The World of Elementary Particle Physics Demystified Eduardo Pontón - IFT & ICTP/SAIFR IFT - Perimeter - ICTP/SAIFR Journeys into Theoretical Physics, July 18-23
Plan 1. What are these lectures about 2. How do we know what we know 3. Field Theory and Symmetries 4. Hidden Symmetry and the Higgs Boson
Part I Our Subject Matter
Particle Physics Perseus Galaxy Cluster What do YOU mean?? Gold Dust? Installation inspired by the search for the Higgs boson (by Becs Andrews) Atoms of Niobium (41) and Selenium (34)
Particle Physics typically understood as the realm of subatomic particles Quantum mechanical effects an essential component!
It will be useful to recall some facts in the context of the birth of Quantum Mechanics!
Planck's law for black-body radiation: For radiation at temperature T, average energy in volume V with frequencies between! and! + d! : hde(!)i = V ~ 2 c 3! 3 d! e ~! 1 = dn(!) ~! e ~! 1 Planck, 1900 Number of modes in V and [!,! + d!] dn(!) = V!2 d! 2 c 3 Einstein s formula for mean energy fluctuations in a black body: h( E) 2 i = hde(!)i2 dn(!) + ~!hde(!)i Einstein, 1909
To derive it, just need to recall a bit of statistical mechanics: Canonical Partition Function: Z = X n e E n Obtain average energy by differentiating w.r.t. : hei 1 Z X n E n e E n = @ log Z @ Differentiating w.r.t. again, we can obtain the mean square energy fluctuation: h( E) 2 i = he 2 i hei 2 = @hei @ Upshot: can easily get the energy fluctuation, if we know the energy as a function of temperature!
Einstein just applied this to Planck s law: h( E) 2 i = @hei @ ~! hde(!)i = dn(!) e ~! 1 and for any frequency: dn(!) ~! 1 Rayleigh-Jeans law ~! 1 ~! Wien s formula dn(!) ~! e h( E) 2 i = hde(!)i2 dn(!) + ~!hde(!)i Then he proceeded to interpret the result
h( E) 2 i = hde(!)i2 dn(!) + ~!hde(!)i To interpret the linear term The quadratic term is exactly what is obtained for classical waves (Homework!) Recall that for an ideal gas, i.e. N non-interacting particles: hei = 3 2 Nk BT = 3N 2 Hence: The concept of wave-particle duality was born: h( E) 2 i = @hei @ = k B T hei the effects of the two causes of fluctuations [waves and particles] act like fluctuations from mutually independent causes (additivity of the two terms) Einstein (1909) Attempts at obtaining this from dynamics (as time averages) could only give one or the other term
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In our typical particle physics experiments, we see the events as particles: they resemble the electron-by-electron setup! But we are interested in the underlying distribution (in different variables) In addition, the experimental conditions we are focusing on are such that the particles are moving close to the speed of light! Theoretician perspective: need to be able to compute quantum mechanical amplitudes that reflect the properties of special relativity: No inertial frame is special (laws appear the same in any) Nothing travels faster than the speed of light (causality structure) Amplitudes must allow a probabilistic interpretation (unitarity) Quantum Mechanics + Special Relativity = Quantum Field Theory
If we want to be more precise: Quantum Field Theory of Point Particles A point particle type specified by: mass & spin (or helicity, if massless) What if the fundamental constituents were string-like, or even more complex? A matter of scales: if our probe cannot resolve the string/brane, we will be able to describe its physics by QFT
The lesson is more general: Protons/nuclei can look point-like under many experimental conditions Atoms/molecules can look point-like to a typical human QFT can be used to describe any such system it has nothing to do with the system being fundamental But QFT becomes essential when the energies are such that particles can be produced the realm we want to explore here!
