Particle Physics WS 2012/13 (14.12.2012)

Stephanie Hansmann-Menzemer Physikalisches Institut, INF 226, 3.101 Content of the Lecture

1. Introduction 8. Elastic and inelastic 1.1 Natural units scattering and the quark model 1.2 Standard model basics

1.3 Relativistic kinematics 9. (QCD)

9.1. Symmetries and conservation laws 2. Interaction of Particles with Matter 9.2. Local gauge invariance

9.3. Bound states 3. Detectors for 9.4. Quark Gluon Plasma 3.1 General Detector Concepts

3.2 PID Detectors

10. w 3.3 Tracking Detectors 10.1. , Wu Experiment, Goldhaber eak Experiment 4. Scattering process and transition amplitudes 10.2. Left right handed couplings

4.1. Fermi’s golden rule

10.3. CKM Matrix interaction 4.2. Lorentz invariant phase space and matrix element

4.3 Decay Width and Lifetime 11. The Standard Model 4.4 Two and Three Bod decay rate, Dalitz plot 11.1 Electroweak unification 4.5 Cross section 11.2 Precision tests

11.3 Higgs mechanism 5. Description of free particles

5.1. Klein-Gordan equation 12. Neutral Meson Mixing

5.2. Dirac equation

5.3. Plane Wave solutions 13. CP Violation

6. QED 14. 6.1 Interaction by particle exchange 6.2 Feynman rules 6.3. Electron-Positron annihilation 6.4. Electron Scattering

7. Radiativ correction and renormalization 2 Content of Today

 Hadronic decays of weak interaction

 Reminder of Parity

 Partiy conservation in QED/QCD

 The ϴ/τ puzzle

 Discovery of Partiy Violation: Wu-Experiment

 Goldhaber-Experiment: Helicity of the

 Structure of vertex current weak IA

3

colour hypercharge Y = λ8/3

Phenemenology of weak IA (charged current)

All particles (except photons and gluons) take part in weak IA.

Massive exchange bosons: W± (m=80 GeV), Z0 (m=91 GeV) polarization 2 [푔μν −푞μ푞ν /푚푊 ] Propagator term for massive =1 particle: -i 2 2 푞 −푚푊

For q < mW/mZ weak IA is negligible small compared to QED/QCD (for large q, weak IA comparable to electromagnetic IA)

Observation of weak IA mainly in decays which are forbidden in strong/elm IA Due to conservation and/or which involve neutrinos

푢 푢 τ(φ) ~ 1.6 10-22s - π0 - -6 K s u τ(μ ) ~ 2.6 10 s s - s W e- φ K- 푠 푢 change of ν 푒 νμ quark flavour u - + μ - -6 푠 K W- e τ(K) ~ 3.1 10 s

ν 푒 4

colour hypercharge Y = λ8/3

Weak Hadronic Decays dominant decay mode at quark level e.g. β decay

u d n → p e- ν 푒 u d - ν W- e W+ e u u

p + ν 푒 e d d n u M2 ~ cos2ϴ ~ 0.95 d c - 푢 푐 W- e ϴc : Cabbibo angle ν 푑 푠 푒 ΔI = 1 subpressed decay modes 3

푢 푢 Weak IA does not conserve isospin, - π0 K s u strangeness or any other quark flavour number. W- e-

ν Lepton numbers is however conserved ΔS = 1 푒 푢 푐 2 2 M ~ sin ϴc ~ 0.05 푑 푠 5

colour hypercharge Y = λ8/3

Reminder of Parity

푖(푝 푥 −퐸푡) particle solution Ψi = ui(E,푝 ) 푒 1 0 0 1 푝 푧 푝푥 −푖푝푦 u1 = 퐸 + 푚 u2 = 퐸 + 푚 퐸+푚 퐸+푚 푝 +푖푝 −푝 푥 푦 푧 퐸+푚 퐸+푚

