有限密度における ベクター中間子の質量変化の検証
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有限密度におけるベクター中間子の質量変化の検証
Introduction Experimental Setup Results Future Plan
Kyoto Univ.a , KEKb, RIKENc, CNS Univ. of Tokyod,
Megumi Naruki, KEK, JapanJ. Chibab, H. En’yoc, Y. Fukaoa, H. Funahashia, H. Hamagakid, M. Ieirib, M. Ishinoe, H. Kandaf , M. Kitaguchia, S. Miharae, K. Miwaa, T. Miyashitaa, T. Murakamia, R. Mutob, T. Nakuraa, K. Ozawad, F. Sakumaa, O. Sasakib,M. Sekimotob, T. Tabaruc, K.H. Tanakab, M. Togawaa, S. Yamadaa,S. Yokkaichic, Y. Yoshimuraa
(KEK-PS E325 Collaboration)
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Hadron Mass
2
vacuum
higgs
vacuum
udu
current quarks ~MeV/c2
hadrons ~GeV/c2
constituent quarks ~300MeV/c2
uu
d
Tqq
,
Hot/Dense Matter
RestorationChiral Symmetry
QCD Vaccum
Spontaneous Breaking of
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dropping mass• Brown-Rho scaling (’91)
– m*/m = 0.8 at = 0 • QCD Sum Rule by Hatsuda & Lee (’92)
– m*/m = 1 - 0.16 /0 for /w– m*/m = 1 - 0.03 /0 for f
• Lattice Calc. by Muroya, Nakamura & Nonaka(’03)
width broadening (at 0)• Klingl, Kaiser, Weise (’97-8)
G*/G~10 for /w/f • Rapp & Wambach (’99) : G*
/G ~2• Oset & Ramos (’01) : DGf = 22MeV • Cabrera & Vicente (’03) : DGf = 33MeV
Mass modification at finite density
w
f
Hatsuda & Lee PRC46(1992)R34
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KEK-PS E325 experiment
measures Invariant Mass of e+e-, K+K-
in 12GeV p + A → , w , f + X reactions
Expected Invariant Mass distribution of and wDecay in vacuum In Copper Nuclei
w
mass modified by the formula : m*/m=1-0.16 /0
Prog.Theor.Phys.95(1996)1009
• low energy : the mass modification at the normal nuclear density• dilepton measurement : free from final state interactions
/w ee
f
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KEK-PS E325 experimentWe measureInvariant Mass of e+e-, K+K-
in 12GeV p + A , w, f + Xslowly moving ,w,f (plab~2GeV/c ) larger probability to decay
inside nucleusBeamprimary proton beam(~109/spill/1.8s)
Targetinteraction length
0.2%/0.05% (C/Cu)radiation length:
0.4/0.5%(C/Cu)
History’93 proposed’96 construction start NIM, A457, 581 (2001) NIM, A516, 390 (2004)
’97 first K+K- data’98 first e+e- data /w: PRL, 86, 5019 (2001)
’99~’02 x100 statistics in e+e- /w: PRL, 96, 092301 (’06) f ee: PRL, 98, 042501 (‘07) a : PRC, 75, 025201 (‘06)
x6 statistics in K+K-
f KK: PRL, 98, 152302 (’07)
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Detector Setup
12GeV proton
beam
Forward LG Calorimeter
Rear LG Calorimeter
Side LG Calorimeter
Front Gas CherenkovRear Gas Cherenkov
Barrel DC
Cylindrical DC
Vertex DC
B0.81Tm
Hodoscope
Aerogel Cherenkov
Forward TOF
Start Timing Counter
1m
M.Sekimoto et al., NIM, A516, 390 (2004).
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Spectrometer PerformanceL p p-
Mass spectra are well reproduced by the simulation
Ks p+ p-
M =496.8±0.3(MC 496.9±0.1) MeV/c2
s = 3.9±0.4(MC 3.5±0.1) MeV/c2
M =1115.71±0.02(MC 1115.53±0.01) MeV/c2
(s = 1.73±0.02(MC 1.62±0.01) MeV/c2)
Expected mass resolution for f = 10.7MeV/c2
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Invariant Mass Spectrum of e+e-
C Cu
we examine how well the data are reproduced with known hadronic sources & combinatorial background
we+e-
fe+e- fe+e-
we+e-
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Invariant Mass Spectrum of e+e-
C Cu
the excess over the known hadronic sources on the low mass side of w peak has been observed.
f e+e- f e+e-
we+e- we+e-
c2/dof=161/140 c2/dof=154/140
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Invariant Mass Spectrum of e+e- (background subtracted)
N/Nw<0.04(stat.)+0.09(sys.) N/Nw<0.10(stat.)+0.21(sys.)
