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all fundamental with no underlying structure

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. Couplings and Charges. All charged particles interact electromagnetically

patience-kelly
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all fundamental with no underlying structure

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  1. 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

  2. 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 (callel 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

  3. 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) P461 - particles I

  4. 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 triplit 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

  5. 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 (deculplet) for spion 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 0f 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

  6. Baryon Wave Functions • Antisymmetric as 3 s=1/2 quarks • 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

  7. 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 • 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 P461 - particles I

  8. Hadron + Quark masses • Mass of hadron = mass of constituent quarks plus 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 < 200 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

  9. Hadrons, Partons and Jets • The quarks and gluons which make up a hadron are called partons • Proton consists of: 3 valence quarks (about 40% of momentum) gluons (about 50% opf the momentum) “sea” quark-antiquark pairs • The sea quarks are constanly 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 0f 0.002 F (G. Blazey et al) P461 - particles I

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