Elementary Particle Physics
Download
Report
Transcript Elementary Particle Physics
Lecture 04 - Hadrons
●
Quarks multiplets
●
Hadron decays
●
Conservation laws
Resonances
FK7003
1
The fundamental forces
Different exchange particles mediate the forces:
electromagnetic
strong
weak
Interaction
Relative
strength
Range
Exchange
Mass
(GeV)
Charge
Spin
Strong
1
Short
( fm)
Gluon
0
0
1
Electromagnetic
1/137
Long
(1/r2)
Photon
0
0
1
Weak
10-9
Short
( 10-3 fm)
W+ W-,Z
80.4,80.4
, 91.2
+e,-e,0
1
Gravitational
10-38
Long (1/r2)
Graviton ?
0
0
2
FK7003
No quantum field
theory yet for gravity
2
The quarks
Quark
Q (e)
Mass
(GeV)
u- up
2/3
0.003
d- down
-1/3
0.005
s- strange
-1/3
0.15
c- charm
2/3
1.2
b- bottom
-1/3
4.2
t-top
2/3
171
Spin ½ particles
Multiplets:
u c t
d s b
+ antiquarks: u , d , s , c , b , t opposite charge: Q -Q
FK7003
3
Hadrons
Two types: mesons quark+antiquark and
baryons quark+quark+quark
Later lectures to show why those combinations are possible.
Full particle listings from the
Review of Particle Physics:
http://pdg.lbl.gov/2008/listings/contents_listings.html
FK7003
4
The quarks
Spin ½ particles
Quark
Q
+ antiparticles
Mass
(GeV)
B
S
C
B
T
(e)
u- up
2/3
0.003
1/3
0
0
0
0
d- down
-1/3
0.005
1/3
0
0
0
0
s- strange
-1/3
0.15
1/3
-1
0
0
0
c- charm
2/3
1.2
1/3
0
1
0
0
b- bottom
-1/3
4.2
1/3
0
0
-1
0
t-top
2/3
171
1/3
0
0
0
1
For antiquarks: internal quantum numbers change sign.
Charge: Q -Q, Baryon number: B - B
Flavour: (strangeness) S -S , ("charmness") C -C , ("bottomness") B - B , T T
Charge is always conserved.
Flavour quantum numbers are conserved in strong and electromagnetic
decays but need not be conserved in weak decays.
FK7003
5
Hadron quantum numbers
Baryons:
Particle
Mass (MeV)
B
Q
S
C
B
p (uud)
938
1
1
0
0
0
n (udu)
940
1
0
0
0
0
L (uds)
1116
1
0
-1
0
0
Lc (udc)
2285
1
1
0
1
0
Lb (udb)
5624
1
0
0
0
-1
General rule for all hadrons.
Total strangeness S strangeness
N s N s = (no. s quarks - no. s quarks)
Similarly C N c N c ; B N b N v (4.01) (obs! No "top" hadrons)
Baryon number: B= quark-baryon-number (4.02)
FK7003
6
Hadron properties
Mesons (bosons)
Particle
Mass (MeV)
B
Q
S
C
B
p+ (ud)
140
0
1
0
0
0
K- (su)
494
0
-1
-1
0
0
D- (cd)
1869
0
-1
0
-1
0
Ds+ (cs )
1971
0
1
0
1
0
(bb)
9460
0
0
0
0
0
FK7003
7
Evidence for a new quantum number:
colour
(4.03)
FK7003
8
Hadrons and the strong force
The strong force occurs between particles carrying
"colour" charge.
Range of the strong force 10 15m.
q (R)
q (G)
Coupling at a vertex: S (more later)
A quark can carry 3 colours: Red (R), Green (G), Blue (B)
q(R)
Gluon (RG)
q (G)
There are eight gluons: (later lecture in detail)
Gluons themselves carry colour and self-interact:
The theory of the strong force is quantum chromodynamics (QCD).
FK7003
9
Colour combinations
We have never seen a quark or gluon!
Nature abhors naked colour.
