# The Weak Force

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```					The Weak Force

?
EM
STRONG

WEAK
The Force Carriers
 Like the Electromagnetic & Strong forces, the Weak force is also
mediated by “force carriers”.

 For the weak force, there are actually 3 force carriers:

W+                W-                          Z0

These “weak force” carriers         This “weak force” carrier
carry electric charge also !         is electrically neutral

The “charge” of the weak interaction is called
“weak charge”
Weak Charge of Quarks & Leptons
Both quarks & leptons carry weak charge
 Both quarks & leptons “couple to” the W and Z force carriers

 Since the W’s have a charge of +1 and –1 they cause a “charge-
changing” interaction. That is when they are emitted or absorbed,
to conserve charge, the “emitting” or “absorbing” particle changes
charge by +1 or –1 unit.

 The emitting or absorbing particle changes into a different particle.
Alternately, when the W decays, it decays into 2 particles which:
(a) Carry weak charge
(b) The sum of their charges equals the charge of the W

 I will mainly talk about the W in the context of decays…
Comparison of the Force Carriers
Property         EM           Strong                    Weak
Force         Photon         Gluon
Carrier
W+, W-             Z0
(g)           (g)
Charge of                                     Electrical &
None           Color                             Weak
force carrier                                     Weak
Quarks &                       All quarks      All quarks
Couples to:     Charged     Quarks only             &               &
leptons                       all leptons     all leptons
Infinite      <10-14 [m]
Range                                       < 2x10-18 [m]   < 2x10-18 [m]

Notice that the weak force only operates at distances ~ < 10-18 [m] !
Particles & Forces
Charged      Neutral
quarks        leptons     leptons
(e,m,t)      (n)

Strong        Y             N             N
Electro-
Magnetic      Y             Y             N

Weak          Y             Y             Y

Quarks carry strong, weak & EM charge !!!!!
Neutrinos
 From the previous table, you saw that neutrinos only interact via
the weak force.

 Also, the weak force only “kicks in” for d <10-18 [m]. Recall that
the nucleus’ size is about 10-15 [m], so this is 1000 times smaller than
the size of the nucleus.

 As a result, neutrinos can pass through a lot of matter, and do
absolutely nothing!!!!

 After all, matter is mostly empty space, right !

 Neutrinos can easily pass right through the earth, almost as if it
wasn’t there!
Neutron decay
This is how neutron decay really proceeds through the
Weak Interaction

e-                     u          u                 u
W-        d        d    u    d            u    d
ne
Neutron       Proton         Proton

u                           u
d    d                   u       d    +        e-   +        ne

Neutron                 Proton
Neutron Decay (cont)

u                     u
d d                  u d        +       W-
Neutron              Proton
e-   +   ne

n                       p           +             e-     +   ne

But in fact, what’s really going on is this:

d                       u           +             e-     +   ne
Feynman diagram for weak decay
du+e     -+n
e

ne
e-
W-

d                                       u
d                                       d   “Spectator
u                                       u    quarks”

Spectator quark(s): Those quarks which do not directly
participate in the interaction or decay.
Feynman diagram for weak decay
(continued)
 Since the spectator quarks do not directly participate in the
decay, we can just omit them…
 This yields the “quark-level” Feynman diagram!

Is charge conserved ?                  ne 0
e - -1
W-

d                                       u
-1/3                                    +2/3

Is Le conserved ?
Decays of “heavy” quarks
The heavy quarks decay to the lighter ones
t Q=+2/3
b    Q=-1/3

c   Q=+2/3

s    Q=-1/3

u     Q=+2/3
d   Q=-1/3
What about the decay of a b-quark?
bc+m      -+n
m
Is charge conserved ?                nm 0
m-       -1
W-

b                                        c
-1/3                                   +2/3

Notice: Here, the W- decays to a m- and nm

Is Lm conserved ?
What about the decay of a c-quark?
cs+m      ++n
m
Is charge conserved ?                 nm 0

m+ +1
W+

c                                     s
2/3                                    -1/3

Notice: Here, I have the W+ decaying to a m+ and nm (could have
been an e+ and ne as well).
Is Lm conserved ?
What about the decay of a b-quark?
su+e     -+n
e
Is charge conserved ?        ne 0
e - -1
W-

s                             u
-1/3                          +2/3

Is Le conserved ?
Decays of heavy quarks to u & d
 A quark can only decay to a lighter quark.
 The W charge has the same sign as the parent quark.

Quark    Charge     Mass
[GeV/c2]
top      +2/3     ~175
tb   W+(100%)
bottom    -1/3      ~4.5
b  c W- (~90%)                    charm     +2/3      ~1.5
b  u W- (~10%)                   strange    -1/3      ~0.2
up       +2/3    ~0.005
c  s W+ (~95%)
c  d W+ (~5%)         down      -1/3    ~0.010

s  u W- (~100%)

d  u W+ (~100%)
“Leptonic” Decay of W
Once the W is produced, it must decay

W-  e- ne                   W+  e + n e
W-  m- nm                   W+  m + n m
W-  t - nt                  W+  t + n t

It’s call “leptonic decay” because the
W is decaying to leptons!

The W can decay to leptons because leptons carry weak charge

But so do quarks …
Since quarks also carry weak charge, we can also get:
-                               +
W  ud                     W  ud
It’s call “hadronic decay” because the
W is decaying to quarks, which will form hadrons!
u
Check charge:
W-                        (-2/3 + -1/3 = -1)
d
b                                        c

But quarks are bound to one another by the strong force, and are not
observed as “free” particle. That is, they are bound up inside hadrons…

What happens next ?
One possibility…
u               Can, in fact,
W-         d
form a p-
b                       c
B-                            u D0
u

B-                                D0
Meson                             Meson

==    p
d           -
u

B-  D0 p-
The process by which quarks “dress themselves” into hadrons
u         u
u                        p0
W-         W-        u                               u

u
d
d                           p-
d
d
As the quarks separate, the “potential energy” stored in this “spring-
like” force increases. Eventually, the potential energy gets large
enough, and nature relives itself by converting this potential energy
into mass energy. That is, quark-antiquark pairs are created ! The
quarks then pair off and form hadrons (which we can see) !
 In fact, this process whereby quark-antiquark pairs are created
can happen more than once !

 One might therefore get 2, 3, or more hadrons from a hadronic
W decay!

 It’s important to note that when the “spring” associated with
the strong force “snaps”, it always produces quarks and antiquarks
of the same type. They are usually the lighter quarks, since they
have lower mass, and thus are created more easily:

uu , dd , ss
Again Energy being transformed into mass !
Feynman Diagrams involving
W force carriers
Decay of a B- Meson
Could end up as:
u               B-  D0 p-

W-                            B-  D0 p-p0
d
b                                        c       B-  D0 p- p+ p-
B-                                             u D0
u                                                etc

Additional particles are created when the strong force produces more
quark-antiquark pairs. They then combine to form hadrons!

 Notice that the charge of the particles other than the D0 add up to the
charge of the W- (Q = -1), as they must!
W Decays

W-  e- ne
W-  m- nm
Can be 1 or more
W-  t - nt                hadrons produced

W+ follows in an analogous way… see previous slides
Interactions involving W’s
Here is one… Don’t worry about these types of interactions…
I want to emphasize the role of W’s in decays of quarks

e + e  n e +n e
+     -

e-                    ne

W-

e+                   ne
time
Check lepton number, charge conservation…
The main points
1. Neutrons decay to protons through the weak
interaction

2. The electron and neutrino in fact come from
the Wene decay.

3. The W can decay into either lepton pairs or
a quark-antiquark pair (ud). In the latter case, the quarks