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Physics 661, lecture 4 1

Physics 661

Particle Physics Phenomenology

October 4, 2001

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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

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• 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

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• 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

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• 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

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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

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Cosmic Rays Underground

Muons

neutrino induced muons

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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

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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

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Neutrinos Underground

Contrary to theexpected ratioνµ/νe ≈ 2, thetwo types ofneutrinos havesimilar spectra

Some new physicsis coming intoplay?

(neutrinooscillations)

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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.

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Neutrinos Underground

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Air ShowersVery High Energycosmic rays willproduce air showerswhen they interactin the atmosphere

2.7

“knee”

“ankle”

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Air Showers• High energy showers (say > 100 TeV) require

arrays of detectors observing large areas

• eg. HiRes Fly’s Eye

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Air Showers• Each detector monitors a different portion

of the sky

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Air Showers

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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

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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

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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

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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

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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

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Particle Acceleration

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Particle Acceleration

Predicts powerlaw: dN/dE ~ E-2

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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”)

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Source of UHE CRs• Colliding Galaxies• Active Galactic Nuclei