−푖(푝 푥 −퐸푡) antiparticle solution Ψi = vi(E,푝 ) 푒 푝 −푖푝 푥 푦 푝푧 퐸+푚 퐸+푚 Partity operator P: −푝푧 푝 +푖푝 v = 퐸 + 푚 v = 퐸 + 푚 푥 푦 1 퐸+푚 2 퐸+푚 1 0 1 0 0 0 1 γ0 = 0 1 0 0 0 0 0 −1 0 These solutions have positive energies. 0 0 0 −1

Spin ½ particles AT REST have intrinsic partiy P = +1

Spin ½ particles AT REST have intrinsic parity P=-1 6 Reminder of Parity

P Ψ(푥 , 푡)= Ψ(−푥, 푡) P2 Ψ(푥 , 푡)= Ψ(푥 , 푡)

Parity is conserved in strong and electromagnetic IA (to be shown next slide)

Parity and momentum operator do not commute! 푃 푝 = −푝푃 ∶ „Operator“

Therefor intrinsic partity is (strictly speaken) defined only for particles AT REST.

If a system of two particles has a relative antular momentum L, total parity is given by:

L P(x1 x2) = P(x1) P(x2) (-1) (*)

Parity of W, Z, photon, gluons: P=-1 (result of gauge theory) [parity of photon and gluons are not well defined, use definition of fields ]

For all other composed and excitd particles (e.g. , proton, ion) use rule (*) and parity conserving IA to determine intrinsic parity.

7 Parity Conservation in QED/QCD − − 푔 푒 푒 M = -q q 푢 (푝 )γμ u (p ) μν 푢 (푝 )γνu (p ) e τ 푒 2 e 1 푞2 τ 4 τ 3 푞 푞 p1 p = - 푒 τ j μ gμν j v 2 푞2 e τ

p4 푞 푞 M = - 푒 τ j j p 푞2 e τ 3 − − P τ τ u γ0 u † 푢 = 푢 γ0 (Pu)†γ0 = (γ0u)†γ0= u†γ0†γ0 = u†γ0γ0 = 푢 γ0

j = 푢 γμ 푢 푢 γ0γμγ0 푢

j0 = 푢 γ0 푢 푢 γ0γ0γ0 푢 = 푢 γ0 푢 = j0

jk = 푢 γ푘 푢 jk = 푢 γ0γ푘γ0 푢 = − 푢 γ푘γ0γ0 푢 = -jk k = 1,2,3

푞 푞 푞푒푞τ 푞푒푞τ 푒 τ 0 0 k k M = - j j - 2 (je jτ - (-je )(- jτ )) = - 2 je jτ 푞2 e τ 푞 푞

parity conservation! 8 Historical ϴ/τ

9

colour hypercharge Y = λ8/3

Wu-Experiment

1956: Lee and Yang:

No evidence for parity conservation in weak IA, thus proposed set of measurements on of them was the Wu-Experiment

Wu-Experiment:

(performed by Mme Wu and collaborators)

10 Wu-Experiment

Partiy conservation: physics stays invariant under parity conservation

Idea: Check that number of emitted in direction of spin (퐽 ) of 60Co and in opposite direction (-퐽 ) are the same.

P퐽 = P(푟 푥 푝 ) = (-푟 ) 푥 푝 = −퐽

P

J=5 J=4

Experiment: Invert polarization of 60Co and compare electron rate in same angle ϴ

photons are preferentially emitted in direction of spin. Use photon distribution to test polarization of 60Co. (elm IA conserves parity) 11 60 MAIN CHALLENGE: Polarization of C0

M=5 Spin of 60Co: J=5 → M = -5,-4, …., 4, 5 ΔE = g μK B

-27 . μK ~ 5.05 x 10 J/T Population of energy levels follows . Boltzmann distribution: . 퐸 − 푘 푇 푒 퐵 M=-5

for ΔE >> kBT only lowest energy level is populated, however for given B field in experiment (2.3 T) very low temperatures needed

g factor depends on gitter structure Example: g= 7.5 (60Co), B = 2.3 T, T = 0.003 K

Δ퐸 푃(푚=−4) − = 푒 푘퐵푇 = 0.074 → 92% polarized 60Co 푃(푚=−5)

60 Solution Part-I: embedding C0 in a paramagnetic material (B ~ μr ; μr ~ 3-4) still temepratures of T=0.01K needed 12 Adiabatic Colling

1926 von Debye proposed method to create low temperature

Fundamental relation of thermodynamics: dU = T dS – p dV

1. Step: isotherm magnetisation - paramagnetic material in helium gas is put into magnetic field - energy levels are split up, only lower once are populated - entropy gets smaller: dS <0 → dU <0, helium gas absorbes heat

2. Step: helium gas removed → thermal isolation of nitrit

3. Step: adiabatic cooling - magnetic field is slowly switched off - split off of energy levels get smaller - system likes to polpulate higher states, Caveat: need magnetic field to 60 however dU = const due to isolation get polarized Co - dS gets larger thus T gets smaller

13 How to combine Cooling and Polarization?

Two competing effects needed in the nitrit-crystal to get high degree of ploarization

1) Need high B field and low temperature to get polarization

2) Switch off B field to lower temperature via adiabatical cooling B field on → warm up, B field off → cool down

How does this work?

Solution: Some paramagnetic material have large anisotropic distribution of g-factors (artefact of crystal structure, different binding mechanisms)

B field for adiabatic cooling in direction with high g-factor Thus large split up of energy levels, thus large cooling effect

B field for polarization in direction of low g-factor, thus only little warm up

14 Wu-Experiment Requirements:

- 2 B fields in orthogonal directions

- detection of emitted electron (cover a small opening angle ϴ)

- detection of emitted gamma (to test polarization of 60Co)

- crystal needs to be located in helium bath first than in vacuum

60Co 15

Wu-Experiment: Results

) ) rate

measure photon anisotropy, to determine

unpolarized degree of polarization warm ( warm

w

to

rate relative relative rate

electron rates are different ounting c depending on the polarization! parity violation warm up with time 1616 Qualitative Explanation

Wu experiment established CP violation!

It was however not precise enough to measure helicity of neutrino H ~ 0.7 ± large uncertainties

Goldhaber experiment 17 Goldhaber Experiment

152 152 Eu + e- → Sm* + νe

152 Sm + γ

Light blue and green arrows indicate possible spin configurations

152 152Eu, J = 0; + e- Sm*, J = 1 + νe

center of mass system

spin of neutrino is in opposite direction than the one of 152Sm*, momentum of is in opposite direction than the one of 152Sm* 18

Goldhaber Experiment 152Sm*, J = 1 152 152 Eu + e- → Sm* + νe

152 Sm + γ 152Sm get's small recoil from photon! 152Sm, J = 0

or

direction of spin of photon is opposite of neutrino

emitted in direction of Sm* emitted in opposite direction of Sm*

Two open question: 1) What is the direction of emission of the photon?

2) What is the polarization of the photon? 19 Resonant Scattering

foto of exeperiment

20 Measurement of Polarization of Photon

iron in B field

21 Goldhaber Experiment: Result

 Due to geometry of experiment, only resonant scattered photons are detected different rescatter object Helicity of detected photons identical to helicity of neutrino.

 Detect photons which pass trough magnetized iron.

B field points in flight direction of photons → measure fraction of (mainly) LH photons

B field points in opposit direction → measure fraction of (mainly) RH photons

Sm 푁 −푁 Scatter ring δ = − + = 0.017 ± 0.003 0.5(푁−+푁+)

N_ : counting rate with magentic field down

N+: counting rate with magnetic field up 22 Goldhaber-Experiment: Result

Result: δ = +0.017 ± 0.003

Theoretical expectation (for 100% polarized photons)

„-“ for h > 0 δ = ± 0.025 „+“ for h < 0

Only 5-8% of electrons in iron are polarized, thus asymmetry of scattering for LH and RH photons is very small, thus heavily wash out the asymmetry.

