Cross-section extraction
using xem2 data
Sebastian Moran Vasquez
1
2
Contents:
3
Cross-section Calculation
Ratio Method
Here we do not correct the data to get the Born cross section, instead we run a simulation and add all the real world effects to it, until it matches the data. Here is when MC enters the analysis.
σ
σ
Born
data
Born
Model
=
MC
data
Y
Y
A(V) : acceptance of the spectrometer
C : kinematic dependent efficiencies (not constant)
V : volume of the phase-space
R(V) : Radiative effects
So, here you don't correct the data, you put your effort into the MC to make it look like the data. Note that the MC data has no idea about the physics of the interaction (cross-sections) or anything like that, the only thing that is doing is transporting electrons with a certain range of energy through the magnets of the spectrometer and populating the phase space.
det
4
Cuts Applied
MC:�
stop_id==0.0 && abs(hsdp)<8 && abs(hpsyptar)<0.032 && abs(hpsxptar)<0.085
Data:�
abs(ptardp)<8 && decal > 0.7 && abs(ptarth)<0.085 && abs(ptarph)<0.032 && npeSum>2
ptarph = yptar
ptarth = xptar
Good way to show impact of cuts:
3 histograms on top of one another:
5
Run Numbers and Parameters
For C12 @ 20 deg:
6
20 bins per p setting
7
σ(Rad) as a function of δ
p=-4.78 p=-5.36 p=-5.878 p=-6.6
p=-3.4 p=-3.81 p=-4.0 p=-4.27
p=-2.42 p=-2.71 p=-3.04
8
σ(Born) as a function of δ
p=-2.42 p=-2.71 p=-3.04
p=-3.4 p=-3.81 p=-4.0 p=-4.27
p=-4.78 p=-5.36 p=-5.878 p=-6.6
9
p=-6.6
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p=-5.878
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p=-5.36
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p=-4.78
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p=-4.27
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p=-4.0
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p=-3.81
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p=-3.4
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p=-3.04
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p=-2.71
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p=-2.42
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Comparison Θ calculated v/s using a fixed Θ=20 deg
So far, in the application of the weight to MC, on a event by event basis, the value for theta has been the central angle of the particular setting, in this case is 20 deg. The idea here is to make a comparison of the effect of calculating a different theta per each event instead of assuming a fixed value.
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Using Θ calculated per each MC event.
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Cross-section ratio comparison Θ calc v/s fixed
Both methods give consistent results until xb~0.8
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Θ fixed Θ calculated per each event
p=-6.6
p=-5.878
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Θ fixed Θ calculated per each event
p=-5.36
p=-4.78
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Θ fixed Θ calculated per each event
p=-4.27
p=-4.00
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Θ fixed Θ calculated per each event
p=-3.81
p=-3.40
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Θ fixed Θ calculated per each event
p=-3.04
p=-2.71
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Θ fixed Θ calculated per each event
p=-2.42
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Inclusion of Efficiencies
3 Efficiencies were considered: From report file (example)
N : Yield
PS: Pre-scale factor
Q: Charge (BCM4A)
Eff: Efficiency factor
If PS3_factor ≠ -1
JA: Later on, need to figure out how ELT, CLT are calculated. For now, ignore ELT
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Effect of including the efficiencies in the cross-section ratios
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32
Inclusion of Al Dummy Subtraction
For p=-6.60 GeV/c
N(LD2)/N(dummy) are the charge normalized yield of LD2/dummy with PS factors and all efficiencies included.
Al and LD2 have the same cuts applied.
