Dear Flemming,
I was planning to submit the corrected one you sent back to me.
As for (pbar/p)**1/3 that just comes from quark counting.
In a thermal model
dN/dP = (Spin Factor) *(Factor of T/M) * exp Mu/T * phase space
density.
For antiparticle/particle ratios everthing cancels except the chemical
potentials. In principle one has 3 chemical potentials for up, down and strange
quarks (ignoring charm, bottom and top). The diffent potentials for up and down
are required to conserver electric charge but in practice the difference between
them is very small. Let mu_q = the potential for a light (up or down) quark and
mu_s be the potential for a strange quark.
Then (pbar/p) = exp -3mu_q/exp (3mu_q/T) since protons have 3 light quarks
= exp(-6mu_q/T) (1)
Kaons have one light quark and one strange one so
k-/k+ = exp((mu_s-mu_q)/T)/exp-(mu_s-muq)/T)
= exp(2mu_s/T) * exp -2Mu_q/T
= exp(2mu_s/T) * (pbar/p)**1/3 (2)
For e+e- k-/k+=pbar/p=1 ==> mu_q = mu_s = 0
The data in Figure 4 approach (pbar/p)**1/3 as (pbar/p)==>1 but the AGS data
are way above, implying a positive strange chemical potential. Thus one
can vu figure 4 as showing that the strange chemical potential decreases
with sqrt(s). The fact that there is one universal curve
implies local strangeness conservation since this implies a constraint on
mu_s. Another way of interpreting k-/k+=(pbar/p)**1/4 uses Eqn (2)
(pbar/p)**1/4=exp(2mu_s/T)*(pbar/p)**1/3
(pbar/p)**-1/12=exp(2mu_s/T)
Using (1) and taking logs gives
-1/12 * -6 mu_q/T = 2 mu_s/T
or mu_S = 1/4 mu_q
This looks like a nice result.
Yours Michael
Quoting Flemming Videbaek <videbaek@sgs1.hirg.bnl.gov>:
> Dear Michael
>
> Could you give me the final version of your abstract as well as indicate
> if
> it has been submitrted.
> And too thanks for your comment to the paper. Is it easy to see that a
> thermal model with constant u give p/p**1/3?
> The we should amke a point of this in the paper; PRL is 'general' so
> such
> simple relsations should be stressed.
>
> Flemming
>
>
> ------------------------------------------------------
> Flemming Videbaek
> Physics Department
> Brookhaven National Laboratory
>
> tlf: 631-344-4106
> fax 631-344-1334
> e-mail: videbaek@bnl.gov
> ----- Original Message -----
> From: "Michael Murray" <murray@CyclotronMail.tamu.edu>
> To: <brahms-l@bnl.gov>
> Sent: Saturday, June 29, 2002 6:32 PM
> Subject: Re: Draft Abstract for Fall DNP Meeting (Michigan State
> University)
>
>
>
>
>
Michael Murray, Cyclotron TAMU, 979 845 1411 x 273, Fax 1899
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