Download Chapter 8, Lecture 1

Nuclear Physics and Quantum Mechanics: Neutron Stars
At the end of their lives, nucleosynthesis in stars stops and the
stars collapse to white dwarfs.
In white dwarfs, the gravitational force is balanced by
“electron degeneracy”. [According to the Pauli-exclusion
principle, no two electrons (fermions) can occupy the same
quantum mechanical state.]
If the star is too massive, M>1.4 Msun (the Chandrasekhar
limit), the electrons become relativistic and P~n5/3  n4/3.
The electron degeneracy pressure is no longer sufficient and
the white dwarf collapses further.
Here the reaction e + p  n + νe takes place. The degeneracy
of the neutrons (fermions) prevents further collapse up to the
Oppenheimer-Volkov limit. Neutron stars.
Pulsars: rapidly
rotating
neutrons stars
with strong
magnetic fields.
The core of the
neutron star is
believed to be
an unusual state
of nuclear
matter.
A strange quark
star may also be
possible.
(Area of current
research)
Today’s Plan
Review Chapter 8: meson mixing and CP
violation
Schedule student presentations
Schedule Final Exam
(two options: Friday May 5 or Monday May 8).
Fill out ECAFE forms.
https://www.hawaii.edu/ecafe/
Review of Chapter 8
Question I:
K 0 , K 0 are eigenstates of the (weak, strong, EM) interaction
Question II:
K10 , K20 are eigenstates of the (weak, strong, EM) interaction
Answers: strong, weak
Ans: Also called the K-short and Klong
Question: Suppose
you start with a pure
K0 beam, what
happens to it as a
function of time ?
Question: How do the
lifetimes of the K1 and
K2 compare ?
QM: Anti-K0
spontaneously
appears
Question: How can one observe kaon mixing in experiment ?
Hint: What are the weak semileptonic decays of neutral kaons to pions ?
(remember the quark content of neutral kaons)
Hint: How can one distinguish a neutral kaon and its antiparticle ?
K 0 ® p -l +n l ; K 0 ® p +l - n l
Gjesdal, S. et al. (1974); Phys. Lett. 52B 113
Question:
What is δ in
this plot of
data ?
Ans: ASL,
semileptonic
asymmetry
d (t) º P + (t) - P - (t) = e
-G st
2
cos(Dmt)
Feynman diagrams for K0-anti K0 mixing
Question: Are the top quark contributions significant ?
Why or Why not ?
Quantum Mechanics: Regeneration
Murray Gell-Mann
Start with a K0 beam in vacuum (produced by a pion beam
hitting a target A).
Question: What happens between the blue target and red target
?
Abraham Pais
Question: What happens after the red (regeneration target) ?
Question: Consider two pairs of mutually perpendicular (crossed
polarizers) linear polarization states of light rotated by 450 to each
other.
Consider the following analogy: let the K0, K0-bar system be
analogous to the first pair of axes and then let the K1, K2 be
analogous to the second pair.
Is this analogy correct ?
Design an experiment analogous to the experiment of Pais and
Piccioni using linear polarizers.
Review (strong and weak eigenstates)
1
| K >=
(| K 0 > + | K 0 >)
2
1
0
| K 2 >=
(| K 0 > - | K 0 >)
2
0
1
1
| K >=
(| K10 > + | K 20 >)
2
0
1
0
0
| K >=
(| K1 > - | K 2 >)
2
0
Analogy: +-45
polarized light
(K0 and K0bar
are crossed
vertical and
horizontal
polarizers)
What is the difference between KS,KL and K1, K2 ?
| K S >=
| K L >=
1
1+ | e |2
1
1+ | e |2
0
0
0
|
K
>
+
e
|
K
>
»|
K
( 1
) 1>
2
0
0
0
|
K
>
+
e
|
K
>
»|
K
( 2
) 2>
1
Question: What is ε ? And how large is it ?
Ans: A measure of CP violation in mixing. The
epsilon parameter is 2 x 10-3 in the kaon system.
Question: How was ε first measured ?
Christenson, J et al. (1964); Phys. Rev. ett. 13 338
© Nobel Foundation 1980
Cronin
Fitch
1964: CP symmetry is violated
CP=-1
CP=+1
B( K L     )  (2.0  0.4) 103
•
•
•
•
Shocking but Alternative
interpretations ruled out
A new particle X: KL g KS + X
A new long-range force
Extra nonlinear terms in the
Schrödinger equation (beyond
quantum mechanics !)
Regeneration of KS on an
unfortunate fly trapped in the
helium bag.
Phys. Rev. Lett. 13, 138 (1964)
There is a small difference between matter & antimatter
CP Violation
• There are small differences between matter
and anti-matter observed in the weak
interaction.
• The small effect is seen only in particles
containing strange quarks called “K-longs”
Jim Cronin, University of Chicago
Val Fitch, Princeton University
Why is CP Violation Interesting ?
• 1967: Andrei Sakharov (brilliant
Russian physicist and dissident): the
cosmic connection linking particle
physics with the existence of the
Universe.
Early Universe
Matter
10,000,000,000
Antimatter
10,000,000,000
Nobel Prizes from Surprising Discoveries about
Weak Interactions of Quarks
Maximal P
violation
1957
T.D. Lee
C.N. Yang
Small CP
violation
1980
J. Cronin
V. Fitch
O(1) CP
violation
and 3
generations
18
M. Kobayashi
T. Maskawa
2008
What is the Feynman diagram
for B0-anti B0 mixing ?
Hint: What is the quark content of a B0 and anti-B0 ?
Hint: Is this a first or second order weak process ?
How to measure particle-antiparticle mixing ?
Question: How does one determine whether mixing has
occurred ?
Hint: look at the charge of the second lepton ?
Ans: Opposite Flavor tags versus Same Flavor tags (form an
asymmetry). N.B. This is NOT CP violating.
Abe, K. et al (Belle collab). (2005); Phys. Rev. D 71 072003
Question: Why is the x-axis, the modulus of t ?
Diagrams for BJ/ψ KS
Question: Why is this process CP violating ?
Ans: The element Vtd is complex and the amplitudes
interfere.
How does one measure CP Violation ?
Why is time dependence required ?
Hint: What is the Charge conjugation for
e+ e- ® ¡(4S) ® B0 B0
Another hint: C=-1 since the reaction proceeds
through a single virtual photon.
| y >=| B0 (t, f )B0 (t ' ,tag) > - | B0 (t ' ,tag)B0 (t, f ) >
Ans: CP violating
goes as sin(ΔmΔt)
Time integrated CP
asymmetries vanish
at the 4S.
Note also need
“flavor tagging”
Some history: Summer of 2001
Belle:
BaBar:
The first example of CP Violation outside of the kaon (strange quark)
system. CP Violating Effects of O(1) rather than O(10-3)
CP Violation from Belle and BaBar
Adapted from Adachi, I. et al. (2012);
Phys. Rev. Lett. 108 171802
Adapted from Aubert, B. et al. (2009);
Phys. Rev. D79 072009
Review questions for Chapter 8
What are the three types of CP violation ?
Ans: I CP violation due to mixing i.e. violation in the wavefunction (ΔS=2)
Ans: II CP violation in the decay amplitude a.k.a. “direct CP
violation”, “epsilon-prime’ (ΔS=1 or ΔB=1)
Ans: III CP violation due to the interference between decays
with and without mixing. (ΔB=2)