Subatomic Physics: Particle Physics. Review April 13th Key Concepts. What s important are the concepts not the facts and figures.

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1 Subatomic Physics: Particle Physics Review April 13th 21 The Standard Model Natural Units Relativistic Dynamics Anti-matter Quarks, Leptons & Hadrons Feynman Diarams and Feynman Rules Decays QED, QCD, Weak What you don t need to know 1 Key Concepts What s important are the concepts not the facts and fiures. Key concepts: The uarks and leptons - particles which interact (decay / scatter). The forces - transmitted by bosons. What each force interacts on - what interactions are allowed. The measurements used to uantify decays and scatterin. Feynman diarams and Feynman rules LHC concepts: Accelerators: how protons are accelerated in the LHC. Detectors: how particles produced in pp scatterin appear in a detector (in our case ATLAS detector), what uantities can be reconstructed. The physics motivation for acceleratin particles to hih enery. 2

2 The Standard Model The Standard Model describes more-or-less everythin we currently know about particle physics: the matter particles and the three of the four forces which describe their interactions. Matter: aka the fermions!e e" u d Leptons!µ µ" Quarks c s!# #" t b Chare, e!1 +2/3!1/3 Matter is rouped into three successively heavier enerations. Each eneration consists of: 2 leptons with Q=!1e, Q= 2 uarks with Q=+2/3e, Q=!1/3e Forces Interactions are propaated by the exchane of bosons Interaction Bosons Q, e Stron luons, Electromanetic photon, $ Weak W ±, Z, ±1 Gravity?? 3 Decays and Scatterins Decays and scatterins are the main processes used to observe and investiate interactions. Decay: one particle decays to two or three other particles, via a boson. e.. µ " %e "&!µ!e!µ p = p + p + p µ e µ " νe νµ!'e Scatterin: two particles collide e.. pp%..., e + e " %µ + µ " W W Hadron collisions: individual constituents (uarks, luons ) interact Important uantity is Lorentz invariant s: sum of collidin particles four momenta s = ( p e + + p e )2 e " " or Z e " µ " Collider: two beams of particles collide Fixed taret: beam of particles incident on a taret e + γ µ + 4

3 Relativistic Dynamics Relativistic Dynamics is used to describe kinematics in decays and scatterin. Four momentum: If we suare four-momentum: p = (E/c, p x, p y, p z ) = (E/c, p ) p 2 = E2 c 2 p p = m2 c 2 In decay the four-momentum is conserved e.. in µ! #e!!$e!µ In a scatterin the four-momentum is conserved e.. e + e " %µ + µ " we et the mass suared! p µ = p e + p νe + p νµ Suare both sides: m 2 µc 2 = (p e + p νe + p νµ ) 2 p e + + p e = p µ + + p µ pinitial = p final pinitial = p final In a scatterin, the suare of the initial four momentum is s. Enery in the Centre of Mass frame is!s, e.. s = ( p e + + p e )2 In both decay and scatterin: boson transfers momentum from initial to final state! 5 Natural units: set c = = 1 Natural Units All uantities can be expressed as a power of enery. Mass, momentum and enery measured in the same units: MeV or GeV Two important uantities for Lorentz transformations: β = v/c γ(v) = 1/ 1 β 2 Natural Units Lorentz boosts: γ = E/m γβ = p /m β = p /E Four momentum: p = (E, p x, p y, p z ) Invariant mass p 2 = E 2 p 2 = m 2 6

4 Quark and Lepton Quantum Numbers Quantum Numbers Leptons: Individual lepton numbers: Le, Lµ, L# Total lepton number L = Le + Lµ + L# Electric Chare, Q All lepton numbers always conserved! Le Lµ L# Quarks: Electric Chare, Q Quark number, N = N()! N( % ) Up, down, strane, charm,bottom & top uark number e.. Nu =N(u)!N( %u ) etc Every uark carries a colour chare: red, blue or reen e" µ" #" Q and N are conserved in all interactions. Nu, Nd, Ns, Nc, Nb, Nt are not always conserved in W-boson interactions.!e!µ!# 7 Anti-matter Every matter particle has an anti-matter partner. E 2 = p 2 c 2 + m 2 c 4 E = ± p 2 c 2 + m 2 c 4 Particle is the positive enery solution Anti-particle is neative enery solution x e! (x,t) E> e + ("x,"t) E< t Feynman s interpretation: neative enery particle with chare Q movin backward in space & time appears as positive enery particle with chare!q movin forward in space & time. Anti-matter particle has: Opposite electric chare, opposite colour chare Same mass & lifetime Opposite N, Le, Lµ & L#!e e" u d Leptons!µ µ" Quarks c s!# #" t b Anti-leptons &!e e+ %u %d &!µ µ+ Anti-uarks %c %s &!# #+ %t %b Chare!1 +2/3!1/3 Chare!2/3 /3 8

