1

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

3

ConservationConservation

4

5

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

6

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

'''

7

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

8

MatterMatter

Hadron (Quark) - sizeBaryon (qqq): proton, neutronMeson ( ): pion, kaon

Lepton – no sizePoint particle

9

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

10

11

StrangenessStrangeness

S= - (# of s - # of )

# of s = number of strange quark

# of = number of anti-strange quark

12

CharmCharm

C= (# of c - # of )

# of c = number of charm quark

# of = number of anti-charm quark

13

BottomBottom

B= - (# of b - # of )

# of b = number of bottom quark

# of = number of anti-bottom quark

14

TopTop

T= (# of t - # of )

# of t = number of top quark

# of = number of anti-top quark

15

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

16

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

17

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

18

Perkins 1.10

19

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

20

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

21

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

22

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

23

26

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

27

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

22

)(

)()(

babaababa

TLMTLM

TLMTLM

E

cL

2

22

E

cA

29

30

31

32

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.