The process in nuclei and the restoration of chiral symmetry

1. Campaign of measurements of the process in N and A

2. The CHAOS spectrometer

3. The A-dependence of and comparison with theories

4. The T-dependence of the process

5. Comparison with other experimental results

6. Conclusions

CHAOS : TRIUMF, Univ. of Colorado (USA), Univ. of Regina (Canada)

Univ. of Melbourne (Australia), Univ. of Sacramento (USA)

Univ. of Tubingen (Germany), Univ. of Trieste and INFN-Ts

The measurements with CHAOS

+,- p ++,- n @ T = 243, 264, 284 and 305 MeV

CHAOS : TRIUMF, Univ. of Colorado (USA), Univ. of Regina (Canada)

Univ. of Melbourne (Australia), Univ. of Sacramento (USA) Univ. of Tubingen (Germany), Univ. of Trieste and INFN-Ts

+ A + +,- X @ T=283 and A: 2H, 12C, 40Ca, 208Pb

+ 45Sc + +,- X @ T= 243, 264, 284 and 305 MeV

The CHAOS spectrometer

Trigger hardware &particle identification

Incoming -beam

283 MeV, + 2H + - p [p]

Magnet return yoke

Magnet dipole tip

Wire chambers

45Sc+,++,-N)44X Phase Space

The invariant mass distribution

Data from the CHAOS databaseF. Bonutti et al., NPA677(2000)213; P.Camerini et al., NPA735(2004)89.

TheoryH.C.Chiang et al., NPA644(1998)77;E.Oset et al., NPA678(2000)424.

2+,++,-N)N Phase Space

C=A

(M) /T N N

(M) /T A A

T: Total x-section(M): Diff. X-section

1. C is weakly related to the detector acceptanceA

2. The normalization of (M) to T removes the dependence of the number of scattering centers.

A A

3. The ratio of (M) to (M) is loosed

from the reaction mechanism C,

since the is a quasifree process.

A A

a) Cdescribes the clear effects of nuclear matter on the system focuses on the medium modifications of meson properties.

A

b) C, a useful observable for a direct comparison between the results from different experiments.

A

A

C; A-dependence of A

C; A-dependence of A

Oset: Full model of the process, standard nuclear effects accounted for, P-wave pionic modes included and the-meson dynamically generated.

Oset and Vicente,PRC60(1999)064621

A theoretical approach to

CHAOS vs Model● Limited acceptance (, Thr.) OK●

T and d/dOs OK

● T & A input parametrs OK

VicenteOsetChiang

Chiang

Pion production in nuclei, a quasifree process N N

Pion-pole: Contact term:

2- & 3-point: N N* ; .....

N N* ;

Standard nuclear effects are accounted for Fermi motion, Pauli blocking, Pion absorption,Quasi-free elastic scattering, …….

+ + + ….….

Role of Nuclear Matter on the (

I=J=system meson dynamically generated:

2m

Role of Nuclear Matter on 'sP-wave coupling of 's to p- & -h states:

N, h

A theoretical approach to in nucleiModel: Giessen, P. Muhlich et al., PLB595(2004)216

Model: Valencia, Nacher et al., NPA695(2001)295

Data: TAPS, Messcherdorp et al., PRL89(2002)222302

Model: Giessen, based on the Valencia’s elementary process, production/propagation of ’s in A via a semi-classical BUU transport model, careful treatment of FSI, no medium effects. Conclusions: “.. The downward shift in M, which TAPS was taken as an indication for chiral symmetry restoration, is reproduced solely by ordinary final state interactions of the two outgoing pions.”

BUT,• Giessen ~ Valencia in the I=0 channel;• Giessen < Velencia in the I=1 channel;• The same threshold strength for I=0 & I=1, where the thresh. enhancement is observed.

Theories should describe the I=0,1 (or 2) channels simultaneously !!!.

C; A-dependence of A

Oset: Full model of the process, standard nuclear effects discussed, P-wave pionic modes included and the-meson dynamically generated.

Oset and Vicente,PRC60(1999)064621

Muhlich: Model based on Oset’s developed for the and reactions, better treatment of FSI of pions with the nucleus, no medium modifications.

Muhlich et al.,PLB595(2004)216

TAPS CHAOS

I=0

I=1

E~420 MeV

~ 2/30

I~0

I=2

E~420 MeV

~ 1/30

C/P.S.; A-dependence of A

Davesne: S-wave pionic modes (LM model developed for =0.50 & tad-pole diagrams) and P-wave pionic modes (P-wave coupling of ’s to particle- and -hole configurations)

Hatsuda: meson generated by the fluctuations of the <qq> chiral order parameter. The existence of implies a strong threshold enhancement of M at c

phenomenon related to the (partial) restoration of the chiral symmetry.

Hatsuda et al., PRL 63(1999)2840

Davesne et al.,PRC62(2000)024604

Chiral Symmetry and in Hadron and Nuclear PhysicsHatsudaKunihiroJido

propagator: D(,)=[2 - m2 – ,)]-1

Effective mass .

=i

: One-loop selfenergy

spectral function: M = -1/ Im D(,) = -Im ,)

2–m2–Re,)]2+[Im,)]2

Partial Restoration of the Chiral Symmetry: m m(JP= 0+) (J

P= 0

-)

LM + tad-pole diagramsMm

m

. ~ 2mcritical

tree-level

4m

. 2

spe

ctra

l fu

ncti

on

GeV

1. critical ~ 0

2. Mild resonant behaviour at 2m

3. A ()I=J=0 resonant state is not required in the vacuum

C; T-dependence of A

Vicente-Oset: av ~ 1/3regardless of T

the reaction is localized at the nucleus surface

V-O, PRC60 (2004) 064621

M (Mev)

Experimental results: TAPS and CB VS CHAOS

CB CHAOS

I = 0

p= 40 8 MeV/c

~ 1/30

I ~ 0

p= 399 MeV/c

~ 1/30

CB: A.Starostin et al., PRL85(2000)5539

CHAOS: P.Camerini et al., PRC64(2001)067601

~ the same final result !

TAPS CHAOS

I=0

E~420 MeV

~ 2/30

I~0

E~420 MeV

~ 1/30

CHAOSTAPS

1. Threshold enhancement for C(Pb/C)

2. Density probed by TAPS: ~2*CHAOS

3. C(Pb/C) doesn’t reflect the higher

density inspected by TAPS Higher densities higher pion distortions

Data: TAPS, Messcherdorp et al., PRL89(2002)222302Data: CHAOS, F.Bonutti et al.,

NPA677(2000)213

S-wave pionic modes pole-position P-wave pionic modesFinal State Interactions

; (M) appears depleted in vacuum due to strong interference effects. Nuclear matter might modify pieces of the amplitude; therefore, canceling out the interference effects and restoring a space-phase like behavior at the 2mππ threshold.

Conclusions

The simultaneous study of the I=0 and I=1, 2 channels is essential to establish the correct size of the -strength.

experimental& theoretical

The interaction is modified by the medium when

strongly

weakly

I=0

I=1,2

In-medium modification of the correlation

partial restoration of the chiral symmetry C~

A N (M) /(M) A N

Cππ is a useful observable for probing medium modification of meson (hadron) properties A

hypothesis: