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all fundamental with no underlying structure Leptons+quarks spin ½ while photon, W, Z, gluons spin 1 No QM theory for gravity Higher generations have larger mass. When/where discovered. Nobel Prize?. g Mostly Europe 1895-1920 Roentgen (sort of)1901

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slide1
all fundamental with no underlying structure
  • Leptons+quarks spin ½ while photon, W, Z, gluons spin 1
  • No QM theory for gravity
  • Higher generations have larger mass

P461 - particles I

when where discovered
When/where discovered

Nobel Prize?

g Mostly Europe 1895-1920 Roentgen (sort of)1901

W/Z CERN 1983 Rubbia/vanderMeer1984

gluon DESY 1979 NO

electron Europe 1895-1905 Thomson 1906

muon Harvard 1937 No

tau SLAC 1975 Perl 1995

ne US 1953 Reines/Cowan 1995

nm BNL 1962 Schwartz/Lederman/Steinberger 1988

nt FNAL 2000 NO

u,d SLAC 1960s Friedman/Kendall/Taylor 1990

s mostly US 1950s NO

c SLAC/BNL 1974 Richter/Ting 1976

b FNAL 1978 NO (Lederman)

t FNAL 1995 NO

muon – Street+Stevenson had “evidence” but Piccione often gets credit in the 1940s as measured lifetime

P461 - particles I

couplings and charges
Couplings and Charges
  • All charged particles interact electromagnetically
  • All particles except gamma and gluon interact weakly (have nonzero “weak” charge) (partially semantics on photon as mixing defined in this way) A WWZ vertex exists
  • Only quarks and gluons interact strongly; have non-zero “strong” charge (called color). This has been tested by:

magnetic moment electron and muon

H energy levels (Lamb shift)

“muonic” atoms. Substitute muon for electron

pi-mu atoms

  • EM charge just electric charge q
  • Weak charge – “weak” isospin in i=1/2 doublets used for charged (W) and have I3-Aq for neutral current (Z)
  • Strong charge – color charge triplet “red” “green” “blue”

P461 - particles I

pi mu coupling
Pi-mu coupling

P461 - particles I

strong force and hadrons
Strong Force and Hadrons
  • p + p -> p + N*
  • N* are excited states of proton or neutron (all of which are baryons)
  • P = uud n = udd (bound by gluons) where u = up quark (charge 2/3) and d = down quark (charge -1/3)
  • About 20 N states spin ½ mass 938 – 2700 MeV
  • About 20 D states spin 3/2
  • Charges = uuu(2) uud(1) udd(0) ddd(-1)
  • N,D decay by strong interaction N  p/n + p with lifetimes of 10-23 sec (pion is quark-antiquark meson). Identify by looking at the invariant mass and other kinematic distributions

P461 - particles I

isospin
ISOSPIN
  • Assume the strong force is ~identical between baryons (p,n,N*) and between three pions
  • Introduce concept of Isospin with (p,n) forming an isopsin doublet I=1/2 and pions in an isopsin triplet I=1, and quarks (u,d) in a I=1/2 doublet
  • Isospin isn’t spin but has the same group algebra SU(2) as spin and so same quantum numbers and addition rules

P461 - particles I

baryons and mesons
Baryons and Mesons
  • 3 quark combinations (like uud) are called baryons. Historically first understood for u,d,s quarks
  • “plotted” in isospin vs strangeness. Have a group of 8 for spin ½ (octet) and 10 (decuplet) for spin 3/2. Fermions and so need antisymmetric wavefunction (and have some duplication of quark flavor like p = uud)
  • Gell-Mann tried to explain using SU(3) but badly broken (seen in different masses) but did point out underlying quarks
  • Mesons are quark-antiquark combinations and so spin 0 or 1. Bosons and need symmetric wavefunction (“simpler” as not duplicating quark flavor)
  • Spin 0 (or spin 1) come in a group of 8 (octet) and a group of 1 (singlet). Again SU(3) sort of explains if there are 3 quarks but badly broken as seen in both the mass variations and the mixing between the singlet and octet

