inleiding subatomaire fysica - high energy physicsfilthaut/teach/isaf/slides.pdf · inleiding...

Inleiding Subatomaire FysicaFrank Filthaut

http://www.hef.ru.nl/~filthaut/teach/isaf/welcome.php:course information, including lecture notes

Tuesday, March 27, 2012

http://www.hef.ru.nl/~filthaut/teach/isaf/welcome.php

http://www.hef.ru.nl/~filthaut/teach/isaf/welcome.php

Course Contents1.Introduction

2.Quantum Electrodynamics

heuristic derivation of Feynman diagrams

3.Strong Interaction and Quantum Chromodynamics

hadrons and the static quark model

dynamics: deep-inelastic scattering

QCD

4.Weak Interaction

leptons: unitarity, gauge bosons

Higgs mechanism

quarks: CKM-matrix, discrete symmetries, CP violation

(neutrino oscillations)

2


Course StrategyMain aim: explain how the Standard Model “works”

Emphasis on theoretical aspects

but information from experiment is indispensable! Wherever relevant or useful, experimental results will be discussed

No time for aspects of instrumentation

but see next pages for generally relevant properties

3


Particles in the Standard Model

4


Current Research

The Higgs boson has not been found yet

an important research topic

There are theoretical problems (“fine tuning” / “hierarchy”) related to the Higgs boson, and the Standard Model cannot describe gravitation

searches for experimental evidence for models for “beyond the Standard Model” physics

The Standard Model does not explain the existence of dark matter and dark energy

interaction with astrophysics (cosmology, ...)

The Standard Model is extraordinarily successful in describing elementary particles and their EM, weak, and strong interactions... but it is incomplete!

5


Not an Aim: understanding of detectors

6


But: which particles are measured?

Typical functionality of a multi-purpose collider detector (see animation):charged particles are identified and and their momenta measured intracking detectors

electrons, positrons, and photons are absorbed, identified, and their energy measured in the electromagnetic calorimeter

strongly interacting particles (hadrons) are absorbed and their energy measured in the hadronic calorimeter

muons are identified (and, in some experiments, their momentum measured) in the muon system

short-lived particles are reconstructed through their decay products

(high-energy) quarks/gluons manifest themselves as hadron jets

neutrinos escape undetected

We will also encounter examples of detectors with more specific measurement purposes

7


Atlas Experiment: Animation

8


Example: Event Display

hadron jets

charged particletrajectories

identified electron or positron

neutrino hypothesis(apparent lack of

momentum conservation)

9

identified muon


Non-relativistic: Schrödinger equation

Continuity equation:

i∂∂ t

ψ(x) =

−∇2

2m+V (x)

ψ(x) −i

∂∂ t

ψ∗(x) =

−∇2

2m+V (x)

ψ∗(x)

i

ψ∗(x)∂∂ t

ψ(x)+ψ(x)∂∂ t

ψ∗=− 1

2m

ψ∗(x)∇2ψ(x)−ψ(x)∇2ψ∗(x)

i∂∂ t

|ψ(x)|2 =− 12m

∇ ·

ψ∗(x)∇ψ(x)−ψ(x)∇ψ∗(x).

ρ(x) = |ψ(x)|2,

j(x) =−i2m

ψ∗(x)∇ψ(x)−ψ(x)∇ψ∗(x)

∂∂ t

ρ(x)+∇ ·j(x) = 0

multiply by ψ* multiply by ψ

10


Week 2


Negative-energy solutions

Identical effect on “the system” (quantum numbers):

emission of an anti-particle

absorption of a (E<0) particle

V

V

t

x

≅

e+ (E>0) e- (-E<0)

2nd order process: scattering of a particle off of two potentials

12


Discovery of the positron

Larger curvature above than below the Pb plate:

particle travels upward

Path length much longer thanexpected for protons: a light particle

Sign of the curvature in the B-field:positively charged particle

13


Perturbation theoryAdd perturbation term V to system H0 which can be solved completely:

Expand wavefunction in terms of unperturbed basis:

This yields an equation describing the time evolution of the respective coefficients:

ψ(x , t) =

n

an(t)φn(x)e−iEnt .

