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Physics 222 UCSD/225b UCSB

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.

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Physics 222 UCSD/225b UCSB

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

  2. 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.

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

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

  5. Where the sign comes from • You express the B0 as superposition of BH and BL in order to be able to do the time evolution trivially. • After the time evolution is done, you then “contract” the BH and BL into the final state. • This gets you another chance for picking up a sign.

  6. BH -> f gives you a “p A” BL -> fbar gives you a “-q Abar” … and so forth. B0 = (BH + BL )/2p B0bar = (BH - BL )/2q … so there’s another place with a minus sign.

  7. = Anatomie of these Equations (1) Unmixed: = Mixed: |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!

  8. = Anatomie of these Equations (2) Unmixed: = Mixed: 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.

  9. 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|.

  10. = Anatomie of these Equations (3) Unmixed: = Mixed: 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.

  11. Relationship between Eigenstates We have: mass eigenstates = BH and BL flavor eigenstates = B0 and B0 CP eigenstates = B+ and B- Define CP eigenstates: => Where we have used that B0 is a pseudoscalar meson.

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