Due to background effects (thermal movements inside the source, polarisation can depend on angle, …) expect for pure LH neutrios 75% polarized photons

Measured photo polarisation: 66 ± 15%, consistent with 75%

Neutrino are left handed particles

23 Structure of Current of Weak IA

μ Vertex current of QCD/QED: j = Ψ γ Ψ M ~ j1j2 conserves parity!

How do potential vertex currents can look like?

In order to have a Lorentz invariant represenation of the matrix element, vertex currents are restricted to be of the form:

Ψ 4 푥4 Ψ, where the 4x4 matrix is a product of γ matrices

nb of components „Boson Spin“ Lorentzinvariant b

ilinear scalar Ψ Ψ 1 0

μ covariants vector Ψ γ Ψ 4 1 ≡

tensor Ψ σμν Ψ 4x4 2

bilinears axial vector Ψ γμγ5 Ψ 4 1

pseudo scalar Ψ γ5 Ψ 1 0

σμν = i/2(γμγν -γνγμ) 24 Axial Vector Current

μ μ 5 Test parity of M ~ jA1jA2 jA = 푢 γ γ u P 0 0 5 0 0 5 0 0 0 0 5 0 5 0 jA = 푢 γ γ 푢 푢 γ γ γ γ 푢 = - 푢 γ γ γ γ 푢 = −푢 γ γ 푢 = -jA

k 푘 5 푢 γ0γ푘γ5γ0푢 = 푢 γ0γ0γ푘γ5푢 = 푢 γ푘γ5푢 = j k jA = 푢 γ γ 푢 A

0 0 k k 0 0 k k M ~ jA,1 jA,2 = jA,1 jA,2 – jA,1 jA,2 (-jA,1 ) (-jA,2 ) – jA,1 jA,2 = jA,1jA,2 parity conservation!

Axial vector currents conserve as well parity

Weak IA must be linear combination of axial and vector coupling

μ μ 5 j1 = 푢 (gV γ + gAγ γ ) u = gVjV,1 + gAjA,1 j2 = gVjV,2 + gAjA,2

2 2 M ~ j1j2 = gV jV,1jV,2 + gA jA,1jA,2 + gVgA(jV,1 jA,2 + jA,1 jV,2)

2 2 gV jV,1jV,2 + gA jA,1jA,2 - gVgA(jV,1 jA,2 + jA,1 jV,2) ≠ M parity violation

푔푉푔퐴 relative strength of parity violation: 2 2 maximal violation for V-A, V+A coupling 25 푔푉 +푔퐴 V-A Coupling of Weak IA

The coefficients gA, gV must be determined from data. For the Charge current interation (W exchange) the parity violation is maximal:

푔 1 weak current: J = -i 푊 Ψ γμ (1-γ5)Ψ 2 2

coupling V-A structure

[V+A coupling would result in only right handed neutrinos exist/take part in IA, in contradiction to Goldhaber experiment] Projection operator on right and left handed cirality states:

5 5 PR = ½(1+γ ) PL = ½(1-γ )

5 5 Ψ = ΨR + ΨL = ½(1+γ )Ψ + ½(1-γ )Ψ

μ μ Remember : QED/QCD vertex: Ψγ φ = Ψ푅 + Ψ퐿 γ φ푅 + φ퐿 μ μ μ μ = Ψ푅γ φ푅 + Ψ푅γ φ퐿 + Ψ퐿γ φ푅 + Ψ퐿γ φ퐿 μ 5 μ Ψγ (1 − γ )φ = Ψ퐿γ φ퐿 Only left handed particles and right handed chirality anti-particles take part in charged current IA 26 Connection to Fermi-Theory

27 Strength of Weak Interaction

28