Transcript bYTEBoss introduction

Particle Physics II – CP violation
Introduction
N. Tuning
Acknowledgements:
Slides based on the course from Marcel Merk and Wouter Verkerke.
Niels Tuning (1)
Outline
•
•
25 February: Introduction
–
Motivation of this course
–
Anti-matter
–
P and C symmetries
3 March: Lecture 1
– CP symmetry
– K-system
• CP violation
• Oscillations
– Cabibbo-GIM mechanism
– Mixing
•
10 March: Lecture 2
– CP violation in the Lagrangian
– CKM matrix, unitarity triangle
– BJ/Psi Ks
•
17 March: Lecture 3
–
3 Types of CP-violation
–
Measuring CP-violation
–
Penguins
–
New physics?
Niels Tuning (2)
Literature
• Slides based on courses from Wouter Verkerke and Marcel Merk.
• W.E. Burcham and M. Jobes, Nuclear and Particle Physics,
chapters 11 and 14.
• Z. Ligeti, hep-ph/0302031, Introduction to Heavy Meson Decays
and CP Asymmetries
• Y. Nir, hep-ph/0109090, CP Violation – A New Era
• H. Quinn, hep-ph/0111177, B Physics and CP Violation
Niels Tuning (3)
Introduction: it’s all about the charged current
• “CP violation” is about the weak interactions,
• In particular, the charged current interactions:
• The interesting stuff happens in the interaction with
quarks
• Therefore, people also refer to this field as “flavour
physics”
Niels Tuning (4)
Motivation 1: Understanding the Standard Model
• “CP violation” is about the weak interactions,
• In particular, the charged current interactions:
• Quarks can only change flavour through charged current
interactions
Niels Tuning (5)
Introduction: it’s all about the charged current
• “CP violation” is about the weak interactions,
• In particular, the charged current interactions:
• In 1st lecture next week:
• P-parity, C-parity, CP-parity
•  the neutrino shows that P-parity is maximally violated
Niels Tuning (6)
Introduction: it’s all about the charged current
• “CP violation” is about the weak interactions,
• In particular, the charged current interactions:
W+
Wb
b
gVub
• In 1st lecture next week:
gV*ub
u
u
• P-parity, C-parity, CP-parity
•  Symmetry related to particle – anti-particle
Niels Tuning (7)
Motivation 2: Understanding the universe
• It’s about differences in matter and anti-matter
– Why would they be different in the first place?
– We see they are different: our universe is matter dominated
Equal amounts
of matter &
anti matter (?)
Matter Dominates !
Niels Tuning (8)
Where and how do we generate the Baryon asymmetry?
• No definitive answer to this question yet!
• In 1967 A. Sacharov formulated a set of general
conditions that any such mechanism has to meet
1) You need a process that violates the baryon number B:
(Baryon number of matter=1, of anti-matter = -1)
2) Both C and CP symmetries should be violated
3) Conditions 1) and 2) should occur during a phase in which there is
no thermal equilibrium
• In these lectures we will focus on 2): CP violation
• Apart from cosmological considerations, I will convince
you that there are more interesting aspects in CP
violation
Niels Tuning (9)
Introduction: it’s all about the charged current
• “CP violation” is about the weak interactions,
• In particular, the charged current interactions:
• Same initial and final state
• Look at interference between B0  fCP and B0  B0  fCP
Niels Tuning (10)
Motivation 3: Sensitive to find new physics
• “CP violation” is about the weak interactions,
• In particular, the charged current interactions:
“Box” diagram: ΔB=2
“Penguin” diagram: ΔB=1
b
s
b s
s
b
μ
μ
Bs
b
s
b̃
g̃
s̃
x
x
s̃
g̃
b̃
s
b
Bs
B0
b
d
g̃
b̃
x
s
K*
s
Bs
μ
s̃
b
g̃
s̃
x
b̃
μ
μ
μ
• Are heavy particles running around in loops?
