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Conservation
Kihyeon Cho
April 5, 2011HEP
What is the world made of?What holds the world together?
Where did we come from?
the smallest things in the worldinteractions (forces) between them
the Universe’s past, present, and future
Particle Physics: physics wheresmall and big things meet,
inner and outer space meet
Tools ?
ContentsContents
Introduction Fermion-BosonHistory
Particle and Antiparticle입자물리학과 노벨상
Quark and LeptonInteractionsConservationNatural Units
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ConservationConservation
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Conservation LawsConservation LawsWhen something doesn’t happen there is usually a reason!
ReadPerkins: Chapters 1.4 , 1.10
n\ pe- or p\ ne+v or \ e That something is a conservation law !
A conserved quantity is related to a symmetry in the Lagrangian thatdescribes the interaction. (“Noether’s Theorem”)A symmetry is associated with a transformation that leaves the Lagrangian invariant.
time invariance leads to energy conservationtranslation invariance leads to linear momentum conservationrotational invariance leads to angular momentum conservation
Familiar Conserved QuantitiesQuantity Strong EM Weak
Commentsenergy Y Y Y sacredlinear momentum Y Y Y sacredang. momentum Y Y Y sacredelectric charge Y Y Y
sacred
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표준모형 표준모형 (Standard Model)(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, ,
bsd
bsd
tbtstd
cbcscd
ubusud
VVVVVVVVV
'''
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Standard ModelStandard Modelb, c are heavier than
other quarks
- heavy flavor quarks
W, Z, top are stand out from the rest.
+2/3e
-1/3e
0
-1
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MatterMatter
Hadron (Quark) - sizeBaryon (qqq): proton, neutronMeson ( ): pion, kaon
Lepton – no sizePoint particle
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DefinitionDefinition
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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StrangenessStrangeness
S= - (# of s - # of )
# of s = number of strange quark
# of = number of anti-strange quark
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CharmCharm
C= (# of c - # of )
# of c = number of charm quark
# of = number of anti-charm quark
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BottomBottom
B= - (# of b - # of )
# of b = number of bottom quark
# of = number of anti-bottom quark
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TopTop
T= (# of t - # of )
# of t = number of top quark
# of = number of anti-top quark
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SummarySummary
d u s c b t
Charge -⅓e ⅔e -⅓e ⅔e -⅓e ⅔e
Baryon ⅓ ⅓ ⅓ ⅓ ⅓ ⅓
Lepton 0 0 0 0 0 0
Strangeness
0 0 -1 0 0 0
Charm 0 0 0 1 0 0
Bottom 0 0 0 0 -1 0
Top 0 0 0 0 0 1
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Conservation RulesConservation RulesConserved
QuantityWeak Electromagnetic Strong
I(Isospin) No
(I=1 or ½)
No Yes
(No in 1996)
S(Strangeness) No
(S=1,0)
Yes Yes
C(charm) No
(C=1,0)
Yes Yes
P(parity) No Yes Yes
C(charge) No Yes Yes
CP No Yes Yes
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Other Conserved QuantitiesOther Conserved Quantities
Quantity Strong EM Weak Comments Baryon number Y Y Y no p+0
Lepton number(s) Y Y Y no -e-Nobel 88, 94, 02 top Y Y N discovered 1995 strangeness Y Y N discovered 1947 charm Y Y N discovered 1974, Nobel 1976 bottom Y Y N discovered 1977 Isospin Y N N proton = neutron (mumd) Charge conjugation (C) Y Y N particle anti-particle Parity (P) Y Y N Nobel prize 1957 CP or Time (T) Y Y y/n small No, Nobel prize 1980 CPT Y Y Y sacred G Parity Y N N works for pions only
Classic example of strangeness violation in a decay: p- (S=-1 S=0)Very subtle example of CP violation:
expect: Kolong+0-
BUT Kolong+-(1 part in 103)
Neutrino oscillations give first evidence of lepton # violation! These experiments were designed to look for baryon # violation!!
Review of interactionsReview of interactions
|C| and/or |S| 0, 1 => No interactions|C| and/or |S| =0 => Strong interaction|C| and/or |S| =1 => Weak InteractionNeutrino => Weak InteractionPhoton => Electromagnetic Interaction
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Perkins 1.10
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ExamplesExamples
B0s → J/ψΦB: 0 → 0 0 L: 0 → 0 0C: 0 → 0 0S: -1 → 0 0 (Strangeness 보존이 안됨 )
B0s => s bbar B=+1, S=-1J/ψ => c cbarΦ => s sbar
ss
ccJ
bsBs
/
0
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Some Reaction ExamplesSome Reaction ExamplesProblems a) Consider the reaction vu+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 vu=1, +=-1 (particle Vs. anti-particle) Reaction not allowed!
b) Consider the reaction ve+pe-+++pMust be weak interaction since neutrino is involved.
conserves all weak interaction quantitiesReaction is allowed
c) Consider the reaction e-+++ (anti-ve)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 #) quantitiesReaction is allowed
dsK
usK
usK
0
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More Reaction ExamplesMore Reaction ExamplesLet’s consider the following reactions to see if they are allowed:
a) K+p ++ b) K-p 0 c) K0+-
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 interactionc) OK via weak interactionDon’t even bother to consider Gravity!
dsK
usK
usK
0
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Example Example Strong EM weak Conclusion
K+p ++
No
(S=2)
No
(No photon)
No
(Meson&
Baryon only)
No
K-p 0 Yes
(S=0)
No Strong
K0+- No
(S=1)
No
(No photon)
Yes Weak
Perkins 1.10
Natural UnitsNatural Units
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Units for High Energy PhysicsUnits for High Energy PhysicsThe most convenient energy unit for HEP is electron volts not Joules Typical nuclear binding energies are MeV (106 eV)
The most convenient mass unit for HEP is MeV/c2 not kg. mass of electron = 0.51 MeV/c2 = 9.1x10-31 kg mass of proton = 938 MeV/c2 = 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
2222 )()( mcpcE 222 mpE
221110121 Energyandand TLMTLMcTLM
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Units for High Energy Physics (Ex.)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/E2, A=constant
Put this formula back into MKS units: A cross section has units L2:
We have 3 equations: a-2=0, 2a+b-4=2, and 4-a-b=0 a=2, b=2 and:
221110121 Energyandand TLMTLMcTLM
44222221
110121
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)(
)()(
babaababa
TLMTLM
TLMTLM
E
cL
2
22
E
cA
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ReferencesReferences
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 - 물리학Newton (2011.3, 2008.10)PDG home page
(http://pdg.lbl.gov)
Thank you.Thank you.