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  +  +,- 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  +  +,- T  =283 and A: 2 H, 12 C, 40 Ca, 208 Pb  + 45 Sc  +  +,- T  = 243, 264, 284 and 305 MeV

The CHAOS spectrometer Trigger hardware & particle identification Incoming  - beam 283 MeV,  + 2 H  +  - p [p] Magnet return yoke Magnet dipole tip Wire chambers

45 Sc  +,  +  +,- N) 44 X Phase Space The  invariant mass distribution Data from the CHAOS database F. Bonutti et al., NPA677(2000)213; P.Camerini et al., NPA735(2004)89. Theory H.C.Chiang et al., NPA644(1998)77; E.Oset et al., NPA678(2000)  +,  +  +,- N)N Phase Space

C   = A  (M  ) /  T N N A A  T : Total x-section  (M  ): Diff. X-section 1. C  is weakly related to the detector acceptance A 2. The normalization of  (M  ) to  T removes the dependence of the number of scattering centers. AA 3. The ratio of  (M  ) to  (M  ) is loosed from the reaction mechanism C , since the  is a quasifree process. A A a) C  describes 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

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 p -> pp CHAOS vs Model ● Limited acceptance ( W, Thr.)OK ● s T and d s /d Os OK ● T & A input parametrsOK Vicente Oset Chiang Pion production in nuclei, a quasifree process p N -> pp N Pion-pole:Contact term: 2- & 3-point: N N* D ;......pN.pN N N* D ;. p N Standard nuclear effects are accounted for Fermi motion, Pauli blocking, Pion absorption, Quasi-free elastic scattering, …… …. Role of Nuclear Matter on the ( pp) I=J=0 system s- meson dynamically generated : 2m p Role of Nuclear Matter on p 's P-wave coupling of p's to p- & D-h states: p p N, D h

A theoretical approach to  in nuclei Model: Giessen, P. Muhlich et al., PLB595(2004)216 Model: Valencia, Nacher et al., NPA695(2001)295 Data: TAPS, Messcherdorp et al., PRL89(2002) 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) 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  ~ 2/3  0     I~0     I=2 E~420 MeV  ~ 1/3  0

C  / P.S.; A-dependence of  A Davesne : S-wave pionic modes (L  M model developed for  =0.5  0 & 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 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 s in Hadron and Nuclear Physics Hatsuda Kunihiro Jido s propagator: D s ( w, r )=[ w 2 - m 2 s – S s (w, r )] -1 Effective mass. r=0, S s =ie. s, p s S s : One-loop selfenergy s spectral function: M s = -1/ p Im D s ( w, r ) = -Im S s (w, r ) [w 2 –m 2 s – Re S s (w, r )] 2 +[Im S s (w, r )] 2 Partial Restoration of the Chiral Symmetry: m s m p   s (J P = 0 + ) p (J P = 0 - ) LsM + tad-pole diagrams M s (w ~2p) = -p [Im S s (w,r)] -1   ~ Q(w-2 m p )(1- ) -1/2. w ~ 2m p  r critical tree-level 4m 2. w 2 p. s spectral function GeV 1. r critical ~ r 0 2. Mild resonant behaviour at 2m p 3. A ( pp ) I=J=0 resonant state is not required in the vacuum

C  ; T-dependence of  A  Vicente-Oset:  av ~ 1/3   regardless of T the reaction is localized at the nucleus surface V-O, PRC60 (2004)

M  (Mev) Experimental results: TAPS and CB VS CHAOS CB CHAOS     I = 0 p  = 40 8 MeV/c  ~ 1/3  0     I ~ 0 p  = 399 MeV/c  ~ 1/3  0 CB: A.Starostin et al., PRL85(2000)5539 CHAOS: P.Camerini et al., PRC64(2001) ~ the same final result ! TAPS CHAOS     I=0  E~420 MeV  ~ 2/3  0     I~0  E~420 MeV  ~ 1/3  0 CHAOS TAPS 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) Data: CHAOS, F.Bonutti et al., NPA677(2000)213

S-wave pionic modes pole-position P-wave pionic modes Final 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 2m ππ 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 C ππ is a useful observable for probing medium modification of meson (hadron) properties A hypothesis: