Elementary Particles Harris Chapter 11 plus some ER
- Slides: 107
Elementary Particles ~ Harris Chapter 11; plus some. ~ ER Chapter 18; yea, right. Rohlf: “Modern Physics from a to Zo” www. pdg. lbl. gov Particle Adventure at http: //pdg. lbl. gov/2005/html/outreach. html
OUTLINE • • The Basics: Harris 11. 4, 11. 3 Cross section calculation techniques: Harris 11. 5 Early proofs of quarks & gluons QED (quantum electro dynamics) QCD (quantum color dynamics) QFD (quantum flavor dynamics) Buzz Words & Unanswered Questions: Harris 11. 6, 11. 7 – – CKM Matrix / Neutrino Oscillations Unification Parity & Time-Reversal Violation the Higgs / where does mass come from?
The basics • Equipment • Fundamental Objects • Fundamental Interactions
Equipment • Electron Collider e- e+ – DESY – Stanford • Proton Collider – Fermi. Lab – CERN p+ p- • Electron fixed target – Bates – CEBAF / JLab ee-
Fundamental Objects leptons 3 generations 3 families 6 flavors quarks 3 generations 3 families 6 flavors all spin ½ objects 0. 511 Me. V ~0 e. V 105 Me. V < 0. 37 Me. V 1784 Me. V < 35 Me. V ~350 Me. V ~700 Me. V 1500 Me. V ~500 Me. V 174000 Me. V 4700 Me. V
Fundamental Objects leptons 3 generations 3 families 6 flavors quarks 3 generations 3 families 6 flavors Binding energy is a major effect proton = uud = 350 + 700 = 1400 >> true mass 938 Me. V
Fundamental Objects leptons 3 generations 3 families 6 flavors quarks 3 generations 3 families 6 flavors all spin ½ objects Electric charge of leptons Electric charge of quarks
Fundamental Objects Field particles or gauge bosons < 6 E-17 e. V other required objects 80, 91 Ge. V Higgs bosons > 114 Ge. V 8 gluons (graviton) --- LR bosons > 715 Ge. V
Fundamental Interactions QCD QED QFD “Charge” Gauge boson color RGB 8 gluons g as ~ 1 G < 1 fm electric charge e Photon g a. EM ~ 1/137 Ze ∞ I. V. B. W± Zo a. WI ~ 10 -5 gw ~ 10 -3 fm agrav ~ 10 -39 -- ∞ flavor “strength” Coupling constant Vertex function Range of influence (graviton) (gravity) mass a = (vertex fn)2
Comments on Fundamental Interactions • • Range • Electric Charge – photons are ‘stable’ DE = 0 c. Dt = ∞ – IVB are ‘unstable’ DE ~ 2 Ge. V c. Dt ~ 0. 1 cm – gluons – no info – – • all quarks and e m t and W± can participate in QED since g has no charge, g cannot interact with g ‘s. Color – only quarks & gluons have color participate in QCD – Since g has color, g can interact with g‘s “glueballs” • Flavor – all quarks and leptons have “flavor”, therefore can participate in QFD
Composite Objects • Hadrons – mesons – qq – baryons – qqq – quaterions – not observed – pentaquarks – i. d. i. • .
Cross Section Techniques Feymann diagrams
How to calculate cross sections d. I Io
simplified* Feymann rules • Each vertex gives – QED: – QCD: – QFD: Ze G g momentum transfer • Each propagator gives – massless: energy of the compound state – massive: Eres = Eo + i G/2 * dropping various constants, spin-info, . . . other details
before p m mo m tu en pf incident particle sca ed tter le c i t ar q pi after fer ns tra pi = pf + q Eres = Eo + i G/2 lifetime total decay width
SP 333 or Time-Dep Perturb Th Example
2 nd order perturb theory Nuclear Physics Example
What makes us think quarks and gluons exist ? • • 2 jet events 3 jet events R-ratio Zo width
CDF detector @ Fermi. Lab http: //www-cdf. fnal. gov/cdfphotos
2 Jet events TASSO / PETRA / DESY
3 Jet events
R-ratio
e- g e+ R = ee+ q- q+ g m- m+
If NRG available in reaction ~ 1000 Me. V, then uds If NRG available in reaction ~ 3000 Me. V, then udsc If NRG available in reaction ~ 10, 000 Me. V, then udscb If NRG available in reaction ~ 180, 000 Me. V, then udscbt
RWB RYB RGB
3·R
3 generations -- the Zo width at available NRG = 90 Ge. V ee+ Zo m- m+ total decay width G = Ge + Gve + Gm + Gvm + Gt + Gvt
QED • Stationary States • Reactions
QED - Stationary States e p Some kind of experiment to excite the system
Note: even though we have quessed a good potential function, we realize that we will have to include s-o, rel KE, Darwin, Lamb shift, . . . -- and the perturbations could have been big.