Niels Tuning (11)
Recap:
• CP-violation (or flavour physics) is about charged
current interactions
• Interesting because:
1) Standard Model:
in the heart of quark
interactions
2) Cosmology:
related to matter – anti-matter
asymetry
3) Beyond Standard Model:
measurements are sensitive to
new particles
Matter
Dominates !
b
s
s
b
Niels Tuning (12)
Personal impression:
• People think it is a complicated part of the Standard Model
(me too:-). Why?
• Non-intuitive concepts?
– Imaginary phase in transition amplitude, T ~ eiφ
– Different bases to express quarks states, d’=0.97 d + 0.22 s + 0.003 b
|K0> ↔ |K0>
– Oscillations (mixing) of mesons:
• Complicated calculations?
2
2
2
2
  B 0  f   Af  g +  t  +  g -  t  + 2   g +  t  g -  t   



2 
0
2
2
1
2
 B  f  Af  g +  t  + 2 g -  t  + 2     g +  t  g -  t   






• Many decay modes? “Beetopaipaigamma…”
– PDG reports 347 decay modes of the B0-meson:
•
Γ1 l+ νl anything
• Γ347 ν ν γ
( 10.33 ± 0.28 ) × 10−2
<4.7 × 10−5
CL=90%
Niels Tuning (13)
Let’s start slowly…
Niels Tuning (14)
What is evidence for the existence of anti-matter?
• Energetic photons produced in matter/anti-matter
annihilation
– Look at spectrum of photons in universe and look for spikes
– Main problem: photons can not travel unlimited distances in the
universe because of interactions with remaining cosmic
background radiation and gases etc…
– Conclusion: No anti-matter in 20Mpc radius.
– How to look further into space?
• Better: Look for anti-Helium nuclei flying through space
– Positrons, anti-protons can occasionally be produced in various
processes, but producing anti-Helium is way too complicated by
‘regular means’: Only viable source of anti-Helium are fusion
processes in ‘anti-stars’
– Presence/absence of anti-Helium says something about existence
of anti-matter in distant regions of space
– Large rest mass of Helium nuclei allows them to travel much
further through space than photons  Conclusions of anti-Helium
searches cover much larger region of space
Niels Tuning (15)
The AMS experiment – Searching for He
• In essence as small particle physics experiment in space
– AMS-01 brought to space through flight of Discovery shuttle
– Can detect and identify many types of cosmic rays
Niels Tuning (16)
Results of the AMS experiment
• Zero anti-helium found, plenty of Helium found
– Rigidity of tracks is measure of particles momentum
– Very high energy Helium nuclei have traveled from far  Says something
about spatial reach of experiment
• ‘Universe with pockets of anti-matter’ hypothesis increasingly
unlikely
– Future AMS-02 experiment will (launch 2007) will have much increased
range
Niels Tuning (17)
Introduction – positron discovery by Anderson
• Result: discovery of a positively charged electron-like
particle dubbed the ‘positron’
– Experimental confirmation of existence of anti-matter!
e+
(23 MeV)
Outgoing particle (low momentum / hi curvature)
6mm Pb
Lead plate to slow down particle
in chamber
Incoming particle (high momentum / low curvature)
e+
(63 MeV)
Niels Tuning (18)
Introduction – positron discovery by Anderson
• 4 years later Anderson confirmed this with g  e+e- in
lead plate using g from Thorium carbide source
Niels Tuning (19)
Introduction – anti-neutrino: Savannah river
• Decisive experiment close to Savannah River nuclear
reactor in South Carolina in 1956 (Nobel prize 1995)
• Idea: nuclear reactor provides enormous anti-neutrino
flux from fission O(1013) /cm2/sec
– Try to detect inverse beta decay: n + p+  n + e+
(Beta decay: n  p+ + e- + n)
n e +  p+ n
p + n  n e+
Cross over eInvert reaction
Niels Tuning (20)
Introduction – anti-neutrino: Savannah river
• How do you detect n + p+  n + e+
– Look for the positron through the reaction
e+ e-  g g
From inverse
beta decay
From detector
material
and detect 2 photons produced simultaneously.
