Elementary Particles The particles we will be looking at in this - - PowerPoint PPT Presentation
Heidi Schellman Northwestern Elementary Particles The particles we will be looking at in this course are either elementary , like the electron , or composite , like the pion and proton . The elementary particles can be characterized by their
Heidi Schellman Northwestern
The particles we will be looking at in this course are either elementary, like the electron, or composite, like the pion and proton. The elementary particles can be characterized by their ”quantum numbers”. A quantum number is a quantity that is conserved by at least some of the fundamental interactions.
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±
2/3 2/3 2/3 −1/3 −1/3 −1/3 Q u a r k s L e p t
s 1.5-3 ~1250 ~173,000 3-7 70-120 ~4200 >0? >0? >0? 0.511 105.66 1777.2 81,400 91,188 Weak Interactions Strong Interactions Electro- magnetism
mass,MeV Charge tandard Model of
3 Generations of Fermions Force Carriers June 2008 ±1
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The stable elementary particles that occur in nature at low energies are the electron, electron-neutrino, the u and d quarks, the gluon and the photon. You don’t see u and d quarks, or gluons directly as they are all bound up in protons and neutrons.
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Feynman Diagrams are both a way of illustrating what is going on in an interaction, and a way of calculating that interaction. What one does is one draws the particles in 1 space dimension and 1 time dimension.
An electron at rest in space-time.
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Here two electrons interact by exchanging a photon. Time flows from left to right. This is how the electromagnetic force works - exchange of a force particle.
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e− γ e− γ e e− γ e− γ e
The scattering of an electron and a photon. You could imagine aiming an X-ray at an atom and knocking out an electron this way.
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e− γ e− γ e e− γ e− γ e
as they come together and then moving apart later.
not have the right mass - it has the center of mass energy and not me. This is called a virtual particle and it can only exist for a time ∆t such that ∆m∆t ≥ ¯ h For a 500 keV photon hitting an electron at rest out of an atom, the ”virtual” electron has a mass of 878 keV. The thing to remember is that energy and momentum are conserved at each point in the interaction, but the masses of particles can wander off for very short periods of time.
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they interact.
propagating through space. Because charge is conserved, electron lines have to continue through the diagram. Once we get into weak interactions, your electron may be able to change into an electron neutrino, but the ”lepton” line can’t break. Same for the quarks - they can change type but you have to conserve quarkness. Photons and other bosons can come and go as needed.
photon to scatter. Feynman diagrams illustrate quantum mechanical amplitudes and the probability we observe in the real world is the square
they can interfere.
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e− e+ e− e+ γ e− e+ e− e+ γ
There are two diagrams as in Compton scattering.
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force carrier for Electro-Magnetism no strong or weak interaction
photon-electron scatter pair-production of electron/positron in field of a nucleus
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Q = -e m = 0.511 MeV/c2 stable couples to γ, W, Z
bremsstrahlung
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photon pair-produces, electrons radiate, products do the same. Length scale for one interaction is X0 ~ 0.3 cm in lead, 9 cm in silicon Shower length ~ X0 log(ZE)
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electron bremsstrahlungs, photon pair-produces, electrons radiate, products do the same. Length scale for one interaction is X0 ~ 0.3 cm in lead, 9 cm in silicon Shower length ~ X0 log(ZE)
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Sampling Calorimeter Uranium Liquid Argon Electrons knocked loose in the Argon are detected Get 15%/sqrt(E) energy resolution V
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Q = -e m = 105.66 MeV/c2 decays to e e couples to γ, W, Z
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28
DIS2010
Tammy Walton APS talk
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If you can detect charged particles, you can measure their momentum by applying a magnetic field
CFT Trigger XY View
Event 8 x (cm) y (cm)
20 40 60
20 40 60
3 2 . 5 3 2 . 2 . 1 1 . 5 1 . 3 1.2 0.9 . 9 0.9 0.8 . 8 0.8 0.8 0.8 . 8 . 8 0.7 0.7 . 7 0.7 . 7 0.6 0.6 0.6 0.6 0.6 . 6 . 6 . 6 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Particles bending in a 2 T magnetic field. The red particles are electrons from a Z decay
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Quark Confinement Strong force is very strong Try to rip one quark out of a proton
u d u
u u d d
u d u
u u d d
s d d s d u
u u d d
d u s s d
pair creation is easier than stretching get a ’jet’ of particles
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Parton View Particle View Partons become ’jets’ Jets momentum similar to parton momentum u dbar p n
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Q = -0 m = 0? stable couples to W, Z
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Q = e m = 80.4 GeV decays to q , q’, l , couples to q, q’, l, v, , Z The W particle is the carrier of the Weak Force v e+ u d W
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Q = 0 m = 91.19 GeV/c2 decays to q , q, l , couples to q, q, l, v, , Z, W The Z particle is also a carrier of the Weak Force v v u u Z0
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The elementary particles we have seen to date have either spin 1
2(fermions)
believed to be spin-2 but has not been detected. Spin is conserved in all interactions.
