“Exotic” hadron-hadron S-wave Interaction Bing-song Zou IHEP, Beijing

Outline 1.“Exotic”  S-wave Interaction Why interested ? How “exotic” ? Similarity between  and  N s-wave scattering What’s the nature of the broad  ? Why it appears narrower in production processes ? Why f 0 (980)’s peak width is so narrow ? 2.   S 0  pp & I=1  S 0  pp near threshold enhancement 3. K  S-wave near threshold enhancement in J/    p K -  vs p p   p   

1.“Exotic”  S-wave Interaction Why interested ? 1) a fundamental strong interaction process and a necessary input for many reactions involving multi-pions 2) I=0  S-wave has the same quantum number of f 0 resonances which include :  /f 0 (600) (  -model,  exchange for NN interaction) and the lightest glueball candidate f 0 (1500)/f 0 (1710)    f0f0

How “Exotic”      pp

CERN-Munich data: B.Hyams et al., Nucl. Phys. B64 (1973) 134.

Exotic I=0 S-wave I=0 D-wave I=1 P-wave I=1 F-wave  (770)   (1690) f 2 (1270) D.V.Bugg, A.Sarantsev,B.S.Zou, Nucl. Phys. B471 (1996) 59

 phase shifts 

 inelasticity 

“Exotic”  S-wave interaction : broad  background with narrow resonances as dips instead of peaks

    p  I=0)  (I=1/2)  N  (I=1/2) Similarity for  and  N s-wave scattering

What’s the nature of the broad  ? Important role by t-channel  exchange for all these processes          =0 = - 2 K  I=2    =1/2 = - 2 K  I=3/2 D. Lohse, J.W. Durso, K. Holinde, J. Speth, Nucl.Phys.A516, 513 (1990) B.S.Zou, D.V.Bugg, Phys. Rev. D50, 591 (1994)

Basic features of I=2  Interaction F.Q.Wu, B.S.Zou et al., Nucl. Phys.A735 (2004) 111 repulsive force by t-channel  attractive force by t-channel f 2 Inelasticity by  S-wave

An important cause for hadron-hadron S-wave interactions appearing “exotic” is t-channel meson-exchange amplitude has a comparable strength as s-channel resonance contribution for S-waves. For higher partial waves, s-channel resonance contribution dominates.

Why broad  appears narrower in production processes than in  elastic scattering? T el = K / ( 1 - i  K ) = K + K i  K + K i  K i  K + … T prod = P / ( 1 - i  K ) = P + P i  K + P i  K i  K + …

el prod T el from Bugg,Sarantsev,Zou Nucl. Phys. B471 (1996) 59 with  pole at ( – i ) GeV T prod = T el * P / K, K = tan  assuming P=1

How about production vertex P ? P(V ’  V     ) T. Mannel, R. Urech, Z. Phys.C73, 541 (1997); Ulf-G. Meißner, J.Oller, Nucl.Phys. A679 (2001) 671; L. Roca, J. Palomar, E. Oset, H.C.Chiang, Nucl. Phys. A744 (2004) 127 F.K.Guo,P.N.Shen, H.C.Chiang, R.G.Ping, Nucl.Phys.A761 (2005) 269 For  ’  J/    , E  small, 1 st term dominates  higher  peak For      , E  large, 2 nd term dominates  lower  peak  peak position is process dependent ! P ~ c 1 + c 2 s

 ’  J/     BES, Phys.Rev. D62 (2000) BES, Phys.Lett. B598 (2004) 149

Why f 0 (980)’s peak width is so narrow ? BES, hep-ex/ M = 965 MeV g 1 = 165 MeV 2 r = g 2 /g 1 = 4.21 r = 0 r = 4.21 Strong coupling to  KK strongly reduce the peak width of f 0 (980)

B.S.Zou, hep-ph/ , “  S-wave interaction and 0 ++ particles” 0 ++ particles with substantial couplings to  :  /f 0 (600), f 0 (980), f 0 (1500), f 0 ( )

BES II Preliminary f 0 (1790) ? BES collaboration, hep-ex/

  S 0  pp & I=1  S 0  pp near threshold enhancement |M| 2 BES Both arbitrary normalization BES, Phys. Rev. Lett. 91, (2003) J/  →  pp p p  p p  COSY-TOF, Eur.Phys.J.A16, 127 (2003)

One-Pion-Exchange and BES pp ( 1 S 0 ) near threshold enhancement Zou B.S., Chiang H.C. Phys.Rev.D69 (2004) NN interaction : 9 (S, I ) = (0,0) 1 (S, I ) = (1,1) -3 (S, I ) = (1,0) or (0,1) {  NN interaction : I=0,  pp ( 1 S 0 ) gets the biggest attractive force ! deuteron

One  exchange FSI &  exchange FSI

 exchange FSI & full FSI by A.Sibirtsev et al. hep-ph/

A.Sibirtsev, J. Haidenbauer, S. Krewald, Ulf-G. Meißner, A.W. Thomas, hep- ph/ P-wave I=0 s-wave I=1 s-wave

Pure I = 1 (I=0) + (I=1) Near threshold enhancement for I=0  NN annihilation E. Klempt, F. Bradamante, A. Martin, J. Richard, Phys. Rept. 368 (2002) 119

BES, Phys. Lett. B472 (2000) 207 PWA Results on J/  to 4  BES, Phys. Lett. B446 (1999) 356 J/  0 -+ resonances decaying to meson channels 0 - +

In summary,  pp near threshold enhancement is very likely due to some broad sub-threshold 0 -+ resonance(s) plus FSI.

3. K  s-wave near threshold enhancement complimentary BES and COSY experiments J/    P K -  vs P P   P    P  &  P  the same  t-channel interaction K -  &    the same interaction  P K - for  * P K + for pentaquarks

Events/ 10 MeV NxNx NxNx NxNx PS, eff. corrected (Arbitrary normalization) Near-threshold enhancement in M K 

BES Collaboration, Phys. Lett. B510 (2001) 75

B.C.Liu and B.S.Zou, Phys. Rev. Lett. 96 (2006) From relative branching ratios of J/    p  N*  p (K-  p (  p  g N*K  /g N*p  /g N*p  ~ 1.3 : 1 : 0.6 Smaller N*(1535) BW mass previous results 0 ~ 2.6 from  N and  N data

P P   P    with  g N*K  /g N*p  = 1.3 without N*(1535) K.Tsushima, A.Sibirtsev, A.Thomas, Phys.Rev.C59 (1999) 369 with N*(1535)

(1) (2) (3) Mass of N*(1535)

A.Zhang, Y. Liu, P. Huang, W. Deng, X.Chen, S.L. Zhu, hep-ph/ : 1/2- and 1/2+ octet N* pentaquarks have similar masses in Jaffe-Wilczek diquark model N*(1535) ~ uud (L=1) +  [ud][us]  s + … N*(1440) ~ uud (n=1) +  [ud][ud]  d + …  *(1405) ~ uds (L=1) +  [ud][su]  u + … Larger [ud][us]  s component in N*(1535) makes it coupling stronger to N  & K , weaker to N  & K  and heavier ! B.C.Liu, B.S.Zou, PRL 96(2006) u d du qq u du qq SS  q ½+ [ud] } L=1  q ½ - [ud] [us] } L=0

Summary for our study on J/    P K -  and P P   P    1)  near-threshold enhancement due to N*(1535) with g N*K  /g N*p  = 1.0 ~ 1.6 compatible with all  data 2) Larger [ud][us]  s component in N*(1535) makes it coupling stronger to strangeness and heavier !