LECTURE 14 HADRONS PHY492 Nuclear and Elementary Particle Physics

LECTURE 14
HADRONS
PHY492 Nuclear and Elementary Particle Physics
Last Two Lectures: Fermions
Leptons :
elementary particles
in the standard model
All have spin = 1/2 February 10, 2014 Quarks :
strongly interacting particles
fundamental constituents of matter,
but cannot be detected directly
All have spin = 1/2 14 PHY492, Lecture 2 Hadrons
February 10, 2014 PHY492, Lecture 14 3 Forces
Electromagnetic interaction : Coulomb potential
1
qQ
4πε0
r Weak interaction : unified theory by A.Salam, S.Weinberg, S.Glashow
→ Electroweak interaction
Strong interaction : Nuclear force
(Hamada-Johnston pot.)
attractive hard core QCD Lagrangian February 10, 2014 PHY492, Lecture 14 4 Flavor Independence
Flavor Independence :
The strong force between two quarks at a fixed distance apart
is independent of which quark flavors u, d, s, c, b, t are involved.
( after taking into account quark mass differences ) s equals to
d
s but differs from u
s u
As a consequence of flavor independence.
hadrons in families have approximately the same masses
( charge multiplets ). Example :
February 10, 2014 π+
π0
π-
139.57 (MeV/c2)
139.49 (MeV/c2) n
p
938.27 (MeV/c2)
939.56 (MeV/c2) 139.57 (MeV/c2) Small correction: electromagnetic force PHY492, Lecture 14 5 Charge independence of nuclear forces
Flavor independence of the strong forces
between u and d quarks leads directly the
charge independence of nuclear forces.
charge symmetry p equals to
p
n n
Structure of
Structure of
AZN
is similar to
11
5 B6
ANZ
11C5
6 (mirror nuclei) February 10, 2014 PHY492, Lecture 14 6 Isospin Symmetry
Isospin symmetry : the symmetry between u and d quarks
(1)
proton and neutron are viewed as the “up” and “down” I3 components of a single particle,
+1/2 the nucleon N with an isospin quantum number I = 1/2
p I3 = +1/2 for proton
I3 = - 1/2 for neutron
(2)
Hadronic resonance state Δ(1232)
with I = 3/2 :
Δ++, Δ+, Δ0,
(uuu)
(uud)
(udd)
I3 +3/2 Δ-
(ddd)
n -1/2 +1/2 -1/2 -3/2 February 10, 2014 PHY492, Lecture 14 7 Quark Model Spectroscopy
The observed hadrons are of three types;
baryons ( qqq ), antibaryons ( qqq ), and mesons ( qq ).
Baryon number baryons
antibaryons
mesons
qqq
qqq
qq
1
-1
0
p = uud, n = udd
π+ = ud, π0 = uu,dd, π- = du Kaons, with unknown quantum number ( strangeness ), were discovered
unexpectedly. With the advent of the quark model in 1964, it was realized
that strangeness S was, apart from its sign, the strangeness quark number,
S = - Ns
S = 1 : K+ (494) = us, K0(498) = ds
S = -1 : K- = us , K0 = ds, Λ = uds Similarly,
charm quantum number
C = Nc = N(c ) – N(c )
≈ = -Nb = - [N(b) – N(b)] bottom quantum number B
February 10, 2014 PHY492, Lecture 14 8 Supermultiplet
The meson states of the qq form with its spin and parity
can be described as the supermultiplet as shown below.
The hypercharge Y is defined as
≈ Y=B+S+C+B+T
Jπ = 0- Jπ = 1/2+ Isospin February 10, 2014 PHY492, Lecture 14 9 Lifetime
Lifetime of hadrons has a close relation to the interaction
involved in the decay. interaction
K*+(us) → K0(ds) + π+(ud) π0(uu,dd) → γ + γ
strong interaction
1.3×10-23 s electromagnetic
interaction
0.8×10-16 s π+(ud) → µ+ + νµ
weak interaction
n(udd) → p(uud) + e- + νe weak interaction
February 10, 2014 lifetime PHY492, Lecture 14 2.6×10-8 s 103 s 10 Magnetic moments
Magnetic moments of hadrons can be explained by the
sums of contributions from the quark magnetic moments.
2Mp
Mp
Mp
µu = 3mu µN , µd = 3md µN , µs = 3m µN s Nuclear magneton
u d s Λ = uds
µΛ = µs S = 0 proton (1/2)
= uud
u u d S = 1 S = 1/2 | proton > =
-
Sz µN
= eh/2Mp
Sz OR 2/3 |d;1/2,-1/2> |uu;1,1>
1/3 |d;1/2, 1/2> |uu;1,0> µproton = 4/3 µu – 1/3 µd = Mp/mu(d) · µN February 10, 2014 PHY492, Lecture 14 11 Feasibility of reactions
Check the following conservation laws;
- Q (charge) must be conserved
- Lepton numbers Leµτ must be conserved
- Quark number Nq (Baryon number B) must be conserved
- Each Nf (f=u,d,s,c,b,t) must be conserved
for strong, electromagnetic interactions
- Mass, energy, momentum conservation. (a) Σ0 → Λ + γ
(b) p + p → Σ+ + n + Κ0 + π+
(c) Ξ- → Λ + π-
(d) Δ+ → p + π0
February 10, 2014 PHY492, Lecture 14 12 Hadron Masses
Ignore what is written in Martin on hadron masses.
•  The idea of “constituent” or “effective” or “bound” mass is
a hand-waving attempt to simplify what can only be
explained quantitatively with relativistic quantum field
theory.
•  I don’t think there’s much point in inventing a confusing
treatment when it’s easier to understand the true concepts
at play.
February 10, 2014 PHY492, Lecture 14 13 Hadron Masses
Let’s start with the idea of gluons (more on this later in Ch 5)
February 10, 2014 PHY492, Lecture 14 14 Hadron Masses
Let’s start with the idea of gluons (more on this later in Ch 5)
February 10, 2014 PHY492, Lecture 14 15 Color Confinement
Let’s start with the idea of gluons (more on this later in Ch 5)
February 10, 2014 PHY492, Lecture 14 16 Color Confinement
Let’s start with the idea of gluons (more on this later in Ch 5)
February 10, 2014 PHY492, Lecture 14 17 Hadron Masses
Let’s start with the idea of gluons (more on this later in Ch 5)
February 10, 2014 PHY492, Lecture 14 18 Hadron Masses
Quarks are bound by gluons, but must obey sensible
quantum orbital states.
February 10, 2014 PHY492, Lecture 14 19 Hadron Masses
The energy stored by the gluons
goes *UP* as the average radial
separation of the quarks
increases.
February 10, 2014 PHY492, Lecture 14 20 Hadron Masses
The energy stored by the gluons
goes *UP* as the average radial
separation of the quarks
increases.
February 10, 2014 PHY492, Lecture 14 21