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Particle Physics Study

Particle Physics Study. 2009/07/27 Grass. From Luigi DiLella , Summer Student Program 2005. Outline. Before We Move to Particle Physics Neutrinos Fundamental Interaction Particle Interactions and Conservation Laws Quarks Elastic Scattering and Ine lastic Scattering

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Particle Physics Study

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  1. Particle Physics Study 2009/07/27 Grass From Luigi DiLella, Summer Student Program 2005

  2. Outline • Before We Move to Particle Physics • Neutrinos • Fundamental Interaction • Particle Interactions and Conservation Laws • Quarks • Elastic Scattering and Inelastic Scattering • “Dynamic” Evidence for Quarks • Elementary Particles

  3. Before We Move to Particle Physics • Thomson’s atomic model • Rutherford’s scattering experiments • E = h ν; λ=h /p • Pauli’s exclusion principle Richard Feynman: Whatever is not expressly forbidden is mandatory.

  4. Neutrinos • n -> p + e- -Expect well defined energy • No electric charge • Spin ½ • No mass • A very small mass b- decay: n  p + e- + n b+ decay: p  n + e+ + n (e.g., 14O814N7 + e+ + n)

  5. Neutrino Detection Prediction of Fermi’s theory: n + p  e+ + n http://www.ps.uci.edu/physics/reinesphotos.html http://www-sk.icrr.u-tokyo.ac.jp/doc/sk/photo/normal.html http://www-personal.umich.edu/~jcv/IMBdiverbig.jpg Steve Dye, HPU

  6. Fundamental Interaction

  7. Strong Interaction gluon • It holdsquarks and gluons together to formprotons, neutrons and other particles. • It is also the force that bindsprotons and neutrons together. In this context it is called the nuclear force (or residual strong force), and it is the residue strong interaction between the quarks that make up the protons and neutrons. • It acts directly only upon elementary quark and gluon particles. • The strong force acting between quarks, unlike other forces, does not diminish in strength with increasing distance, after a limit (about the size of a hadron) has been reached. It remains at a strength of about 100 000 newtons, no matter how far away from each other the particles are, after this limiting distance has been reached.

  8. Weak interaction • 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. Particle Interactions and Conservation Laws • Conservation of Baryon Number • Conservation of Lepton Number • Conservation of Strangeness O.K. No ! O.K. No ! O.K. No ! S = +1: K+, K° ; S = –1: L, S±, S° ;S = –2 : X°, X– ; S = 0 : all other particles (and opposite strangeness –S for the corresponding antiparticles) No ! O.K.

  10. Quarks 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. Elastic ScatteringInelastic Scattering

  12. Deep Inelastic Scattering • If we can use electrons to "see" protons inside the nucleus, can we also use them to see inside protons? • The direct evidence for the existence of quarks inside the proton is provided by deep inelastic scattering. The idea is to accelerate electrons to very high energies, then allow them to interact with a stationary proton, and investigate what happens.  But why is this called deep inelastic scattering? • At high energies, the wavelengths associated with the electrons are much smaller than the size of a proton.  Hence the electrons can probe distances that are small compared with the proton - that is, DEEP within the proton.   However, the high energies tend to disrupt the proton, so that it produces several new particles (hadrons).  This means the scattering is INELASTIC because the target has been changed in the process. • Deep inelastic scattering may be viewed in two ways: as inelastic scattering off a proton because it has constituents inside, or as elastic scattering from one of the constituents inside (ignoring the whole proton and other constituents). We are able to say that the constituents appear to be point-like and so can be considered to be fundamental particles.  

