Rough Schedule. Units often used in Elementary Particle Physics

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Curtis Long
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1 Rouh Schedule (1) The course orientation and a special lecture on "Understandin of radio activities now in Sendai". (2) Rutherford Scatterin and Concepts for Experiments. (3) Accelerators and Particle Detectors. (4) Elementary Particles and their Interactions. (5) Quark model of Hadrons and Oscillation of Neutral Kaon. (6) Symmetries, P, C, and CP violations. (7) Neutrinos (8) The Standard Model (Gaue symmetry, His, etc.) 1 Units often used in Elementary Particle Physics Exa [E-] Tera [T-] Gia [G-] Mea [M-] kilo [k-] mili [m-] micro [µ-] nano [n-] pico [p-] femto [f-] * Lenth: 1[fm]=1x10-15 m (~size of proton) *Time: 1[µs], 1[ns], Used in experiments [s](time a liht passes throuh a proton), used in theories. * Velocity: Relative velocity with respect to liht velocity [c] is used. β=v/c Example, v=1.5x10 8 [m/s]=0.5c! β=0.5 Mostly β~1 for hih enery physics. 2

2 Units often used in Elementary Particle Physics Exa [E-] Tera [T-] Gia [G-] Mea [M-] kilo [k-] mili [m-] micro [µ-] nano [n-] pico [p-] femto [f-] * Enery: 1 electron volt = 1[eV]=1.6x10-19 [J] 1[eV]=The enery that a particle with electric chare e (=1.6x10-19 [C]) obtains when accelerated by 1[V] voltae ap. The total enery of Avoadro number of particles which have 1eV of enery each is 100,000[J] 1[eV]~10,000[K] 3 Units often used in Elementary Particle Physics Exa [E-] Tera [T-] Gia [G-] Mea [M-] kilo [k-] mili [m-] micro [µ-] nano [n-] pico [p-] femto [f-] * Mass: The equivalent enery of a particle with mass m at rest is E 0 =mc 2.!m=E 0 /c 2 m is expressed as unit [ev/c 2 ] 1[eV/c 2 ]=1.8 x10-36 []. [/c 2 ] is often omitted. We say "electron mass is 511 kilo electron volt." 4

3 Units often used in Elementary Particle Physics Exa [E-] Tera [T-] Gia [G-] Mea [M-] kilo [k-] mili [m-] micro [µ-] nano [n-] pico [p-] femto [f-] * Momentum: [p]=[mv]=[ev/c] There is a relation E 2 = ( pc) 2 + ( m 0 c 2 ) 2 Units often used in Elementary Particle Physics Exa [E-] Tera [T-] Gia [G-] Mea [M-] kilo [k-] mili [m-] micro [µ-] nano [n-] pico [p-] femto [f-] * Anular momentum: L = [p*r]=[(ev/c)*x] =[ev s]. very often expressed by relative manitude to the reduced Planck constant:! = h /2π = ev s Anular momentum of l=1 state! L =1!. l=1 = 1(MeV/c) x 0.005fm s =1 2 [!] [!] is very often omitted. [ ] electron spin! We say "electron spin is ½ (one-half)." [ ]

4 ((,,,, )) )),, )),, c β=v/c v=1.5x10 8 [m/s]! β = 0.5 (( (( )) )) (( ((! 2 " c (( (( ((,,,, (( 1 $ t " = & t v 1 ( v c) 2 % c x ' c=1 1 Lorentz ), t " = transformation 2 ( 1 β 2 Schroediner Equation i! ψ t = &!2 " ) ( 2 +V+ ψ ' 2m *!=1. i ψ t = & 1 '( 2m ( t βx) " ) 2 +V * + ψ natural unit expression fine structure constant (( 1 [!c] ~ 200[ MeV fm] α = e2 = 1 4πε !c 200 MeV fm [ ] ~ [ ] 137 Example: We can calculate the potential enery of the Hydroen tom from the radius (a 0 ~5x10-11 [m]), usin "back of the envelope calculation". [ ] [ ] V H = e2 1 = α ev m ~ 4πε 0 a 0 a m physicists memorize this. ~ 1.4[ MeV fm] ~ 28[ ev] 8

Particle Physics => Understand the History of the Universe Particle Physics 9,, (( )) )),,,,

6x10-5 [ev/kelvin]):boltzmann constant T Rouhly 1eV~10,000K E Temperature ~ particle collision

3meV (cosmic MW, current universe) 300K ~30meV (room temp.

5 Particle Physics => Understand the History of the Universe Particle Physics 9,, (( )) )),,,, Relation between temperature and particle enery E=k B T, k B (=8.6x10-5 [ev/kelvin]):boltzmann constant T Rouhly 1eV~10,000K E Temperature ~ particle collision enery! possibility of reactions between the particles 3K ~0.3meV (cosmic MW, current universe) 300K ~30meV (room temp., neutrino mass) 100,000K ~10eV (ionization of hydroen atom) K~ 100MeV (Hadron masses) K~ 100GeV (Weak Boson, His masses) K~ 10TeV (max accelerator enery (LHC)) K~10 20 ev (max cosmic ray enery)

6 ,, (( )) )),,,, t=0: BiBan The collision eneries are so hard that the four interactions (electromanetic, weak, stron and ravity) behaved same. t~10-43 s, E=10 28 ev The ravity was separated from the other three interactions. t~10-37 s, R~10-19 m, E=10 24 ev Inflation. The universe expanded quickly. Collision enery became weaker and the stron and EW interactions were separated. t~10-10 s, R~1cm, E ~100GeV, "Plasma" of elementary particles. γ +γ e + + e, q + q, W + +W,! EW interactions were separated into EM and Weak interactions.,, (( )) )),,,, t >10-5 s, R>1000m, E~100MeV Quarks bound to form hadrons u + d π +, u + u + d p t >10 2 s, R>3,000,000km, E<100KeV Unstable particles decay out. π + µ + +ν µ e + +ν e +ν µ +ν µ Protons and neutrons bind to form deuteron n + p D +γ t >3x10 5 y, E<1eV Nucleus and electrons bind to form atom. p+e!h Atoms bind to from molecules C+2H 2 " CH 4 12

