The first exam is over. There is not that much to say about it, it's just over. But afterwards I allways ask myself why I've been so nervous. Anyway I had a nice weekend off and
finally found my "dejeuner en fourrure" of Meret Oppenheim at the
MoMA. The last time I was there, the last time I had guests from Switzerland, I missed it.
Thanks to
Martin for figuring out
this decay. It is a double weak decay.
|s> --W
---> |u>
|u> --W
+--> |d>
The W
- and the W
+ combine to form the Pi
0. But I still don't know why this decay is so dominant (it is over 99% of all Xi
0 decays) over the following:
|ssu> --W
---> |uus> = Sigma
+
with only one W exchange. The mass differences aren't
that big.
When I post physics problems here, it is just to get rid of them. Because when I reread them after a certain time, I normally must admit that they resulted by a misunderstanding of mine. So I hope this will again be the case. I apologize for boring those of my readers who don't care about details of particle physics. I know, I only
state these problems here without explanation. So it is quite impossible to understand for non-physicists. That's worse for me though, since you can't help me with some nice hints.
Ok, then:
How does the following decay take place?
Xi0 = |ssu> ->
Lambda = |uds> +
Pi0 = |uuBar> + |ddBar>
It must be a
weak charged current
as far as I know these are the only flavour changing decays. But there is nothing charged about it. The initial and the final state particles are all neutral.
Nevertheless it is the dominant decay for the Xi
0, (see the
Particle Data Group page.)
Good the Olympics are on their way, so people might forget about this ridiculous Rechtschreibereform. It's a shame, but it made its way through to
Preposterous.
Anyway most people probabely think we are most happy here in Germany since we have time to complain about the bad influence of "Schifffahrt" on our kids.
The
answer to question two is quite simple:
It turned out that the wavefunction corresponding to Spin * Space * Flavour
of a Baryon is symmetric under exchange of any two quarks. That was the
reason why the coulour quantum number was postulated in the first place.
Let's write the wavefunction of a Baryon as a product
psi = J(Spin) * S(pace) * F(lavour) * C(oulour)
Now consider a Baryon consisting of three quarks of the same flavour,
say the Delta++.The F function must be symmetric otherwise
it vanishes.So J and S have to be both antisymmetric or both symmetric.
if they are both antisymmetric the S part can't be build by a product of
three groundstate wavefunctions since that again would vanish.
So the lightest possible Baryon with identical quark content is the
one with symmetric S and J (and F)
you expect all of the quarks to have an s-wavefunction and therefore they must
have parallel Spins J = 3/2.
Some
more questions on particle physics:
- Suppose the light quarks u,d,s were really mass degenerate, then the lightest Mesons would split in a singlett (eta_1) and an octett with the flavour neutral states pi_0 and eta_8. The wave function for these states are
|pi_0> = (|d dBar> - |u uBar>)
|eta_8> = ( |d dBar> + |u uBar> -2|s sBar>)
respectively.
Do these particles have exactly the same quantum numbers? And if they do, how do you know that they both exist? Just because group theory tells you that there is an octett.
The physical eta particles are heavier than the pi_0 and can decay into to 3 pions, is this still possible if there were perfect mass degeneracy? Because then you could identify the eta_8 through this decay mode. But still, how do you know that you are observing a eta decaying say to gammas rather than a pion?
-
Baryon multipletts: There exists a decuplett with J = 3/2, and an octett with J = 1/2. The decuplett states with at least two different quark types can be considered as excited states of the octett. But the Delta- (|ddd>), Delta++ (|uuu>) and the Omega(|sss>) have no counterpart in the octett. So why must the spins of identical quark flavours be aligned?
Some things I would do if there weren't these exams:
- an extensive tour on the "marche aux puces" of this town. (I really don't know the English expression for it, but I am improving anyway, I remember the day when didn't know the German word for "Brockenhaus", i.e. "Trödler".)
- go to Neukölln to visit the church St. Schutzengel, (it is about to be sold, see the actual Zitty magazine, or contact the catholic (if I remember it correctly) church if interested.)
- go on another bike trip, just a little bit longer than the last one and to a region with some nice mountains to climb.
Schau an, da gibt es nicht weit von
meiner Heimat eine
Magdalena Einsiedelei und ich wusste nix davon. Das ist ja mal ein Spaziergang ins Freiburgische wert.
Wenn nun auch Frau Buhlmans
Verbot von Studiengebühren fällt, und die unionsregierten Länder Gebühren einführen, die SPD regierten hingegen nicht, dann könnte das tatsächlich zu einem zwei Klassensystem führen. Denn die Studenten, die die Gebühren nicht zahlen wollen, oder nicht zahlen können und keinen Kredit aufnehmen wollen, werden in SPD Lande umsiedeln und diejenigen, die reich genug sind oder aber für eine bessere Ausstattung und eine bessere Betreuung (was hoffentlich ein sekundär Effekt von Gebühren = mehr Geld, und studentischer Abwanderung = besseres Verhältnis von Lehrenden zu Studenten, ist) bereit sind, sich zu verschulden, werden in CDU Lande ziehen.
Well, I am still surfing the web instead of studying. There is a nice
post of Chad Orzel on a phycisists every day life.
Chemical elements, biological species and mountains are often called after their discoverer or the place where the have been found. (At least the ones you don't encounter in an normal Western everyday life.) Particles aren't, with two exceptions: the J of the J/psi and the
Higgs. But Mr. Ting at least conformed with the naming standard of the particle community, reducing his name to a letter. (J is similar to the Chinese sign for Ting). So there remains the Higgs. (I don't now who called it "Higgs", most probabely it wasn't
Peter Higgs himself).
But maybe there is no Higgs at all, that would save the matter.
