From Luigi DiLella, Summer Student Program 2005

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4   decay: n  p + e  +   decay: p  n + e  +  (e.g., 14 O 8  14 N 7 + e + + )

20 January 2005 Steve Dye, HPU Prediction of Fermi’s theory: + p  e + + n

6 InteractionStrong ElectromagneticWeak Gravitation MediatorsGluonsPhotonsW and Z bosonsgravitons Relative Strength Range (m) ∞ ∞

7 gluon

8 It is the only force affecting neutrinos. It is the only interaction capable of changing flavor. It is the only interaction which violates parity symmetry P (because it almost exclusively acts on left-handed particles). It is also the only one which violates CP (CP Symmetry). It is mediated by massive gauge bosons. This unusual feature is explained in the Standard Model by the Higgs mechanism.

9 Conservation of Baryon Number Conservation of Lepton Number Conservation of Strangeness No ! O.K. No ! O.K. S = +  : K +, K° ; S = –  : ,  ±,  ° ; S = –  :  °,  – ; S = 0 : all other particles (and opposite strangeness –S for the corresponding antiparticles) No !O.K. No ! O.K.

10 QuarkSymbolSpinCharge Baryon Number SCBT Mass* UpU1/2+2/31/ MeV DownD1/2-1/31/ MeV CharmC1/2+2/31/ MeV StrangeS1/2-1/31/ MeV TopT1/2+2/31/ GeV BottomB1/2-1/31/30005 GeV Ex: uud -> p ;Q=1, spin=1/2, Baryon Number=1 udd -> n ;Q=0,spin=1/2, Baryon Number=1

11 In this process, the kinetic energy of the incident particles is conserved, only their direction of propagation is modified. Conservation of Kinetic energy : Conservation of momentum : In this process, the kinetic energy of an incident particle is not conserved. Conservation of momentum Ex: Compton Scattering, Deep Inelastic Scattering.

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14 Electron elastic scattering from a point-like charge  e  at high energies: differential cross-section in the collision centre-of-mass (Mott’s formula) Scattering from an extended charge distribution: multiply  M by a “form factor”:  Q  = ħ / D : mass of the exchanged virtual photon D: linear size of target region contributing to scattering Increasing  Q  decreasing target electric charge  Q   (GeV  ) F(Q)F(Q) F (  Q   ) =  for a point-like particle  the proton is not a point-like particle

15 F(Q)F(Q)  Q   (GeV  ) incident electron ( E e, p ) scattered electron ( E e ’, p’ ) incident proton ( E p, – p )   Hadrons (mesons, baryons) Total hadronic energy : For deeply inelastic collisions, the cross-section depends only weakly on  Q   suggesting a collision with a POINT-LIKE object

16 Deep inelastic electron – proton collisions are elastic collisions with point-like, electrically charged, spin ½ constituents of the proton carrying a fraction x of the incident proton momentum Each constituent type is described by its electric charge e i (units of  e  ) and by its x distribution (dN i  dx) (“structure function”) If these constituents are the u and d quarks, then deep inelastic e – p collisions provide information on a particular combination of structure functions: Comparison with  – p and  – p deep inelastic collisions at high energies under the assumption that these collisions are also elastic scatterings on quarks  + p   – + hadrons :  + d   – + u (depends on dN d  dx )  + p   + + hadrons :  + u   + + d (depends on dN u  dx ) (Neutrino interactions do not depend on electric charge) All experimental results on deep inelastic e – p,  – p,  – p collisions are consistent with e u  =  and  e d  =  the proton constituents are the quarks

17 Two beams circulating in opposite directions in the same magnetic ring and colliding head-on e+e+ e–e– E, p E, – p A two-step process: e + + e –  virtual photon  f + f f : any electrically charged elementary spin ½ particle ( , quark) (excluding e + e – elastic scattering) Virtual photon energy – momentum : E  =  E, p  =   Q  = E   – p   c  =  E  Cross - section for e + e –  f f :  = e   (ħc)   e f : electric charge of particle f (units  e  )  = v  c of outgoing particle f (formula precisely verified for e + e –   +  – ) Assumption: e + e –  quark ( q ) + antiquark ( q )  hadrons  at energies E  m q c  (for q = u, d, s)    :

18 R Q =  E (GeV)  For Q .  GeV R  . If each quark exists in three different states, R   is consistent with  x (  ). This would solve the  – problem.  Between  and .  GeV, the peaks and structures are due to the production of quark-antiquark bound states and resonances of a fourth quark (“charm”, c) of electric charge +   Above .  GeV R . . Expect R  (from u, d, s) +  x (  ) = .  from the addition of the c quark alone. So the data suggest pair production of an additional elementary spin ½ particle with electric charge =  (later identified as the  – lepton (no strong interaction) with mass   MeV/c  ).

19 the interactions between quarks based on “Colour Symmetry” Quantum ChromoDynamics (QCD) formulated in the early  ’s  Each quark exists in three states of a new quantum number named “colour”  Particles with colour interact strongly through the exchange of spin 1 particles named “gluons”, in analogy with electrically charged particles interacting electromagnetically through the exchange of spin 1 photons A MAJOR DIFFERENCE WITH THE ELECTROMAGNETIC INTERACTION Electric charge: positive or negative Photons have no electric charge and there is no direct photon-photon interaction Colour: three varieties Mathematical consequence of colour symmetry: the existence of eight gluons with eight variety of colours, with direct gluon – gluon interaction  The observed hadrons (baryons, mesons ) are colourless combinations of coloured quarks and gluons  The strong interactions between baryons, mesons is an “apparent” interaction between colourless objects, in analogy with the apparent electromagnetic interaction between electrically neutral atoms

20 Free quarks, gluons have never been observed experimentally; only indirect evidence from the study of hadrons – WHY? CONFINEMENT: coloured particles are confined within colourless hadrons because of the behaviour of the colour forces at large distances The attractive force between coloured particles increases with distance  increase of potential energy  production of quark – antiquark pairs which neutralize colour  formation of colourless hadrons (hadronization) CONFINEMENT, HADRONIZATION: properties deduced from observation. So far, the properties of colour forces at large distance have no precise mathematical formulation in QCD. At high energies (e.g., in e + e –  q + q ) expect the hadrons to be produced along the initial direction of the q – q pair  production of hadronic “jets”

The Higgs spin  particle (NOT YET DISCOVERED) responsible for generating the masses of all particles

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24 Neutrino detection Target: surface S, thickness dx containing n protons cm –  Incident : Flux  [ cm –  s –  ] (uniform over surface S) dx Prediction of Fermi’s theory: + p  e + + n  – p interaction probability in thickness dx of hydrogen-rich material (e.g., H  O) p interaction rate =  S n  dx interactions per second  : – proton cross-section (effective proton area, as seen by the incident  ) p interaction probability = n  dx = dx  Interaction mean free path: =  n  Interaction probability for finite target thickness T =  – exp(–T  )  ( p)   –  cm  for  MeV    150 light-years of water ! Interaction probability  T  very small (~  –  per metre H  O)  need very intense sources for antineutrino detection