• Savannah river Detector:
– Tank with 200 liters of water with 40 kg of CdCl2 dissolved in it.
– Surrounded by 110 photomultipliers for photon detection
• Clean signal found  direct proof of existence of neutrino
– Nobel prize 1995
•
ν + n  p+ + e- not observed
– ν≠ν , Lepton number must be conserved
Niels Tuning (21)
Introduction - What about the other anti-particles?
• Dirac equation: for every (spin ½) particle there is an
anti-particle
– It took a bit longer, but more were discovered
Anti-proton (1955) and anti-neutron (1955) using cyclotrons
• Reactions with particles and anti-particles
– Q: How do you produce anti-particles anyway?
– A: In pairs with particles, e.g. g  e+ e• But this is not the whole story as we will see later
• General rule: crossing symmetry
– In any existing reaction you can move a particle through the
arrow while turning it into an anti-particle
– Example:
e- g  e- g (Compton scattering)
g g  e+ e- (Pair creation)
Move e- to right
Move g to left
(g = g)
Niels Tuning (22)
Definition and discovery
of C,P,CP violation
Niels Tuning (23)
Continuous vs discrete symmetries
• Space, time translation & orientation symmetries are all
continuous symmetries
– Each symmetry operation associated with one ore more
continuous parameter
• There are also discrete symmetries
– Charge sign flip (Q  -Q) : C parity
– Spatial sign flip ( x,y,z  -x,-y,-z) : P parity
– Time sign flip (t  -t) : T parity
• Are these discrete symmetries exact symmetries that
are observed by all physics in nature?
– Key issue of this course
Niels Tuning (24)
Example: People believe in symmetry…
Instruction for Abel Tasman, explorer of Australia (1642):
•
“Since many rich mines and other treasures have been found in
countries north of the equator between 15o and 40o latitude, there is
no doubt that countries alike exist south of the equator.
The provinces in Peru and Chili rich of gold and silver, all positioned
south of the equator, are revealing proofs hereof.”
Niels Tuning (25)
Three Discrete Symmetries
• Parity, P
– Parity reflects a system through the origin. Converts
right-handed coordinate systems to left-handed ones.
– Vectors change sign but axial vectors remain unchanged
• x  -x , p  -p, but L = x  p  L
• Charge Conjugation, C
– Charge conjugation turns a particle into its anti-particle
• e
+
 e- , K
-
K
+
-
+
• Time Reversal, T
– Changes, for example, the direction of motion of particles
• t  -t
Niels Tuning (26)
P-parity experiments
• Before 1956 physicists were convinced that the laws of
nature were left-right symmetric. Strange?
– A “gedanken” experiment:
Consider two perfectly mirror symmetric cars:
Gas pedal
Gas pedal
driver
driver
“L”
“L” and “R” are fully symmetric,
Each nut, bolt, molecule etc.
However the engine is a black box
“R”
Person “L” gets in, starts, ….. 60 km/h
Person “R” gets in, starts, ….. What happens?
• What would happen if the ignition mechanism uses, say,
60Co b decay?
Niels Tuning (27)
The situation in 1956
• Nothing hints at the existence of any kind of Parity
violating physics…
– Reminder: Parity: (x,y,z)  (-x,-y,-z)
– If universe is parity-symmetric, inverting all spatial coordinates would
not changes laws of physics
• 1956: Lee and Yang publish a paper Question of Parity
Conservation in Weak Interactions/
– Suggestion: Weak interaction might violate Parity symmetry.
• Originated from discussions at April HEP conference in
Rochester, NY. Following Yang's presentation Richard
Feynman brought up the question of non-conservation of
parity.
– Feynman himself later said, "I thought the idea (of parity violation)
unlikely, but possible, and a very exciting possibility." Indeed
Feynman later made a fifty dollar bet with a friend that parity would
not be violated.
