1)     Write down

a)     the eigenvalue equation for the position operator. Describe briefly what property the eigenstate has.

b)     the eigenvalue equation for the momentum operator. Describe briefly what property the eigenstate has.

X |x> = xo |x>

The state describes a particle in a defienit locataion

P |x> = po |x>

The state describes a particle in a defienit momentun













2)     What is the difference between a global and a local (gauge) transformation? Explain using rotations.


turn every coordinate axis by a variable amount at each point is space =local












3)     Why are local transformations important?


They are used to generate the interaction a la general rel.













4)     Can the Σ decay by emitting a Zo ? Why or why not ? Please include the processes you considered.




For uds coupled to a uds + neutrino neutrinobar the reaction can proceed. This is the same as the Σ Λ+γ. The z0 is massive so it cant be free like th photon. About 75 MeV mass difference the z0 must then decay into neutrinos or a q qbar if there were enough mass


The available mass 1,192.642 - 1,115.683 =77 MeV no pions can be created thus e+e- and neutrinos are the ony option



































5)     Standard Model

a)     What is a Baryon?

any compound quark obj where number of quarks and anti quarks is different

typically we have 3 quark objects as baryon and qqbar as nmesons

b)     What is flavor?

a label for each of the types of quarks: up, dwon strang charm


c)     What is a meson?

q qbar equal number of quaks and anti quarks


d)     What is an exotic hadron?

anything other than a qqbar or qqq


e)     What is isospin?

inernal Q# that puts up/down into doblet






















1)     Which of the following interactions should occur? If the reaction is possible what force causes the reaction. If the interaction doesnt occur what reasons can you use to rule it out?




Reason or Force



Weak decay doesnt conserve energy







Weak pion beta decay






Charge conservation


Weak (no charge for neutrino)


flavor changing neutral current Zo


Baryon number udsu(dbar) not conserved.


2)     Provide as many distinct lowest order Feynman as possible for the following reactions:






















3)     For classical Coulomb scattering of an electron from a very massive + target, the impact parameter is related to the scattering angle as shown below. Express the cross section in terms of rather than. Dont worry about the overall sign of your answer.








4)     CP violation

a.      Kaons have been observed to decay into two and three pion final states. What does that imply about parity and why?

parity not onserved

b.     What is the parity of the two pion state?


c.      The mass eigenstates of the kaon are the and .What happens to these states under C and P.

CP|K> = |K> and CP|K> = |K>

d.     Construct new states that are eigenstates of CP K1, K2.

| KS> = ( |K> + |K> ) / 2 with CP = +1

|KL> = ( |K> - |K> ) / 2 with CP = -1


e.      Are these the states that are experimentally observed via 2 pion and three pion decay? Why or why not?

almost but very rarely there can be a decay to the

f.       Given that CP is violated what other transformation is must have a small associated violation?

time reversal