PHYS 5326 – Lecture #5
Wednesday, Jan. 29, 2003
Dr. Jae Yu
1.
2.
3.
4.
5.
QCD Evolution of PDFs
Measurement of Sin2qW
Formalism of Sin2qW in n-N DIS
Improvements in Sin2qW
Interpretation and Link to Higgs
Wednesday, Jan. 29, 2003
PHYS 5326, Spring 2003
Jae Yu
1
Factorization
nm,(`nm)
k
k’
s=f*sp
m-, (m+)
pm, qm
W+(W-)
q=k-k’
Partonic hard scatter sp
q, (`q)
xP
P
}
EHad
Non-perturbative, infra-red part f
Wednesday, Jan. 29, 2003
PHYS 5326, Spring 2003
Jae Yu
2
DGLAP QCD Evolution Equations
• The evolution equations by Dokshitzer-Gribov-LipatovAltarelli-Parisi provide mechanism to evolve PDF’s to
any kinematic regime or momentum scale
(
( )
)
2
i

m
dq NS x, M 2
i
s

q
q

u
+
d


V
V
2
d ln M
2
i
(
)
(
)
( )
2
i

m
dq S x, M 2
i
s

q
+
q

i
d ln M 2
2
( )
dG x, M 2  s m 2

2
d ln M
2
 x
dy NS
2
x y q y, M Pqq  y 
(
1
)

dy  NS
2
s x
2
s  x
x y q y, M Pqq  y  + G y, M PqG  y 
(
1
)
(
)
 x 
dy  S
2
s  x
2
x y q y, M PGq  y  + G y, M PGG  y 
1
(
)
(
)
Pij(x/y): Splitting function that is the probability of parton i with momentum y get resolved as
parton j with momentum x<y
Wednesday, Jan. 29, 2003
PHYS 5326, Spring 2003
Jae Yu
3
Feynman Diagrams for Parton Splitting
NLO: O(s2)
LO: O(s)
Wednesday, Jan. 29, 2003
PHYS 5326, Spring 2003
Jae Yu
4
Electroweak Threory
• Standard Model unifies Weak and EM to SU(2)xU(1)
gauge theory
– Weak neutral current interaction
– Measured physical parameters related to mixing parameters
for the couplings
g2 2 M W
g'  gtanθ W , e  gsinθ W , GF 
,
 cosθ W
2
8M W M Z
• Neutrinos in this picture are unique because they only
interact through left-handed weak interactions  Probe
weak sector only
– Less complication in some measurements, such as proton
structure
Wednesday, Jan. 29, 2003
PHYS 5326, Spring 2003
Jae Yu
5
sin2qW and n-N scattering
• In the electroweak sector of the Standard Model, it is not known a priori what
the mixture of electrically neutral electomagnetic and weak mediator is
This fractional mixture is given by the mixing angle
• Within the on-shell renormalization scheme, sin2qW is:
sin q
On- Shell
2
w
M W2
 1 0 M Z2
•Provides independent measurement of MW & information to pin down MHiggs via
higher order loop corrections, in comparable uncertainty to direct measurements
•Measures light quark couplings  Sensitive to other types (anomalous) of
couplings
•In other words, sensitive to physics beyond SM  New vector bosons,
compositeness,n-oscillations, etc
Wednesday, Jan. 29, 2003
PHYS 5326, Spring 2003
Jae Yu
6
Higher Order Corrections
• LO GSW requires three parameters: , GF and MZ
• Higher order corrections bring in dependence two
additional parameters: MTop and MHiggs
n
q
W
W

t W `b
W
W
W
s  O ( W4 )
Wednesday, Jan. 29, 2003
n
m
q’
q
PHYS 5326, Spring 2003
Jae Yu
W
n
Z
W
t  `t
W
Z
W
s  O ( W4 )
q
7
How is sin2qW measured?
( 3)
coupling  I weak
( 3)
coupling  I weak
- QEM sin 2 qW
• Cross section ratios between NC and CC proportional to sin2qW
• Llewellyn Smith Formula:
n (n )
R

σnNC(n )
σnCC(n )
Wednesday, Jan. 29, 2003
n (n )


σ
1
5
 ρ 2  - sin2 θ W + sin4 θ W  1 + nCC(n )
2
9
σ CC


PHYS 5326, Spring 2003
Jae Yu
8




Original Experiments
•
•
•
Conventional neutrino beam from /k decays
Focus all signs of /k for neutrinos and antineutrinos
Only nm in the beam (NC events are mixed)
•
Very small cross section  Heavy neutrino target
ne are the killers (CC events look the same as NC events)

Wednesday, Jan. 29, 2003
PHYS 5326, Spring 2003
Jae Yu
9
How Can Events be Separated?
Event Length
Charged
Current
Events
Neutral
Current
Events
Wednesday, Jan. 29, 2003
y-view
Nothing is
coming in!!!
m
x-view
m
y-view
Nothing is
coming in!!!
x-view
PHYS 5326, Spring 2003
Jae Yu
Nothing is
going out!!!
10
Experimental Variable
Define an Experimental Length variable
Distinguishes CC from NC experimentally in statistical manner
Compare experimentally measured ratio
R Exp
Wednesday, Jan. 29, 2003
NNC Candidates
NShor t
L  L Cut



NLong
L  L Cut
NCC Candidates
to theoretical prediction of Rn
PHYS 5326, Spring 2003
Jae Yu
11
Past Experimental Results
-Shell
sin2θ On
W
 MW
M2W
 1 - 2  0.2277  0.0036
MZ
On-Shell
 80.14  0.19GeV/c 2
The yellow band represents a correlated uncertainty!!
Wednesday, Jan. 29, 2003
PHYS 5326, Spring 2003
Jae Yu
12
Improvements on Measurements
• Asses the uncertainties from previous
measurements
• Determine what the sources of largest
theoretical and experimental
uncertainties are
• Provide new methods to reduce large
uncertainties
Wednesday, Jan. 29, 2003
PHYS 5326, Spring 2003
Jae Yu
13
2
sin qW
Theoretical Uncertainty
• Significant correlated error from CC production of charm quark (mc)
modeled by slow rescaling mechanism
• Suggestion by Paschos-Wolfenstein by separating n and`n beams:
-
R 
σnNC - σnNC
σnCC - σnCC
n
n
1
 R -R
2
 ρ  - sin θ W  
1- r
2

2
Reduce charm CC production error by subtracting sea quark contributions
Only valence u, d, and s contributes while sea quark contributions cancel out
Massive quark production through Cabbio suppressed dv quarks only
Wednesday, Jan. 29, 2003
PHYS 5326, Spring 2003
Jae Yu
14
Homework Assignments
• Draw a few additional Feynman diagrams for
higher order GSW corrections to n-N scattering
at the same order as those on pg 7 in this lecture
– Due: One week from today, Wed., Feb. 5
Wednesday, Jan. 29, 2003
PHYS 5326, Spring 2003
Jae Yu
15