H = H0 +V (x , t), H0φn = Enφn with

d3xφ∗n(x)φm(x) = δnm.

i∂ψ(x , t)

∂t=

n

φn(x)e−iEnt

Enan(t) +

dan(t)dt

= (H0 + V (x , t))ψ =

n

(H0 + V (x , t))an(t)φn(x)e−iEnt

=

n

(En + V (x , t))an(t)φn(x)e−iEnt

⇒ i

n

dan(t)dt

φn(x)e−iEnt =

n

V (x , t)an(t)φn(x)e−iEnt

14


Perturbation theory (2)

Multiply by ϕ*f eiE

ft and integrate over space:

Integrate (formally) over time, assuming initial state i:

Make Lorentz-covariant:

This yields:

NB: in the last two equations only first-order terms were retained

daf (t)dt

= −i

n

an(t)e−i(En − Ef )t · Vfn(t), with Vfn(t) =

d3xφ∗f (x)V (x , t)φn(x)

af (t) = δfi

+ (−i) t

−Tdt Vfi (t )e−i(Ei − Ef )t

+ (−i)2

n

t

−Tdt Vfn(t )e−i(En − Ef )t ·

t

−Tdt Vni (t )e−i(Ei − En)t + ...

φn(x) ≡ φn(x)e−iEnt ⇒ af (t) = −i t

−Tdt

d3xφ∗

f (x)V (x)φi (x).

t → ∞ : Tfi → −i

d4xφ∗f (x)V (x)φi (x)

15


Week 3


Delbrück scatteringObserved (1973, G. Jarlskog et al.) in scattering of high-energy (E ~ 7 GeV) photons off uranium

effect ~ Z4

Small scattering angles (~ mrad)!


Electron Magnetic MomentDirac equation reduced to two-component spinors:

Spatial (LHS) part:

RHS, non-relativistic limit:

Conclusion:

σ · (p + eA)

2uA = ((E + eA0)2 − m2)uA

σ · (p + eA)

2= σiσj

pipj + e2AiAj + e(piAj + Aipj )

= (δij + iijkσk )

pipj + e2AiAj + e(piAj + Aipj )

= pipi + e2AiAi + e(piAi + Aipi ) + ie(piAj + Aipj )ijkσk

= (p + eA)2 + e(∇× A) · σ= (p + eA)2 + eσ · B

((E + eA0)2 − m2) = ((m + (E + eA0 − m))2 − m2) ≈ 2m(E + eA0 − m)

(E − m)uA =

(p + eA)2

2m− eA0 +

e2m

σ · B

uA

18


Week 4


Discovery of the charged pion(and of the muon...)

π±

μ±

e±

1.charged pion is stopped2.pion decays3.resulting muon is stopped4.muon decays5.electron/positron escapes

20


Discovery of “strange” particles

charged kaon:angle and energy e-

V0 (KS, Λ): “vertices”,momenta of outgoing particles


Lifetimes of “strange” particles

particle mass (MeV) lifetime (s) (main) decay modesspin 0

K− 494 1.2 · 10−8 µ−νµ, π−π0

K0S 498 9 · 10−11 π+π−, π0π0

K0L 498 5 · 10−8 π±e∓νe, π±µ∓νµ, π+π−π0, π0π0π0

spin 1/2Λ 1116 2.6 · 10−10 pπ−, nπ0

Σ+ 1189 8 · 10−11 pπ0, nπ+

Σ0 1193 7 · 10−20 ΛγΣ− 1197 1.5 · 10−10 nπ−

Ξ− 1322 1.6 · 10−10 Λπ−

Ξ0 1315 3 · 10−10 Λπ0

Σ+, Σ- are not antiparticles!

KS and KL are “mixtures” of K0 and K0

will be covered in context of weak interaction

—


Week 5


Meson octets

,_ +0

K K

KK

π π πη

_

0 +

_0

S = 0

Q = −1 Q = 1Q = 0

S = 1

S = −1

,_ +0

K

K_

S = 0

Q = −1 Q = 1Q = 0

ρ ρ ρω

K_* *0

0* K *+

S = 1

S = −1

JP=0- JP=1-

24


Baryon octet and decuplet

ΣΣΣ

n p

Ξ Ξ

Λ,

_

_ +

0

0

Q = −1 Q = 0 Q = 1

S = 0

S = −1

S = −2

ΣΣΣ

Ξ Ξ

Δ Δ Δ Δ

Ω_

_0* *

*_ 0* *

_ 0 + ++

+

Q = −1

Q = 0

Q = 1

Q = 2

S = 0

S = −1

S = −2

S = −3

JP=1/2+ JP=3/2+

25


Discovery of the Ω- particle

Photographed using a “bubble chamber” nearly boiling fluid, charged particles cause bubbles