Niels Tuning (28)
Parity symmetry – The situation in 1956
• When the paper appeared, physicists were not
immediately prompted into action. The proposition of
parity non-conservation was not unequivocally denied;
rather, the possibility appeared so unlikely that
experimental proof did not warrant immediate attention.
• The physicist Freeman Dyson wrote of his reaction to
the paper: "A copy of it was sent to me and I read it. I
read it twice. I said, `This is very interesting,' or words
to that effect. But I had not the imagination to say, `By
golly, if this is true it opens up a whole new branch of
physics.' And I think other physicists, with very few
exceptions, at that time were as unimaginative as I."
Niels Tuning (29)
Parity symmetry – the experiment
• Madame Wu
– Another immigrant was now to play
the next major role,
Madame Chien-Shiung Wu.
• Arriving at Berkely in 1936 from Shanghai, Wu was one
of the most ardently pursued coeds on campus. But she
was also a hard worker who abhorred the marked absence
of women from the American scientific establishment.
She says, " ... it is shameful that there are so few women
in science... In China there are many, many women in physics.
There is a misconception in America that women scientists
are all dowdy spinsters. This is the fault of men. In Chinese
society, a woman is valued for what she is, and men encourage
her to accomplishments --- yet she retains eternally feminine."
• Idea from experiment in collaboration with Lee
and Yang: Look at spin of decay products of
polarized radioactive nucleus
– Production mechanism involves exclusively weak
interaction
Niels Tuning (30)
Intermezzo: Spin and Parity
• How does the decay of a particle with spin tell you
something about parity?
• Gedanken-experiment: decay of X  a + b
– Spin: |1,1> 
|½, ½ > + |½, ½>

– It is important that X is maximally polarized: only then there is a
single solution for the spin of the decay products. If not, e.g.
• |1,0>  |½, +½> + |½, -½>
• |1,0>  |½, -½> + |½, +½>
Niels Tuning (31)
Intermezzo: Spin and Parity and Helicity
• We introduce a new quantity: Helicity = the projection
of the spin on the direction of flight of a particle
Sp
H
Sp
H=+1 (“right-handed”)
H=-1 (“left-handed”)
Niels Tuning (32)
Intermezzo: Spin and Parity and Helicity
• Spin is quantized  Helicity is quantized
– Possible H values for S=1/2: H=-1 and H=+1
– Most particles are linear combination of H=+1 and H=-1 states
– Angular distribution for particles observed in specific helicity
eigenstate:
I(q)RH = 1 - (v/c) cos q
I(q)LH = 1 + (v/c) cos q +
H=+1 (“right-handed”)
Constant
If both helicities
are produced
equally in decay.
Superposition
of H=+1
and H=-1
states
If not angular
distribution will
not be flat
H=-1 (“left-handed”)
Niels Tuning (33)
Note on Helicity
• Note that Helicity is not generally a Lorentz- invariant
observable
– Sign of particle momentum p is relative to observer.
– A second observer ‘overtaking’ the particle from the lab observer
perspective will see the particle moving in the opposite direction
(p’ = -p)  It see the opposite Helicity
• Exception for massless particles:
– You cannot overtake massless particles moving at speed of light
– Helicity for massless particles is Lorentz-invariant intrinsic
property
Niels Tuning (34)
A realistic experiment: the Wu experiment (1956)
• Observe radioactive decay of Cobalt-60
nuclei
– The process involved:
60
–
60 Ni
28
60 Co
27
is spin-5 and
ne are spin-½
27Co 
60
28Ni + e + ne
S=1/2
is spin4, both e- and
– If you start with fully polarized Co (SZ=5) the
experiment is essentially the same (i.e. there is only
one spin solution for the decay)
|5,+5>  |4,+4> + |½ ,+½> + |½,+½>
S=4
S=1/2
Niels Tuning (35)
The Wu experiment – 1956
• Experimental challenge:
how do you obtain a
sample of Co(60) where
the spins are aligned in
one direction
– Wu’s solution: adiabatic
demagnitization of Co(60)
in magnetic fields at very
low temperatures (~1/100
K!). Extremely challenging
in 1956!