JA: Suggest using N for number, Y for normalized yields
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Effect of including dummy subtraction in the cross-section ratios
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35
Inclusion of BCM4A Charge Correction
Q_corr = Q * (1. + (0.37 / Q_I))
From report file:
BCM4A Beam Cut Current
BCM4A Beam Cut Charge
The cross-section ratio is re-calculated using Q_corr instead of Q
36
Charge Symmetry
Background (CSB)
Correction
20 deg 26 deg 35 deg
2.42 2.71 3.04 3.4 1.95 2.21 2.52 2.86 1.26 1.44 1.63 1.85 2.11 2.40
LD2 ✅ ✅ ✅ ✅ ✅ ❌ ✅ ❌ ✅ ✅ ✅ ✅ ✅ ✅
He3 ✅ ✅ ✅ ✅ ----------------------- ✅ ✅ ✅ ✅ ❌ ❌
He4 ✅ ✅ ✅ ✅ ----------------------- ✅ ✅ ✅ ✅ ✅ ✅
Li6 ✅ ❌ ✅ ❌ ----------------------- ------------------------------------
Li7 ✅ ❌ ✅ ❌ ----------------------- ------------------------------------
Be9 ✅ ❌ ✅ ❌ ----------------------- ------------------------------------
B10 ✅ ❌ ✅ ❌ ----------------------- ✅ ❌ ✅ ✅ ❌ ❌
B11 ✅ ❌ ✅ ❌ ----------------------- ✅ ❌ ✅ ✅ ❌ ❌
C12 ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅
Al27 ✅ ❌ ✅ ❌ ----------------------- ------------------------------------
Ca40 ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅ ✅
Ca48 ✅ ❌ ✅ ❌ ----------------------- ✅ ✅ ✅ ✅ ✅ ✅
Ti48 ✅ ❌ ✅ ❌ ----------------------- ------------------------------------
Fe54 ✅ ❌ ✅ ❌ ----------------------- ------------------------------------
Ni58 ✅ ❌ ✅ ❌ ----------------------- ------------------------------------
Cu63 ✅ ✅ ✅ ✅ ----------------------- ❌ ✅ ✅ ✅ ✅ ✅
Ni64 ✅ ❌ ✅ ❌ ----------------------- ------------------------------------
Ag108 ✅ ❌ ✅ ❌ ----------------------- ------------------------------------
Sn119 ✅ ❌ ✅ ❌ ----------------------- ------------------------------------
Au197 ✅ ❌ ✅ ❌ ----------------------- ✅ ✅ ✅ ✅ ❌ ❌
Th232 ✅ ❌ ✅ ❌ ----------------------- ------------------------------------
Dummy ✅ ❌ ✅ ❌ ✅ ❌ ✅ ❌ ✅ ✅ ✅ ✅ ❌ ❌
Positive polarity runs per each target/setting
Only e+ runs, not e- runs for these settings
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20°
26°
35°
π⁰ → 2𝛾 → e⁺ + e⁻
CSB Correction
From 6GeV era. E02-019
Region of interest for CSB studies
Expectation: very large effect at low p and large angles
Notes: The results are using all the “subsets 1” data, ELCLEAN for e+ and ELREAL for e- . Also TRIG3Mult>=1 was used in this study.
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20°
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20°
Trying to use offset in the fit function
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Using all data (full coverage in some targets only)
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Using all data (full coverage in some targets only)
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Using only the settings that are present for all targets
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Using only the settings that are present for all targets
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Full vs Limited Coverage Comparison
vs
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48
Adding ratio plots to see if there is a systematic shift more clearly
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Adding ratio plots to see if there is a systematic shift more clearly
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Full vs Limited Coverage Comparison
vs
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52
The largest relative uncertainty on the e+/e- ratio from the fit normalization is about 2%.
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Residuals
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55
Sources of uncertainty in the e+/e fit
Fit uncertainty (slide 52):
Shape imperfections/extrapolation error (slide 55):
Charge asymmetry
Total: sqrt(5^2+1^1+1^2)% up to E’=3.2. Add the linearly increasing piece in quadrature.
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57
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Relative Errors Ratios for different targets
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60
I was missing copper
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Systematics Table
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Quantifying scaling
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64
Show only the right one for APS
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68
Detector Calibration
Corrections applied to Final Yield
Data Analysis, Current Status
All of them applied to the cross sections already
Next Steps:
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70
26°
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35°
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How to apply the CSB to the cross section?