5 Free uarks are never observed. Hadrons Quarks are always found in bound colour-neutral states: Mesons: a uark and an anti-uark Baryons: three uarks Anti-baryons: three anti-uarks Colour confinement The uarks are confined to hadrons due to stron force luon self-interactions couplin constant (S increases as uarks become further apart Interactions: scatterin and decays Consider the interactions of the individual uarks inside the hadrons. e.. at the LHC its the individual uarks and luons that interact! 9 Partons We must consider interactions of individual constituents, partons, of the proton. At hih eneries (e.. at the LHC) protons consist of the followin partons: three net uarks: u, u, d uarks and anti-uarks in pairs e.. u u, $ d $d, s s $ or c c$ luons,, (from interaction of consistent uarks and anti-uarks) Sketches of the proton illustratin the parton content: 1

6 LHC Collisions LHC collisions will be a mixture of: uark-uark, uark-luon, luonluon, anti-uark!uark, anti-uark!luon etc. We do not know on a collision-by-collision basis which of these scatterins took place. Variable Feynman x is used to characterise the proton s parton content x = p parton p proton < x < 1. The flavours of uarks and luon found in the proton as a function of x. 11 Detector Sinals Chared particles leave several position measurements in the trackin detector. Positions are joined up to trace out a track, used to reconstruct the momentum. Measures p Eneries of electrons, photons and hadrons are absorbed in calorimeter, allowin enery to be measured. Measure E. Neutrinos do not interact at all in detector. Observed imbalance in momentum perpendicular to the beam. If beam is alon z-direction, measure px(&), py(&) but not pz(&). Quarks hadronise, producin series of hadrons. Appear in detector as narrow jet of particles. 12

7 Particle Sinals in the ATLAS Detector 13 Accelerators Variable electric and/or manetic fields are used to accelerate bunches of chared particles. Linear accelerators (linacs) are use hih freuency E-field to accelerate chared particles in a straiht line to obtain hiher eneries Circular accelerators (synchrotrons) are used accelerate chared particles around a circle, to obtain hiher eneries and to store the particles. Synchrotron accelerators use variable B-field strenth and hih freuency E-field, synchronised with particle speed to accelerate chared particles to relativistic eneries. Manets are series of dipole (bendin) and uadrapole (focussin) manets Stored particles in a synchrotron lose enery due to synchrotron radiation. This must be added back into the beam at each turn. 14

8 Feynman Diarams Feynman diarams are used to illustrate and calculate rates of decays and scatterin.!µ e.. muon decay: µ! #e!!$e!µ µ "!'e e.. e + e " %µ + µ " scatterin W e " µ " W " or Z e + Use the Feynman Rules to calculate the matrix element, M, from diaram For decay the partial width of the decay, ', is proportional to M 2 For scatterin the cross section, ), is proportional to M 2 Use four momentum conservation to calculate boson four momentum, γ µ + Time e " Muon decay e + e " %µ + µ " scatterin = p µ p νµ = p e + p νe = p e + + p e = p µ + + p µ 15 Feynman Rules The matrix element, M, is the amplitude, per unit time, for a iven process to happen. We calculate M from: the vertex couplins at the vertex the boson propaator term The Feynman Rules Write down the couplin at the each vertex: chare of the fermion (for EM), S (for QCD) W (for W-*-! vertex), WV (for W-- vertex), Work out the four-momentum transferred by the boson, Write down the propaator term for each boson: e " e + e $ 1/( 2 m 2 boson) γ e µ " µ + M is proportional to vertex couplins and propaator terms e.. M(e + e µ + µ ) = e 2 / 2 If process involves hadrons: consider interactions of the constituent uarks 16