QED - Reactions related to 2 vertices
g e+ g ee- earrows are added to help identify particles versus antiparticles e- e+ g e+ e+ g e- e+ e- e-
In a real experiment: e+ e+ e- e- s= + + a. EM ~ 1/137 e+ e- + + a. EM + (a. EM)2 +. . . QED is renormalizable , higher order diagrams can be accounted for by choosing an effective value for ‘e’ QED cross sections are ‘easy’ to calculate.
QCD • Stationary States • Reactions
QCD - Stationary States
confinement term ‘Coulomb’ term K 1 ~ 50 Me. Vfm K 2 ~ 1000 Me. V/fm ? ? As a matter of fact, must have V 0 by about 1 fm.
RUBBER BANDS stretch & break 2 ends U = ½ k (Dx)2 4 ends QUARK PAIRS stretch & break the color field
QCD - Reactions K 1 ~ 50 Me. Vfm K 2 ~ 1000 Me. V/fm At r ~ 0. 5 fm, a. QCD ~ 1. 5
How-To: quark-quark reactions meson ? spectator quarks Which pairs of quarks interacted?
u. G u. R d. G u. R u. G
d. R d. G q = uds. . . u. R u. G Because a. QCD > 1, higher order diagrams more important, can’t use perturbation theory. “QCD is non-renormalizable. ” (in this form) must use another technique to do calcs “string theory”
The black box: s= a. QCD ~ 1. 2 + + q+ q- + + + a. QCD (a. QCD)2 +. . . QCD is not-renormalizable , the power series expansion cannot be made to converge. QCD cross sections are ‘impossible’ to calculate with perturbation theory. string theories
Hadronization meson ? Free quarks not observed
Hadronization meson ? The q’s can have more complicated pairings than indicated meson ?
Hadronization
p+ p o L + o K ER Fig 18 -9 a
QFD • Stationary States • Reactions
QFD – Stationary States need neutral & colorless system • bound system of neutrinos – not experimentally feasible • excited states of leptons – e* not observed below 90 Ge. V (1990) – would imply lepton compositeness must learn about QFD from reactions
QFD - Reactions e- Zo e+ Experimentally; gw = 1. 7 !!! QFD is considered “weak” only because Zo, W± are massive !
g e+ g ee- earrows are added to help identify particles versus antiparticles e- e+ g e+ e+ g e- e+ e- e-
W+ QFD – charged current d (-1/3) u W- (2/3) W- v (0) u (2/3) e (-1) d (-1/3) e W-
Zo QFD – neutral current u (2/3) u Zo (2/3) e e e+ Zo Zo e
Zo u (2/3) c QFD – “flavor changing neutral currents” (2/3) Zo Zo d (-1/3) s (-1/3) NOT OBSERVED – or at least very rare
neutrino experiments ? ? Wd (-1/3) u (2/3)
neutrino experiments e v Wd (-1/3) e+ u (2/3) W+ v only interact with neg quarks u d (2/3) (-1/3) …converse…
Discovery of the Top Quark
Discovery of t quark Eo + i G/2 Eo = 174, 000 Me. V G = 1560 Me. V Signature: high nrg e+ accompanied by b-hadrons e+ t ~ 4. 2 * 10 -25 sec W+ t (2/3) b (-1/3) t never has a chance to form a long-lived composite with another quark; no R-ratio rise will be observed
Other Curious Mini-topics and Buzz Words • CPT – Parity Violation – Regeneration of the kaons – Time Reversal Violation • CKM & MNS Matrix – Quark mixing – Neutrino Mass-Mixing, a. k. a Neutrino Oscillations • • Unification Electroweak Interaction Where’s the Higgs? Why are there only LH neutrinos?
CPT • Parity – – – P: r = -r P: p = -p P: L = P: (r x p) = L P: S = S P: Ylm = (-)l Ylm • Charge Conjug – – – C: e = e+ = C: p = C: v = C: S = -S C: I = -I • Time Reversal – – T: r = r T: p = -p T: L = - L T: S = - S In classical physics, processes are invariant under operations of C, P, and T separately. Lorentz Transformations (Sp. Rel) require processes invariant under CPT combined. handwaving proof: http: //en. wikipedia. org/wiki/CPT_symmetry
Parity Violation p Helicity – relative orientation of p & S S RH Bizarre fact: only LH neutrinos exist only RH antineutrinos exist -- an artifact of how the WI works (WR) S v LH p Parity is maximally violated in the WI because the WI involves neutrinos.
CS Wu (1957) Demonstration of C and P violation but with combined CP conserved
CS Wu (1957) Demonstration of C and P violation but with combined CP conserved
CS Wu (1957) Demonstration of C and P violation but with combined CP conserved
CS Wu (1957) Demonstration of C and P violation but with combined CP conserved CPT theorem implies if (CP) OK, then T must be OK too.
