Questions and answers for homeworks in 4420, Sp 97

>Sorry to bother you with trivial junk like this but...

Not at all!

>
>On page 584 of F&H, the fifth decay mode of the Sigma+ is listed as
>dagger[n pi+ gamma.  I'm just wondering if this is a wild typo or did the
>particle physicists run out of greek letters, or do F&H take perverse
>pleasure in hiding footnotes?  I tried to view the particle tables on your
>web page, but I could not "display" them.  I could download some of them,
>but it would be rather time consuming with my snail of a modem.

I think it must be a typo. Either that, or it was probably a footnote
in the data tables (from which those apendices were copied!)  I think
the particle tables you want are postscript, so indeed will take time
on a slow modem. Sorry about that. (The main solution is to look up the
journal article in the library!) 

By the way, the weird entry you're looking at in F+H, just ignore the
dagger and left bracket.


>
>If trying to do problem 1 with the F&H table is unreasonable, please let
>me know.  I'm just a little too lazy to drive back into Boulder to
>photocopy from the journal.  But I'll eventually find myself over that
>way.

F+H should have enough info for parts a, b, and part of d, as well as
the rest of the homework. (Except the Clebshes, which you have a copy
of)

F+H *don't* have info about the hyperon *resonances*, which you need to
do part c and d. (The sigma 1.39) 

What you need is the link that says:

 SIGMA BARYON RESONANCES (S = -1, I = 1) 

 Sigma(1385) P(13) 
 Display or Copy PostScript file, (7 pages, 159615 bytes) 

(Yes, I guess 160kb is a bit painful, sorry!  If you just set your
modem going, perhaps it will take less time downloading that one
(actually 7) page, rather than driving back into Boulder...  (Or,
finish that problem up Monday morning:-)

Hope this helps.

Steve

>Hi, I've got one quick question for you.
>In regards to determining the quark model for the sigma + particle:
>I determined that I = 1 for sigma+, which means that I3 = 1.

I'm with you so far.

>Now, Q = 1/2 + I3, so Q = 3/2

I think this is the problem! That formula as you've written it is
*special* for the nucleon.  The factor of "1/2" on the right side is,
more generally, Y/2. (where Y is the hypercharge of the object,
A+S+...  Since you know that the sigma+ has Q=+1 (that's what the plus
means in its name!) then you can *deduce* that it must have hypercharge
of 0. Since it is a baryon (it's in the baryon section of the data
tables!) then it must have S=-1. etc. You actually got all this below, except
for the Q part...

>
>Sigma+ is a baryon, so it must be composed of 3 quarks.
>
Yup

>All quarks have Q = +/- 1/3 or +/- 2/3.

In fact, all *quarks* have Q=-1/3, or +2/3. (The opposite signs
are for the *anti*quarks, which don't make up baryons. They make up
anti-baryons)
>
>The sigma+ must have one strange quark in it so S = 1, which
>has Q = -1/3.

Yup

>There is no combination whatsoever of q's that will yield a
>total Q of 3/2 if the individual Q's are added to get a total,
>assuming all of the above conclusions are true.

Everything you say is perfect, the only mistake was right at the
beginning, where you used the un-generalized formula to relate Q and
I3. (See F+H eqn 8.30) The total Q should be 1. Hopefully that will save the
day.

>
>How the heck can the sigma+ possibly have a charge of 3/2???
>The other two q's must have a total charge of 7/6 if the charge
>on the strange quark is -1/3. I don't see any way that that can
>be true, unless there is some wierd new quark I don't know about.
>
>Any help you can give me would be appreciated!
>
>Thanks,

Does this help?