CSB subtraction done before dummy subtraction
Results for C12, HMS
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Results for Ca40 , HMS
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With CSB corr
Without CSB corr
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Isoscalar corrections
Different parameterizations for σn/σp
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New delta correction
This time the correction is applied as a weight to the MC yield, not as a redefinition of the variable (previous case)
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Effect of the delta correction to the cross section
Carbon, HMS
20 deg
35 deg
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80
Isoscalar corrections
Different parameterizations for σn/σp
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New delta correction
This time the correction is applied as a weight to the MC yield, not as a redefinition of the variable (previous case)
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Effect of the delta correction to the cross section
Carbon, HMS
20 deg
35 deg
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No Cuts
ngcer>2
ngcer>2 + |δ|<8.0
pions electrons
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No Cuts
ngcer>2
ngcer>2 + |δ|<8.0
ngcer<1.0
p=-6.60
p=-5.878
p=-5.36
p=-4.78
p=-4.27
p=-3.81
p=-3.40
p=-3.04
p=-2.71
p=-2.42
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Coulomb Corrections
90
The expectation is that @ x~1 the ratio goes below one, look into that
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MC Ytar correction
weight = -0.00812174*ytar*ytar - 0.0000415678*ytar+1.00021 ; Applied to MC yield as a weight
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weight = TMath::Sqrt(1+xptar*xptar + yptar*yptar); Applied to MC yield as a weight
MC Jacobian Correction
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delta_corr = 0.990337*δ - 0.00236077*δ^2 + 0.000286814*δ^3 + 2.09878E-6*δ^4 - 2.4867E-6*δ^5 + 1.8646E-7*δ^6 ; Redefinition of the variable, is not a weight
MC delta Correction
98
delta_corr = 0.990337*δ - 0.00236077*δ^2 + 0.000286814*δ^3 + 2.09878E-6*δ^4 - 2.4867E-6*δ^5 + 1.8646E-7*δ^6 ; Redefinition of the variable, is not a weight
MC delta Correction
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100
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Delta correction plotted as a function of delta
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103
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Applying the delta cut before or after the correction
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Applying the delta cut before or after the correction
Conclusion: We should apply the cut after we implement the correction, otherwise we are losing events at the edges.
|δ| < 8.0 -> INCORRECT
|δ_corrected| < 8.0 -> CORRECT
P = -2.42
P = -6.60
.
.
.
106
Using the variables at the interaction point vs reconstructed ones
20 deg
26 deg
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35 deg
Effect on the cross section as a function of x.
20 deg
108
26 deg
35 deg
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Useful plots
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111
For lower p settings the xs doesn’t vary much, but for higher p settings the xs varies rapidly
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F2 Structure Functions Studies
Study based on the paper ‘Scaling of the F2 structure function in nuclei and quark distributions at x > 1’ (https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.105.212502)
Relationship between x and ξ
Muon scattering
Neutrino scattering
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Scaling of the nuclear structure functions
QE peak
DIS
SRC tail
Resonances
Scaling violations at high x, specially at x>1
F(x,Q2)
F(ξ,Q2)
114
To help explaining ‘x and xi scaling of the nuclear structure function at large x’
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C12 D2
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Runs stability-check
HMS and SHMS work with the first 3 of the PS1 PS2 … in the report file. The first one is ¾ that has huge contamination and should not be used for physics analysis, is more to study efficiency and background contamination. The other 2 are more reliable, they are ELREAL, and ELCLEAN, they ask for additional cuts in the cerenkov, look at people’s thesis to understand it better. The ¾ trigger runs should have a substantial increase in the CNY.
