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

Introduction to Lecture 5

Frank Krauss

IPPP Durham

U Durham, Epiphany term 2009

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

Outline

1 Parity violation

2 Fermi’s theory

3 Two neutrino’s

4 CP-violation

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

Parity violation Decays of charged Two decay modes of the charged kaons massively different. Thus, two different particles assumed in the 1950’s: + + + + + 0 τ → π + π + π− and θ → π + π . 8 Lifetime in both modes: τ ≈ 10− s; therefore a weak decay. Difference: Parity. Reasoning: Two- and three- 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 Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

β-decay of First test of this hypothesis: β-decay of cobalt, performed by C.S.Wu (Madame Wu) and E.Ambler in 1956. Idea: Observe some spatial in 60 60 Co → Ni + e− +ν ¯. Give some reference direction in space, add some magnetic field to align the of the cooled cobalt nuclei. Measure the emission of the against or with the spin direction of the nuclei and construct asymmetry. Neither spin nor the magnetic field change under mirror reflections (they are axial vectors - like cross products), but does.

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

Handedness and CP-invariance In principle this allows to distinguish left- and right-handed coordinate systems and to communicate (e.g. to an alien) which one we’re using. However, repeating a defining experiment like the cobalt one in an antimatter world, the additional effect of the matter-antimatter kicks in. It is interesting to note that the also violates Cˆ , in such a way that invariance under the product Cˆ Pˆ is preserved to a very high degree.

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

Fermi’s theory Basic idea In the 1950’s only three known: , , neutrino. Best place to study all of them: weak interactions of leptons. In practise, however, this leaves µ-decay only. Therefore, second best class of processes: β-decay and decays of and kaons. Theory for them at that had been formulated by Fermi in 1933:

For the processes n → p + e− +ν ¯ use the amplitude M = GF (ψ¯pΓψn)(ψ¯e Γψν ),

where GF is a and information about the spin composition of the interaction is encoded in the Γ’s. Note: This theory assumes that at a single point in space-time the wave-function of the (ψn) is replaced by the wave-functions of the , the electron and the incoming neutrino (or, equivalently, the outgoing anti-neutrino).

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

Currents

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

Can extract GF from rate of β decay or similar. Easier when replacing the proton and neutron with u and d-. But Γ’s more problematic. Huge step forward by establishing P-violating nature. In 1956 Feynman and Gell-Mann proposed them to be a combination of vector and axial-vector components, accounting for the parity violation. Ultimately: construct currents of the form ψ¯Γψ for s → u and d → u hadronic and for e → ν and µ → ν leptonic transitions. Can then stick them together to generate the amplitude. N.B.: Will need prefactors to account for relative s → u/d → u strength.

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

Spin, helicity and Need a better understanding of P-violation. Reminder: can be described by two components. At low they can be interpreted as the different spin states. For large velocities, spins w.r.t. a given external axis are not so useful any more. Therefore define spin w.r.t. the axis of motion: helicity. But this is not under Lorentz transformations (simple argument: boost particle in its rest frame). Alternatively, use the ’s chirality (or handedness). Both helicity and chirality flip under parity. In fact, the definitions exactly coincide for massless fermions.

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

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 Pˆ conserved as many plus as minus helicity electrons are emitted. Defining a polarisation N+ − N P = − N+ + N − P = ±1 translates into all electrons being helicity ±1. Therefore, if all electrons are left-handed, P = −v/c. Experimentally: all electrons emitted in β-decay are left-handed.

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

Neutrino helicity This finding constrains the Γ’s very tightly. Assuming that the structure of the weak interaction is universal for all fermions, this implies that only left-handed fermions and right-handed anti-fermions take part in weak interactions. Since the interact only through the weak interaction (and through , 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 and collaborators. It is considered to be one of the most clever experiments in the history of particle physics (see next slide). Similar experiments have been done, e.g. with the decays of + + + π → µ + νµ. Since the π is a spin-0 particle, the spins of the muon and the neutrino must always be opposite. Measuring the muon spin (helicity) therefore allows to deduce the neutrino helicity.

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

The Goldhaber experiment (1958) Use the inverse β-decay of the spin-0 nucleus 152Eu: the electron is captured (instead of being emitted) producing an excited (spin-1) 152SM nucleus, emitting a neutrino. the nucleus decays then into its spin-0 ground state and a . 152 152 152 e− + Eu(J = 0) →  SM(J = 1) → SM(J = 0) + γ + ν Due to the of the involved particles, the nucleus remains at rest and the neutrino and the photon are emitted back-to-back, with -0. Because of the nucleus before and after being spin-0, their spins must be opposite and add up to the electron spin. In order to measure the photon helicity, magnetic material is used. Depending on the ’ helicity, they are either absorbed by the material or not. Thus, controlling the magnetic material allows to “dial” the photon helicity.

