:

Chris Parkes

CP Violation Part IIntroductory concepts

Slides available on my web pagehttp://www.hep.manchester.ac.uk/u/parkes/

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Outline

THEORETICAL CONCEPTS (with a bit of experiment)

I. Introductory conceptsMatter and antimatter

Symmetries and conservation laws

Discrete symmetries P, C and T

II. CP Violation in the Standard ModelKaons and discovery of CP violation

Mixing in neutral mesons

Cabibbo theory and GIM mechanism

The CKM matrix and the Unitarity Triangle

Types of CP violation

Matter and antimatter

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“Surely something is wanting in our conception of the universe... positive and negative electricity, north and south magnetism…”Matter antimatter Symmetry

“matter and antimatter may further co-exist in bodies of small mass” Particle Antiparticle Oscillations

Prof. Physics, Manchester – physics building named after

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Adding Relativity to QM See Advanced QM II

Free particle Em

2

2p Apply QM prescription ip

Get Schrödinger Equationdt

im

22

2Missing phenomena:Anti-particles, pair production, spin

Or non relativisticWhereas relativistically

mpmvE22

1 22

42222 cmcE p

22

2

2

2

1

mc

dtcKlein-Gordon Equation

Applying QM prescription again gives:

Quadratic equation 2 solutionsOne for particle, one for anti-particleDirac Equation 4 solutionsparticle, anti-particle each with spin up +1/2, spin down -1/2

Anti-particles: Dirac

Combine quantum mechanics and special relativity, linear in δt

Half of the solutions have negative energy

Or positive energy anti-particlesSame mass/spin… opposite charge

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predicted 1931

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Antiparticles – Interpretation of negative energy solutions

Westminster Abbey

- Dirac: in terms of ‘holes’ like in semiconductors - Feynman & Stückelberg: as particles traveling backwards in time, equivalent to antiparticles traveling forward in time

both lead to the prediction of antiparticles !

Paul A.M. DiracE

mc2

etc..

etc..

positron

-mc2

electron

positron

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Discovery of the positron (1/2)

1932 discovery by Carl Anderson of a positively-charged particle “just like the electron”. Named the “positron”

First experimental confirmation of existence of antimatter!

Lead plate to slow down particlein chamber

Incoming particle (high momentum / low curvature)

Outgoing particle (low momentum / high curvature)

Cosmic rays with a cloud camber

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Discovery of the positron (2/2)

4 years later Anderson confirmed this with g e+e- in lead plate using g from a radioactive source

Dirac equation: for every (spin ½) particle there is an antiparticle

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Dirac: predicted 1931

Positron observed 1932

Antiproton observed 1959Bevatron

Anti-deuteron 1965PS CERN / AGS Brookhaven

Anti-Hydrogen 1995CERN LEAR

Spectroscopystarts 2011CERN LEAR (ALPHA)

Antihydrogen Production

Fixed Target Experiments (too hot, few!)– First anti-hydrogen– < 100 atoms CERN (1995), Fermilab– Anti-protons on atomic target

‘Cold’ ingredients (Antiproton Decelerator)– ATHENA (2002), ATRAP, ALPHA, ASACUSA– Hundreds of Millions produced since 2002.

ALPHA Experiment

Will Bertsche

G.Bauer et al. (1996) Phys. Lett. B 368 (3)

M. Amoretti et al. (2002). Nature 419 (6906): 456

Antihydrogen Trapping

Antihydrogen: How do you trap something electrically neutral ? Atomic Magnetic moment in minimum-B trap

– T < 0.5 K! Quench magnets and detect annihilation ALPHA Traps hundreds of atoms for up to 1000 seconds!

– Hence can start spectroscopy studies

Nature 468, 355 (2010). Nature Physics, 7, 558-564 (2011) Will Bertsche

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Matter and antimatter

Differences in matter and antimatter Do they behave differently ? Yes – the subject of these lectures We see they are different: our universe is matter dominated

Equal amounts of matter & antimatter (?)

Matter Dominates !

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Tracker: measure deflection R=pc/|Z|e, direction gives Z signTime of Flight: measure velocity betaTracker/TOF: energy loss (see Frontiers 1) measure |Z|

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Search for anti-nuclei in space

AMS experiment: A particle physics experiment in space Search of anti-helium in cosmic rays AMS-01 put in space in June 1998 with Discovery shuttle

Lots of He foundNo anti-He found !