26


Baryon masses in the spin interaction model

Particle Predicted mass (GeV) Measured mass (GeV)n, p 0.89 0.939Λ 1.08 1.116Σ 1.15 1.193Ξ 1.32 1.318∆ 1.07 1.232Σ∗ 1.34 1.385Ξ∗ 1.50 1.533Ω− 1.68 1.673

M = m1 + m2 + m3 + A

S1 · S2

m1m2+

S1 · S3

m1m3+

S2 · S3

m2m3


Meson masses in the spin interaction model

Particle Predicted mass (GeV) Measured mass (GeV)π 0.15 0.137K 0.46 0.496η 0.57 0.549ρ 0.77 0.770ω 0.77 0.782K∗ 0.87 0.892φ 1.03 1.020

M = mq + mq + ASq · Sq

mqmq


Discovery of the J/Ψ particle

J Ψ


Spectroscopy of heavy mesons

2

4

6

8

10

12

ME

SO

N M

AS

S (

GE

V)

c J/

’c

’

hc c0

c1

c2

b

’b

’

’’

b0b1(1P)b2

b0b1(2P)b2

(1D)

hb(1P)

hb(2P)

Bc

BsB

B*

s

B*

DsD

exptfix parameters

postdictionspredictions

30


Inelastic electron-proton scatteringExperiments by Friedman, Kendall, Taylor et al., 1969:

Ee ≲ 20 GeV

measurement of inclusive cross sections (i.e., not only e-p final states are being considered)

First indication of the proton’s composite nature


Bjørken scaling

Q2

2mpx W2(x , Q2)

Experiment: deep-inelastic electron-proton scattering,

Ee ≲ 20 GeV

x=0.25


Week 6


Gell-Mann matrices

λ1 =

0 1 01 0 00 0 0

λ2 =

0 −i 0i 0 00 0 0

λ3 =

1 0 00 −1 00 0 0

λ4 =

0 0 10 0 01 0 0

λ5 =

0 0 −i0 0 0i 0 0

λ6 =

0 0 00 0 10 1 0

λ7 =

0 0 00 0 −i0 i 0

λ8 = 1√3

1 0 00 1 00 0 −2

34


Q2 dependence of αs

0

0.1

0.2

0.3

1 10 102

! GeV

!s(!

)

(source: PDG)


Measurements of F2(x,Q2)

log-log scale!

data for different values of x moved by a factor 2i (for readability)

Q2 (GeV

2)

F2(x

,Q2)

* 2

i x

H1ZEUSBCDMS

E665NMCSLAC

10-3

10-2

10-1

1

10

102

103

104

105

106

107

108

109

10-1

1 10 102

103

104

105

106

(source: PDG)


Measurements of F2(x,Q2)

same data versus x

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

10-6

10-5

10-4

10-3

10-2

10-1

1x

F2(x

,Q2)

ZEUS

H1

SLAC

BCDMS

NMC

0

1

2

3

4

5

6

7

10-7

10-6

10-5

10-4

10-3

10-2

10-1

1x

F2 c

c(x

,Q2)

+ c

(Q)

H1

ZEUS

EMC

0

0.025

0.05

0.075

0.1

0.125

0.15

0.175

0.2

10-6

10-5

10-4

10-3

10-2

10-1

x

F2 b

b(x

,Q2)

+ k

(Q)

(source: PDG)


e+e- ⟶hadrons: jets

Events with 3 jets: first direct evidence for the existence of the gluon


e+e-⟶hadrons: cross section

10-1

1

10

102

0.5 1 1.5 2 2.5 3

Sum of exclusivemeasurements

Inclusivemeasurements

3 loop pQCD

Naive quark model

u, d, s

!

"

#

!!