¾
trigger
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Effect on the cross-sections and xs ratio
20 deg
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26 deg
120
35 deg
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ELREAL
3/4
20 deg
20.005 deg,
ladder 2
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ELREAL
3/4
20 deg
Those are boiling runs! Not production runs
20.005 deg,
ladder 2
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ELREAL
3/4
20 deg
20.005 deg,
ladder 2
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ELREAL
3/4
20 deg
remove
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26 deg
ELREAL
3/4
126
26 deg
ELREAL
3/4
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26 deg
ELREAL
3/4
128
35 deg
ELREAL
3/4
129
35 deg
ELREAL
3/4
130
35 deg
ELREAL
3/4
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Outliers in the run stability studies:
Taking only two p-settings
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Taking a closer look at setting p=-3.4 GeV
1.04
1.02
0.98
Comparison for different cuts
133
Taking a closer look at setting p=-3.4 GeV -> H.bcm.bcm4a.AvgCurrent distributions
6569
5910
4925
4920
5904
BCM4A Current: 8.462 uA
BCM4A Beam Cut Current: 24.604 uA
BCM4A Current: 53.947 uA
BCM4A Beam Cut Current: 57.059 uA
BCM4A Current: 38.117 uA
BCM4A Beam Cut Current: 42.232 uA
BCM4A Current: 34.202 uA
BCM4A Beam Cut Current: 36.837 uA
BCM4A Current: 39.201 uA
BCM4A Beam Cut Current: 39.552 uA
I-beam taken from HMS_runlist.dat
I-beam = 60
I-beam = 40
I-beam = 50
I-beam = 40
I-beam = 40
Data is taken every 2 sec or 1000 events, whatever is shorter
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Taking a closer look at setting p=-4.27 GeV -> H.bcm.bcm4a.AvgCurrent distributions
4875
5883
6554
4866
5876
I-beam taken from HMS_runlist.dat
I-beam = 50
I-beam = 55
I-beam = 60
I-beam = 40
I-beam = 40
BCM4A Current: 36.270 uA
BCM4A Beam Cut Current: 43.554 uA
BCM4A Current: 54.077 uA
BCM4A Beam Cut Current: 57.608 uA
BCM4A Current: 39.512 uA
BCM4A Beam Cut Current: 51.863 uA
BCM4A Current: 24.393 uA
BCM4A Beam Cut Current: 32.247 uA
BCM4A Current: 36.673 uA
BCM4A Beam Cut Current: 38.790 uA
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Without the inclusion of BCM4A Charge Correction ( boiling studies)
Using Q_corrected
Using Q_UNcorrected
The discrepancy gets worse using the uncorrected charge
Q_corr = Q_uncorr * (1 + 0.37/Q_I) ; Q_I : BCM4A Beam Cut Current
{H.BCM4A.scalerChargeCut/H.1MHz.scalerTimeCut:%.3f} uA
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Comparison of some distributions for runs in p=-3.4 GeV @ 20 deg
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141
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Study of the offsets in the simulation file.
0.06 Beam x offset (cm) +x = beam left
0.06 Beam y offset (cm) +y = up
0.0 Target z offset (cm)+z = downstream (0.25)
0.1 Spectrometer x offset (cm) +x = down
0.10 Spectrometer y offset (cm)
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With Offset Without Offset
Data
MC un-weighted
MC weighted
-2.42
GeV/c
-4.78
GeV/c
-5.78
GeV/c
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Binning in x v/s binning in delta
x=0.68
x=0.76
x=0.52
x=0.60
x=0.84
x=0.92
x=1.0
x=1.08
x=1.24
x=1.16
p=-5.878 GeV
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Reference Plots
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Comparison All Targets
150
He3 had some
pressure leakage problems during
data taking.
Melting studies
needed for Sn
20 deg, HMS
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152
26 deg, HMS
35 deg, HMS
Add Ca40 and Ca48!!
