lecture sm 12

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Schning/Rodejohann 1 Standard Model of Particle Physics SS 2013

Lecture:

Standard Model of Particle Physics

Heidelberg SS 2013

Weak Interactions II

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Important Experiments

Wu-Experiment (1957): radioactive decay of Co60

Goldhaber-Experiment (1958): radioactive decay of Eu152

Muon Decay: Michel spectrum

Pion Decay: branching ratios

Nuclear Beta Decays

Neutrino-Nucleon Scattering (neutrino antineutrino)

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Neutron Decay

L =G

2(d (15)u) (v (1

5) e)

Lagrangian d u:

Decay Width

=GF

2c1

2 5

153

with

c1

= cos C

= 782 keV

Note: the dand u mass eigenstates are not weak eigenstates the neutron decay is not a simple d u decay (quarks are not free)

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Test of Lorentz Structure?

+

vectorcoupling

0*helicity -1 +1

n p e-

+

n p e-

Fermi transition Gamov Teller transition

-1

Momentum

Spin

axialvectorcouplingMomentum

Spin

0*helicity - +1-1- -

?

What is the relative contribution of V and A couplings in nuclear decays?

L =G

2(n (15)p) ( v (1

5) e)

Use a more general Lagrangian:

=cA

cVwith

The strength of the axial-coupling is related to the neutron lifetime!

=cA

cV

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Measurement of the Neutron Lifetime

Techniques:

(ultra) cold neutron traps

in-beam decays

electron detectors

proton detectors

electron-proton coincidence method

n pe e

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Neutron Trap II

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Results Neutron Lifetime

Significant tensions between

experiments!

Best value (PDG 2010): n = 885.7 s

derived from this value: =cA

cV

= 1.26940.0028

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Prediction for cA/c

v

Valence quark wave function of the neutron :

Detailed calculation of vector/axial-vector contributions gives:

cA/c

v= 5/3

Mismatch between experimentand prediction due to:

Relativistic corrections

Neglected sea quarks in the neutron

QCD corrections

e-

e

W-

-p

n

QCD correctionsmodify axial-coupling

spin flip

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Prediction for cA/c

v

Valence quark wave function of the neutron :

Detailed calculation of vector/axial-vector contributions gives:

cA/c

v= 5/3

Mismatch between experimentand prediction due to:

Relativistic corrections

Neglected sea quarks in the neutron

QCD corrections

e-

e

W-

-u

d

gluon

QCD correctionsmodify axial-coupling

spin flip

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Overview Weak Decay Processes

leptonic decay

semileptonic decays

semileptonic decays (S=1)hadronic weak decays (S=1)

heavy quark decays (C=1, B=1, T=1)

Weak decays of quarks and leptons (fermions)

W-Boson decays:

n pe e

e e

p e

e p

Q qW

W l lW q q

Charged currents can mediateinteractions between differentlepton and quark generations(mixing)

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K-Meson Decays

GF2ms

5

Lifetime ~ 10-8

sms 150 MeV

K+ 0 0 +K+ 0 l+

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Weak Decays of B-mesons

GF

2

mb

5

Lifetime ~ 1.5 psmb 4.5 GeV

B0 D+ B0 D0 0 B0 D+ l

l

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Decay of the Top quark

GF2 mt

5

Lifetime ~ 10-25 s

mt172GeV

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Summary Weak Interaction

left handedfermions: (

ee

)L

( )L (

)L (

u

d )L (c

s)L (t

b )L(I3=+ 1 /2I3=1 /2 )

right handedfermions:

e , ReR

, RR

, RR

uRdR

cRsR

tRbR

I3=0

W-bosons couple only on fermions with weak isospin!

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Weak Scattering Experiments

Question:What is the difference between:

A) scattering experiments in classical mechanics

B) weak scattering experiments?

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Weak Scattering Experiments

Video of a classical scattering experiment

Question:What is the difference between:

A) scattering experiments in classical mechanics

B) weak scattering experiments?

Answer:

Despite the fact that em

=1/127 is much smaller

than weak

~1/30electromagnetic interactions

(A) is much more dangerous than (B)weak interactions
http://home/schoning/heidelberg/lehre/SM13/Material/Stupid.mp4http://home/schoning/heidelberg/lehre/SM13/Material/Stupid.mp4

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Strength of Weak InteractionQuestion:

Why is the weak interaction so weak if

weak~1/30 ismuch stronger than

em=1/127 ?

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em=1/127 ?

Answer:

1. Coupling

elm. IA weak IA

e ( 0.3) g ( 0.65) (e , g=4 )

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em=1/127 ?