2

3

4

5

6

7

3 3.5 4 4.5 5

Mark-IMark-I + LGWMark-IIPLUTODASPCrystal BallBES

J/$ $(2S)

$3770

$4040

$4160

$4415

c

2

3

4

5

6

7

8

9.5 10 10.5 11

MD-1 ARGUS CLEO CUSB DHHM

Crystal Ball CLEO II DASP LENA

!(1S)!(2S)

!(3S)

!(4S)

b

R

!s [GeV]

(source: PDG)

normalised to σ(e+e-→μ+μ -)


Week 7


Neutrino-nucleon scattering

in both cases: muon neutrinos

shown: σ/E

(source: PDG)


Evidence for the Z boson

Gargamelle experiment (bubble chamber), 1973

atomic electron

γ conversion

γ conversion

(source: CERN)


Week 8


Discovery of the Z bosonUA1 experiment, 1983

e±

e∓

(source: CERN)


Number of neutrino generationsTotale Z boson decay width ΓZ: width of the resonance

Partial decay width Γhad: cross section at the peak of the resonance

same for the decay to lepton pairs

more complicated for decay to e+e-: interference

Radiative corrections need to be applied!

in particular, initial state photon radiation Ecm [GeV]

! had [

nb]

! from fitQED unfolded

measurements, error barsincreased by factor 10

ALEPHDELPHIL3OPAL

!0

"Z

MZ

10

20

30

40

86 88 90 92 94

ΓZ = Γhad + Γ + Γνν


Extra slides


Parity violation as a tool

τ-→π-ντ decays

Eπ in the lab frame directly related to decay angle θ in the τ rest frame

Used at LEP 1 to measureτ polarisation

this too arises from parity violation, but in the production and decay of the Z boson 0

500

1000

0 0.5 1E! / E

beam

Nu

mb

er

of

De

ca

ys

!

"#

$_

#_

(source: CERN)


Evidence for the decay KL→π+π-

Consider large decay times (so that only KL remain)

Reconstruct π+π-

invariant mass (m*) and direction with respect to the beam (cosθ)

other particles: combinatorial backgrounds

Kaons from the beam clearly visible


CP violation in other decays

Volume 52B, number 1 PHYSICS LETTERS 16 September 1974

Their charge asymmetry is evaluated as a function of T' and p ' in bins of width At ' = 0.5 ! 10-10s and p ' = f

2 GeV/c starting at rmi n = 2.25 ! 10 -10 s and Pmin = 7 GeV/c.

The mass difference Am is determined by a comparison of the time dependence of the measured charge asym-

metry with the theoretical expectation fi(r', Am, y) for the set of parameters to be determined. The theoretical

function ~ and its derivatives are calculated by Monte Carlo techniques from eq. (2). This treatment accounts for

the following:

- The K~3 matrix elements according to V - A theory with linear formfactors for the hadronic current [3] and

radiative corrections [4].

- The observed beam profile, and the experimental resolution and acceptance.

- Transformation from the true kaon momentum p and lifetime r to the measured quantities p ' and r ' .

- The shape of the kaon momentum spectrum and the dilution factor A(p) as obtained in the K~2 analysis [1 ]

The influence of the actual form of the matrix element on the charge asymmetry is weak. The shape of the

momentum spectrum enters only indirectly in the transformation from r to r ' . The K S lifetime and the K L charge

asymmetries are taken from previous results of the same experiment [ 1 ,2 ] . The results of the best fits to the

measured charge asymmetries are shown in figs. 1 and 2. The A S - A Q fac tory is left free in the fits. The uncor-

rected values for the KL-K S mass difference are:

Am(Ke3 ) = (0.5287 -+ 0.0040) ! 1010 s -1 , A m ( K 3 ) = (0.526 + 0.0085) ! 1010 s -1 .

0 0 8 -

008 -

0.04 -

0.02 -

Z

4. +

Z

o i

Z

i

v

- 0 0 2 -

B

-0.04

-01)6

-0 .08

CHARGE ASYMMETRY IN THE DECAYS K°----~Tc;e'*v

+~,~- + + i L

i

"I .

dl I • I l I • a t

I I I I I i

20

K ° DECAY TIME x ' (lO'l°sec)

Fig. 1. The charge asymmetry as a function of the reconstructed decay time r' for the Ke3 decays. The experimental data are compared to the best fit as indicated by the solid line.

116

~ 10 τ(KS)

dΓ(K0 → π+e−νe, t)− dΓ(K0 → π−e+νe, t)dΓ(K0 → π+e−νe, t) + dΓ(K0 → π−e+νe, t)


Solar neutrino fluxdetectable in Davis’s experiment


Super-Kamiokande detector

50 kton water, viewed by phototubes


Oscillations: Super-Kamiokande

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

1 10 102

103

104

L/E (km/GeV)

Data

/Pre

dic

tion (

nu

ll osc.)!

relation between zenith angle and path length


Oscillations: KamLAND


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