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Download Alessandro Bettini Introduction to Elementary Particle Physics
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History: After the arms control efforts of both Republican and Democratic presidents: US and Russia own 93% and have about 5000 nuclear warheads each. Today’s plan Particles are waves: another example Energy loss for light charged particles Interactions of photons with matter Sources of particles: Cosmic rays and Accelerators Cherenkov radiation Quiz in the 2nd half of class on Wednesday. http://www.phys.hawaii.edu/~teb/phys490/490.html https://arxiv.org/pdf/1610.08297v1.pdf QM Particles are waves: a new example Suppose that dark matter is composed of scalar particles with mass m~10-22 eV (instead of particles with m~100-200 GeV), what is the deBroglie wavelength of such entities ? 196 ´10 6 eV ´10 -15 m 15 l~ = 2 ´10 m XXX, wrong -22 10 eV Takes into account velocity of dark matter (4 orders of magnitude) Ionization loss for “heavy” charged particles -dE r Zz 2 ì 2mc 2gb 2 2 ü =K ln( - b )ý 2 í dx Ab î I þ where K= 30.7keV m 2 kg -1 Hans Bethe Figure: PDG Should be called the Bethe formula. Felix Bloch had nothing to do with it Some features to note: 1) energy loss per unit length ~1/β2 2) energy loss grows logarithmically at large β (relativistic rise) 3) A minimum ionizing particle (“a mip” ~0.1-0.2 MeV m2 kg-1 ρ) Question: What do the colors mean ? ALICE heavy ion/nuclear physics TPC at the LHC. Question: What is the d band ? Why is it so far to the right ? Energy loss of electrons In addition to ionization loss, there is a second mechanism for “light” charged particles called “bremsstrahlung” Question: What does the German word “bremsstrahlung” mean ? Ans: braking radiation. Question: How does the probability of bremsstrahlung depend on the mass of the particle ? Ans: ~1/m2 (will protons “brems” ? How about muons ?) Here P is power, b is the impact parameter Interactions of photons in matter What are the three mechanisms here ? PDG Note that this plot is on a log-log scale. Question: At what energies does Compton scattering dominate for Pb ? Pair production kinematics Question: Can a photon (γ) decay to an e+epair in vacuum ? Explain. s f = 2me2 + 2(E+ E- - p+ p- cosq ) > 2me2 > 0 Do you see why the 2me2 term appears ? So what about the reaction e+ + e- γ, is that allowed ? How can pair production occur ? g + N ® e + e- + N What about bremsstrahlung, which is the process, e-e- + γ ? m = (Eg + E + 2Eg Ee ) - ( p + pg + 2 pe pg cosq ) 2 e 2 2 e 2 e 2 me2 = mg2 + me2 + 2Eg Ee - 2 pe pg cosq Do you follow ? 2Eg (Ee - pe cosq ) = 0 but Eg ¹ 0 Ans: Also forbidden in vacuum. Need a nucleon to conserve energy-momentum e + N ® e +g + N ± ± See Bettini p.11 for a related argument Famous pedagogical cosmic ray figure from CERN Note the electromagnetic and hadronic components of the cascade from the primary cosmic ray. Composition of cosmic rays Rossi found that cosmic rays have a soft component absorbed by a few cm’s of lead and a hard component that passes through. Question: What is the origin of these components ? A high energy cosmic ray (proton) may produce a shower of particles high in the atmosphere. Will produce charged pions (lifetime 26ns) p ® m nm; p ® m nm + + - - The muons have a lifetime of 2.2 μsec (and if boosted can make it to ground level) m ® e + n m + n e (and c.c.) + + Other processes: p 0 ® gg Bruno Rossi Chicago, (1905-1993) Cornell, MIT Question: What does c.c. mean ? Ans: Charge conjugate Electromagnetic showers Some radiation lengths: Air X0=300m; Fe X0~2cm; Pb X0~5.6 mm Question: How can we characterize the energy loss as a function of length for an electromagnetic shower ? Ans: Use the concept of radiation length, denoted X0 dE dx = E X0 E(x) = E0 e What is the solution for E(x) ? - x X0 The cross-over point between ionization loss and radiation loss is the critical energy, Ec. 600MeV Ec = Z Particle Physics started with cosmic ray physics. Later with the development of particle accelerators, it became more effective to study particles in accelerator