introduction to particle physics lecture 5krauss/lectures/introtoparticle... · 2009. 9. 22. ·...

Parity violation Fermi’s theory Two neutrino’s CP-violation

Introduction to particle physicsLecture 5

Frank Krauss

IPPP Durham

U Durham, Epiphany term 2009

F. Krauss IPPP

Introduction to particle physics Lecture 5


Outline

1 Parity violation

2 Fermi’s theory

3 Two neutrino’s

4 CP-violation

F. Krauss IPPP



Parity violation

Decays of charged kaons

Two decay modes of the charged kaons massively different.Thus, two different particles assumed in the 1950’s:

τ+ → π+ + π+ + π− and θ+ → π+ + π0.

Lifetime in both modes: τ ≈ 10−8 s; therefore a weak decay.

Difference: Parity.Reasoning: Two- and three-pion final states have different

parities, if both in s-wave. Therefore either the decaying

particle(s) have different parities or the interaction

responsible must violate parity!

T.D.Lee and C.N.Yang postulate (1956):Weak interactions violate parity,

i.e. can distinguish between left- and right-handed

coordinate systems. This is not the case for strong or

electromagnetic interactions.

F. Krauss IPPP



β-decay of cobalt

First test of this hypothesis: β-decay of cobalt,performed by C.S.Wu (Madame Wu) andE.Ambler in 1956.

Idea: Observe some spatial asymmetry in60Co →60 Ni + e− + ν.

Give some reference direction in space, add somemagnetic field to align the spin of the cooledcobalt nuclei.

Measure the emission of the electrons against orwith the spin direction of the nuclei and constructasymmetry.

Neither spin nor the magnetic field change undermirror reflections (they are axial vectors - likecross products), but momentum does.

F. Krauss IPPP



Handedness and CP-invarianceIn principle this allows to distinguish left- and right-handedcoordinate systems and to communicate (e.g. to an alien) which onewe’re using.

However, repeating a definingexperiment like the cobalt one inan antimatter world, the additionaleffect of the matter-antimattersymmetry kicks in. It is interestingto note that the weak interactionalso violates C , in such a way thatinvariance under the product C P ispreserved to a very high degree.

F. Krauss IPPP



Fermi’s theory

Basic ideaIn the 1950’s only three leptons known: electron, muon, neutrino.

Best place to study all of them: weak interactions of leptons.In practise, however, this leaves µ-decay only. Therefore, secondbest class of processes: β-decay and decays of pions and kaons.

Theory for them at that time had been formulated by Fermi in 1933:

For the processes n → p + e− + ν use the amplitudeM = GF (ψpΓψn)(ψeΓψν),

where GF is a coupling constant and information about the spincomposition of the interaction is encoded in the Γ’s.

Note: This theory assumes that at a single point in space-time thewave-function of the neutron (ψn) is replaced by the wave-functionsof the proton, the electron and the incoming neutrino (or,equivalently, the outgoing anti-neutrino).

F. Krauss IPPP



CurrentsObvious problem: How to fix GF and the structures Γ?

Can extract GF from rate of β decay or similar. Easier whenreplacing the proton and neutron with u and d-quarks.

But Γ’s more problematic. Huge step forward by establishingP-violating nature. In 1956 Feynman and Gell-Mann proposed themto be a combination of vector and axial-vector components,accounting for the parity violation.

Ultimately: construct currents of the form ψΓψ for s → u andd → u hadronic and for e → ν and µ→ ν leptonic transitions. Canthen stick them together to generate the amplitude.N.B.: Will need prefactors to account for relative s → u/d → u strength.

F. Krauss IPPP



Spin, helicity and chirality

Need a better understanding of P-violation.

Reminder: Fermions can be described by two components. At lowvelocities they can be interpreted as the different spin states.

For large velocities, spins w.r.t. a given external axis are not souseful any more. Therefore define spin w.r.t. the axis of motion:helicity. But this is not invariant under Lorentz transformations(simple argument: boost particle in its rest frame).

Alternatively, use the fermion’s chirality (or handedness).

