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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 gr

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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

P461 - particles I

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

- 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

P461 - particles I

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

- 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

- 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 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

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 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

- quark antiquark combinations. Governed by SU(2) (spin) and strangenessSU(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

- Mass of hadron = mass of constituent quarks plus binding energy. As gluons have F=kx, increase in energy with separationpositive “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

- 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

p

c

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

b

P461 - particles I

Lepton and Baryon Conservation

- Strong and EM conserve particle type. Weak can change but always leptonlepton or quarkquark
- 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

- 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 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

- 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

- 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)

- 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

- 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

- 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 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

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

- 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

- 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

- 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

- 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

- Transition leptonneutrino 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

- 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

- 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 Decay

- Very small rate of ts or td
- the quark states have a color factor of 3

t

b

W

P461 - particles I

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 bm)
- 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

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

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

- 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

- 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

- 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

- Almost 100% of the time muons decay by
- Q(muon decay) > Q(pionmuon 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

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 PH=-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

- 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+ 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.

- 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

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