PHYS 5326 – Lecture #4
Wednesday, Jan. 31, 2007
Dr. Jae Yu
1.
2.
3.
4.
5.
QCD Evolution of PDF
Measurement of Sin2qW
Formalism of Sin2qW in n-N DIS
Improvements in Sin2qW
Interpretation of Sin2qW and Its Link to Higgs
Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
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. 31, 2007
PHYS 5326, Spring 2007
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
dq NS ( x, M 2 )
d ln M 2
dq S ( x, M 2 )
d ln M 2
2

m
1 dy
)
x
s(
i
i
NS
2
  q - q  uV + dV 
q ( y, M ) Pqq  

x
2
y
i
 y
2

m
1 dy 
)
s(
i
i
NS
2
s  x
2
s  x 
 q + q 
 q ( y, M ) Pqq   + G ( y, M ) PqG   

x
2
y
i
 y
 y 
dG ( x, M 2 )  s ( m 2 ) 1 dy  S
 x 
2
s  x
2

 q ( y, M ) PGq   + G ( y, M ) PGG   
2

x
d ln M
2
y 
 y
 y 
Pij(x/y): Splitting function which describes the probability for a parton i with momentum y get
resolved as a parton j with momentum x<y
Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
3
Feynman Diagrams for Parton Splitting
NLO: O(s2)
LO: O(s)
Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
4
Electroweak Theory
• 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
MW
g '  g tan qW e  g sin qW GF 
 cos qW
2
8M W
MZ
• 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. 31, 2007
PHYS 5326, Spring 2007
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 electromagnetic 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. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
6
EW Higher Order Corrections
• LO GSW requires three parameters: , GF and MZ
• Higher order corrections bring in dependences to
two additional parameters: MTop and MHiggs
n
q
W
W

t W `b
W
W
W
s  O ( W4 )
Wednesday, Jan. 31, 2007
n
m
q’
q
PHYS 5326, Spring 2007
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
n (n )


1
5
σ
σnNC(n )
2
2
4
 n (n )  ρ  - sin θ W + sin θ W  1 + nCC(n )
2
9
σ CC
σ CC


Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
8

 

The Original Experiment
•
•
•
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. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
9
How Can Events be Separated?
Event Length
Charged
Current
Events
Neutral
Current
Events
Wednesday, Jan. 31, 2007
y-view
Nothing is
coming in!!!
m
x-view
m
y-view
Nothing is
coming in!!!
x-view
PHYS 5326, Spring 2007
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. 31, 2007
NNC Candidates
NShort
L  L Cut



NLong
L  L Cut
NCC Candidates
to theoretical prediction of Rn
PHYS 5326, Spring 2007
Jae Yu
11
Past Experimental Results
-Shell
sin2θ On
W
M2W
 1 - 2  0.2277  0.0036
MZ
 MW On-Shell  80.14  0.19GeV/c 2
The yellow band represents a correlated uncertainty!!
Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
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. 31, 2007
PHYS 5326, Spring 2007
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:
n
n
n
n
1


R
R
σ
σ
2
2
NC
 ρ  - sin θ W  
R -  nNC
n
1- r
2

σ CC - σ CC
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. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
14
Improving Experimental Uncertainties
• Electron neutrinos, ne, in the beam fakes NC events from CC
interactions
– If the production cross section is well known, the effect will be
smaller but since majority come from neutral K (KL) whose x-sec is
known only to 20%, this is a source of large experimental
uncertainty
• Need to come up with a beamline that separates neutrinos from
anti-neutrinos
Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
15
Event Contamination and Backgrounds
•SHORT nm CC’s (20% n, 10% `n)
m exit and rangeout
•SHORT ne CC’s (5%)
neNeX
•Cosmic Rays (0.9%)
•LONG nm NC’s (0.7%)
hadron shower
punch-through effects
•Hard m Brem(0.2%)
Deep m events
Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
16
Other Detector Effects
Sources of experimental uncertainties kept small, through modeling using n and TB data
Size(dsin2qW)
Effect
Tools
Zvert
0.001/inch
m+m- events
Xvert & Yvert
0.001
MC
Counter Noise
0.00035
TB m’s
Counter Efficiency
0.0002
n events
Counter active area
0.0025/inch
n CC, TB
Hadron shower length
0.0015/cntr
TB ’s and k’s
Energy scale
0.001/1%
TB
Muon Energy Deposit
0.004
n CC
Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
17
Measurements of ne Flux
•
•
( -)
Use well known processes (Ke3: K   e n e )
Shower Shape Analysis can provide direct measurement ne events,
though less precise