Both helicity and chirality flip under parity. In fact, the definitionsexactly coincide for massless fermions.

F. Krauss IPPP



Experimental check: Electron polarisation in β-decays

P violation induces an asymmetry in the e−-direction in β decay.

It also affects the helicities of the electrons. With P conserved asmany plus as minus helicity electrons are emitted.

Defining a polarisation

P =N+ − N−

N+ + N−

P = ±1 translates into all electrons being helicity ±1. Therefore, ifall electrons are left-handed, P = −v/c .

Experimentally: all electrons emitted in β-decay are left-handed.

F. Krauss IPPP



Neutrino helicity

This finding constrains the Γ’s very tightly.

Assuming that the structure of the weak interaction is universal forall fermions, this implies that only left-handed fermions andright-handed anti-fermions take part in weak interactions.

Since the neutrinos interact only through the weak interaction (andthrough gravity, to be precise), only left-handed neutrinos seen.

To verify this, a simple β-decay can be used.

The first experiment of this kind was done by M.Goldhaber andcollaborators. It is considered to be one of the most cleverexperiments in the history of particle physics (see next slide).

Similar experiments have been done, e.g. with the decays ofπ+ → µ+ + νµ. Since the π+ is a spin-0 particle, the spins of themuon and the neutrino must always be opposite. Measuring themuon spin (helicity) therefore allows to deduce the neutrino helicity.

F. Krauss IPPP



The Goldhaber experiment (1958)

Use the inverse β-decay of the spin-0 nucleus 152Eu:

the electron is captured (instead of being emitted) producing anexcited (spin-1) 152

SM nucleus, emitting a neutrino.the nucleus decays then into its spin-0 ground state and a photon.

e− +152 Eu(J = 0) →[

152SM(J = 1) →152 SM(J = 0) + γ]

+ ν

Due to the masses of the involved particles, the nucleus remains atrest and the neutrino and the photon are emitted back-to-back, withangular momentum-0.

Because of the nucleus before and after being spin-0, their spinsmust be opposite and add up to the electron spin.

In order to measure the photon helicity, magnetic material is used.Depending on the photons’ helicity, they are either absorbed by thematerial or not. Thus, controlling the magnetic material allows to“dial” the photon helicity.

F. Krauss IPPP



Lepton number

Basic ideaA simple question: Are the neutrinos emitted in neutron β-decay thesame as those emitted in proton β-decay?

Compare β decays of n and p: n → p + e− + ν and p → n + e+ + ν.Suggests that in the former case an anti-neutrino ν is emitted.

This allows to formulate a law lepton-number conservation:Assigning a lepton number of +1 to electron, muons and neutrinos,and of −1 to their anti-particles, i.e. positrons, anti-muons andanti-neutrinos, and a lepton number of 0 to all other particles, thenin any reaction lepton number is conserved.

Examples:

ν + p → e+ + n is allowedν + n → e− + p is forbidden.

F. Krauss IPPP



The absence of µ → eγ

In the framework of Fermi-theory, reactions of the type µ− → e− +γwould be allowed. A Feynman diagram related to this would looklike the muon decaying into a neutrino plus a pion, which recombineto form an electron. However, this has never been observed.

The solution to this puzzle lies in postulating the existence of two

types of neutrinos, one associated to the electron and oneassociated to the muon such that the corresponding currents inFermi theory read

(ψeΓψνe) and (ψµΓψνµ

).

Lepton-number conservation replaced by lepton-type number

conservation:

electron number = +1 for e− and νe , = −1 for e+ and νe , and = 0for all other particlessimilar for muon number (and tau number, see later).

F. Krauss IPPP



The two-neutrino experiment

The main problem when experimenting with neutrinos is to producethem in large quantities. One option, at low energies, is by using thehuge fluxes coming from nuclear reactors (electron neutrinos). Atlarge energies, accelerators must be used.

To this end, for instance, high-energy protons are collided with aberyllium target, producing large numbers of, e.g. pions. They inturn decay into muons and muon-neutrinos. The latter can beisolated by large amounts of material - iron. If there was only oneneutrino species, the remaining neutrinos in the experiment could, inprinciple, initiate two kinds of reactions with equal likelihood, namely

ν + n → µ− + p and ν + n → e− + p.

