1

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)

Hadron Mass

2

vacuum

higgs

vacuum

qq

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

3

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

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

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

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.