kaons - Physics 443 February 2008 Kaons 1 Quarks According...

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Physics 443 February 2008 Kaons 1 Quarks According to the Standard Model there are 3 generations of quarks, with two quarks in each generation. Quarks have electric charge, color charge and weak charge. The electric charge couples the quarks by electromagnetic forces. The color charge couples them by the strong force, and the weak charge by the weak force. Within each generation one of the quarks has electric charge 2 3 e and the other - 1 3 e where e is the charge of an electron. The 6 quark flavors are up( u ), down( d ), charm( c ), strange( s ), top( t ), and bottom( b ). u d 0 c s 0 t b 0 (1) The u, c and t have charge 2 3 e and d 0 , s 0 , and b 0 have charge - 1 3 . For each quark, there is an antiquark with opposite electric charge. Thanks the mech- anism of confinement, we never see free quarks, but only quark bound states. There are bound states of 3 quarks, like the proton ( uud ) and neutron ( udd ) with charges 1 and 0 respectively. The 3 quark states are called baryons. Every possible 3 quark combination of the light quarks ( u , d , and s ) has been observed. The masses of the quarks are very different as shown in the table. Except for the pro- ton, the 3 quark bound states are all unstable. There are also quark anti-quark states like the π + ( u ¯ d ), π - ud ), K 0 sd ), K + su ), ¯ K 0 ( s ¯ d ), etc. with charges 1, -1, 0, 1, 0. The quark anti-quark states are called mesons. Every quark antiquark pair will appear as a meson. Quark masses (MeV/c 2 ) u 10 d 10 s 80 c 1.55 b 4700 t 175000 We usually produce mesons in strong or electromagnetic interactions. They decay by weak interactions. Strong and electromagnetic interactions conserve quark flavor. The number of quarks - antiquarks of each flavor in the initial state is the same as the number in the final state. That is N q - N ¯ q 1
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is conserved. So a u quark cannot turn into a d in a strong interaction. On the other hand, weak interactions couple the charge 2 3 quark with the charge - 1 3 quark in each generation and the weak interaction is mediated by the charged vector boson call the W . The W has electric charge ± 1. The interactions are represented by Feynmann diagrams. Some of the allowed weak interaction vertices are shown in Figure 1. d 0 s 0 ¯ s 0 u c ¯ c A A A A A A A A A W - W - W + A A A W - d ¯ u Figure 1: Weak interaction charged current vertices Time runs up in the diagrams. Note that charge is conserved at each vertex. That is, the sum of the electric charges of the quarks and W’s coming into the vertex is the same as the sum of electric charges leaving the vertex. The bar indicates the antiparticle so ¯ q is the anti q . Since we never see free quarks, the vertices indicated above are just pieces of more complicated interactions that involves mesons and baryons. An important subtlety is that the quark flavors that we identify for par- ticipation in weak interactions according to 1 are not quite the same as the quarks states that couple by strong interaction. In particular the weak states s 0 and d 0 are linear combinations of the strong states s and d . Namely s 0 = s cos θ c - d sin θ c d 0 = d cos θ c + s sin θ c The mixing angle θ c
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