7 ,, (( )) )),,,, t >10 9 y, E<1meV Stars and alaxies are formed. DNA and life is enerated t ~1.3x10 10 y, E~0.3meV Now, we are here and thinkin about the universe. The evolution of the universe is closely related to the properties of elementary particles and its interactions. To understand the history of our universe, we need to know the properties of elementary particles. 13 Elementary Particle Physics We have "standard model of elementary particles". It succeeds to explain most of the the experimental results (except for neutrino oscillation). It is built on the relativistic quantum mechanics with aue symmetry to introduce interactions and His mechanism to produce particle masses. It includes 6 quarks, 6 leptons 4 types of aue bosons and 1 His boson. 14

8 There are two types of elementary particles (1) Fermions: Spin=1/2 * Fermi-Dirac statistics (Pauli's exclusion principle) * Buildin block of matter. (2) Bosons: Spin=0, 1 * Bose Einstein Statistics (basic principle of the laser) * Mediate forces. Spin: Classical analoy = self-rotation Many of the cases, it is OK to imaine so. But there is limitations Spin=1 = Anular momentum of p-orbit electron of H Spin=1/2 = half of it. 15 (1) Fermion: Spin=1/2 # spin-up ψ = % 1& $ 0' ( spin-down # ψ = % 0& $ 1' ( Name Chare 1 st (eneration) 2 nd (eneration) 3 rd (eneration) Lepton -1 e μ τ 0 ν e ν µ ν τ Quark +2/3 u (up) c (charm) t (top) -1/3 d (down) s (strane) b (bottom) 16

9 (2) Boson: Spin=1 # 1& % ( s z =+1 ψ = 0 % ( $ 0' # 0& % ( s z =0 ψ = 1 % ( $ 0' # 0& % ( s z =-1 ψ = 0 % ( $ 1' Gaue bosons chare EM Weak Stron γ(photon) Z 0 (luon) ±1 W ± Spin=0 His boson ψ =1 chare 0 H 0 17 The Standard Model of# Elementary Particle Physics His H 0 18

10 The size of elementary particles electron <10-18 m γ proton quarks ~10-15 m ~10-10 m H atom 19 Mass of Elementary Particles Uranium Hydroen 1eV/c 2 =1.8x10-36 mass (MeV/c 2 ) 1.E+07 1.E+06 1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E-07 1.E-08 1.E-09 1.E-10 His γ, t Z 0 c b W ± s τ d µ u e νe (Direct) (m1<<m2<m3 assumed) m eneration γ <6x10-17 ev/c 2 ν3 ν2 20

Interactions: (1) bind particles Electro-Manetic Interactions electron γ F = 1 e 2 4πε 0 r, U = 1 e 2 2 4πε 0 r proton H atom Stron Interactions e 2 4πε 0 = 1 137.

11 Interactions: (1) bind particles Electro-Manetic Interactions electron γ F = 1 e 2 4πε 0 r, U = 1 e 2 2 4πε 0 r proton H atom Stron Interactions e 2 4πε 0 = ! "c [ ] α "c [ ] α: fine structure constant. Characteristic strenth of EM interaction (~1%) 21 Interactions: (2) let particles decay β-decays n p + e +ν e n p d d d W - Caused by Weak Interactions ν e e - 22

12 Interactions:! (3)scatter! particles Probability of a + b a + b collision by various interactions σ=10-26 cm 2 1/100 σ=10-28 cm 2 1/1,000,000,000 σ=10-37 cm 2 pp Stron interaction γp EM interaction 2 nd order EM interaction γγ νν Weak interaction EPPB Suekane 23 beam enery Interactions Without interactions nothin happens. Our complex structure of the universe is made by the interactions. Basics of Interaction How scatterin happens? example: ElectroManetic scatterin e + u e + u e - e - What is oin on here? 24

k f =k i +q q γ +2e/3 k i (2) u-quark with four momentum k i absorbs the photon and is scattered to the momentum k f =k i +q e - p i p f =p i

13 e - p i -e γ p f =p i q q (1) electron with four momentum p i emits photon with momentum q. The electron is kicked back and momentum becomes p f =p i -q. k f =k i +q q γ +2e/3 k i (2) u-quark with four momentum k i absorbs the photon and is scattered to the momentum k f =k i +q e - p i p f =p i q -e q γ k f =k i +q +2e/3 k i (1)+(2) This is a diaram of scatterin with EM interactions 25 e - -2e 2 /3 e - It is NOT a direct contact of particles. electron γ proton In hydroen atom, the proton and electron do not touch each other. But electron feels the EM force. H atom

14 e - Z Ζ 0 Z ν e e - W W - d W e - Neutral Current Weak Interaction e + u e + u Chared Current Weak Interactio e + u ν e + d d G d R S ( RG ) Stron Interaction S u G d R + u G d G + u R u R YES Quarks u,d,c,s,b,t Fermion (spin=1/2) Stron Interaction () YES NO Leptons Namin of Fermions Electromanetic Interaction (γ) NO hared leptons e,µ,τ Neutrinos ν e,ν µ,ν τ 28

The story of the Universe

The story of the Universe From the Bi Ban to today's Universe Quantum ravity era Grand unification era Electroweak era Protons and neutrons form Nuclei are formed Atoms and liht era Galaxy formation Today