Y2 Neutrino Physics (spring term 2017)

Dr E Goudzovski eg@hep.ph.bham.ac.uk

http://epweb2.ph.bham.ac.uk/user/goudzovski/Y2neutrino

Lecture 1

Introduction to particle physics

The neutrino

1

The most common known particle in the Universe

The sun produces ~1038 neutrinos per second But most neutrinos are relics of the Big Bang (~1010 years old) About 300 neutrinos in every cm3 of space

The most “anti-social” known particle

Low-energy neutrino mean free path in ordinary matter: light years ~1024 neutrinos will pass through your body in your lifetime, only ~1 will interact with you

The most elusive known particle

Postulated in 1930; took 26 years to detect Took another 40 years to establish non-zero masses Neutrino detection poses an irresistible experimental challenge

Insight into many aspects of particle physics and beyond

Least understood particle of the Standard Model Emerging fields: neutrino geophysics, neutrino astrophysics

Practical details

2

The course homepage (linked to Canvas):

http://epweb2.ph.bham.ac.uk/user/goudzovski/Y2neutrino

Notes for each lecture

preliminary version: all notes are available;

final version: within 24 hours after the lecture.

Recommended reading lists.

Brief summary of examinable material.

Continuous assessment:

Three problem sheets (weeks 6, 8, 10).

Problem sheets include material up to the Friday lecture.

Examination:

For most of you, combined exam with Nuclear physics.

This lecture

3

Introduction to particle physics

The system of units.

Particle physics distance and energy scale.

Basics of relativistic kinematics; four-momenta.

Reaction thresholds.

Texbooks:

B.R. Martin and G. Shaw. Particle physics. Chapters 1, 2.

D. Perkins. Introduction to high energy physics. Chapter 1.

D. Griffiths. Introduction to Elementary Particles. Chapters 1, 3.

SI units

4

Second: [dimension symbol: T]

Duration of 9,192,631,770 periods of the radiation

corresponding to the transition between the two hyperfine levels

of the ground state of the 133Cs atom

Metre: [dimension symbol: L]

Length of the path travelled by light in vacuum during

a time interval of 1/299,792,458 of a second

[NB: the speed of light is a universal constant]

Kilogram: [dimension symbol: M]

The mass of the international prototype of the kilogram

Re-definition proposed, e.g. via the Planck constant The system of units is evolving

Most SI units are derived from the basic units, e.g.

Energy (E = mv2/2): J = kg m2/s2 dimension: ML2T2

Power (P = E/t): W = J/s dimension: ML2T3

Natural units

5

Natural units based on the language of particle physics:

(1) from quantum mechanics: unit of action ħ [~ 1.1×10−34 Js]

(2) from relativity: the speed of light c [~ 3×108 m/s]

(3) from particle physics: unit of energy GeV [~ 1.6×10−10 J]

Simplify the calculations by setting ħ = c = 1.

Then all quantities have dimensions of powers of energy

(convenient for dimensional estimates)

Energy: GeV Time: GeV1

Momentum: GeV Length: GeV1

Mass: GeV Area: GeV2

Our standard units of basic quantities are

Energy: GeV Time: ħ / GeV

Momentum: GeV/c Length: ħc / GeV

Mass: GeV/c2 Area: (ħc / GeV)2

(1 GeV = kinetic energy gained by an electron accelerated by a potential difference of 109 Volts)

Natural units: examples

6

The standard unit of mass:

m0 = 1 GeV = (1.6×10−19 C × 109 V) / c2 = 1.8×10−27 kg.

( proton mass)

Height: ~1016 GeV1

Mass: ~1029 GeV

Time to the end of this lecture:

~ 3×1027 GeV1

Useful for conversion: ħc = 197 MeV fm, where 1 fm = 10−15 m.

The standard unit of length:

L0 = 1 GeV1 = ħc/(m0c2) = 197 MeV fm / 1 GeV = 0.2×10−15 m.

( reduced Compton wavelength of the proton)

The standard unit of time:

t0 = 1 GeV 1 = L0/c = (0.2×10−15 m / 3×108 m/s) = 0.7×10−24 s.

(typical lifetime of hadronic resonances)

(A non-assessed problem: check these computations)

Particle physics: scale

7

Atom: the Bohr radius

a0 = ħ/(cme) ~

~ 1010 m = 105 fm

Nucleus R ~ a0(me/mp) ~ 1014 m = 10 fm

Protons and neutrons R ~ 1015 m = 1 fm

(4He illustrated)

Quarks:

point-like particles

R < 1019 m = 104 fm

Particle physics

Nuclear physics

Uncertainty principle: de Broglie wavelength

Large Hadron Collider (LHC):

Rutherford experiments (1909):

1 fm (fermi or femtometre) = 1015 m

(New compositeness limits from the LHC: 4+4 TeV beams)

Q1: What is the size of an atom?

