Dear Steve,
I first saw antiparticle/particle ratios expressed in terms of
chemical potentials in a talk by Rafelski. The mu_s=mu_q/4 is unique to us
since no-one has shown such a wide range of pbar/p vs k-/k+ yet.
Michael
Quoting "Stephen J. Sanders" <ssanders@ku.edu>:
> Dear Jens Jorgen,
> Thanks for the clarification on the calculation! I was missing the
> second term in the k-/k+ ratio. Is there a good reference for
> this? Just based on the papers that we cite, I would have taken
> the particle production to scale as
> 1/exp[{E - mu_b B - mu_s S}/T],
> with B and S being the baryon and
> strangeness numbers for the resulting hadrons.
>
> Regards,
> Steve
>
> on 7/7/02 5:36 AM, Jens Jørgen Gaardhøje at gardhoje@nbi.dk wrote:
>
> > Dear Steve,
> > Thanks for your precise and relevant comments. They are now in version
> 3.05,
> > which I will however not circulate until monday evening - to minimize
> > confusion among the crowd.
> >
> > The Becattini curve has yet to find its way into figure 4. (CLAUS !?)
> >
> > I have gone through the calc. again and find no mistake in the
> relationship
> > mu_s=1/4 . mu_q.
> >
> > pbar/p = exp( -2mu_b/T) = exp(-6mu_q/T)
> >
> > k-/k+ = exp( 2 mu_s/T) . exp( -2 mu_q/T) ; since K- has an anti-u and
> a s,
> > and antiparticles contribute with opposite sign chem. pot. etc.
> >
> > This leads to the relation k-/k+= exp(2mu_s/T) . (pbar/p)**1/3 (1)
> >
> > We observe k-/k+ = (pbar/p)**1/4.
> >
> > equating k-/k+ above with the RH side leds to the quoted identity.
> >
> > Another approach would have been to fit the data to an expression like
> (1)
> > and let mu_s and T vary. => CLAUS CAN YOU DO THAT??
> >
> > Please let me know if we agree on the formalism.
> > cheers
> > JJ
> >
> >
> > ____________________________________________________________
> > Jens Jørgen Gaardhøje, Assoc. Prof., Dr. Sc.
> > Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark.
> > Tlf: (+45) 35 32 53 09, secr. (+45) 35 32 52 09, Fax: (+45) 35 32 50
> 16.
> > UNESCO Natl. Comm., secr. (+45) 33 92 52 16.
> > Email: gardhoje@nbi.dk.
> > ____________________________________________________________
> >
> >
> > ----- Original Message -----
> > From: "Stephen J. Sanders" <ssanders@ku.edu>
> > To: <brahms-l@bnl.gov>
> > Sent: Saturday, July 06, 2002 11:34 PM
> > Subject: Comments on version 3.04
> >
> >
> >> Dear Jens Jorgen and Claus,
> >> Overall the paper seems to tell an interesting story. Nice job.
> >> Some comments:
> >>
> >> PRL required full postal addresses. For the US institutions, this
> means
> > you
> >> will need to
> >> supply the states and postal zip codes.
> >>
> >> Abstract:
> >> "ratios at midrapidity" (typo in draft)
> >> "from mu_b=120 MeV at forward rapidity to mu_b ~25MeV at
> mid-rapidity"
> >> (otherwise the reader will
> >> assume a parallel structure to the previous sentence where one
> >> goes FROM midrapidity TO
> >> forward rapidity)
> >>
> >> Paragraph 1.
> >> "...considerable transparency is expected for Au+Au collisions, even
> > for
> >> central events."
> >> (current sentence is poorly formed and confusing)
> >> "...near midrapidity and pbar/p and K-/K+ particle number ratios
> with
> >> values near unity."
> >> (current sentence poorly formed...)
> >> "...described above, reminiscent..." (remove "a" before
> reminiscent)
> >>
> >> Paragraph 3.
> >> "...ratios are approaching unity, with values of 0.75+-0.04(pbar/p),
> >> 0.95+-0.05(K-/K+), and
> >> 1.01+-0.04(pi-/pi+), respectively."
> >> (What does "over 0.95+-0.05" mean?!!!! Is this a claim that we
> don't
> >> believe the quoted uncertainty?
> >>
> >> Paragraph 5.
> >> "p=5.5 and 8GeV/c, respectively." (add comma)
> >>
> >> Paragraph 6.
> >> "The primary event trigger was based on two Zero Degree Calorimeters
> >> (ZDCs) located +/-18m
> >> from the nominal IP [12]. The reaction centrality was determined
> > using
> >> a plastic
> >> scintillator tile array surrounding the intersection region[7,8,12].
> >> Beam-Beam Counters (BBCs),
> >> consisting of two arrays of Cherenkov radiators positions +-2.15 m
> > from
> >> the IP, measured charged
> >> hadrons in the pseudorapidity range 3.0<|eta|<3.8. For the 25% most
> >> central collisions, the BBCs
> >> allow collision vertex determination with a resolution of sig_z~0.65
> > cm
> >> and supply the start time
> >> for the time-of-flight measurement with sig_t<~30 ps."
> >> (Otherwise ZDC is used in Paragraphs 8, but never defined.)
> >>
> >> Paragraph 8.
> >> "...expected \beta^{-1} vs. momentum behavior for..." (add
> behavior)
> >> "...BBC-ZDC..." (We used BBC in the multiplicity papers and it
> > would
> >> be nice to be consistent...)
> >>
> >> Paragraph 9.
> >> "In the MRS the background contribution to the proton yields,
> > arising
> >> mainly..." (Otherwise,
> >> I'm not sure what is meant by "from protons"...)
> >>
> >> Paragraph 11.
> >> "{\it etc.}" (add period to indicate abbreviation of "et cetera")
> >>
> >> Paragraph 12.
> >> "Systematic uncertainties are estimated as 2% in the case of pions
> > and
> >> kaons and as 4% in the case
> >> of protons." (Both instances of "to" should be changed to "as".)
> >>
> >> "...invariant plateau around midrapidity as proposed by Bjorken."
> > (add
> >> "as")
> >>
> >> Paragraph 14.
> >> (Here I am suggesting a rewording that would have made this
> > discussion
> >> clearer to me after reading
> >> the EARLIER Braun-Munzinger papers, which we don't cite. However, I
> >> am also not
> >> getting your expression of mu_s=1/4 mu_q, so I may be missing
> >> something else....(I find
> >> mu_s = mu_b/4 rather than mu_q/4))
> >>
> >> " ...expressed by a power low K-/K+=(pbar/p)^{1/4}. The exponent
> > gives
> >> the scaling factor between
> >> the strange and baryon chemical potentials. For a vanishing
> >> strange-quark chemical
> >> potential \mu_{qs}, this
> >> exponent is expected to have a value of 1/3 (where mu_{qs}=\mu_B/3 -
> >> \mu_S). The present
> >> result sugests \mu_S = \mu_B / 4."
> >>
> >> Figure Caption 4.
> >> Becattini results stated in caption is not shown (on my figure...)
> >>
> >> Regards,
> >> Steve
> >>
> >>
> >>
> >
>
Michael Murray, Cyclotron TAMU, 979 845 1411 x 273, Fax 1899
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