P461 - particles I

baryons and mesons8
Baryons and Mesons
  • Use group theory to understand: -what states are allowed - “mixing” (how decay) - state changes (step-up/down) - magnetic moments of
  • as masses are so different this only partially works – broken
  • SU(2) Isospin –very good (u/d quark same mass) SU(3) for s-quark – good with caveats SU(4) with c-quark – not so good

P461 - particles I

baryons
Baryons

D0

also

P461 - particles I

baryon wave functions
Baryon Wave Functions
  • Totally Antisymmetric as 3 s=1/2 quarks - Fermions
  • S=3/2. spin part must be symmetric (all “aligned”). There are some states which are quark symmetric (uuu,ddd,sss). As all members of the same multiplet have the same symmetries  quark and spin are both symmetric
  • to be antisymmetric, obey Pauli exclusion, need a new quantum number “color” which comes in 3 (at least) indices. Color wavefunctions:

P461 - particles I

baryon wave functions11
Baryon Wave Functions
  • S=1/2. color part is like S=3/2. So spin*quark flavor = symmetric. Adding 3 spin = ½ to give S=1/2 produces “mixed” spin symmetry.
  • First combine two quarks giving symmetric 1<->2
  • Add on third quark to get first term
  • Cycle 1  2  3  1 8 more terms. And then multiply by 6 color terms from S=3/2 page (4*9*6=216 terms)
  • Why no charge 2 or charge -1particles like the proton or neutron exist  the need for an antisymmetric wavefunction makes the proton the lightest baryon (which is a good thing for us)

P461 - particles I

meson wave functions
Meson Wave Functions
  • quark antiquark combinations. Governed by SU(2) (spin) and strangenessSU(3) (SU(4)) for c-quark). But broken symmetries
  • pions have no s quarks. The h’s (or the w+f) mix to find real particles  break SU(3)

meson mass Decay

p 135,140 no s

h 550 little s

h’ 958 mostly s

r 770 no s

w 782 little s

f 1019 85% KK, 15% ppp

P461 - particles I

hadron quark masses
Hadron + Quark masses
  • Mass of hadron = mass of constituent quarks plus binding energy. As gluons have F=kx, increase in energy with separationpositive “binding” energy
  • Bare quark masses: u = 1-5 MeV d = 3-9 MeV s = 75-170 MeV c = 1.15 – 1.35 GeV b = 4.0–4.4 GeV t = 169-179 GeV
  • Top quark decay so quickly it never binds into a hadron. No binding energy correction and so best determined mass value (though < 300 t quark decays observed)
  • Other quark masses determined from measured hadron masses and binding energy model pion = “2 u/d quarks” = 135 Mev proton = “3 u/d quarks” = 940 MeV kaon = “1 s and 1 u/d” = 500 MeV Omega = “3 s quarks” = 1672 MeV
  • High energy p-p interactions really q-q (or quark-gluon or gluon-gluon). “partons” emerge but then hadronize. Called “jets” whose energy and momentum are mostly original quark or gluon

P461 - particles I

hadrons partons and jets
Hadrons, Partons and Jets
  • The quarks and gluons which make up a hadron are called partons (Feynman, Field, Bjorken)
  • Proton consists of: -3 valence quarks (about 40% of momentum) -gluons (about 50% opf the momentum) -“sea” quark-antiquark pairs
  • The sea quarks are constantly being made/annihilated from gluons and can include heavier quarks (s,c,b) with probability mass-dependent
  • X = p/p(total) is the momentum fraction and each type of particle has a probability to have a given X (parton distribution function or pdf)
  • PDFs mostly measured in experiments using nu,e,mu,p etc. Some theoretical modeling
  • Even at highest energy collisions, quarks still pointlike particles (no structure) as distances of 0.002 F (G. Blazey et al)
  • single quark produces other gluons and quarks  jet. Have similar fragmentation function

P461 - particles I

fragmentation functions

u,d,s

Fragmentation functions

p

c

fraction of energy which quark (or gluon) has for either particle or jet

b

P461 - particles I

lepton and baryon conservation
Lepton and Baryon Conservation
  • Strong and EM conserve particle type. Weak can change but always leptonlepton or quarkquark
  • So number of quarks (#quarks-#antiquarks) conserved. Sometimes called baryon conservation B.
  • Number of each type (e,mu,tau) conserved L conservation
  • Can always create particle-antiparticle pair
  • But universe breaks B,L conservation as there is more matter than antimatter
  • At small time after big bang #baryons = #antibaryons = #leptons = #antileptons (modulo spin/color/etc) = ~#photons (as can convert to particle-antiparticle pairs)
  • Now baryon/photon ratio 10-10

