Physics 222 UCSD/225b UCSB Lecture 17 Comments to HW2

Concept for measuring  m Measure the flavor of the meson at production. –Referred to as “flavor tagging” Measure the flavor at decay. –Via flavor specific final state. Measure meson momentum and flight distance. –Calculate proper time from this. Put it all together to measure probability for finding a meson with opposite flavor at decay from the flavor at production. –Do this as a function of proper time.

Mixing Probability for meson to keep its flavor: Probability for meson to switch flavor:

Important Sign Probability for meson to keep its flavor: Probability for meson to switch flavor:

Where the sign comes from You express the B 0 as superposition of B H and B L in order to be able to do the time evolution trivially. After the time evolution is done, you then “contract” the B H and B L into the final state. This gets you another chance for picking up a sign.

B H -> f gives you a “p A” B L -> fbar gives you a “-q Abar” … and so forth. B 0 = (B H + B L )/2p B 0 bar = (B H - B L )/2q … so there’s another place with a minus sign.

Anatomie of these Equations (1) = Mixed: = Unmixed: |q/p| =1 unless there is CP violation in mixing itself. |A| = |A| unless there is CP violation in the decay. We will discuss both of these in more detail in next lecture!

Anatomie of these Equations (2) = Mixed: = Unmixed: cos  mt enters with different sign for mixed and unmixed! Unmixed - Mixed Unmixed + Mixed = Assuming no CP violation in mixing or decay. Will explain when this is a reasonable assumption in next lecture.

What’s swept under the rug: I was cavalier here, (well you were supposed to figure this out in the homework). Unmixed = Mixed = For CP violation you then can take: = Where we assumed here that |A| = |Abar|.

Anatomie of these Equations (3) = Mixed: = Unmixed: Now assume that you did not tag the flavor at production, and there is no CP violation in mixing or decay, i.e. |q/p|=1 and |A| = |A| All you see is the sum of two exponentials for the two lifetimes.

Relationship between Eigenstates We have: mass eigenstates = B H and B L flavor eigenstates = B 0 and B 0 CP eigenstates = B + and B - Define CP eigenstates: => Where we have used that B 0 is a pseudoscalar meson.