The Quantum Harmonic Oscillator (if you need a review) Quadratic Hamiltonian: H = 1 2 ˆp2 +! 2ˆx 2 r ~ ˆx = 2! a + a Define creation and annihilation operators via: r ~! ˆp = i a a 2 H = N + 1 Which diagonalize the Hamiltonian: ~! N = a a 2 n-quanta/particle states obeying Bose-Einstein statistics: 1i = a 0i ni = 1 p n! (a ) n 0i [a, a ]=1 [a, a] =[a,a ]=0
Let us go back to the wave-particle puzzle h( E) 2 i = hde(!)i2 dn(!) + ~!hde(!)i which had to wait until 1925 for a satisfactory solution (Pasqual Jordan in the Dreimännerarbeit) Since the E&M field (in a box) is a set of decoupled simple harmonic oscillators, we can quantize each one, following the quantum mechanical treatment known to apply to a single oscillator. Considering a 1D case: (as Jordan did) r ~ box of size L and wavevectors k n = n/l =! n (x, t) = X n 2! n a n e i! nt+k n x +h.c. [a n,a n 0 ]= n,n 0 [a n,a n 0]=[a n,a n 0 ]=0
Considering a 1D case: box of size L and wavevectors r ~ k n = n/l =! n (x, t) = X n 2! n a n e i! nt+k n x +h.c. [a n,a n 0 ]= n,n 0 [a n,a n 0]=[a n,a n 0 ]=0 The energy density is found to be H = 1 2L Z L 0 dx (@ t ) 2 +(@ x ) 2 = X n (N n + 1 2 )~! n By putting the oscillators in a thermal bath at temperature T, and computing the mean square energy fluctuations in a small segment a << L, the two terms were recovered: h( E) 2 i = hde(!)i2 dn(!) + ~!hde(!)i For a detailed derivation see: Duncan & Janssen, arxiv:0709.3812 These considerations, together with the seminal papers by Dirac (1926,1927), gave birth to Quantum Field Theory
Upshot: the canonical quantization of a field (continuous) incorporates automatically the concept of a particle (discreteness)
In addition: the formalism allows to describe the creation and destruction of quanta (particles) (provided energy and momentum can be conserved) Note also that the quantum mechanical treatment of the E&M field had to be intrinsically relativistic
Dimensional Analysis The only difference between a rut and a grave are the dimensions Ellen Glasgow Existence of (maximum) universal speed: c = 299 792 458 m/s Universal unit of action: ~ =6.582 119 514(40) 10 16 ev s Universal Boltzmann constant: k B =8.617 3324 (78) ev/k Since we are interested in quantum, relativistic systems, better to measure velocities and action in units of c and! ~ Natural units: c = ~ = k B =1 Then any mass/energy scale is associated with a length scale through the Compton wavelength: and to a time scale through c. o = ~/(mc) Everything is energy and that s all there is to it. Match the frequency of the reality you want and you cannot help but get that reality. It can be no other way. This is physics. Pseudo-scientific quote, probably from a channeler named Darryl Anka who has assigned the words to an entity named Bashar!!
Dimensional Analysis Some useful reference scales: Most of the mass we see around us comes from the mass of protons/neutrons Nucleon mass: m p 1 GeV = 10 9 ev 10 27 kg Associated length scale: o p (1/5) 10 15 m = (1/5) Fermi Associated time scale: 10 24 s Note: the charge radius of the proton is about 1 Fermi Sometimes dimensionless constants have a crucial effect on the physics. Compare to the hydrogen atom. The underlying mass scale is: m e 0.5 MeV = 0.5 10 6 ev m p /2000 Relevant energy scale is and the length scale is a 0 = o e / E 0 = 1 2 2 m e 10 ev o e 2000 o p A big, non-relativistic system because 1/137 1
The Standard Model Mendeleev s Table
Particles and Particles
Rutherford at his Lab. A Paradigm
Seeing Particles ~B P.A.M. Dirac (1931) Discovery of the Positron (1932) C. Anderson Cloud chamber s picture of cosmic radiation
Simpler Times Cloud Chamber (muons, alpha and beta radiation) Alpha Particles (Polonium)
16 GeV beam entering a liquid-h 2 bubble chamber at CERN (~1970)
The discovery of neutral currents by the Gargamelle bubble chamber (1973)
... A Long Way
Find an LHC Guide/FAQ with lots of interesting information at: http://cds.cern.ch/record/1165534/files/cern- Brochure-2009-003-Eng.pdf