Answer:

1. Coupling

2. Propagator

elm. IA weak IA

Q2=1 eV2

Q2=1 MeV2

Q2=1 TeV2

e ( 0.3) g ( 0.65) (e , g=4 )

i g

q2

i g + qq /mW2

q2mW

2

i g

mW2

=8GF

2

lowenergy

Ratio(elm./weak)

0.641022

0.641010

0.64102 (

1

q2

)/(1

mW2

)

mW

~ 80 GeV

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Strength of Weak Interaction

At high mass scales E~100 GeV the weak interaction is

stronger than the electromagnetic interaction

Neutrino-nucleon scattering experiments require neutrino beams

of about E

~100 GeV to test weak interactions at reasonable

rates ~O(1pb) because of the propagator effect

(

e e) G

F

2s

e

e

neutrino-electron scattering

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Production of (Myon) Neutrino Beams

Production reactions:

CHARM Detector

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CHARM Detector

CHARM Detector

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CHARM Detector

Why marble?

20

40Ca(CO

3) is an iso-scalar target (same amount ofdand u quarks)

CHARMII Detector

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CHARMII Detector

CHARMII Detector

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CHARMII Detector

Detection of Myon Neutrinos in CC

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Detection of Myon Neutrinos in CC

N

X

long track identified as muon(minimum ionising particle)

length of track is a measureof the muon energy

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(Anti-) Neutrino-Nucleon Scattering

dd

( d

u) =GF

2

42s

neutrino-nucleon scattering

d

d

( u +

d) =GF

2

42

t

antineutrino-nucleon scattering

u

+

d

-

d

u

W

W

Neutrino-Nucleon:

Anti-Neutrino-Nucleon:

t

(A i ) N i N l S i

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dd

( d

u) =GF

2

42s


d

d

( u +

d) =GF

2

42

t


u

+

d

-

d

u

W

J=0

W

Neutrino-Nucleon:


(A ti ) N t i N l S tt i

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dd

( d

u) =GF

2

42s


d

d

( u +

d) =GF

2

42

t


u

+

d

-

d

u

W

J=0

W

J=1

Neutrino-Nucleon:


(A ti ) N t i N l S tt i

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dd

( d

u) =GF

2

42s


d

d

( u +

d) =GF

2

42

t


u

+

d

-

d

u

W

t/s = (1cos)2 = (1y)2

J=0

W

J=1

Neutrino-Nucleon:


dd

(N

X) 1

2

GF2

42x S

dd

(N+

X) 1

2

GF2

42x

t

sS

isoscalar target

Lorentz Invariant Kinematics of the

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Deep Inelastic Scattering Process

The virtuality of the exchanged

photon is given by:

Q2 = q2 = ( p p ')2

q

p

p '

positron

nucleon

W-boson

1sin

4 / 2

N

x P

Relative energy loss (inelasticity):

y = E

= q Pp P

x = q2

2 q P= Q

2

S y

relative fraction of parton momentum:

S = 2 p Pwith cms energy:

neutrino

Measurement of the Differential

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N and anti-N Cross Section

CDHS

Neutrino-Nucleon:


ddy

( N

X) 1

2

GF2

x S

d

dy(

N + X)

1

2

GF2

x S (1y)2

isoscalar target

small deviations from above equations due to x-dependence!

Measurement of the Total N and

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anti-N Cross Section

From simple quarkcounting:(isoscalar target)

(N)

(N)= 3

Parton dynamicsmore complex

Sea Quarks!

measured value ~2is significantly smaller!

Example: Proton Parton Densities

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Example: Proton Parton Densities

Significant component from sea quarks!

multiply by 20!

(Anti ) Neutrino Nucleon Scattering

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d

u

u +

d

u

+

d

-

d

u

W

W

u d

d +

u

+

-

d

uW

W

_

_

d

u

_

_

Unfolding the Valence Quark

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Distributions

dv + dsea + (usea) 2dv + dsea + (usea)

2uv

+ usea

+ (dsea

) uv

+ usea

+ (dsea

)

_ _

_ _

Structure Functions

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S uc u e u c o sRelations:

Measurement:

Extraction of parton densities:

F2

Results xF3

Results

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F2

Results xF3

Results

Comparison N versus lepton-N

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Scattering

Structure function results

obtained in weak interactions

agree well with result obtained

in electromagnetic interactions!

Due to different couplings:

Ratio of d /u

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Ratio of dv/u

v

Result: dV/u

V 0ifx 1

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lecture sm 12

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