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Physics 661, lecture 4 1
Physics 661
Particle Physics Phenomenology
October 4, 2001
Physics 661, lecture 4 2
Cosmic Rays• Outline
– Primary cosmic ray spectrum and abundances– Cosmic rays in the atmosphere– Cosmic rays at the Earth’s surface– Cosmic rays underground (started)
– Air showers– Interactions with the CMB– Particle acceleration
Physics 661, lecture 4 3
• The weakest force is gravity• The coupling becomes large only at a very
large energy scale, known as the Planck scale• Planck scale is given by equation
(hc/GN)1/2 = 1.2 x 10 19 GeV
• Quantum gravitational effects becomeimportant only at this scale
Problem Set Background
Physics 661, lecture 4 4
• At what energy would a proton incident on aproton at rest be able to produce an antiproton
• The required reaction is p p → p p p p• This reaction would require an energy in the
center-of-mass of 4 mp
• So, ECM2 = (Ep + mp)2 - (pp - 0)2 > (4mp)2
• = Ep2 + 2 Epmp + mp
2 - pp2
• = 2 Epmp + 2 mp2 > (4mp)2
• Epmp > 7 mp2
• Ep > 7 mp
Helpful Example
Physics 661, lecture 4 5
• Curvature of a relativistic charged particlein a magnetic field
• Lorentz force: F = q v/c x B
• Motion: dp/dt = F
• Radius of curvature (ρ): Fn = pv / ρ so q (v/c) B = pv / ρ or ρ = cp/qB p (GeV/c) = 0.3 B(Tesla) ρ(meters) q
Background on Curvature in B Field
Physics 661, lecture 4 6
Background on Curvature in B Field
p∆p = dp/dt ∆x/v
∆xθ
θ
ρ ∆p / p = ∆x / ρ
dp/dt (∆x/v) /p = ∆x / ρ
FN = vp / ρ
Physics 661, lecture 4 7
Cosmic Rays Underground
Muons
neutrino induced muons
Physics 661, lecture 4 8
Neutrinos Underground• σ ≈ 0.5 x 10-38 cm2 Eν/GeV
• λ = 1/(σN) ≈ 1014 cm /(Eν/GeV) ≈ 4x104 Dearth /(Eν/GeV)
• Neutrino componentsunderground– Solar neutrinos
• E ~ MeV– Cosmic ray induced in Earth’s
atmosphere• E ≥ GeV
– Other sources
Physics 661, lecture 4 9
Neutrinos Underground• Cosmic Ray induced neutrinos should be in
the ratio νµ/νe ≈ 2– pions are produced in atmosphere
• π → µ νµ
• µ → e νe νµ
Physics 661, lecture 4 10
Neutrinos Underground
Contrary to theexpected ratioνµ/νe ≈ 2, thetwo types ofneutrinos havesimilar spectra
Some new physicsis coming intoplay?
(neutrinooscillations)
Physics 661, lecture 4 11
Neutrinos Underground(Zenith angle dependence)
• Evidence for neutrino oscillations (ν1 → ν2)
Shaded boxes show the expectation. The dashedlines show the expectation in the presence of derivedoscillation parameters.
Physics 661, lecture 4 12
Neutrinos Underground
Physics 661, lecture 4 13
Air ShowersVery High Energycosmic rays willproduce air showerswhen they interactin the atmosphere
2.7
“knee”
“ankle”
Physics 661, lecture 4 14
Air Showers• High energy showers (say > 100 TeV) require
arrays of detectors observing large areas
• eg. HiRes Fly’s Eye
Physics 661, lecture 4 15
Air Showers• Each detector monitors a different portion
of the sky
Physics 661, lecture 4 16
Air Showers
Physics 661, lecture 4 17
Lifetimes of cosmic rays• The interstellar magnetic field is about 10-11
Tesla. The diameter of the Milky Way’s diskis about 100,000 light-years. How high anenergy cosmic ray will be trapped in thisfield?
• 105 ly = 105 (3 x 1010 cm/sec) (π x 107sec/yr) = 1023 cm• p (GeV/c) = 0.3 B(Tesla) ρ(meters) q =0.3 (10-11)(5x1022) = 1.5 x 1011 GeV/c = 1.5 x 1020 eV
Physics 661, lecture 4 18
Lifetimes of cosmic rays• The cosmic rays can travel through roughly 5
gm/cm2 before interacting• The disk of the Milky Way has a density of
about 1/cm3 = 1.67 x 10-24 gm/cm3
• Therefore, the lifetime of cosmic raystrapped in the Milky Way is
t = 5 gm/cm2 / N c = 5 / (1.67 x 10-24 3 x 1010) seconds = 1014 seconds = 3 x 106 years
Physics 661, lecture 4 19
Interactions with the CMBThe CMB provides asource of collisions whichcuts off high energy CRs
When the cosmic rayenergy exceeds1020 eV, pion productionis possible, the crosssection is large, and thereis a cut-off
ΕγEp
Physics 661, lecture 4 20
Interactions with the CMBExistence of cosmic rays
above Greisen-Zatsepin-Kuzmin limit suggest
• possibly propagation ofexotic particle
• and/or decays oftopological defects
• or ultra-massive relicparticles
• More data is needed
Physics 661, lecture 4 21
Particle Acceleration• Mechanism is an open question• Conventional scenario:
– all high energy charged particles are accelerated inmagnetized astrophysical shocks, whose size and typicalmagnetic field strength determines the maximal achievableenergy, similarly to man-made particle accelerators.
• Most likely astrophysical accelerators for cosmicrays up to the “knee,” and possibly up to the “ankle”– shocks associated with remnants of past Galactic supernova
explosions• Extragalactic component
– powerful objects such as active galactic nuclei are assumed
Physics 661, lecture 4 22
Particle Acceleration
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Particle Acceleration
Predicts powerlaw: dN/dE ~ E-2
Physics 661, lecture 4 24
Source of UHE CRs• Large, energetic structures, where shock
waves are likely (eg. Supernovae, collidinggalaxies, AGNs)
• SN 1006– non-thermal X-rays
• SNs can probably only go up to 1015 eV (“knee”)
Physics 661, lecture 4 25
Source of UHE CRs• Colliding Galaxies• Active Galactic Nuclei