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

Lepton number

Basic idea A simple question: Are the neutrinos emitted in neutron β-decay the same 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-neutrinoν ¯ is emitted. This allows to formulate a law -number conservation: Assigning a lepton number of +1 to electron, and neutrinos, and of −1 to their anti-particles, i.e. positrons, anti-muons and anti-neutrinos, and a lepton number of 0 to all other particles, then in any reaction lepton number is conserved. Examples: ν¯ + p → e+ + n is allowed − ν¯ + n → e + p is forbidden.

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

The absence of µ → eγ

In the framework of Fermi-theory, reactions of the type µ− → e− + γ would be allowed. A related to this would look like the muon decaying into a neutrino plus a pion, which recombine to 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 one associated to the muon such that the corresponding currents in Fermi theory read ¯ ¯ (ψe Γψνe ) and (ψµΓψνµ ). Lepton-number conservation replaced by lepton-type number conservation: − + electron number = +1 for e and νe , = −1 for e andν ¯e , and = 0 for all other particles similar for muon number (and tau number, see later).

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

The two-neutrino experiment The main problem when experimenting with neutrinos is to produce them in large quantities. One option, at low , is by using the huge fluxes coming from nuclear reactors (electron neutrinos). At large energies, accelerators must be used. To this end, for instance, high- are collided with a beryllium target, producing large numbers of, e.g. pions. They in turn decay into muons and muon-neutrinos. The latter can be isolated by large amounts of material - iron. If there was only one neutrino species, the remaining neutrinos in the experiment could, in principle, 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 Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

CˆPˆ-invariance and neutral kaons

Eigenstates Weak interactions violate both Pˆ and Cˆ. ± ± (The latter from observing e spins in µ decays) But hope: Maybe exact cancellation such that product CˆPˆ conserved? To test: Find particle states that are either even or odd under CˆPˆ and check that the final state in its decays is also CˆPˆ-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 wave function for odd particles. Neutral |K 0i = |¯sdi is (odd under parity), but C|ˆ K 0i = K¯ 0 = |sd¯i. Therefore neither K 0 nor K¯ 0 is eigenstate of CˆPˆ.

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

Eigenstates (cont’d) But linear combinations |K 0 i = 1 |K 0i ± |K¯ 0i 1,2 √2  are CˆPˆ-eigenstates. 0 0 ˆˆ 0 0 |K1 i is even, |K2 i is odd: CP|K1,2i = ±|K1,2i 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 0i or K¯ 0i, the flavour eigenstate. 0 The kaon decaying in weak interactions is |K1,2i, the CˆPˆ-eigenstate. The two different kaons typically decay like (remember: Pˆ is multiplicative) 0 −10 K1 → 2π τ = 0.9 · 10 s 0 −8 K2 → 3π τ = 5.2 · 10 s. The lifetime differences are due to the phase space.

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

Consequences If a neutral kaon is produced in strong interactions, typically it is clear whether it carries a s or an ¯s. For instance: 0 0 π− + p → K + Λ , level: |du¯i + |uudi → |d¯si + |udsi Immediately after its production, the |K 0i becomes an equal 0 0 admixture of the two states, |K1 i and |K2 i. The two states have different lifetimes. The longer the kaon state 0 survives, the more likely it is that it is a |K2 i. When it decays, there is therefore a 50% chance that it is a K¯ 0, the anti-particle of the originally created state. The fun increases, when a K¯ 0 and a K 0 state are produced coherently. Then they are quantum-mechanically entangled. One of 0 them will decay quite early, as a K1 . At this point the other one 0 must be a K2 .

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

CˆPˆ-violation In 1964 Christenson, Cronin, Fitch and Turlay tried to check whether CˆPˆ is exactly conserved. 0 Setup: Pair-produce two neutral kaons and select a beam of K2 . 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: CˆPˆ is slightly violated. 0 → K1,2 are not quite the particles seen by weak interaction. Instead it is the short- and long-lived kaons 0 0 0 0 0 0 KS = K1 − εK2 and KL = K2 + εK1 , − respectively, with ε ≈ 2 · 10 3 parametrising CˆPˆ-violation. → There are observable consequences, like, e.g. different rates in 0 − + 0 + − K2 → π + e + νe and K2 → π + e +ν ¯e .

F. Krauss IPPP Introduction to particle physics Lecture 5 Parity violation Fermi’s theory Two neutrino’s CP-violation

Summary Discussed parity and its violation in weak interactions. Introduced Fermi’s theory of weak interaction, which is an effective theory - 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: CˆPˆ-violation. To read: Coughlan, Dodd & Gripaios, “The ideas of particle physics”, Sec 11-14.

F. Krauss IPPP Introduction to particle physics Lecture 5