Physics 56400 Introduction to Elementary Particle Physics I

Lecture 12 Fall 2018 Semester Prof. Matthew Jones Parity Violation in Weak Interactions • We already saw that, perhaps, weak interactions do not conserve parity. • In fact, weak interactions maximally violate parity conservation Helicity and Chirality

• Helicity is the projection of the spin onto the momentum axis: 휆 = 푠Ԧ ∙ 푝Ƹ • Right-handed fermions have 휆 = +1/2 • Left-handed fermions have 휆 = −1/2 • Helicity is not Lorentz invariant – You can boost to a frame in which the direction of 푝Ԧ has been reversed • Chirality similar to helicity but it is Lorentz invariant – We will study it in more detail when we look at QED • In the limit where 푣 → 푐, they are the same. Helicity and Chirality • It would seem that the weak interaction only acts on left- handed fermions or right-handed anti-fermions • This is exact for chirality and almost exact for helicity • Neutrinos are so light (essentially massless) that for all practical purposes there are only left-handed neutrinos and right-handed anti-neutrinos – There might(?) be right-handed neutrinos or left-handed anti- neutrinos, but nothing couples to them • The weak interaction strongly prefers to couple to the left-handed helicity components of charged leptons (or right-handed anti-leptons). • In the limit where 푣 → 푐, the weak interaction does not couple to right-handed leptons (or left-handed anti- leptons). Leptonic Decays of Pions 푒−, 휇−

휋−

휈푒ҧ , 휈휇ҧ 푝Ԧ 2 Γ = ℳ휋 8휋푀 푓푖 푝Ԧ • Decay to muons: = 0.0086 8휋푀 푝Ԧ • Decay to electrons: = 0.0200 8휋푀 − • We might expect the decay to 푒 휈푒ҧ to dominate but it does not… Leptonic Decays of Pions

• To conserve angular momentum, both final state particles must have right-handed helicity. • The anti-neutrinos are essentially massless so they are always right-handed.

• But 훽휇 = 0.27 while 훽푒 = 0.99997 • There is a much greater probability of finding the muon in a left-handed chirality state. • This is called “helicity suppression” Leptonic Decays of Kaons

− − 퐵푟 퐾 → 푒 휈푒ҧ −5 − − = 2.5 × 10 퐵푟(퐾 → 휇 휈휇ҧ )

훽휇 = 0.9190, 훽푒 = 0.999998

• Although the weak interaction does not conserve parity, perhaps it conserves CP Neutral Kaons • Kaons produced by strong interactions have eigenstates 퐾0 = (푑푠ҧ) and 퐾ഥ0 = 푠푑ҧ • Both have parity P=-1 but they can mix to form CP eigenstates: 1 퐾 = 퐾0 + 퐾ഥ0 CP=+1 1 2 1 퐾 = 퐾0 − 퐾ഥ0 CP=-1 2 2 + − • The 퐾1 can decay to 휋 휋 (CP even) while the 퐾2 must decay to a state with 3 pions (CP even). K-long and K-short

• The decay to two pions (푝 = 209 MeV) has much greater available phase-space than the decay to three pions (푝푚푎푥 = 139 MeV) • For this reason, they decay rate to two pions is greater than the decay rate to three pions

• The 퐾2 lifetime is longer than the lifetime of the 퐾1: 0 휏 퐾퐿 = 51.16 휇푠, 푐휏 = 15.34 m 0 휏 퐾푆 = 0.09 ns, 푐휏 = 2.68 cm • These are the physical states with well-defined masses that propagate in free space. Strong vs Weak Eigenstates • When a strange quark is produced via the strong interaction, the flavor state is well defined 0 0 • It is an equal mixture of the 퐾2 ≈ 퐾퐿 and 퐾1 ≈ 퐾푆 eigenstates: 0 1 1 0 0 퐾 = 퐾1 + 퐾2 ≈ 퐾푆 + 퐾퐿 2 2 0 1 1 0 0 퐾ഥ = 퐾1 − 퐾2 ≈ 퐾푆 − 퐾퐿 2 2 • Initially, we have equal probability of observing 0 0 either 퐾퐿 or 퐾푆 decay. • However, the short-lived component decays faster 0 and eventually we will have a pure 퐾퐿 component. Regeneration

0 • When a pure beam of 퐾퐿 interact with mater, the (푑푠ҧ) and (푠푑ҧ) components have different cross sections. – Only (푠푑ҧ) can annihilate down-quarks in nuclei • This changes the (initially equal) fraction of (푑푠ҧ) and (푠푑ҧ) in the beam 0 • The beam that emerges has a new 퐾푆 component • In fact, this component is coherent with the 0 unreacted 퐾퐿 component (Pais & Piccioni, 1955) CP Violation

0 • Since we can prepare a pure beam of 퐾퐿 , it is easy (Ha!) to search for CP violation in the form of 0 + − 퐾퐿 → 휋 휋 • Fitch-Kronin experiment (Brookhaven, 1964) CP Violation

0 0 • So the 퐾푆 and 퐾퐿 are not quite 퐾1 and 퐾2 eigenstates. 0 1 퐾푆 = 퐾1 + 휀퐾2 1 + 휀 2 0 1 퐾퐿 = 휀퐾1 + 퐾2 1 + 휀 2 • It turns out that 푅푒 휀 ~10−3 which is small, but definitely not zero. Kaon Oscillations