P461 - particles I

hadron production decay
Hadron production + Decay
  • Allowed production channels are simply quark counting
  • Can make/destroy quark-antiquark pairs with the total “flavor” (upness = #up-#antiup, downness, etc) staying the same
  • All decays allowed by mass conservation occur quickly (<10-21 sec) with a few decaying by EM with lifetimes of ~10-16 sec) Those forbidden are long-lived and decay weakly and do not conserve flavor.

P461 - particles I

hadrons and qcd
Hadrons and QCD
  • Hadrons are made from quarks bound together by gluons
  • EM force QuantumElectroDynamics QED strong is QuantumChromoDynamics QCD
  • Strong force “color” is equivalent to electric charge except three different (identical) charges red-green-blue. Each type of quark has electric charge (2/3 up -1/3 down, etc) and either r g b (or antired, antiblue, antigreen) color charge
  • Unlike charge=0 photon, gluons can have color charge. 8 such charges (like blue-antigreen) combos, 2 are colorless. Gluon exchange usually color exchange. Can have gluon-gluon interaction

P461 - particles I

quark gluon coupling
quark-gluon coupling
  • why q-qbar and qqq combinations are stable
  • 8 gluons each with color and anticolor. All “orthogonal”. 2 are colorless gluons
  • coupling gluon-quark = +c coupling gluon-antiquark = -c

r

b

vertex 1 +c

r

vertex 2 +c

b

vertex 2 -c

P461 - particles I

group theory
Group Theory
  • W/Z bosons and gluons carry weak charge and color charge (respectively)Bosons couple to Bosons
  • SU(2) and SU(3) which have 3 and 8 “base” vectors can be used to represent weak and strong forces. The base vectors are the W+,W-,Z and the 8 gluons. Exact (non-broken) symmetry
  • The group algebra tells us about boson interaction. So for W/Z use
  • SU(2) used for 3D rotations angular momentum (orbital and spin) isospin (hadrons – broken) weak interactions  weak “isospin”

P461 - particles I

group theory su 3
Group Theory – SU(3)
  • 3x3 unitary matrices with det=1. 2n2-n2-1=8 parameters. Have group algebra
  • and representation of generators
  • and 3 color states

P461 - particles I

pions
Pions
  • Use as strong interaction example
  • Produce in strong interactions
  • Measure pion spin. Mirror reactions have same matrix element but different phase space/kinematics term. “easy” part of phase space is just the 2s+1 spin degeneracy term
  • Find S=0 for pions

P461 - particles I

more pions
More Pions
  • Useful to think of pions as I=1 isospin triplet and p,n is I=1/2 doublet (from quark plots)
  • Look at reactions:
  • p p -> d pi+ Total

I ½ ½ 0 1 1

Iz ½ ½ 0 1 1

p n -> d pi0 Total

I ½ ½ 0 1 0 or 1

Iz ½ - ½ 0 0 0

  • in the past we combined 2 spin ½ states to form S=0 or 1

P461 - particles I

more pions25
More Pions
  • Reverse this and say eigentstate |p,n> is combination of I=1 and I=0
  • reactions:
  • then take the “dot product” between |p,n> and |d,pi0> brings in a 1/sqrt(2) (the Clebsch-Gordon coefficient)
  • Square to get A/B cross section ratio of 1/2

P461 - particles I

em decay of hadrons
EM Decay of Hadrons

u

g

  • If a photon is involved in a decay (either final state or virtual) then the decay is at least partially electromagnetic
  • Can’t have u-ubar quark go to a single photon as have to conserve energy and momentum (and angular momentum)
  • Rate is less than a strong decay as have coupling of 1/137 compared to strong of about 0.2. Also have 2 vertices in pi decay and so (1/137)2
  • EM decays always proceed if allowed but usually only small contribution if strong also allowed