0

Nmeas /NMC
1.05  0.03 (n e )
( )
Weighted average
used for ne
dRnexp~0.0005
1.01  0.04 n e
 ne from very short events (En>180 GeV)
• Precise measurement of ne flux in the tail region of flux  ~35% more
`ne in `n than predicted
• Had to require (Ehad<180 GeV)
due to ADC saturation
Results in sin2qw shifts by +0.002
Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
18
MC to Relate Rnexp to Rn and sin2qW
• Parton Distribution Model
– Correct for details of PDF model  Used CCFR data for PDF
– Model cross over from short nm CC events
•
Neutrino Fluxes
- nm,ne,`nm,`ne in the two running modes
- ne CC events always look short
•
Shower length modeling
– Correct for short events that look long
•
Detector response vs energy, position, and time
– Continuous testbeam running minimizes systematics
Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
19
sin2qW Fit to Rnexp and R`nexp
Thanks to the separate beam  Measure Rn’s separately
exp
Use MC to simultaneously fit Rn and Rnexp to sin2qW and mc, and sin2qW and 
•
•
n (n )
R
•
•
n (n )


σnNC(n )
1
5
σ
 n (n )  ρ2  - sin2θ W + sin4 θ W  1 + nCC(n )
2
9
σ CC
σ CC



 

Rn Sensitive to sin2qW while R`n isn’t, so Rn is used to extract sin2qW and R`n to
control systematics
Single parameter fit, using SM values for EW parameters (0=1)
sin2θ W  0.2277  0.0013 (stat)  0.0009 (syst)
mc  1.32  0.09 (stat)  0.06 (syst) w/ m
2
c
 1.38  0.14 GeV/c as input
•Two parameter fit for sin2qW and 0 yields
sin2θ W  0.2265  0.0031
Wednesday, Jan. 31, 2007
ρ0  0.9983  0.040
PHYS 5326, Spring 2007
Jae Yu
Syst. Error dominated
since we cannot take
advantage of sea
quark cancellation
20
NuTeV sin2qW Uncertainties
Dominant
uncertainty
d sin2qW
Source of Uncertainty
Statistical
0.00135
ne flux
0.00039
Event Length
0.00046
Energy Measurements
0.00018
Total Experimental Systematics
0.00063
CC Charm production, sea quarks
0.00047
Higher Twist
0.00014
Non-isoscalar target
0.00005
sn /sn
0.00022
RadiativeCorrection
0.00011
RL
0.00032
Total Physics Model Systmatics
0.00064
Total Systematic Uncertainty
0.00162
DMW (GeV/c2)
Wednesday, Jan. 31, 2007
1-Loop Electroweak Radiative
Corrections based on Bardin,
Dokuchaeva JINR-E2-86-2 60 (1986)
-shell)
δsin2θ(On
W
 M2t - ( 175GeV )2 
 -0.00022  

 ( 50GeV )2 


 MH 
+0.00032  ln 

 150GeV 
0.08
PHYS 5326, Spring 2007
Jae Yu
21
NuTeV vs CCFR Uncertainty Comparisons
}Beamline worked!
}Technique worked!
Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
22
Comparison of New sin2qW
-Shell
sin2 θ On
 0.2277  0.0013 (stat)  0.0009 (syst)
W
2
sin θ
On-shell
W
M 2W
 1- 2
MZ
 M W On-Shell  80.14  0.08 GeV/c 2
Comparable precision but value smaller than other measurements
Wednesday, Jan. 31, 2007
PHYS 5326, Spring 2007
Jae Yu
23