1. 1 Conservation Kihyeon Cho April 5, 2011 HEP

2. What is the world made of? What holds the world together? Where did we come from? the smallest things in the world interactions (forces) between them the Universe’s past, present, and future Particle Physics: physics where small and big things meet, inner and outer space meet Tools ?

3. Contents Introduction Fermion-Boson History  Particle and Antiparticle  입자물리학과 노벨상 Quark and Lepton Interactions Conservation Natural Units 3

4. Conservation 4

5. 5 Conservation Laws When something doesn’t happen there is usually a reason! Read Perkins: Chapters 1.4, 1.10 That something is a conservation law ! A conserved quantity is related to a symmetry in the Lagrangian that describes the interaction. (“Noether’s Theorem”) A symmetry is associated with a transformation that leaves the Lagrangian invariant. time invariance leads to energy conservation translation invariance leads to linear momentum conservation rotational invariance leads to angular momentum conservation Familiar Conserved Quantities Quantity Strong EM Weak Comments energyYYYsacred linear momentumYYYsacred ang. momentumYYYsacred electric chargeYYYsacred

6. 6 표준모형 (Standard Model) What does world made of?  6 quarks  u, d, c, s, t, b  Meson (q qbar)  Baryon (qqq)  6 leptons  e, muon, tau  e, , 

7. 7 Standard Model b, c are heavier than other quarks - heavy flavor quarks W, Z, top are stand out from the rest. +2/3e -1/3e 0

8. 8 Matter Hadron (Quark) - size  Baryon (qqq): proton, neutron  Meson ( ): pion, kaon Lepton – no size  Point particle

9. 9 Definition Baryon number B =1/3 for quark B= -1/3 for anti-quark B= 0 for lepton B = (# of quark – # of anti-quark) /3 ex) Proton = +1 (uud) (=3/3) Neutron = +1 (udd) (=3/3) pion = 0 (u ubar) (=(1-1)/3) Lepton number L= # of lepton – # of anti-lepton ex) e - = +1, = -1 Proton = 0 Neutron = 0

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11. 11 Strangeness S= - (# of s - # of ) # of s = number of strange quark # of = number of anti-strange quark

12. 12 Charm C= (# of c - # of ) # of c = number of charm quark # of = number of anti-charm quark

13. 13 Bottom B= - (# of b - # of ) # of b = number of bottom quark # of = number of anti-bottom quark

14. 14 Top T= (# of t - # of ) # of t = number of top quark # of = number of anti-top quark

15. 15 Summary duscbt Charge-⅓e-⅓e⅔e⅔e-⅓e-⅓e⅔e⅔e-⅓e-⅓e⅔e⅔e Baryon⅓⅓⅓⅓⅓⅓ Lepton000000 Strange ness 00000 Charm000100 Bottom00000 Top000001

16. 16 Conservation Rules Conserved Quantity WeakElectromagneticStrong I(Isospin)No (  I=1 or ½) NoYes (No in 1996) S(Strangeness)No (  S=1,0) Yes C(charm)No (  C=1,0) Yes P(parity)NoYes C(charge)NoYes CPNoYes

17. 17 Other Conserved Quantities Quantity Strong EM Weak Comments Baryon numberYYYno p  +  0 Lepton number(s)YYYno  -  e -  Nobel 88, 94, 02 topYYNdiscovered 1995 strangenessYYNdiscovered 1947 charmYYNdiscovered 1974, Nobel 1976 bottomYYNdiscovered 1977 Isospin YNNproton = neutron (m u  m d ) Charge conjugation (C) YYNparticle  anti-particle Parity (P)YYNNobel prize 1957 CP or Time (T)YYy/nsmall No, Nobel prize 1980 CPTYYYsacred G ParityYNNworks for pions only Classic example of strangeness violation in a decay:  p  - (S=-1  S=0) Very subtle example of CP violation: expect:K o long  +  0  - BUT K o long  +  - (  1 part in 10 3 ) Neutrino oscillations give first evidence of lepton # violation! These experiments were designed to look for baryon # violation!!