C Cu
most of decay in nucleus due to their short lifetime; t ~ 1.3fm
/w ratio is consistent with zero. 95%C.L. allowed regions:
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Invariant Mass Spectrum of e+e-
C Cu
we examine how well the data are reproduced with known hadronic sources & combinatorial background
we+e-
fe+e- fe+e-
we+e-
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e+e- Invariant Mass Distributions
C Cuf f
[GeV/c2] [GeV/c2]• fit with MC shape & quadratic curve• a hint on the spectrum of Cu data.• longer lifetime; t~50fm kinematical dependence
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To see bg dependenceSlowly moving f mesons have a larger probability to decay inside the target nucleus.We divided the data into three by bg ( = p/m ); bg<1.25, 1.25<bg<1.75 and 1.75<bg.
bg distribution
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Invariant mass spectra of f e+e-bg<1.25 (Slow) 1.25<bg<1.75 1.75<bg (Fast)
Larg
e N
ucle
usSm
all N
ucle
us
Rejected at 99% confidence level PRL 98(2007)042501
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Model Calculationw/ medium modification
/w ee
f
, w f
m*/m 1 – k1 /w/0 1 – k1f /0
G*/G 1 1 + k2 /0
generation pointsurface uniform
a=0.710±0.021 a=0.937±0.049momentum dist. measureddensity distribution Woods-Saxon, radius: C:2.3fm/Cu:4.1fm
• dropping mass: M()/M(0) = 1 – k1 (/0) (Hatsuda & Lee)• width broadening: G()/G(0) = 1 + k2 (/0) (k2:5~10)
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Fit Results of Model Calculation
the excesses for both C and Cu are well reproduced by the model including the 9% mass decrease at 0.
m*/m = 1 - 0.092 /0
C Cu
[GeV/c2] [GeV/c2]
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Width Broadening
C Cu
k1 = 0.08 k2 = 1
the best fit values are; k1 = 9.2 ± 0.6% k2 <0.32(90%C.L.) ( Preliminary)
events[/10MeV/c2] events[/10MeV/c2]
「 GeV/c2] 「 GeV/c2]
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Invariant spectra of fe+e-
fit with modified M.C. ( k1=0.034, k2=2.6 )bg<1.25 (Slow) 1.25<bg<1.75 1.75<bg (Fast)
Larg
e N
ucle
usSm
all N
ucle
us
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Fit Results of model calculationm*/m = 1 – k1 /0, G*/G = 1 + k2
/0
The data were well reproduced with the model;
m/w decreases by 9%,mf decreases by 3% andGf increases by 3.6 at 0
Best Fit Values, w f
k1 9.2 ± 0.2% 3.4+0.6-0.7%
k2 0 (fixed) 2.6+1.8-1.2
/w 0.7 ± 0.1 (C)0.9 ± 0.2 (Cu)
-
Contours for k1 and k2 of fe+e-
syst. error is not included
prediction
0 0.5 1 /0
1
0.9
0.8
0.7
fit result /w
fit result f
m(
)/m(0
)
Contours for k1 and /w
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J-PARC E16 Electron pair spectrometer
to explore the chiral symmetry in QCDhigh momentum beam line
Hadron Hall 50-GeV PS
T1 Target
Beam Dump
Switch Yard A-Line
Split Point T0 Target
E16
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J-PARC E16 Electron pair spectrometer
to explore the chiral symmetry in QCD
107 interaction (10 X E325) 1010 protons/spill with 0.1% interaction length target GEM TrackereID : Gas Cherenkov + Lead GlassLarge Acceptance (5 X E325)
primary proton beam at high momentum beam line + large acceptance electron spectrometer
velocity dependencenuclear number dependence (p Pb)centrality dependence systematic study of mass modification
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SummaryWe have observed the excess over the known hadronic sources at the low-mass side of w. Obtained / w ratio indicates that the excess is mainly due to the modification of .We also observed the excess at the low-mass side of f, only at the low bg region of Cu data.The data were well reproduced by the model calculation based on the mass modification. The fit results show that;/w : the mass decreases by 9% at 0 .f : the mass decreases by 3%, and the width increases by a factor of 3.6 at 0.
The mass modification is not statistically significant for the K+K- invariant mass distributions.The observed nuclear mass-number dependences of fe+e- and fK+K- are consistent. – We have obtained limits on the in-medium decay width broadenings
for both the fe+e- and fK+K- decay channels.