Observing chiral partners in nuclear medium

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1 Observing chiral partners in nuclear medium Su Houng Lee. Order Parameters of chiral symmetry breaking - Correlation function of chiral partners. f (8) and w meson 3. Measuring the mass shift of f (8) 4. Conclusion ef: SHL, T. Hatsuda, PD 4, 87 (996) Y. Kwon, SHL, K. Morita, G. Wolf, PD86,344 () SHL, S. Cho, IJMP E (3) 338 P. Gubler, T. Kunihiro, SHL in preparation

2 UA() breaking and chiral symmetry breaking QCD Lagrangian U u d N U L, L, F N F u U d L, L, SU U A () breaking Chiral sym breaking N SUN U F F N s GG 4 N U SU F f - Understanding the generation of hadron masses - mass? a h r? Confinement

3 Chiral symmetry restoration at finite T and r W. Weise 3% reduction at nuclear matter What will happen to hadron masses : A bridge between QCD and eperiment?. Soft modes, scalar meson: Hatsuda, Kunihiro (8,87). Pseudoscalar mesons: Bernard, Jaffe, Meissner (88), Klimt, Lutz, Vogel, Weise (9) 3. Brown-ho: 9 4. Vector mesons: Hatsuda, Lee (9) + many more 3

4 Chiral order parameter. Correlation function of chiral partners vs VV AA Cohen 96. U A () breaking effects in Correlators h' h' Hatsuda, Lee 96 4

5 Chiral symmetry breaking (m) : order parameter Quark condensate i lim TrS (,) lim Tr S(,) i S, L n= Chiral symmetry breaking order parameter : any operator that checks the eistence of this link L L L n= Casher Banks formula: nontrivial zero mode ( l =) contribution using i D l where l l l l

6 6 Other order parameters: correlator,, 4 i i d V a a,,,) ( Tr i S i S S (,) Tr ), ( Tr S S n= n= Other order parameters: V - A correlator (mass difference),, 4 i i d V a a a a,,,) ( Tr i S i S S a a n= L N c O O

7 Meson with one heavy uark : S-P, H H i, i H 4 d H V Tr S H (,) S, i S, i L n= Baryon sector : L L* T T T T u i Cd H, ui Cd H u Cd H, ucd H 4 d V Tr S(,) S, i S, S H, i L n= 7

8 U A () effect. Correlation function of chiral partners vs VV AA Cohen 96. U A () breaking effects in Correlators h' h' Hatsuda, Lee 96 8

9 U A () effect : effective order parameter (Lee, Hatsuda 96) Topologically nontrivial contributions Z dae S Glue det D m Z Z n... Z Z n u L u L n= d L n= d s L s N F n s 4 d 4 GG n nl 9

10 h correlator : n nonzero part Lee, Hatsuda (96) a a i, i i, i 4 ik d e V For SU(3) : V d 4 u 4 d d u d ys ys y permutations n u L u n= d L d const 3 s L s For SU() : Always non zero V d 4 u d d u n const u L u n= d L d For -point function: U() A will be restored when chiral symmetry is restored for N F =3 But Non trivial to check because Z but always broken for N F = Also is not good to check UA() effect when flavor is larger than that is why it is called the chiral order parameter in SU(N)SU(N) case. dae S Glue det D m

11 h mass? Witten-Veneziano formula - I P ik k i de GG, GG P k Gluons only from low energy theorem ik n i de j, j k k P P k n With uarks using s j GG 4 Large Nc argument k GG glueball GG meson P glueballs k mn mesons k m n G G G G G G G G Need h meson P Nc GG h' with m O h ' k m h ' GG h' ) P m ( k h ' N c Nc

12 W-V formula at finite density: Y. Kwon, SHL, K. Morita, G. Wolf, PD86,344 () Most model calculations GG h' m h ' P 4 3 d. r r nm G Very small change Therefore, m h ' m h /

13 How can we observe restoration of chiral symmetry. can not be directly related to physical observable in a model independent way. VV AA could be considered Whole spectrum not necessary (Glozeman: Chiral symmetry is restored for ecited states+ QCD duality) Ground states that couple to each current can be compared SS PP and VV AA r and a Both states should have small intrinsic width and eperimentally observable 3

14 How can we observe mass shift CBELSA/TAPS coll (V. Metag, M. Nanova et al) h' h 6 V w 9 9 MeV i7 MeV 37 MeV i. MeV V h ' Vacuum values Mass Width w 78.6 MeV 8.49 MeV h MeV.98 MeV 4

15 f (8) and w meson. Chiral partners VV AA. CLAS measurement

16 f (8) observation by CLAS 6

17 Light vector mesons J PC = -- Mass Width J PC = ++ Mass Width r 77. a 6-6 w f 8 4. f 4.66 f In SU(): r and a are chiral partners r a In SU(3): The I= singlet and octet states are mied ideally w L L u u d d f s s mass degeneracy between r and w : Due to suppression of disconnected diagram r u u d d Similar miing and mass degeneracy between a and f (8) L L w and f (8) are chiral partners with small width 7

18 f(8) mass shift in QCD sum rules - G G OPE -.=Q large J u u d d 4 i C ( ) d e J n n. m. n J ln Op.. Borel transformed Dispersion relation BT. OPE Cn m, M ( ) M n n n! M G n dse s / M r s r s f s M f c s s rs fe cont M M ; M f / M OPE s M f s s M f OPE cont / M M M ; s OPE cont M M ; s 8

19 f(8) mass shift in QCD sum rules - Borel curve Most important input r N m r Mass shift N 4 MeV MeV m f 8 MeV 3 MeV 9

20 f(8) measurement by CLAS at J-Lab [PC93,6 (6)] observation Missing mass analysis for h Could be done on nuclear target

21 Summary. Chiral order parameter: or VV AA. f (8) and w are chiral partners with small width: Masses are epected to change in nuclear medium by partial chiral symmetry restoration 3. Photoproduction of f (8) on proton can be generalized to nuclear target will mass of chiral partners change? 4. Direct observation of chiral symmetry restoration understand mass generation in hadrons