18. Review of interactions |  C| and/or |  S|  0, 1 => No interactions |  C| and/or |  S| =0 => Strong interaction |  C| and/or |  S| =1 => Weak Interaction Neutrino => Weak Interaction Photon => Electromagnetic Interaction 18 Perkins 1.10

19. 19 Examples B 0 s → J/ψΦ B: 0 → 0 0 L: 0 → 0 0 C: 0 → 0 0 S: -1 → 0 0 (Strangeness 보존이 안됨 ) B 0 s => s bbar B=+1, S=-1 J/ψ => c cbar Φ => s sbar

20. 20 Some Reaction Examples Problems a) Consider the reaction v u +p  + +n What force is involved here? Since neutrinos are involved, it must be WEAK interaction. Is this reaction allowed or forbidden? Consider quantities conserved by weak interaction: lepton #, baryon #, q, E, p, L, etc. muon lepton number of v u =1,  + =-1 (particle Vs. anti-particle) Reaction not allowed! b) Consider the reaction v e +p  e - +  + +p Must be weak interaction since neutrino is involved. conserves all weak interaction quantities Reaction is allowed c) Consider the reaction  e - +  + + (anti-v e ) Must be weak interaction since neutrino is involved. conserves electron lepton #, but not baryon # (1  0) Reaction is not allowed d) Consider the reaction K +  - +  0 + (anti-v  ) Must be weak interaction since neutrino is involved. conserves all weak interaction (e.g. muon lepton #) quantities Reaction is allowed

21. 21 More Reaction Examples Let’s consider the following reactions to see if they are allowed: a) K + p  +  + b) K - p  0 c) K 0  +  - First we should figure out which forces are involved in the reaction. All three reactions involve only strongly interacting particles (no leptons) so it is natural to consider the strong interaction first. a)Not possible via strong interaction since strangeness is violated (1  -1) b)Ok via strong interaction (e.g. strangeness –1  -1) c)Not possible via strong interaction since strangeness is violated (1  0) If a reaction is possible through the strong force then it will happen that way! Next, consider if reactions a) and c) could occur through the electromagnetic interaction. Since there are no photons involved in this reaction (initial or final state) we can neglect EM. Also, EM conserves strangeness. Next, consider if reactions a) and c) could occur through the weak interaction. Here we must distinguish between interactions (collisions) as in a) and decays as in c). The probability of an interaction (e.g. a) involving only baryons and mesons occurring through the weak interactions is so small that we neglect it. Reaction c) is a decay. Many particles decay via the weak interaction through strangeness changing decays, so this can (and does) occur via the weak interaction. To summarize: a)Not possible via weak interaction c)OK via weak interaction Don’t even bother to consider Gravity!

22. 22 Example StrongEMweakConclusion K + p  +  + No (  S=2) No (No photon) No (Meson& Baryon only) No K - p  0 Yes (  S=0) NoStrong K 0  +  - No (  S=1) No (No photon) YesWeak Perkins 1.10

23. Natural Units 23

26. 26 Units for High Energy Physics The most convenient energy unit for HEP is electron volts not Joules Typical nuclear binding energies are MeV (10 6 eV) The most convenient mass unit for HEP is MeV/c 2 not kg. mass of electron = 0.51 MeV/c 2 = 9.1x10 -31 kg mass of proton = 938 MeV/c 2 = 1.67x10 -27 kg The most convenient system of units for HEP are NATURAL Units Planck’s constant ( =h/2  )=1, speed of light =1, Energy in eV (or MeV) Easy to write equations: Relativistic relationship between energy, momentum and mass: Becomes: Converting between systems is “easy”: In MKS units

27. 27 Units for High Energy Physics (Ex.) Converting between systems is “easy”: In MKS units Example: The cross section (  ) for the reaction e + e -  +  - is:  th =A/E 2, A=constant Put this formula back into MKS units: A cross section has units L 2 : We have 3 equations: a-2=0, 2a+b-4=2, and 4-a-b=0  a=2, b=2 and:

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32. 32 References Class P720.02 by Richard Kass (2003) B.G Cheon’s Summer School (2002) S.H Yang’s Colloquium (2001) Class by Jungil Lee (2004) 노벨상이 만든 세상 - 물리학 Newton (2011.3, 2008.10) PDG home page (http://pdg.lbl.gov)http://pdg.lbl.gov

33. Thank you.