P780.02 Spring 2003 L12
Richard Kass
Weak Interactions & Neutral Currents
Until the the mid-1970’s all known weak interaction processes could be described
by the exchange of a charged, spin 1 boson, the W boson.
The initial and final state quarks or leptons differed by one unit of electric charge.
Weak interactions mediated by a W-boson are called “charged current” interactions.
A key prediction of the Glashow-Weinberg-Salam model was the
existence of weak interactions mediated by the Z0, a neutral vector boson.
In the GWS model the Z0 did not change the flavor of the lepton or quark.
Recall: the GIM mechanism was invented to eliminate (first order) neutral current
reactions where the flavor of the quark or lepton changed.
The measured branching fractions of K0+- and K++ne provided evidence
for the absence of strangeness changing neutral currents.
M&S CH 9.1
BR( K 0      ) 7  10 9

 10  8


0.64
BR( K   n  )
n
+
Charged current
u
-
+
W+
strangeness changing
neutral current
??0
s
d
s
P780.02 Spring 2003 L12
Richard Kass
Weak Interactions & Neutral Currents
The GIM mechanism eliminated strangeness changing neutral currents by adding
a fourth quark (charm):
sin   d 
 d    cos
  
 s    sin  c
 
cos c  s 
c
If we add the two amplitudes together we get:
d
d
??0
s
s
??0
d d   d d cos 2  c  s s sin 2 c  [d s  s d ] cos  c sin  c
s s   d d sin 2  c  s s cos 2  c  [d s  s d ] cos  c sin  c
d d   s s   d d  s s
The strangeness changing terms are gone but there are
still neutral current terms!
In 1973 the first experimental evidence for neutral
currents was found using the reaction:
n  e  n   e
This reaction cannot occur by W exchange!
P780.02 Spring 2003 L12
Richard Kass
How do we produce a neutrino beam?
Where do the neutrinos come from ?
Proton-nucleon collisions produce lots of p's and K's which decay into neutrinos.
Neutrino Beam
Anti-Neutrino Beam
Branching Ratio
pn
pn
0.999
10-4
pene
pene
Kn
Kn
0.63
10-5
Kene
Kene
0.03
Kp0n
Kp0n
0.05
Kp0ene
Kp0ene
Also get neutrinos from muon decay:
   n n ee    n n ee
have branching ratios of 100%.
Rough calculation of n/ne ratio:
a) neglect neutrinos from muon decay.
b) assume we produce 10X as many pions as kaons in a proton-nucleus collision.
(p  n )  (K  n  ) 10BR(p     n  )  BR(K    n )  BR( K  p o  n  )





o 
# ne
( p  ne )  (K  n e )
10BR( p  e ne )  BR(K  e ne )  BR(K  p e ne )
# n 10  0.999  0.63  0.03 10.7


 210
# ne 10  10 4 10 5  0.05 .05
# n
Relatively easy to make a beam of high energy n's, but hard to make a "pure" beam
of high energy ne's. To make a pure beam of ne's use nuclear beta decay which is
below the energy threshold to produce muons.
P780.02 Spring 2003 L12
Richard Kass
Neutrino Induced Neutral Current Interactions
Many other examples of neutral current interactions were discovered in the 1970’s
W exchange (charged current):
n+N  -+X
Z exchange (neutral current):
n+N  n+X
Neutrino cross section for neutral currents predicted to be 1/3 of charged current cross section.
Typical layout for a neutrino beam line.
“Observation of Neutrino-Like Interactions Without Muon Or
Electrons in the Gargamelle Neutrino Experiment” PL, V45, 1973.
“CC”= charged current event (e or  in final state)
“NC”= neutral current event (no e or  in final state)
Gargamelle was the name of the bubble chamber (BC).
Expect neutrino interactions to be uniformly distributed in BC.
Background from neutrons and K0’s expected mostly in front of BC.
Data in good agreement with expectation of Standard Model.
NC 
1
20 4
2
   sin W  sin W  0.21  0.03
CC n 2
27
NC 
1
20 4
2
   sin W  sin W  0.45  0.09
CC n 2
9
expect :
NC 
NC 

 
CC n CC n
Distributions along beam axis
P780.02 Spring 2003 L12
Richard Kass
Weak Interactions & Neutral Currents
By 1983 CERN was able to produce “real” Z’s and W’s and measure their properties:
mass, branching fractions, and decay distributions.
By 1989 accelerators that could produce Z0’s via e+e-Z were online:
SLC @ SLAC and LEP @ CERN
By 1999 CERN could produce W’s via e+e-W+W-.
The model of Glashow, Weinberg and Salam becomes the Standard Model.
In the standard model the coupling of the Z to quarks and leptons is different than
the coupling of the W to quarks and leptons.
The W has a “V-A” coupling to quarks and leptons: g(1g5)
The Z coupling to quarks and leptons is much more complicated than the W’s:
g(cvfcafg5)g(I3fI3f g52Qfsin2W)
I3 is the third component of “weak” isospin
W 28 degrees
f=fermion type
W is the “Weinberg angle”
M&S 9.2.1, C.6.3
The Weinberg angle is a fundamental parameter of the standard model.
It relates the “strength” of the W and Z boson couplings to the EM coupling:
gEM=gWsinW
gEM=gZsinWcosW
M&S use gEM=gZcosW, eq. 9.8. However, this is NOT the factor that would be used to describe coupling of
the Z boson to fermions described on the next slide. The correct factor is g EM=gZsinWcosW.
P780.02 Spring 2003 L12
Richard Kass
Weak Interactions & Neutral Currents
The standard model gives us the following for the Z boson coupling
to a fermion anti-fermion pair:
g(cvfcafg5)g(I3fI3f g52Qfsin2W)
f
fermion (f)
cv
ca
I3
Q
ne, n, nt
1/2
1/2
1/2
0
gZg(cvfcafg5)
e, , t
-1/2+2sin2W -1/2
-1/2
-1
u, c, t
1/2-4/3sin2W 1/2
1/2
2/3
d, s, b
-1/2-2/3sin2W -1/2
-1/2
-1/3
f
Z0
In the standard model the masses of the W and Z are related by:
MW=MZcosW
2 1/ 2
2 gW 


MW  

G
 F 
1/ 2


p

 
2
 2GF sin W 

37.4
GeV/c 2
sin W
First order calculation
Interesting new development (2001) with measurement of sin2W.
World average for sin2W =0.22270.0003 (mainly from LEP @ CERN)
NuTeV result for sin2W = 0.22770.0013(stat) 0.0009(syst)
NuTeV is a Fermilab neutrino experiment.
Their result for sin2W disagrees with previous measurements, may point to
physics beyond standard model.