Niels Tuning (36)
The Wu experiment – 1956
• The surprising result: the counting rate is different
– Electrons are preferentially emitted in direction opposite of
60Co spin!
– Careful analysis of results shows that experimental data is consistent
with emission of left-handed (H=-1) electrons only at any angle!!
‘Backward’ Counting rate
w.r.t unpolarized rate
60Co
polarization decreases
as function of time
‘Forward’ Counting rate
w.r.t unpolarized rate
Niels Tuning (37)
The Wu experiment – 1956
• Physics conclusion:
– Angular distribution of electrons shows that only pairs of lefthanded electrons / right-handed anti-neutrinos are emitted
regardless of the emission angle
– Since right-handed electrons are known to exist (for electrons H is
not Lorentz-invariant anyway), this means
no left-handed anti-neutrinos are produced in weak decay
• Parity is violated in weak processes
– Not just a little bit but 100%
• How can you see that
60Co
violates parity symmetry?
– If there is parity symmetry there should exist no measurement
that can distinguish our universe from a parity-flipped universe,
but we can!
Niels Tuning (38)
Our universe vs a parity-flipped universe
• What happens to helicity in parity-flipped universe?
– Momentum flips sign
– Spin stays the same
– Helicity is product and flips sign
Sp
H
Sp
Orientation of spin
Direction of motion
righthanded
H=+1
P
Orientation of spin
Direction of motion
lefthanded
H=-1
• Conclusion:
– Any process that produces right-handed anti-neutrinos in our universe will
produce left-handed anti-neutrinos in the mirrored universe.
– If left and right-handed neutrinos are not produced at the same rate the
physics in the mirrored universe is different
Niels Tuning (39)
Parity violation in weak decays
• Apply parity operation to
60Co
decay
P-Flipped universe
Our universe
e-
RH ne
RH ne
e-
LH ne
e-
e-
LH ne
Niels Tuning (40)
Parity violation in weak decays
• Apply parity operation to
Our universe
(RH anti-neutrinos only)
Forbidden
Allowed
60Co
decay
P-Flipped universe
(LH anti-neutrinos only)
Forbidden
Allowed
e-
RH ne
RH ne
e-
LH ne
e-
e-
LH ne
Preferential direction of electrons
is backward
Preferential direction of electrons
is forward
Niels Tuning (41)
So P is violated, what’s next?
• Wu’s experiment was shortly followed by another clever
experiment by L. Lederman: Look at decay p+  m+ nm
– Pion has spin 0, m,nm both have spin ½
 spin of decay products must be oppositely aligned
 Helicity of muon is same as that of neutrino.
m+
p+
nm
• Nice feature: can also measure polarization of
both neutrino (p+ decay) and anti-neutrino (p- decay)
• Ledermans result: All neutrinos are left-handed and
all anti-neutrinos are right-handed
Niels Tuning (42)
Charge conjugation symmetry
• Introducing C-symmetry
– The C(harge) conjugation is the operation which exchanges
particles and anti-particles (not just electric charge)
– It is a discrete symmetry, just like P, i.e. C2 = 1
m+
p+
nm(LH)
OK
m-
p-
nm(LH)
OK
C
• C symmetry is broken by the weak interaction,
– just like P
Niels Tuning (43)
The Weak force and C,P parity violation
• What about C+P  CP symmetry?
– CP symmetry is parity conjugation (x,y,z  -x,-y,z)
followed by charge conjugation (X  X)
nm
m+
m-
Intrinsic
spin
p+
m+
P p+
CP
C p-
nm
CP appears to
be preserved
in weak
interaction!
nm
Niels Tuning (44)
Conserved properties associated with C and P
• C and P are still good symmetries in any reaction not
involving the weak interaction
– Can associate a conserved value with them (Noether Theorem)
• Each hadron has a conserved P and C quantum number
– What are the values of the quantum numbers
– Evaluate the eigenvalue of the P and C operators on each hadron
P|y> = p|y>
• What values of C and P are possible for hadrons?