g

ubar

P461 - particles I

c cbar and b bbar mesons
c-cbar and b-bbar Mesons
  • Similar to u-ubar, d-dbar, and s-sbar
  • “excited” states similar to atoms 1S, 2S, 3S…1P, 2P…photon emitted in transitions. Mass spectrum can be modeled by QCD
  • If mass > 2*meson mass can decay strongly
  • But if mass <2*meson decays EM. “easiest” way is through virtual photons (suppressed for pions due to spin)

m+

c

g

m-

cbar

P461 - particles I

c cbar and b bbar meson em decays
c-cbar and b-bbar Meson EM-Decays
  • Can be any particle-antiparticle pair whose pass is less than psi or upsilon: electron-positron, u-ubar, d-dbar, s-sbar
  • rate into each channel depends on charge2(EM coupling) and mass (phase space)
  • Some of the decays into hadrons proceed through virtual photon and some through a virtual (colorless) gluon)

c

g

cbar

P461 - particles I

electromagnetic production of hadrons
Electromagnetic production of Hadrons
  • Same matrix element as decay. Electron-positron pair make a virtual photon which then “decays” to quark-antiquark pairs. (or mu+-mu-, etc)
  • electron-positron pair has a given invariant mass which the virtual photon acquires. Any quark-antiquark pair lighter than this can be produced
  • The q-qbar pair can acquire other quark pairs from the available energy to make hadrons. Any combination which conserves quark counting, energy and angular momentum OK

q

e+

g

qbar

e-

P461 - particles I

weak decays
Weak Decays
  • If no strong or EM decays are allowed, hadrons decay weakly (except for stable proton)
  • Exactly the same as lepton decays. Exactly the same as beta decays
  • Charge current Weak interactions proceed be exchange of W+ or W-. Couples to 2 members of weak doublets (provided enough energy)

U

d

d

u

d

u

W

e

n

P461 - particles I

decays of leptons
Decays of Leptons
  • Transition leptonneutrino emits virtual W which then “decays” to all kinematically available doublet pairs
  • For taus, mass=1800 MeV and W can decay into e+n,m+n, and u+d (s by mixing). 3 colors for quarks and so rate ~3 times higher.

W

e

P461 - particles I

weak decays of hadrons
Weak Decays of Hadrons
  • Can have “beta” decay with same number of quarks in final state (semileptonic)
  • or quark-antiquark combine (leptonic)
  • or can have purely hadronic decays
  • Rates will be different: 2-body vs 3-body phase space; different spin factors

W

e

P461 - particles I

top quark decay
Top Quark Decay
  • Simplest weak decay (and hadronic).
  • M(top)>>Mw (175 GeV vs 81 GeV) and so W is real (not virtual) and there is no suppression of different final states due to phase space
  • the t quark decays before it becomes a hadron. The outgoing b/c/s/u/d quarks are seen as jets

t

b

W

c

u

P461 - particles I

top quark decay35
Top Quark Decay
  • Very small rate of ts or td
  • the quark states have a color factor of 3

t

b

W

P461 - particles I

how to discover the top quark
How to Discover the Top Quark
  • make sure it wasn’t discovered before you start collecting data (CDF run 88-89 top mass too heavy)
  • build detector with good detection of electrons, muons, jets, “missing energy”, and some B-ID (D0 Run I bm)
  • have detector work from Day 1. D0 Run I: 3 inner detectors severe problems, muon detector some problems but good enough. U-LA cal perfect
  • collect enough data with right kinematics so statistically can’t be background. mostly W+>2 jets
  • Total: 17 events in data collected from 1992-1995 with estimated background of 3.8 events

P461 - particles I

the first top quark event
The First Top Quark Event

muon

electron

P461 - particles I

the first top quark event38
The First Top Quark Event

jet

P461 - particles I

another top quark event
Another Top Quark Event

jets

electron

P461 - particles I

decay rates pions
Decay Rates: Pions

u

dbar

  • Look at pion branching fractions (BF)
  • The Beta decay is the easiest. ~Same as neutron beta decay
  • Q= 4.1 MeV. Assume FT=1600 s. LogF=3.2 (from plot) F= 1600
  • for just this decay gives “partial” T=1600/F=1 sec or partial width = 1 sec-1