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How measured?Nucleosynthesis – abundance of light elements depends on Nbaryons/Nphotons

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Proton decay so far unobserved in experiment, limit is lifetime > 1032 years

Observed BUT magnitude (as we will discuss later) is too small

In thermal equilibrium N(Baryons) = N(anti-Baryons) since in equilibrium

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Dynamic Generation of Baryon Asymmetry in Universe

CP Violation & Baryon Number Asymmetry

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Key Points So Far

• Existence of anti-matter is predicted by the combination of• Relativity and Quantum Mechanics

• No ‘primordial’ anti-matter observed

• Need CP symmetry breaking to explain the absence of antimatter

Symmetriesand conservation laws

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Symmetries and conservation laws

Role of symmetries in Physics: Conservation laws greatly simplify building of theories

Well-known examples (of continuous symmetries): translational momentum conservation rotational angular momentum conservation time energy conservation

Fundamental discrete symmetries we will study- Parity (P) – spatial inversion- Charge conjugation (C) – particle antiparticle transformation- Time reversal (T)- CP, CPT

Emmy Noether

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The 3 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 antiparticle

e+ e- , K- K+

Time Reversal, T– Changes, for example, the direction of motion of particles

t -t

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P operator acts on a state |(r, t)> as

),(),(

),(),(2 ttP

ttP P

rr

rr

Hence eigenstates P=±1

|(r, t)>= cos x has P=+1, even

|(r, t)>= sin x has P=-1, odd

|(r, t)>= cos x + sin x, no eigenvalue

e.g. hydrogen atom wavefn

|(r,, )>=(r)Ylm(,)

P Ylm(,) Yl

m(-,+)

=(-1)l Ylm(,)

So atomic s,d +ve, p,f –ve PHence, electric dipole transition l=1Pg=- 1

Parity - spatial inversion (1/2)

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Parity multiplicative: |> = |a> |b> , P=PaPb

Proton Convention Pp=+1

Quantum Field Theory Parity of fermion opposite parity of anti-fermion Parity of boson same parity as anti-particle

Angular momentum Use intrinsic parity with GROUND STATES Also multiply spatial config. term (-1) l

Conserved in strong & electromagnetic interactions

scalar, pseudo-scalar, vector, axial(pseudo)-vector, etc.

JP = 0+, 0-, 1-, 1+ -,o,K-,Ko all 0- , photon 1-

Parity - spatial inversion (2/2)

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Left-handed=spin anti-parallel to momentumRight-handed= spin parallel to momentum

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Spin in direction of momentum

Spin in opposite direction of momentum

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Charge conjugation

C operator acts on a state |(x, t)> as),(),(

),(),(2 ttC

ttC C

rr

rr

Particle to antiparticle transformation

Only a particle that is its own antiparticle can be eigenstate of C ! e.g. C |o> = ±1 |o>

o g + g (BR~99%)

EM sources change sign under C,hence C|g> = -1

Thus, C|o> =(-1)2 |o> = +1 |o>

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Measuring Helicity of the Neutrino

152 * 152Sm SmJ= 1 0 1

g

Goldhaber et. al. 1958

Electron captureK shell, l=0

photon emission

Consider the following decay:

Eu at restSelect photons in Sm* dirn

Neutrino, SmIn opposite dirns

e-

• Momenta, p

• spin

OR

gS=+ ½

S=- ½Left-handed

S=+ 1

S=- 1

right-handed

Left-handed

right-handed

• Helicities of forward photon and neutrino same• Measure photon helicity, find neutrino helicity

See textbook

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Neutrino Helicity Experiment Tricky bit: identify forward γ Use resonant scattering!

Measure γ polarisation with different B-field orientations

152 152 * 152Sm Sm Smg g

magnetic field

Pb

NaI

PMT

152Sm152Sm

152Eu

γγ

Fe

Similar experiment with Hg carried out for anti-neutrinos

Vary magnetic field to vary photon absorbtion.Photons absorbed by e- in iron only if spins of photon and electronopposite.

)21()

21()1(

)21()

21()1(

'

ee SSSg

Forward photons,(opposite p to neutrino),Have slightly higher p than backwardand cause resonant scattering

Only left-handed neutrinos exist

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C P

CPParity InversionSpatialmirror

Charge InversionParticle-antiparticlemirror

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left-handed

right-handed

Parity

left-handed

right-handed

Charge & Parity

• Massless approximation (Goldhaber et al., Phys Rev 109 1015 (1958)

Neutrino helicity

✗

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T - time reversal

Invertion of the time coordinate: t -t– Changes, for example, the direction of motion of particles

Invariance checks: detailed balances a + b c + d becomes under T c + d a + b

Conserved in strong & electromagnetic interactions

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CPT invariance

CPT THEOREMAny Lorentz-invariant local quantum field theoryis invariant under the combination of C, P and T

G. Lűders, W. Pauli, J. Schwinger (1954)

Consequences: particles / antiparticles have Opposite quantum numbers Equal mass and lifetime Equal magnetic moments of opposite sign

Fields with Integer spins commute, half-integer spins anti-commute (Pauli exclusion principle)

Tests: Best experimental test of CPT invariance:

Non-CPT-invariant theories have been formulated,

but are not satisfactory

1810~)( 000

KKKmmm

(see PDG review on “CPT invariance Tests in Neutral Kaon decays”)

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Key Points So Far

• Existence of anti-matter is predicted by the combination of• Relativity and Quantum Mechanics

• No ‘primordial’ anti-matter observed

• Need CP symmetry breaking to explain the absence of antimatter

• Three Fundamental discrete symmetries: C, P , T

• C, P, and CP are conserved in strong and electromagnetic interactions

• C, P completely broken in weak interactions, but initially CP looks OK

• CPT is a very good symmetry

• (if CP is broken, therefore T is broken)