– Symmetry operation squared gives unity so eigenvalue squared
must be 1
– Possible C and P values are +1 and -1.
• Meaning of P quantum number
– If P=1 then P|y> = +1|y> (wave function symmetric in space)
if P=-1 then P|y> = -1 |y> (wave function anti-symmetric in
space)
Niels Tuning (45)
Figuring out P eigenvalues for hadrons
• QFT rules for particle vs. anti-particles
– Parity of particle and anti-particle must be opposite for fermions (spin-N+1/2)
– Parity of bosons (spin N) is same for particle and anti-particle
• Definition of convention (i.e. arbitrary choice in def. of q vs q)
– Quarks have positive parity  Anti-quarks have negative parity
– e- has positive parity as well.
– (Can define other way around: Notation different, physics same)
• Parity is a multiplicative quantum number for composites
– For composite AB the parity is P(A)*P(B), Thus:
– Baryons have P=1*1*1=1, anti-baryons have P=-1*-1*-1=-1
– (Anti-)mesons have P=1*-1 = -1
• Excited states (with orbital angular momentum)
– Get an extra factor (-1) l where l is the orbital L quantum number
– Note that parity formalism is parallel to total angular momentum J=L+S
formalism, it has an intrinsic component and an orbital component
• NB: Photon is spin-1 particle has intrinsic P of -1
Niels Tuning (46)
Parity eigenvalues for selected hadrons
• The p+ meson
– Quark and anti-quark composite: intrinsic P = (1)*(-1) = -1
– Orbital ground state  no extra term
– P(p+)=-1
Meaning: P|p+> = -1|p+>
• The neutron
– Three quark composite: intrinsic P = (1)*(1)*(1) = 1
– Orbital ground state  no extra term
– P(n) = +1
• The K1(1270)
– Quark anti-quark composite: intrinsic P = (1)*(-1) = -1
– Orbital excitation with L=1  extra term (-1)1
– P(K1) = +1
Niels Tuning (47)
Figuring out C eigenvalues for hadrons
• Only particles that are their own anti-particles are C
eigenstates because C|x>  |x> = c|x>
– E.g. p0,h,h’,r0,f,w,y and photon
• C eigenvalues of quark-anti-quark pairs is determined by
L and S angular momenta: C = (-1)L+S
– Rule applies to all above mesons
• C eigenvalue of photon is -1
– Since photon is carrier of EM force, which obviously changes sign
under C conjugation
• Example of C conservation:
– Process p0  g g
C=+1(p0 has spin 0)  (-1)*(-1)
– Process p0  g g g does not occur (and would violate C conservation)
Niels Tuning (48)
What do we know now?
• C.S. Wu discovered from 60Co decays that the weak
interaction is 100% asymmetric in P-conjugation
– We can distinguish our universe from a parity flipped universe
by examining 60Co decays
• L. Lederman et al. discovered from π+ decays that the
weak interaction is 100% asymmetric in C-conjugation
as well, but that CP-symmetry appears to be
preserved
– First important ingredient towards understanding matter/antimatter asymmetry of the universe:
weak force violates matter/anti-matter(=C) symmetry!
– C violation is a required ingredient, but not enough as we will
learn later
• Next: a precision test of CP symmetry conservation in
the weak interaction
Niels Tuning (49)
Outline
•
•
25 February: Introduction
–
Motivation of this course
–
Anti-matter
–
P and C symmetries
3 March: Lecture 1
– CP symmetry
– K-system
• CP violation
• Oscillations
– Cabibbo-GIM mechanism
– Mixing
•
10 March: Lecture 2
– CP violation in the Lagrangian
– CKM matrix, unitarity triangle
– BJ/Psi Ks
•
17 March: Lecture 3
–
3 Types of CP-violation
–
Measuring CP-violation
–
Penguins
–
New physics?
Niels Tuning (50)