P461 - particles I

pi decay to e nu vs mu nu
Pi Decay to e-nu vs mu-nu

nu

L+

  • Depends on phase space and spin factors
  • in pion rest frame pion has S=0
  • 2 spin=1/2 combine to give S=0. Nominally can either be both right-handed or both left-handed
  • But parity violated in weak interactions. If m=0  all S=1/2 particles are LH and all S=1/2 antiparticles are RH
  • neutrino mass = 0  LH
  • electron and muon mass not = 0 and so can have some “wrong” helicity. Antparticles which are LH.But easier for muon as heavier mass

P461 - particles I

polarization of spin 1 2 particles
Polarization of Spin 1/2 Particles
  • Obtain through Dirac equation and polarization operators. Polarization defined
  • the degree of polarization then depends on velocity. The fraction in the “right” and “wrong” helicity states are:
  • fraction “wrong” = 0 if m=0 and v=c
  • for a given energy, electron has higher velocity than muon and so less likely to have “wrong” helicity

P461 - particles I

pion decay kinematics
Pion Decay Kinematics
  • 2 Body decay. Conserve energy and momentum
  • can then calculate the velocity of the electron or muon
  • look at the fraction in the “wrong” helicity to get relative spin suppression of decay to electrons

P461 - particles I

pion decay phase space
Pion Decay Phase Space
  • Lorentz invariant phase space plus energy and momentum conservation
  • gives the 2-body phase space factor (partially a computational trick)
  • as the electron is lighter, more phase space (3.3 times the muon)
  • Branching Fraction ratio is spin suppression times phase space

P461 - particles I

muon decay
Muon Decay
  • Almost 100% of the time muons decay by
  • Q(muon decay) > Q(pionmuon decay) but there is significant spin suppression and so muon’s lifetime ~100 longer than pions
  • spin 1/2 muon  1/2 mostly LH (e) plus 1/2 all LH( nu) plus 1/2 all RH (antinu)
  • 3 body phase space and some areas of Dalitz plot suppressed as S=3/2
  • electron tends to follow muon direction and “remember” the muon polarization. Dirac equation plus a spin rotation matrix can give the angular distribution of the electron relative to the muon direction/polarization

P461 - particles I

detecting parity violation in muon decay

Jm

Jn

p+

n

m+

Jn

Je

Jm

n

e+

m+

n

Jn

Detecting Parity Violation in muon decay
  • Massless neutrinos are fully polarized, P=-1 for neutrino and P=+1 for antineutrino (defines helicity)
  • Consider + + e+ decay. Since neutrinos are left-handed PH=-1, muons should also be polarised with polarisation P=-v/c (muons are non-relativistic, so both helicity states are allowed).
  • If muons conserve polarization when they come to rest, the electrons from muon decay should also be polarized and have an angular dependence:

p+ m+ + nm

m+e+ + ne +nm

P461 - particles I

parity violation in e decay
Parity violation in + + e+ decay
  • Experiment by Garwin, Lederman, Weinrich aimed to confirm parity violation through the measurements of I(q) for positrons.
  • 85 MeV pion beam (+ ) from cyclotron.
  • 10% of muons in the beam: need to be separated from pions.
  • Pions were stopped in the carbon absorber (20 cm thick)
  • Counters 1-2 were used to separate muons
  • Muons were stopped in the carbon target below counter 2.

P461 - particles I

parity violation in e decay48
Parity violation in + + e+ decay
  • Positrons from muon decay were detected by a telescope 3-4, which required particles of range >8 g/cm2 (25 MeV positrons).
  • Events: concidence between counters 1-2 (muon) plus coincidence between counters 3-4 (positron) delayed by 0.75-2.0 ms.
  • Goal: to measure I(q) for positrons.
  • Conventional way: move detecting system (telescope 3-4) around carbon target measuring intensities at various q. But very complicated.
  • More sophisticated method: precession of muon spin in magnetic field. Vertical magnetic field in a shielded box around the target.
  • The intensity distribution in angle was carried around with the muon spin.

P461 - particles I

results of the experiment by garwin et al
Results of the experiment by Garwin et al.
  • Changing the field (the magnetising current), they could change the rate (frequency) of the spin precession, which will be reflected in the angular distribution of the emitted positrons.
  • Garwin et al. plotted the positron rate as a function of magnetising current (magnetic field) and compared it to the expected distribution:

P461 - particles I