Elementary Particles ~ Harris Chapter 11; plus some. ~ ER Chapter 18; yea, right. Rohlf: “Modern Physics from  to Z o ” Particle Adventure at

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 –DESY –Stanford Proton Collider –FermiLab –CERN Electron fixed target –Bates –CEBAF / JLab e+e+ ee p+p+ pp ee ee

Fundamental Objects leptons quarks 3 generations 3 families 6 flavors 3 generations 3 families 6 flavors MeV ~0 eV 105 MeV < 0.37 MeV 1784 MeV < 35 MeV ~350 MeV ~700 MeV 1500 MeV ~500 MeV MeV 4700 MeV all spin ½ objects

Fundamental Objects leptons quarks 3 generations 3 families 6 flavors 3 generations 3 families 6 flavors Binding energy is a major effect proton = uud = = 1400 >> true mass 938 MeV

Fundamental Objects leptons quarks 3 generations 3 families 6 flavors 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 other required objects 8 gluons (graviton) < 6E  17 eV 80, 91 GeV --- Higgs bosons LR bosons > 114 GeV> 715 GeV

Fundamental Interactions “Charge” Gauge boson “strength” Coupling constant Vertex function Range of influence QCD color RGB 8 gluons g  s ~ 1 G< 1 fm QED electric charge e Photon  EM ~ 1/137 Ze ∞ QFD flavor I.V.B. W ± Z o  WI ~ 10  g w ~ 10  fm (gravity) mass (graviton)  grav ~ 10  -- ∞  = (vertex fn) 2

Comments on Fundamental Interactions Range – photons are ‘stable’   E = 0  c  t = ∞ – IVB are ‘unstable’   E ~ 2 GeV  c  t ~ 0.1 cm – gluons – no info Electric Charge – all quarks and e  and W ± can participate in QED – since  has no charge,  cannot interact with  ‘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 dI IoIo

simplified* Feymann rules Each vertex gives –QED: Ze –QCD: G –QFD: g Each propagator gives –massless: –massive: momentum transfer energy of the compound state * dropping various constants, spin-info,... other details E res = E o + i  /2

p i incident particle p f scattered particle q momentum transfer p i = p f + q before after E res = E o + i  /2 total decay width lifetime

SP333 or Time-Dep Perturb Th Example

Nuclear Physics Example 2 nd order perturb theory

What makes us think quarks and gluons exist ? 2 jet events 3 jet events R-ratio Z o width

CDF FermiLab

2 Jet events TASSO / PETRA / DESY

3 Jet events

R-ratio

    ee ee qq qq ee ee R =

If NRG available in reaction ~ 1000 MeV, then uds If NRG available in reaction ~ 3000 MeV, then udsc If NRG available in reaction ~ 10,000 MeV, then udscb If NRG available in reaction ~ 180,000 MeV, then udscbt

RWB RYB RGB

3·R3·R

3 generations -- the Z o width  =  e +  ve +   +  v  +   +  v  total decay width    ee ee at available NRG = 90 GeV

QED Stationary States Reactions

QED - Stationary States Some kind of experiment to excite the system p e

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

 ee ee  ee ee  ee ee ee ee arrows are added to help identify particles versus antiparticles  ee ee ee ee

In a real experiment: ee ee ee ee ee ee  EM (  EM ) 2  EM ~ 1/137  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

K 1 ~ 50 MeVfm K 2 ~ 1000 MeV/fm ? ? confinement term ‘Coulomb’ term As a matter of fact, must have V  0 by about 1 fm.

stretch & break the color field RUBBER BANDS U = ½ k (  x) 2 2 ends 4 ends stretch & break QUARK PAIRS

QCD - Reactions K 1 ~ 50 MeVfm K 2 ~ 1000 MeV/fm At r ~ 0.5 fm,  QCD ~ 1.5

How-To: quark-quark reactions meson ? spectator quarks Which pairs of quarks interacted?

uRuR uGuG uRuR uGuG dGdG dRdR

uRuR uGuG dGdG dRdR q = uds... Because  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: qq qq  QCD (  QCD ) 2  QCD ~ 1.2  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 +     o + K o ER Fig 18-9a

p  +   + K +

QFD Stationary States Reactions

QFD – Stationary States bound system of neutrinos –not experimentally feasible excited states of leptons –e* not observed below 90 GeV (1990) –would imply lepton compositeness  must learn about QFD from reactions need neutral & colorless system

 ee ee QFD - Reactions Experimentally; g w = 1.7 !!! QFD is considered “weak” only because Z o, W ± are massive !

 ee ee  ee ee  ee ee ee ee arrows are added to help identify particles versus antiparticles  ee ee ee ee

