Introduction to the Standard Model of Particle Physics

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PHY557 Midterm 1 Fall 2000 PHY557 – Midterm Examination I Short answer problems (110 points) a. QCD: list at least two pieces of experimental evidence for the existence of the color quantum number. ( 6 pnts ) i ) The existence of the fully flavor-spin-orbital symmetric states ++ , , or , which never- theless describe fermions. Antisymmetry under color provides the necessary overall antisym- metry. ii ) Another piece of evidence comes from the pi-zero lifetime (which would be incor- rectly predicted by a factor three without color), and iii ) from the measurement of electron- positron annihilation into muons versus annihilation into quarks (i.e. hadrons): this ratio would be three times larger if color did not exist. b. Examine the following processes, and state for each one whether it is possible or impossible, according to the Standard Model (which does not include GUTs, with their potential violation of the conservation of lepton number and baryon number). In the former case, state which in- teraction is responsible; in the latter case cite a conservation law that prevents it from occur- ring. (Following the usual custom, I will not indicate the charge when it is unambiguous, thus γ , Λ , and n are neutral; p is positive.) ( 32 pnts ) (a) p + p π + + π + π 0 S (annihilation) (b) π 0 γ + γ EM ( q+q γ + γ ) (c) π + π 0 + e + + ν e W (small Q value) (d) Σ n + π W ( s u+W * ) (e) ++ n + π + + π + X (energy cons.) (f) ν e + p n + e + W (if s > m n + m e ) (g) D 0 K + π + W ( c s+W * + ) (h) p + p Σ + + n + K 0 + π + + π 0 S (if s > Σ f m f ) (i) ρ 0 π 0 + π 0 X (B-E stats) (j) p + p p + p + p + p S (if s >4 m p ) (k) D + K + + π + + π X ( c ≠> s ) (l) π + + n π 0 + p S (m) Σ 0 Λ + γ EM + ½ + magn.) (n) Ξ Λ + π W (s u+W * ) (o) π + p Λ + K 0 X (strangeness) (p) Σ n + e + ν e W (s u+W * ) c. Starting from a fully-stretched state ud : i ) show that the π 0 (or ρ 0 ) will be a state composed of ( ) 1 2 dd uu + − = ( ) 1 2 dd uu . ii ) Show that the ω = ( ) 1 2 dd uu + is orthogonal to ρ 0 and an iso-singlet. iii ) Using the observed decays of the φ (1020) meson, argue that its quark con- tent is ss . ( 12 pnts ) i ) Taking I ρ + = I | ud = [( 3 / 4 ) ( 1 / 4 )] {| dd + | ( ) u u } = 1 / 2 {| dd + | ( ) u u } = ρ 0 . ii ) The orthonormal state is the singlet ω = 1 / 2 {| dd | ( ) u u }; using the orthonormality of the | dd and | uu states one finds ω || ρ 0 = 1 1 = 0. iii ) The dominant decay modes of the φ (1020) meson are into Kaons, even though the Q-value of those decays is minute, about 40 MeV. That indicates that the parent meson contained the strange quarks that appear in the de- cay Kaons. In this picture, ρπ and 3 π decay modes originate from the annihilation of the ss quarks in the φ into gluon(s).
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PHY557 Midterm 2 Fall 2000 d. Consider the neutral vector mesons ρ , ω , φ , and J/ ψ , which all have J PC = 1 . Assuming that their (electromagnetic!) decay into an electron-positron pair proceeds via
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