Q2: What is the size of an atomic nucleus?

Visible light:

Relativistic kinematics

Lorentz-factor: (quantifies relativistic effects,

e.g. the time dilation)

Momentum and energy:

For massive particles,

E,p when 1.

Therefore <1.

Speed =v/c

E,p vs for proton

(m = 0.938 GeV/c2)

Energy E

Asymptotic

behaviour

Momentum p

Energ

y, m

om

entu

m (

GeV)

8 Classical theory: p=mc

E0=m, p0=0

Speed:

Massive and massless particles

9

Mass-energy-momentum relation:

In natural units:

Momentum p Energ

y E

Massive objects:

speed normalized to speed of light:

Massless objects (e.g. photons)

always travel at the speed of light:

The classical limit:

10

Rest energy: mass-energy equivalence

E0=mc2

Classical

kinetic energy

Example 1: a jet airliner at cruise speed is a classical object

Example 2: an electron produced in a beta decay; typically

a relativistic object

Four-momentum

11

Four-momentum of a particle:

Lorentz invariant

Inner product of four-momenta and the norm of a four-momentum:

For a system of particles:

The mass of a particle (or invariant mass of a system):

(i.e. the same when evaluated in

any inertial reference frame)

Considering that ,

Four-vectors: quantities that transform

according to the Lorentz transformation.

In the centre-of-momentum (COM) reference frame,

NB: throughout this course, “centre-of-momentum frame”

and “centre-of-mass frame” have the same meaning.

Invariant mass of the system evaluated in the COM frame:

Invariant mass of a system

12

Equality (m=mi) is possible only if all particles

are at rest in the COM frame (so that Ei=mi).

Conclusion: the invariant mass of a system

(Lorentz invariant, i.e. can be evaluated in any reference frame)

is greater than or equal to the sum of masses of constituents.

Reaction thresholds

13

Threshold energy of the reaction (fixed target):

Initial state four-momenta (laboratory frame):

(“target”)

Conservation of four-momentum:

Initial state, laboratory frame Alternative notations

A B

Final state

Threshold: a simple example

14

Anti-proton production on atomic nuclei

Produced in pairs to

conserve the baryon number

(at rest)

Threshold energy of the initial proton:

7mp for hydrogen target (mA=mp), 3mp for heavy nuclei) Target recoil (nuclear recoil) term

A more interesting example

15

Cosmic rays (mainly p) interacting with cosmic microwave background (CMB):

Not a fixed target experiment! The reaction threshold:

Ultra-relativistic regime:

Lowest threshold is for head-on collision: =,

CMB temperature: T=2.7K, corresponding energy: E = kBT = 2.3×104 eV.

(cf. proton energy at the LHC ~1013 eV)

(+: same quark content as proton; m = 1232 MeV, mp = 938 MeV)

2

Cosmic ray energy limit

16

Ultra-high energy cosmic ray

energy spectrum measurements

Greisen-Zatsepin-Kuzmin

(GZK) limit on cosmic ray energy,

predicted in 1966

The Pierre Auger experiment:

one of the 1600 water Cherenkov

tanks distributed over ~3,000 km2

(Mendosa, Argentina)

Proton energy required to interact with CMB:

~ 10 Joules

Energy, eV

Collider & fixed target experiments

17

A

Fixed target experiments:

Head-on collisions in laboratory

frame with opposite momenta:

Collider experiments:

“Energy frontier” experiments. Example: LHC at CERN, ECM = 13 TeV.

B

A B

High energy fixed target experiment:

ultra-relativistic beam (EA≫mA, mB)

However easy to achieve high luminosity: “intensity frontier” experiments

Example: E=400 GeV protons

(m=938MeV/c2) from the

CERN SPS accelerator

on a proton target

:

Summary

18

The natural system of units (ħ=c=1) is used in particle physics:

all quantities are expressed in powers of energy (GeV).

By the Heisenberg’s uncertainty principle, momentum required

to probe a distance scale is p 1/ (in natural units).

Particle accelerators are the most powerful microscopes.

Elementary particles often travel at speeds close to c:

relativistic (rather than classical) kinematics applies.

Lorentz-invariance and conservation of the 4-momenta provide

a useful tool to solve simple kinematic problems

(reaction thresholds, accelerator energy reach, etc.)