experiments. Question: Are cosmic rays still relevant beyond astrophysics and understanding violent phenomena in the universe ? One answer: (1) Still the source of the highest energy particles. (2) Understand how to accelerate particles to such high energies The first stage of accelerators uses electric field to accelerate charged particles (electron, protons, heavy ions) to high energies. F = qE Þ Ed = qV = U Use DC High Voltage up to about 20 MeV. For higher energies, use high frequency AC voltage and carefully time each bunch of particles to obtain a series of accelerating kicks. In a circular accelerator, use an radio-frequency (RF) voltage source. Why are the tubes getting longer ? (in proton accelerators). Ans: protons get boosted as they travel down the linac and the effective length appears shorter as they progress down the tube. To maintain the correct RF timing, need the arrangement above. (Electrons start out relativistic) A few accelerator basics: focus on the synchrotron following Bettini. A synchrotron contains a large number of dipole magnets to confine the beam and quadrupole magnets to keep the beam stable. p(GeV) = 0.3B(T )R(m) Example: If the radius of curvature of a synchrotron ring is 1 km and there is a constant B field of 3.3 T supplied by dipoles, what is the maximum energy that can be stored ? pmax = (0.3)(3.3T )10 m = 10 GeV = 1TeV 3 3 For conventional electromagnets, Bmax~1.4 T; For superconducting magnets Bmax~ 9.0 T FNAL and LHC and the HERA proton ring used superconducting magnets There are RF (radio frequency cavities) to maintain the energy. The beam circulates in a vacuum tube and is grouped into “bunches”. Question: Why not continuous beams ? p.34 Bettini “The particle accelerator is unstable; such an accelerator cannot work” RF cavities Veksler and McMillan Quadrupole magnets Courant, Snyder and Livingston Probably invented by N. Christofilos The first electron-positron collider ADA at Frascati (courtesy of Archivio Audio-Video, INFN-LNF) G. K. O’Neil had conceived and built the first e- e- “storage ring” at Stanford in the late 1950’s. Bruno Touschek built the first (250 MeV) e+e- storage ring and collider at Frascati, Italy. This was followed by improved machines at BINP in Novosibirsk, Russia and at SLAC in Stanford, CA. Annello Di Accumulazione The old Fermilab accelerator complex in Batavia, Il. Old New The CERN accelerator complex in Geneva, Switzerland Old version Proton and heavy ion machine Circumference 27km Some acronyms: LHC=Large Hadron Collider ISR=Intersecting Storage Rings, SPS =Super Proton Synchrotron PS=Proton Synchrotron CMS=Compact Muon Solenoid ATLAS=A Toroidal LHC Apparatus LHCb = LHC beauty ALICE=A Large Ion Collider Experiment Feb 2016: First Turns at SuperKEKB (4 GeV e+’s and 7 GeV e-’s) June 28, 2016 (LER beam current at 1000 mA, HER at 870 mA) Jan 2018: Matter-antiMatter collisions will produce pairs of quantum mechanically entangled (B-anti B) mesons First new particle collider since the LHC (intensity frontier rather than energy frontier; e+ e- rather than p p) There is a large difference between an electron and proton accelerator: electrons emit synchrotron radiation (SR) when they bend. For a 10 GeV/c electron in a 1 km radius ring, the SR loss is about 1 MeV/turn. 4p e b g DESR = ( ) 3 r 2 3 4 Question: Can one build a 1 TeV e+e- collider in a km or few km radius ring ? Ans: No, in a 1 km ring, since the SR losses go like E4 ; the SR loss would be 1012 x 1 MeV= 106 TeV/turn. Question: How can you make a 1 TeV e+emachine ? Question: Is the SR background useful ? Ans: ILC (a linear collider, 30 km long in Japan) Cosmic accelerator example What is the maximum energy of a cosmic ray proton confined in the solar system ? Assume R~ 1013m as the radius of the solar system and an average magnetic field B=1 nT p(GeV) = 0.3B(T )R(m) -9 E = p = 0.3(1´10 T )(10 m) = 3000GeV = 3TeV 13 What is the maximum energy of a cosmic ray proton confined in the galaxy ? (assume R=1021m and B=0.05 nT) E = p = 0.3(0.05 ´10 -9 T )(10 21 m) = 1.5 ´109GeV = 1.5 ´1018 eV What can one conclude about a 1019 eV cosmic ray ?