Neutral Kaon System In our quark model mc 2 = 498 Me. V (a. k. a. QCD eigenstates) mc 2 = 498 Me. V Dmc 2 = 4 * 10 -12 Me. V
Neutral Kaon System can change into by the 2 nd order reaction Time scale ~10 -9 sec
Neutral Kaon System Produced in collisions (QCD/SI) in-flight only affected by WI / QFD Weak / QFD Eigenstates mc 2 = 498 Me. V Dmc 2 = 4 * 10 -6 Me. V t = 0. 89 * 10 -10 sec t = 5 * 10 -8 sec
Neutral Kaon System: Regeneration Collision regions (QCD) QCD eigenstates WI eigenstates QCD eigenstates
Time Reversal Violation (CP Violation) left What does CP do to the kaons? right C CP: Ko. S = + Ko. S CP: Ko. L =- Ko. L P
Time Reversal Violation (CP Violation)
Time Reversal Violation (CP Violation) Decays are consistent with CP good K o. S p p K o. L p p p However ~ 0. 2% of Ko. L decays have p p CP violated on a small scale T violated on a small scale Is this a problem with “standard model”, new “force”, new …. ?
Time Reversal Violation (CP Violation) Is this a problem with “standard model”, new “force”, new …. ? • • bottom system npol Apol scattering neutron electric dipole moment Cs electric dipole moment CP violation has now been observed in the D( ), B ( ), and Bs ( ) systems. The balance of decay rates, oscillations, lifetime splitting determines how bizaare the system behaves in the lab.
CKM matrix Cabibbo-Kobayashi-Maskawa matrix are QCD or ‘mass’ eigenstates d u e. W- s u W- W- W- ve m- vm
CKM matrix are QCD or ‘mass’ eigenstates In the presence of the weak interaction the states are perturbed weak eigenstates
CKM matrix – alternate form Written in terms of angles mixing each pair of quarks (Euler angles) q 1=12 o q 2= q 3= d= With approx values:
If quark mixing, why not…?
MNS matrix Maki-Nakagawa-Sakata matrix q 12 ~ 34 o q 13 < 13 o q 23 ~ 45 o d = ?
Neutrino Oscillations • Solar Neutrino Expts – Homestake Mine, SD (Ray Davis) – Explanation w/i previously existing physics with proper calculation (MSW effect) – MSW effect: ve propagate through dense electrons in Sun • Atmospheric (vacuum oscill) – Super Kamiokande – Improper ratio of vm to ve events. • Reactor Based (vacuum oscill) – Kam. LAND, 53 reactors, anti-ve from fission product decay. – Event rate and energy spectrum – Energy spectrum inconsistent with ‘no oscillation’ • Accelerator Based (vacuum oscill) – Fermi. Lab vs Los Alamos
Vacuum Neutrino Oscillation approx difference btw wavefunctions http: //en. wikipedia. org/wiki/MNS_matrix
Vacuum Neutrino Oscillation For just the ve and vm, relax notation q 12 q ~ 34 o
Electron neutrino oscillations, long range. Here and in the following diagrams black means electron neutrino, blue means muon neutrino and red means tau neutrino. http: //en. wikipedia. org/wiki/Image: Electron_neutrino_oscillation_long. png
Electron neutrino oscillations, short range http: //en. wikipedia. org/wiki/Image: Electron_neutrino_oscillation_short. png
Unification -- trying to express all forces as aspects of one • Motivations – Theory…gauge/phase…transformation…blah, blah… – The Zo and g are interchangable in all diagrams • And no flavor-changing neutral currents – Relative strengths seem to converge
Electroweak Interaction ER pg 702 -b -- one Hamiltonian works for both forces 4 -component field: ( B, W 1, W 2, W 3 ) g = cos qw B + sin qw W 3 EW Interaction ( g or A, W+, W-, Zo ) Zo = -sin qw B + cos qw W 3 W± = W 1 ± i W 2 sin qw = 0. 23 QED Q: Why are IVB so heavy? QFD
Electroweak Interaction • Successful Predictions / Treatments – Zo and g interference at e+e- > 15 Ge. V, ~10% – Parity violating effects in atomic transitions • Optical rotation of light forbidden transitions & high Z – Polarization effects in scattering of polarized electrons off nuclei –. –. –.
Is gravity a force? Or Quantum Gravity? There a number of proposed quantum gravity theories: String theory/superstring theory/M-theory Supergravity Ad. S/CFT correspondence Wheeler-de. Witt equation Loop quantum gravity Euclidean quantum gravity Causal Sets Twistor theory Sakharov induced gravity Regge calculus Acoustic metric and other analog models of gravity Process physics Causal Dynamical Triangulation An Exceptionally Simple Theory of Everything
Where’s the Higgs? What’s the Higgs?
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