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Hi everybody,

This is short clarification about the low mass dileptons. The question
was: HOW THE CALCULATED RHO MODIFICATION, in whatever model, IS
RELATED TO CHIRAL RESTORATION.

(I replied to Uli about dileptons last Fri., and now we all got a msg from 
Wambach. I think it is helpful to restate the points I tried to make
at Chamonix on this once again.)

Answer 1 (the strict one): suppose IN THE SAME MODEL one calculates
axial (a1) modification. Then strict (Weinberg-type finite T) sum
rules coming directly from QCD (see a paper by Kapusta and myself, PRD
1994) tells you that some integral of their difference is $f_\pi(T)$
and another integral is basically the condensate $<\bar q q(T)
>^2$. The discussed modifications are all of a type, that these
integrals would be LESS THAN IN VACUUM. So THERE IS a relationto
chiral restoration. At the restoration point both integrals should
vanish.

Answer 2 (not a strict one, but a CONJECTURE): IN A SO called mixed
phase (whether there is really the first order or just smooth rapid
cross over, does not matter) we expect some continuity between all
quantities, when we approach the QGP. VECTOR AND AXIAL: SPECTRAL
DENSITY should do this as well. Therefore we expect MORE THAN
VANISHING DIFFERENCE between them. We expect resonances to be melted
and that BOTH should tend to the so called PARTONIC RATE, typical for
quark annihilation. The latter should have a certain magnitude down to
twice quark effective mass(T), which is expected to be relatively
small around T_c.  (As noticed in my paper with M.Hung, the
perturbative Klimov-Weldon mass is only about a pion mass, at T_C...)

For example, a scenario when rho and a1 move half way TOWARD EACH
OTHER and nothing else changes (e.g. as Pisarski proposed some time
ago based on some hadronic Lagrangian) would be ACCEPTABLE for point
1, showing the chiral restoration, but UNACCEPTABLE for point 2.

Existing CERES data are, from my perspective, surprisingly supportive
to conjecture 2. If the dilepton production rate in all of the mixed
phase region (say, defined by the energy density .2 to 2 GeV/fm) be
the PARTONIC RATE already, it would describe them rather well (several
hints from others such as Zahed et al, also R.Rapp and myself, in
progress).

(Finally, to avoid confusion: a q. asked by Berndt at Chamonix was how
this agrees with the earlier statements that the QGP radiation DOES
NOT explain dilepton data. A: In those works the partonic rate was
applied to the QGP part of space-time ONLY, while now I am speaking
about using it DURING THE WHOLE MIXED PHASE, ``hadron part"
included. This makes a big difference in absolute magnitude, since
dilute hadron part occupy larger space-time volume.)

Does it mean we have a QGP features at rather low energy density
already?  Well: the data quality is expected to improve dramatically
due to the detector upgrade. Thus I would wait a bit before making
such an important conclusion...