  13. “Dynamic” Evidence for Quarks Electron – proton scattering using a 20 GeV electron beam from the Stanford two – mile Linear Accelerator (1968 – 69). • The modern version of Rutherford’s original experiment: • resolving power  wavelength associated with 20 GeV electron  10-15 cm Three magnetic spectrometers to detect the scattered electron: • 20 GeV spectrometer (to study elastic scattering e– + p  e– + p) • 8 GeV spectrometer (to study inelastic scattering e– + p  e– + hadrons) • 1.6 GeV spectrometer (to study extremely inelastic collisions)

  14. F(|Q2|) |Q2| (GeV2) Electron – proton scattering 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 sM 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 F (|Q2| ) = 1 for a point-like particle  the proton is not a point-like particle

  15. scattered electron ( Ee’ , p’ ) incident electron ( Ee , p ) q g incident proton ( Ep , – p ) Hadrons (mesons, baryons) Total hadronic energy : F(|Q2|) |Q2| (GeV2) Inelastic electron – proton collisions For deeply inelastic collisions, the cross-section depends only weakly on |Q2| , suggesting a collision with a POINT-LIKE object

  16. Comparison with nm – p and nm – p deep inelastic collisions at high energies under the assumption that these collisions are also elastic scatterings on quarks nm + p m– + hadrons : nm + dm– + u (depends on dNd/dx ) nm + p m+ + hadrons : nm + um+ + d (depends on dNu/dx ) All experimental results on deep inelastic e – p , nm – p, nm – p collisions are consistent with eu2 = 4 / 9 anded2 = 1 / 9 the proton constituents are the quarks Interpretation of deep inelastic e - p collisions 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 ei (units of | e |) and by its x distribution (dNi/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: (Neutrino interactions do not depend on electric charge)

  17. e+ e– E , p E , – p A two-step process: e+ + e– virtual photon f + f f : any electrically charged elementary spin ½ particle (m , quark) (excluding e+e– elastic scattering) Cross - section for e+e–f f : a = e2/(ħc) 1/137 ef : electric charge of particle f (units |e |) b = v/c of outgoing particle f (formula precisely verified fore+e–m+m–) Assumption: e+e– quark ( q ) + antiquark ( q )  hadrons  at energies E>>mqc2 (for q = u , d , s)b1: Physics with e+e– Colliders Two beams circulating in opposite directions in the same magnetic ring and colliding head-on Virtual photon energy – momentum : Eg = 2E , pg = 0Q2 = Eg2 – pg2c 2 = 4E 2

  18. R Q = 2E (GeV) Experimental results from the Stanford e+e– collider SPEAR (1974 –75): • For Q< 3. 6 GeV R 2. If each quark exists in three different states, R2 is consistent with 3x ( 2 / 3). This would solve the W– problem. • Between 3 and 4.5 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 +2/3 • Above 4.6 GeV R 4.3. Expect R 2 (from u, d, s) + 3 x (4 / 9) = 3.3 from the addition of the c quark alone. So the data suggest pair production of an additional elementary spin ½ particle with electric charge = 1 (later identified as the t – lepton (no strong interaction) with mass 1777 MeV/c2 ).

  19. The Modern Theory of Strong Interactions the interactions between quarks based on “Colour Symmetry” Quantum ChromoDynamics (QCD) formulated in the early 1970’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. 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” 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.

  21. Elementary Particles The Higgs spin 0 particle (NOT YET DISCOVERED) responsible for generating the masses of all particles http://en.wikipedia.org/wiki/File:Elementary_particle_interactions.svg http://www-visualmedia.fnal.gov/VMS_Site/gallery/stillphotos/2005/0400/05-0440-01D.hr.jpg

  22. The End

  23. Neutrino detection Prediction of Fermi’s theory: n + p  e+ + n n – p interaction probability in thickness dx of hydrogen-rich material (e.g., H2O) Incident n: Flux F [ n cm–2 s–1 ] (uniform over surface S) Target: surface S, thickness dx containing n protons cm–3 dx n p interaction rate = FS nsdx interactions per second n p interaction probability = nsdx = dx / l s : n – proton cross-section (effective proton area, as seen by the incident n ) s( n p) 10–4 3 cm2 for 3 MeV n l 150 light-years of water ! Interaction mean free path: l = 1 /ns Interaction probability for finite target thickness T = 1 – exp(–T/ l) Interaction probability T / l very small (~10–18 per metre H2O)  need very intense sources for antineutrino detection

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