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This is the conserved charge that results from gauge invariance in electricity and magnetism. As far as we know, it is absolutely conserved. The electron is assumed to have charge −1 in units of e, the electron charge. The Fine Structure Constant α = e2 ¯ hc is often used in formulas instead of an explicit e2.
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Color charge is the strong interaction analog of electric charge. The strong interaction equivalent of the photon is the gluon. There are 3 color charges. A quark can be red, green or blue or anti-red, anti-green or anti-blue. Gluons can have 8 color combinations like red-anti-blue or green-anti-red.
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The strong force comes about by the exchange of massless gluons.
Not all particles feel the strong force. The ones that don’t, electrons and neutrinos, are called leptons while the ones that do are called quarks . The word hadrons is also used for strongly interacting particles and generally means the bound quark state we see in the lab, like protons and pi-mesons.
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Meson like the π0, K+ and φ which are made up of quark-anti-quark pairs have color-anti-color charges. Baryons like the proton are made up 3 colored quarks, with 3 different colors so the net color is 0. The strong color force is so strong that you can’t separate the charges and never see a colored object in the lab, only the combination ’red’-’green’-’blue’
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Each particle also has a charge for the weak interactions, which defines how it will interact with the carriers of the weak force, the W and Z0 bosons. Fermions come in weak doublets like the u and d quarks.
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Particle EM charge Strong Charge Weak Isospin e
1 2, − 1 2
νe
1 2, + 1 2
u quark + 2
3e
red,green or blue
1 2, + 1 2
d quark − 1
3e
red, green or blue
1 2, − 1 2
γ 0, 0 W ± ±e 1, ±1 Z0 1, 0 Gluon color a + anti-color b 0, 0
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In addition to the everyday particles, there seem to be 2 more ”generations”
have not figured out what the basic symmetry of nature which leads to the
that any fourth must have masses well above those of known particles. Generation number is not absolute. The weak interactions allow particles to change generations and hence the higher generation particles to decay to the less massive lower generations.
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π+ π+
−
π+ π+
s
π−
Vcs Vcd Vud Vud
The W obviously changes particle type, since it changes charge, so you would expect to see things like e → Wνe as a vertex. But it also turns out to be able to change ”generation”. We know there are at least two additional generations of particles which have been discovered, starting with the muon in the late 1930’s, the strange quark in the 1950’s, the muon neutrino in the 1960’s, the charm and bottom quark and the tau lepton in the 1970’s and the top quark and tau neutrino in the 1990’s.
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π+ π+
−
π+ π+
s
π−
Vcs Vcd Vud Vud
The W boson can mediate transitions between the generations - this is probably good, as otherwise all of those big top and bottom quarks would be stable and weighing everything down. The degree to which the W joins generations is described by two mixing matrices, one for quarks and one for the leptons. The reason this happens is that what we see in the lab are the mass eigenstates of the particles, the ones with definite mass. But the W couples to an admixture of the mass eigenstates.
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d′ s′ b′ Vud Vus Vub Vcd Vcs Vcb Vtd Vts Vtb d s b (1) This is a rotation matrix, and has 4 free parameters, once one applies the constraint that it be unitary. One of those parameters is a complex phase!
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In the 2 × 2 formalism using only the u, d, s, c quarks the mixing is d′ s′ cos θC sin θC − sin θC cos θC d s where the Cabibbo angle θC is such that Vud ≃ Vcs = cos θC ≃ 0.973 and Vus = −Vdc = sin θC ≃ 0.227 These angles determine the relative fractions of D → Kπ, KK,and ππ seen in charmed meson decays and also suppress the decay K0 → µ+µ−. This suppression was introduced by Glashow Iliolopoulos and Maiani who predicted that a charm quark analogous to the u quark would be found. They were right.
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In addition to the s - d mixing there is a 4% mixing between b and s states. So a c quark can decay to either Wd or Ws with relative weights |Vcd|2 and |Vcs|2. In principle it could also decay to a Wb but energy conservation prevents the later two from happening as the b are heavier.
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The neutrinos have a similar mixing matrix where the elements are NOT small.
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