9 Decays We use decays and scatterin cross section to understand interactions. A decay can only occur if m initial > m final The stroner the interaction, the uicker the particle will decay. Measurable uantities: Force Typical lifetime: # Dimensions: time. Lifetimes total width: '= /# Dimensions: enery. Stron 1!2-1!23 s Partial width of decay mode e.. '(# " #µ "!'µ!#) Γ(τ µ ν µ ν τ ) M(τ µ ν µ ν τ ) 2 The total width is the sum of all the individual decay modes e.. The branchin ratio is the fraction of time a particle decays into a particular final state, e.. The sum of all possible branchin ratios adds to 1. EM Weak 1!2-1!16 s 1! s Γ τ = Γ(τ µ ν µ ν τ ) + Γ(τ e ν e ν τ ) + Γ(τ ν τ + hadrons) BR(τ µ ν µ ν τ ) = Γ(τ µ ν µ ν τ ) Γ τ 17 Scatterins The cross section of a scatterin process is proportional to the matrix element suared. σ(e + e µ + µ ) M(e + e µ + µ ) 2 e.. (from two slides back) σ(e + e µ + µ ) e 4 / 4 This relationship is only proportional, you do not have the tools (yet) to calculate the full cross section. But still useful for calculatin the ratios of cross sections, or dynamics of the scatterin process, e.. if is a function of the incident anle. 18

10 Forces & Interactions Three forces to consider: stron (QCD), electromanetic (QED) & weak. Weak force has two bosons: W and Z Forces are propaated by the exchane of bosons. Bosons exchane four momentum,, between the initial and final state Strenth of interaction is acts on some properties of the particle, e.. electromanetic force is couples to electric chares of interactin particles Stron exchane of luons couples to colour chare Electromanetic exchane of photons couples to electric chare Weak Neutral Current Weak Chared Current exchane of Z boson exchane of W ± boson couples to all fermions couples to all fermions The exchaned bosons are often virtual (as opposed to real). Virtual: suare of four momentum is not mass suared: 2 = E 2 p p = m 2 boson Allowed by HUP; we can never directly detect virtual bosons: only their effects. Quantum Electrodynamics QED is uantum theory of electromanetic interactions. All chared particles interact via QED All interactions are described by fermion-fermion-photon (") vertex: Fermion emits or absorbs a photon "#fermion anti-fermion or fermion anti-fermion#" Fermion flavour does not chane when it emits or absorbs a photon e.. an e " remains an e ", b-uark remains a b-uark Strenth of vertex is proportional to chare of fermion Cross sections, decay width M 2 write in powers of ( α = e2 1 4π 137 QED conserves: Q, Nu, Nd, Ns, Nc, Nb, Nt, Le, Lµ, L# 19 2

11 Quantum Chromodynamics QCD is uantum theory of stron interactions. Acts on colour chared i.e. only uarks and luons interact via QCD uark-uark-luon vertex: A uark emits or absorbs a luon luon#uark + anti-uark or uark + anti-uark#luon Quark flavour does not chane, but colour chare chanes As luons also carry colour chare, the luons interact with other luons Potential between two uarks is: V QCD (r) = 4 α s 3 r + kr uark-luon interaction Almost impossible to pull two uarks apart: colour confinement Colour field lines luon-luon interactions Weak Interactions Weak Force is propaated by massive W ± and Z bosons Weak force interacts on all uarks and leptons. Chared current chanes the flavour of the fermion: Allowed flavour chanes: B, Le, Lµ and L# conserved e! (!e µ " (!µ # " (!# QCD Electric field lines QCD conserves: Q, Le, Lµ, L#, Nu, Nd, Ns, Nc, Nt, Nb No flavour chanes! e + (!'e µ + (!'µ # + (!'# (Q=+2/3 uark) ( (Q=!1/3 uark) (Q=!2/3 anti-uark) ( (Q=/3 anti-uark) α S α S = S 2/4π ~ 1 e - w α w = w 2 4π Strenth of chared current: Leptons vertices, universal couplin: W Quark vertices, depends on uark flavour e.. for W-u-d: WVud Neutral current no fermion flavour chane. Handy hint: neutrinos are only involved in weak interactions. w V ckm u W d F W + B ν e W - Z Weak force conserves: Q, Le, Lµ, L# 21 22

12 What you don t need to know... The masses of the particles; they are iven on the constant sheet! Except: neutrino mass is so small you can always inore it m! )! electron mass so small you can inore it compared to other masses. W and Z bosons are much more massive than all lepton and hadron masses. The lifetimes of the particles, they will be iven if reuired. But remember typical lifetimes for the different forces. The uark content of the hadrons. Except proton is uud anti-proton is: %u %u d neutron is udd anti-neutron is: %u d d You can work out the chare of a particle from its symbol e.. Q(* ++ )=+2e exceptions: p and n don t have superscript (but I hope you know the chare of these) uarks have chare +2/3e,!1/3e 23 Handy Hints Neutrinos: Only the weak force acts on neutrinos. Photons: Only the electromanetic force can produce photons. Flavour chane: Only W-boson can cause flavour chane Flavour chane is a chane in Nu, Nd, Ns, Nc, Nb, Nt 24