Cherenkov
Vertex DC
Front Gas Cherenkov
8
C
w(783)
counts/10MeV/c2
e+ e-
counts/10MeV/c2
Observed Invariant Mass Spectra
Cu
f(1020)
K+Kthreshold
f(1020)
counts/4MeV/c2
K +K -
counts/4MeV/c2
f(1020)
C
w(783)
Cu
f(1020)
9
Result of
+
r/we e
M.Naruki et al., PRL, 96, 092301 (2006).
10
e+e- Invariant Mass Spectra
from 2002 run data
(~70% of total data)
counts/10MeV/c2
C
w(783)
C & Cu targets
acceptance uncorrected
f(1020)
M<0.2GeV/c2 is suppressed
by the detector acceptance
 fit the spectra with known sources
11
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,
estimated spectrum
chamber resolution,
using GEANT4
detector acceptance, etc.)
background
– combinatorial background obtained
by the event mixing method
fit parameter
– relative abundance of these
components is determined
by the fitting
fe+e-
experimental
effects
relativistic
+
Breit-Wigner
internal
radiative
correction
Fitting Results
Cu
C
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 0.60-0.76GeV/c2 is excluded from the fit, because
the fit including this region results in failure at 99.9% C.L.. 13
Fitting Results (BG subtracted)
events[/10MeV/c2]
C
events[/10MeV/c2]
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
Toy Model Calculation
• pole mass: m*/m = 1-kr/r0 (Hatsuda-Lee formula)
• generated at surface of incident
p
e
r/w
e
hemisphere of target nucleus
– aw~2/3 [nucl-ex/0603013]
– decay inside a nucleus:
C
Cu
r 52%
66%
w
10%
5%
Cu
r=4.1fm
C
r=2.3fm
• nuclear density distribution : Woods-Saxon
• mass spectrum: relativistic Breit-Wigner Shape
• no width modification
15
Fitting Results by the Toy Model
m*/m = 1 - 0.092 r/r0
r/w = 0.7±0.1
C
r/w = 0.9±0.2
Cu
the excesses for C and Cu are well reproduced
by the model including the mass modification.
16
Result of
+
fe e
R.Muto et al., nucl-ex/0511019
17
fe+e- Invariant Mass Spectra
from 2001 & 2002 run data
C & Cu targets
f(1020)
acceptance uncorrected
fit with
– simulated mass shape of f
(evaluated as same as r/w)
– polynomial curve background
 examine the mass shape as a function of bg (=p/m)
(anomaly could be enhanced for slowly moving mesons)
18
Fitting Results
1.25<bg<1.75
1.75<bg (Fast)
Large Nucleus
Small Nucleus
bg<1.25 (Slow)
Rejected at 99% confidence level
19
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
20
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
to increase the
decay probability
in a nucleus
(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/0603013]
p
f
– decay inside a nucleus (for bg<1.25):
f
C
Cu
3%
6%
21
Fitting Results by the Toy Model
m*/m = 1 - 0.04 r/r0, G*/G = 1 + 2 r/r0
1.25<bg<1.75
1.75<bg (Fast)
Large Nucleus Small Nucleus
bg<1.25 (Slow)
well reproduce the data, even slow/Cu
22
Result of
+
fK K
F.Sakuma et al., nucl-ex/0606029
23
from 2001 run data
C & Cu targets
counts/4MeV/c2
fK+K- Invariant Mass Spectra
C
f(1020)
acceptance uncorrected
fit with
– simulated mass shape of f
(evaluated as same as r/w)
– combinatorial background obtained
by the event mixing method
 examine the mass shape as a function of bg
24
Fitting Results
1.7<bg<2.2
2.2<bg (Fast)
Large Nucleus
Small Nucleus
bg<1.7 (Slow)
Mass-spectrum changes are NOT statistically significant
However, impossible to compare fe+e- with fK+K-, directly
Kinematical Distributions of observed f
the detector acceptance is
different between e+e- and K+Kvery limited statistics for fK+Kin bg<1.25 where the modification
is observed in fe+e-
the histograms for fK+Kare scaled by a factor ~3
26
Result of nuclear
mass-number
dependences of
+
+
fe e & fK K
F.Sakuma et al., nucl-ex/0606029
27
Vector Meson, f
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
simple example
f mass decreases
 GfK+K- becomes small
K mass decreases
 GfK+K- becomes large
f mass
K+Kthreshold
r0:normal nuclear density
f : T.Hatsuda, S.H.Lee,
Phys. Rev. C46(1992)R34.
K : H.Fujii, T.Tatsumi,
PTPS 120(1995)289.
28
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
 ( A)   ( A  1)  A
a
a  af  K + K   af e+ e
 Nf  K + K  ( A1 )
 ln 
 Nf e+ e ( A1 )
(A1>A2)
Nf  K + K  ( A2 ) 
 ln ( A1 A2 )
Nf e+ e ( A2 ) 

afK+K- becomes larger than afe+eThe difference of a is expected to be
enhanced in slowly moving f mesons
29
Results of Nuclear Mass-Number Dependence a
bg
rapidity
=
a=
-
K+K-
e+ e-
pT
ae+e- with corrected for the
K+K- acceptance
bg
averaged
(0.13+/-0.12)
possible modification
of the decay widths is
discussed
afK+K- and afe+e- are consistent
30
Discussion on GfK+K- and Gfe+eGf* Gf0  1 + ktot ( r r0 ) ,
Gf*  K + K  Gf0  K + K   1 + k K ( r r0 ) ,
Gf* e+ e Gf0 e+ e  1 + ke ( r r0 )
We expect k tot k K since the f meson
mainly decays into KK as long as such
decays are kinematically allowed.
① The values of expected a are obtained by the MC.
– f mesons are uniformly produced in a nucleus and decayed according
to the values of kK and ke.
② The measured a provides constraints on kK and ke.
31
Discussion on GfK+K- and Gfe+e③ The constraint on kK is obtained from the K+K- spectra.
Cu
excluded from
the fitting
surplus
Nin/Nout ~ Nsurplus/Nf
– 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
MC
data
kK
Nsurplus/Nf = 0.044+/-0.037+/-0.058 (C)
0.076+/-0.025+/-0.043 (Cu)
kK=2.1+/-1.2+/-2.0 (C&Cu)
Discussion on GfK+K- and Gfe+e-
Gf* Gf0  1 + ktot ( r r0 ) ,
Gf*  K + K  Gf0  K + K   1 + k K ( r r0 ) ,
Gf* e+ e Gf0 e+ e  1 + ke ( r r0 )
k tot
kK
④ 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
33
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+eand 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
34
channels.
Backup
35
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.
36
Contours for k1 and k2 of fe+ePole 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 = 0.034 ± 0.007
k2 = 2.6 ±1.3
Acceptance Correction for a
bg
bg
extrapolate afe+efor the kaon
acceptance
assumption : afe+e- is linearly
dependent on the y-pT plane in
our detector acceptance
values of
divide e+efit the data with
mean & RMS
data into 3x3
the linear function
for each bin
bins in the
y-pT plane
bg
slice
38

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