CERN Accelerating science

• Jochen Wambach - Sun, 25 Oct 1998
  

Dear Colleagues,

in response to the comments by Ulrich Heinz on low-mass
dileptons I wish to clarify my views on this subject:

(1) I have tried to argue that the only model-independent
    conclusion that can be drawn from chiral symmetry
    is the mixing of the vector- and axial-vector correlators.
    At the chiral phase transition these have to become 
    identical. In that sense dilepton pairs clearly must
    carry the signal for chiral symmetry restoration.
    
(2) How this mixing occurs cannot be inferred from first
    principles but is subject to specific models. I 
    discussed that 'dropping vector meson masses' which
    postulate a direct relationship between the masses and
    the chiral condensate are inconsistent with low-density
    and low-temperature expansions deduced from 'chiral
    perturbation theory' and hence chiral symmetry. It
    is therefore hard to see, why such a relationship
    should hold. It can however not be excluded, at present,
    that vector meson masses drop very close to the phase 
    boundary. The 'window' must however be rather small,
    since 'chiral perturbation theory' is valid up to 
    temperatures of 100-120 MeV and baryon densities up
    to saturation density.
    
(3) I believe a more likely scenario for chiral symmetry
    restoration (at least in the I=1 channel, i.e. for
    the rho meson) is substantial broadening through
    collisions in the hadronic gas and the mixing with
    the a_1 meson. As we now know consistently from many 
    calculations collisional broadening of the rho-meson 
    in a baryon-rich environment is substantial, resulting 
    in rather featureless dilepton spectra which are able to 
    describe the data. Such a broadening is further increased
    by mixing with the a_1 meson. A 'melting of the rho meson' 
    suggests that it looses its 'identity' near the phase 
    transition and smoothly merges into the quark-antiquark 
    continuum of pQCD. As for narrow vacuum resonances such 
    as the omega- and the phi-meson the situation is less clear.
    Calculations of the broadening have not reached the same degree
    of agreement as for the rho-meson. Especially for the 
    omega meson it is also unclear how 'chiral singlets' behave
    as the phase boundary is approached. It will therefore be
    extremely important to have 'high-resolution' experiments
    to resolve the omega- and phi-resonances in the dilepton 
    spectrum.
    
    
best regards,

Jochen Wambach