Every particle in nature is colourless/colour singlet
FK7003
10
A strong reaction:
FK7003
11
QCD Description of the Strong Nuclear
Force
Yukawa model proposed pion exchange
Interaction results from internal gluon lines and
quark exchange
FK7003
12
Some words about decays
Impossible to quote a set of simple rules for lifetimes which are correct in all cases.
There are some general observations which can be made.
Lifetimes: strong 1022 1024 s , weak 107 1013 s , electromagnetic 1016 1021 s
These are approximate and there are exceptions.
Eg A B + C
Decay rate from golden rule: 2p f | H int | i
f | H int | i
2
2
E ' (2.4)
- depends on the dynamics of the force causing the decay.
E ' relates the amount of phase space available for the decay.
If mA
mB + mC there is little phase space for the decay and the decay is
suppressed. Eg neutron lifetime
15 minutes.
The strong force has a peculiar rule, known as OZI suppression which we'll
also cover today.
FK7003
13
Strong decay
p+
u
p +p
+
d
u
u
d
p
u
u
u
u
d
d
u
FK7003
p+
p
14
OZI rule
f decays preferentially to K+K- than p+ p0 p even
though it is less energetically favourable.
Decays in which all gluon lines can be ”cut” are
suppressed.
Rule proposed by Okubo, Zweig and Iizuka in 1960s
FK7003
15
FK7003
16
Weak decays of hadrons
n p + e + e
S 0
L p +p
L
S 1!
s
Strangeness is violated.
d
u
}
p
Strangeness (and the other flavour quantum numbers, C,B) are not
conserved in weak decays.
FK7003
17
Conserved quantities/symmetries
Quantity
Strong
Weak
Electromagnetic
Energy
Linear momentum
Angular momentum
Baryon number
Lepton number
Isospin
-
-
Flavour (S,C,B)
-
Charges (em, strong
and weak forces)
Parity (P)
-
C-parity (C)
-
G-parity (G)
-
-
CP
-
T
-
CPT
FK7003
18
Short-lived particles
Free particle moving in + x direction with energy ER
Ψ(x,t) ei(xp ERt) ei(xp ) e i ( ERt) φ(x)ψ(t) (4.04)
Unstable add exponential time dependence.
ψ '(t) ψ(t)e
Γt
2
e
i ( ER i ) t
2
(4.05)
Modify energy term for unstable particle: ER ER i
Ψ '(x,t) φ(x)ψ '(t) e
Γ
(4.06)
2
i ( ER i ) t
i(xp )
2
e
(4.07)
1
| Ψ 'Ψ '* |2 e t (4.08) where τ mean (proper) lifetime
Γ
A stable particle (Γ 0 ) is a plane wave corresponding to a
particle of a single energy ER .Consider new waveform to be an infinite sum of
waves corresponding to particles of different energies
FK7003
19
Use Fourier transform to get E -dependent wave function
Φ(E) ψ '(t)eiEt dt e
t i ( ER E )
2
dt
1
(4.09)
0
0
i ER E +
2
1
2
Probability density Φ (E)
(4.10)
- Breit Wigner
2
2
ER E
4
Seen in decays of nuclear and
atomic energy levels.
Ndecay
Nmax
0.5 Nmax
ER
FK7003
Γ
2
ER
ER
Γ
2
20
Resonances
Measured mass fromdecay :
Shape of excited state mass
distribution follows
Breit-Wigner distribution
Rate
1
m m0
2
+
4
2
p +p
(4.11)
m E
Mass reconstructed fromdecay :
1
Δm (4.12)
τ
Δmτ 1 (nu) Δm c 2 τ
p + +p
Γ
(MKS)
Consistent with uncertainty principle
E t (1.27)
Owing to the short lifetimes - strong decays
often appear as resonances.
FK7003
770 MeV – ”nominal” mass
21
Summary
●
Hadrons introduced
●
Decays via em, weak and strong forces.
●
Conservation laws
●
Width of a resonance provides a lifetime
FK7003
22