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MC
Data
Li6
p=-2.42
p=-2.71
p=-3.04
p=-3.40
p=-3.81
p=-4.27
p=-4.78
p=-5.36
p=-5.88
p=-6.60
p=-6.60
p=-2.42
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zoom
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156
Looking for ‘Subsets’ in the run production
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158
SubSet 1 SubSet 2
SubSet 1 SubSet 2
SubSet 1 SubSet 2
SubSet 1 SubSet 2 SubSet 3
p=-5.36, runs 5854, 5855, 5856
Comparison ratio yield data to MC for different subsets
If I remove 5856 the results are better …
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SubSet 1 SubSet 2
SubSet 2
SubSet 1
SubSet 3
SubSet 5
SubSet 7
SubSet 4
SubSet 6
SubSet 8
Comparison ratio yield data to
MC for different subsets
SubSet 10
SubSet 9
SubSet 2
SubSet 1
SubSet 3
SubSet 4
160
Closer look at the p=-5.36 GeV case for C12 @ 20 deg
SubSet 1 SubSet 2 SubSet 3
p=-5.36, runs 5854, 5855, 5856
Excluding run 5856 from subset 2
Run 5856
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SubSet 1 SubSet 2
X vs Y Raster Coordinates
subset 1
subset2
Run 5808
162
For He4 @ 20 deg
SubSet 1 SubSet 2
Run 5798
subset 1
subset2
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BCM4A Beam Cut Charge: {H.BCM4A.scalerChargeCut:%.3f} uC
E SING FID TRACK EFFIC : {HMSScinDide.npassed/(HMSScinShoulde.npassed+0.0001):%8.4f} +- {(sqrt(HMSScinShoulde.npassed- HMSScinDide.npassed)/(HMSScinShoulde.npassed+.0001)):%8.4f}
HMSScinDide HMSScinShoulde && H.dc.ntrack > 0
HMSScinShoulde HMSScinShould && H.cal.etotnorm > 0.8 && H.cer.npeSum > 2.5
HMSScinShould HMSScinGood && HMSGoodBetanotrk
HMSScinGood H.hod.goodscinhit == 1
HMSGoodBetanotrk H.hod.betanotrack > 0.8 && H.hod.betanotrack < 1.3
Understanding the Numbers
from report files:
source:
https://github.com/JeffersonLab/hallc_replay_XEM/blob/pass1/TEMPLATES/HMS/PRODUCTION/hstackana_production.template
164
Pre-Scaled Ps3 HMS Computer Live Time : {(hcut_TRIG3.npassed / (H.hTRIG3.scaler/ghconfig_ti_ps_factors[2]))*100.0:%3.4f} %
Pre-Scaled Ps3 Total Live Time (EDTM) : {(hcut_edtm_accepted.npassed / (H.EDTM.scaler/ghconfig_ti_ps_factors[2]))*100.0:%3.4f} %
Understanding the Numbers
from report files:
source:
https://github.com/JeffersonLab/hallc_replay_XEM/blob/pass1/TEMPLATES/HMS/PRODUCTION/hstackana_production.template
hcut_TRIG3 T.hms.hTRIG3_tdcTimeRaw > 0
hcut_edtm_accepted T.hms.hEDTM_tdcTimeRaw != 0.0
Ps3_factor = {ghconfig_ti_ps_factors[2]}
EDTM Triggers : {H.EDTM.scaler}
hTRIG3 : {H.hTRIG3.scaler} [ {(H.hTRIG3.scaler/H.1MHz.scalerTime)/1000.:%.3f} kHz ]
165
26 degrees, HMS, C12
These runs failed: 6380 6393 6394 6397 6398 , message: not in tape library
166
35 degrees, HMS, C12
These runs failed: 6380 , 6393, 6394 , 6397 , 6398, 6348 message: not in tape library
167
SHMS 26 deg
Runs that failed (positive polarity): 17472, 17473, 17456,17457,17458 : good run, no report file
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Introduction to superfast quarks
Phase diagram for baryonic matter
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170
171
172
Quark-Gluon duality
“Fundamental connection between low and high energy regimes”
173
Invariant mass (W) for the electron scattering from a moving proton in the nucleus as a function of initial momentum (towards the virtual photon) for different x and Q2 values of the scattering.
When you model e-A scattering as inclusive e-p (with a moving proton) we can access large W values in the e-p subsystem.
Even at x=1 or x=1.5 we can have DIS in the e-p scattering if we go to high enough Q2.