However, in the first experiment of this kind L.Lederman,M.Schwartz and J.Steinberger used 25 years of accelerator time,producing around 1014 neutrinos yielding 51 muons and no electrons,establishing the existence of two kinds of neutrinos.

F. Krauss IPPP



CP-invariance and neutral kaons

Eigenstates

Weak interactions violate both P and C.(The latter from observing e± spins in µ

± decays)

But hope: Maybe exact cancellation such that product CPconserved?

To test: Find particle states that are either even or odd under CPand check that the final state in its decays is also CP-even or odd.

Candidate states must be neutral, i.e. have charge 0.

Parity does not change the nature of particle state, only sign of wavefunction for odd particles.

Neutral kaon |K 0〉 = |sd〉 is pseudoscalar (odd under parity), butC|K 0〉 = K 0 = |sd〉.

Therefore neither K 0 nor K 0 is eigenstate of CP.

F. Krauss IPPP



Eigenstates (cont’d)

But linear combinations

|K 01,2〉 = 1

√

2

(

|K 0〉 ± |K 0〉)

are CP-eigenstates.

|K 01 〉 is even, |K 0

2 〉 is odd: CP|K 01,2〉 = ±|K 0

1,2〉

Which are the physically observable states, the “true” neutral kaons?Answer depends on the interaction.

The kaon being produced in strong interactions is either |K 0〉 orK 0〉, the flavour eigenstate.The kaon decaying in weak interactions is |K 0

1,2〉, the

CP-eigenstate.The two different kaons typically decay like (remember: P is multiplicative)

K 01 → 2π τ = 0.9 · 10−10 s

K 02 → 3π τ = 5.2 · 10−8 s.

The lifetime differences are due to the phase space.

F. Krauss IPPP



Consequences

If a neutral kaon is produced in strong interactions, typically it isclear whether it carries a s or an s. For instance:

π− + p → K 0 + Λ0, quark level: |du〉 + |uud〉 → |ds〉 + |uds〉

Immediately after its production, the |K 0〉 becomes an equaladmixture of the two states, |K 0

1 〉 and |K 02 〉.

The two states have different lifetimes. The longer the kaon statesurvives, the more likely it is that it is a |K 0

2 〉.

When it decays, there is therefore a 50% chance that it is a K 0, theanti-particle of the originally created state.

The fun increases, when a K 0 and a K 0 state are producedcoherently. Then they are quantum-mechanically entangled. One ofthem will decay quite early, as a K 0

1 . At this point the other onemust be a K 0

2 .

F. Krauss IPPP



CP-violationIn 1964 Christenson, Cronin, Fitch and Turlay tried to checkwhether CP is exactly conserved.

Setup: Pair-produce two neutral kaons and select a beam of K 02 .

Check that it never decays into two pions.

Result: Out of about 23000 decays, 50 produced pion pairs,exceeding any background rate that could reasonably be expected.

Conclusion: CP is slightly violated.

→ K 01,2 are not quite the particles seen by weak interaction.

Instead it is the short- and long-lived kaons

K 0S = K 0

1 − εK 02 and K 0

L = K 02 + εK 0

1 ,

respectively, with ε ≈ 2 · 10−3 parametrising CP-violation.→ There are observable consequences, like, e.g. different rates in

K 02 → π

− + e+ + νe and K 02 → π

+ + e− + νe .

F. Krauss IPPP



Summary

Discussed parity and its violation in weak interactions.

Introduced Fermi’s theory of weak interaction, which is an effectivetheory - the full theory will be discussed in the next lecture.

Found lepton number and lepton family number conservation,related to the existence of two neutrinos.

Discussed a subtle effect: CP-violation.

To read: Coughlan, Dodd & Gripaios, “The ideas of particlephysics”, Sec 11-14.

F. Krauss IPPP


introduction to particle physics lecture 5krauss/lectures/introtoparticle... · 2009. 9. 22. ·...

Documents