WW u d (2/3) (  1/3) QFD – charged current WW u d (2/3) (  1/3) WW v e (0) (  1) WW e

ZZ u u (2/3) (  /3) QFD – neutral current e e e ZZ ZZ ZZ e +

ZZ s d (  1/3) ( - 1/3) QFD – “flavor changing neutral currents” ZZ ZZ c u (2/3) NOT OBSERVED – or at least very rare

neutrino experiments d u (-1/3) (2/3) ? ? WW

neutrino experiments d u (-1/3) (2/3) v e WW u d (-1/3) (2/3) e + WW v only interact with neg quarks …converse…

Discovery of the Top Quark

Discovery of t quark t b (-1/3) (2/3) e + WW Signature: high nrg e+ accompanied by b-hadrons E o + i  /2 E o = 174,000 MeV  = 1560 MeV t ~ 4.2 * 10  sec 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:Y lm = (-) l Y lm 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 (SpRel) require processes invariant under CPT combined. handwaving proof:

Parity Violation Helicity – relative orientation of p & S p S Bizarre fact: only LH neutrinos exist only RH antineutrinos exist -- an artifact of how the WI works (W R ) RH p S v LH 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

CPT theorem implies if (CP) OK, then T must be OK too.

Neutral Kaon System In our quark model (a.k.a. QCD eigenstates) mc 2 = 498 MeV  mc 2 = 4 * 10  12 MeV

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) Weak / QFD Eigenstates mc 2 = 498 MeV  mc 2 = 4 * 10  6 MeV  = 0.89 * 10  10 sec  = 5 * 10  8 sec in-flight only affected by WI / QFD

Neutral Kaon System: Regeneration Collision regions (QCD) QCD eigenstates QCD eigenstates WI eigenstates

Time Reversal Violation (CP Violation) C P What does CP do to the kaons? left right CP: K o S = + K o S CP: K o L =  K o L

Time Reversal Violation (CP Violation)

K o S   K o L   Decays are consistent with CP good However ~ 0.2% of K o L decays have   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) bottom system n pol A pol scattering neutron electric dipole moment Cs electric dipole moment Is this a problem with “standard model”, new “force”, new …. ? 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 WW WW WW u   ee d veve vv WW u s

CKM matrix are QCD or ‘mass’ eigenstates In the presence of the weak interaction the states are perturbed weak eigenstates

CKM matrix – alternate form  1 =12 o  2 =  3 =  = With approx values: Written in terms of angles mixing each pair of quarks (Euler angles)

If quark mixing, why not…?

MNS matrix Maki-Nakagawa-Sakata matrix  12 ~ 34 o  13 < 13 o  23 ~ 45 o  = ?

Neutrino Oscillations Solar Neutrino Expts –Homestake Mine, SD (Ray Davis) –Explanation w/i previously existing physics with proper calculation (MSW effect) –MSW effect: v e propagate through dense electrons in Sun Atmospheric (vacuum oscill) –Super Kamiokande –Improper ratio of v  to v e events. Reactor Based (vacuum oscill) –KamLAND, 53 reactors, anti-v e from fission product decay. –Event rate and energy spectrum –Energy spectrum inconsistent with ‘no oscillation’ Accelerator Based (vacuum oscill) –FermiLab vs Los Alamos

Vacuum Neutrino Oscillation approx difference btw wavefunctions

Vacuum Neutrino Oscillation For just the v e and v , relax notation  12   ~ 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.

Electron neutrino oscillations, short range

Unification -- trying to express all forces as aspects of one Motivations –Theory…gauge/phase…transformation…blah, blah, blah… –The Z o and  are interchangable in all diagrams And no flavor-changing neutral currents –Relative strengths seem to converge

Electroweak Interaction ER pg 702-b EW Interaction QEDQFD 4-component field : ( B, W 1, W 2, W 3 ) (  or , W +, W , Z o )  = cos  w B + sin  w W 3   =  sin  w B + cos  w W 3 W ± = W 1 ± i W 2 sin  w = one Hamiltonian works for both forces Q: Why are IVB so heavy?

Electroweak Interaction Successful Predictions / Treatments –Z o and  interference at e + e  > 15 GeV, ~10% –Parity violating effects in atomic transitions Optical rotation of light for forbidden transitions & high Z –Polarization effects in scattering of polarized electrons off nuclei –.

Is gravity a force? Or Quantum Gravity? There are a number of proposed quantum gravity theories: String theoryString theory/superstring theory/M-theorysuperstring theoryM-theory Supergravity AdS/CFT correspondence Wheeler-deWitt equation Loop quantum gravity Euclidean quantum gravity Causal Sets Twistor theory Sakharov induced gravity Regge calculus Acoustic metricAcoustic 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?