• Suppose the strong interaction produced an initial state with S=+1: 0 1 0 0 퐾 = 푑푠ҧ ≈ 퐾푆 + 퐾퐿 2 • The phases of each state evolves with time: 1 −푖푚푆푡−Γ푆푡/2 0 −푖푚퐿푡−Γ퐿푡/2 0 Ψ 푡 ۧ = 푒 퐾푆 + 푒 퐾퐿| 2 0 0 • The probability of observing a 퐾푆 or 퐾퐿 decay is: 2 1 푃 퐾0 = 퐾0 Ψ 푡 = 푒−Γ푆푡 푆 푆 2 2 1 푃 퐾0 = 퐾0 Ψ 푡 = 푒−Γ퐿푡 퐿 퐿 2 Kaon Oscillations

• But, we can also write ۧ Ψ 푡| 1 = 푒−푖푚푆푡−Γ푆푡/2 + 푒−푖푚퐿푡−Γ퐿푡/2 퐾0 2 1 + [ 푒−푖푚푆푡−Γ푆푡/2 − 푒−푖푚퐿푡−Γ퐿푡/2 퐾ഥ0 2 • The probability of observing a 퐾0 state is then 푃 퐾0 = 퐾0 Ψ 푡 2 Γ +Γ 푡 1 − 푆 퐿 = 푒−Γ푆푡 + 푒−Γ퐿푡 + 2푒 2 푅푒 푒푖Δ푚 푡 4 1 푒−Γ푆푡 + 푒−Γ퐿푡 = [ + 푒−Γഥ푡 cos Δ푚푡 ] 2 2 Kaon Oscillations

0 • Before the 퐾푆 component has completely decayed, it can interfere constructively or destructively with the 0 퐾퐿 component.

These are Δ푆 = 2 transitions. Cabibbo Rotation

• Cabibbo observed that amplitudes for the Δ푆 = 0 weak transitions

푢 ↔ 푑 푒 ↔ 휈푒 휇 ↔ 휈휇 were similar, but amplitudes for Δ푆 = 1 transitions were smaller by about a factor of 4. • In 1963, Cabibbo suggested that the weak interaction couples to a linear combination of 푑 and 푠 quarks: ′ 푑 = 푑 cos 휃퐶 + 푠 sin 휃퐶 ′ 푠 = −푑 sin 휃퐶 + 푠 cos 휃퐶 Cabibbo Rotation

• Probabilities for weak transitions then look like this: 2 2 푢 푑 ~ cos 휃퐶 ≈ 1 2 2 푢 푠 ~ sin 휃퐶 ≈ 0.05 • But then we should observe 퐾0 → 휇+휇− with a large branching fraction whereas in fact 퐵푟 퐾0 → 휇+휇− < 8 × 10−10 GIM Suppression

• In 1970, Glashow, Illiopoulos, and Maiani proposed that this amplitude must be cancelled by another process:

• This required that there be a charge +2/3 partner to the strange quark in the same family. Observation of (풄풄ത) States

Brookhaven 30 GeV AGS

SPEAR 푒+푒− storage ring Observation of (풄풄ത) States

• Interpretation: – The states had a very small width because of OZI suppression

푑 휋− = ቊ 푢ത 푐 푢 Suppressed decay 퐽/휓 = ൜ 휋0 = ൜ 푐ҧ 푢ത 푝푚푎푥 = 1448 MeV 푢 휋+ = ൜ 푑ҧ

Γ = 5.55 keV Observation of (풄풄ത) States

• This is a vector meson with the same quantum numbers as the photon Observation of (풄풄ത) States • SLAC continued to scan the beam energy above the 퐽/휓 mass and observed another narrow resonance.

푚 휓′ = 3686.1 MeV Γ = 2.33 keV

If this really was evidence for a new quark, where were the charm flavored mesons?

휓′ → 퐽Τ휓 휋+휋− Observation of (풄풄ത) States • The lightest charm flavored mesons (“open charm”) are the 퐷 mesons: 푚 퐷+ = 1869.7 MeV 푚 퐷0 = 1864.8 MeV • Bound states of (푐푐ҧ) will not decay to D mesons unless 푚푐푐ҧ > 2푚퐷 ~ 3740 MeV • Eventually, the 휓(3770) was observed with a much larger width: Γ = 27.2 MeV (more characteristic of strongly decaying resonance) Charm Spectroscopy

• Charm quarks are heavy and the bound state of (푐푐ҧ) is practically nonrelativistic. • The energies of bound states can be calculated using the same techniques used to calculate the emission spectrum of Hydrogen atoms. – The 퐽/휓 is the 퐽푃퐶 = 1−− ground state – The 휓′ is the 푛 = 2 radial excitation – The 휓′′ is the 푛 = 3 radial excitation Charm Spectroscopy • Quantum numbers of Hydrogen-like systems:

We also need to couple the spins of the quarks to the orbital angular momentum:

푆Ԧ = 푠Ԧ1 + 푠Ԧ2 퐽Ԧ = 퐿 + 푆Ԧ Weak Decays of Charm Mesons

• Cabibbo favored transitions: 푢 ↔ 푑 cos 휃 푐 ↔ 푠 퐶 • Cabibbo suppressed transitions: 푢 ↔ 푠 푐 ↔ 푑 sin 휃퐶