P_initial is the projection of the initial momentum of the nucleon in the q direction
For QE case (W2 = m2) p_in = m(1-x)
DIS
174
27Al(e, e′ )X
Fixed beam energy and scattering angle
….. QE
- - - IN
—— IN + QE
The inelastic contribution remains dominant at increasingly larger values of x.
In order to probe these values of initial momentum the DIS contribution should dominate the QE contribution
175
Quasi-Elastic Reaction
176
Previous attempts:
Very small tail at x≥1
Tail consistent with significant SRCs
The first signal of the existence of superfast quarks
scaling in the region x ≥ 1.
Inconsistent results!
177
Cross section of the inclusive A(e, e′ )X reaction
Structure Functions
(describe the distribution of quarks inside the nucleon)
;
— No modification of nucleon SF
…… Binding modification of the nucleon
DIS SF
— NN SRC
…… Mean field nuclear interaction only
- - - Multi-nucleon correlation model
178
QCD factorization theorem
Key principle in quantum chromodynamics (QCD) that allows for the separation (or "factorization") of short-distance (perturbative) physics from long-distance (non-perturbative) physics in processes like deep inelastic scattering (DIS)
Hard scattering -> pQCD
Cross section (DIS) = convolution ( perturbative , non perturbative )
Perturbative -> interaction between virtual photon and quark, high momentum transfer, strong coupling constant is small and can be treated perturbatively
Non-perturbative = PDFs, that is, the probability of finding a quark or gluon inside a hadron (like a proton) with a certain fraction of its momentum. PDFs have to be extracted from experimental data
Cancels Initial and Final State Interactions: The factorization theorem assumes that initial and final state interactions cancel out, meaning that the quarks and gluons' interactions with the remnants of the proton don’t affect the process at leading order. This cancellation is critical for the clean interpretation of scattering experiments.
179
Here the valence quarks should no play a significant role
valence quarks region
What is certain about the EMC effect is : valence quarks in nucleus carry less momentum than in a nucleon
180
Theoretical Models
Model
181
For x=1.5
— Convolution model
— Hard gluon exchange
…… Six-quark model
- - - Convolution model + bound nucleon m modification
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183
XEM2 Trigger Layout
184
Efficiencies:
Eff = how many times it did fire / how many times it should have fired
Ideally we want Eff around 1, but since we don't have perfect detectors, then we will have deviations from unity. Since we are testing when it did not fire when it should have we need to allow ourselves to work with events that did not fire, that's why we want to use ¾ trigger runs.
185
Solid:
Cryo:
186
Acceptance studies:
Collimator
HMS side view
Slit system
Zcoll = 166.37 cm from the center of the target to collimator entrance
The large collimator defines the acceptance
(dispersive)
(non-dispersive)
Test: physical collimator defining the acceptance vs software cut defining the acceptance
187
LD2
C12
188
Carbon, data, 20 deg, HMS LD2, data, 20 deg, HMS
189
Carbon, MC, 20 deg, HMS LD2, MC, 20 deg, HMS
190
Carbon, data, 35 deg, HMS LD2, data, 35 deg, HMS
191
Results for Deuterium, C12, and Ca40 for 20, 26, and 35 degrees
192
193
194
195
196
197
Comparison results using mc_single_arm and mc_single_arm_xem
198
Comparison results OUTV3 and OUTV4, Cross-section Models
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200
201
Idea: make this test at 20 (statistics) and 26 (overlap HMS SHMS), for C, D2 and Ca40
The solid angle cuts are noticeably larger than the collimator, so, the physical collimator defines the acceptance. Even if we reconstruct particles slightly outside we keep the cut open enough that we keep those events, even if they were reconstructed in the wrong place.
Plots:
xptar vs yptar
166.37 * xptar vs ytar + 166.37*yptar
202
Pion Backgrounds Studies
203
204
To-do list:
Next big steps: HMS at 26 degrees. SHMS at 26 degrees (cross-check). HMS and SHMS at 35 degrees.
205
Include this one in the default set of cuts
default set of cuts
Just for CSB studies
Take a look at the calorimeter cut , pion contamination … this is for csb correction
206
Task for today:