1. MUMON / emulsion total flux uncertainty
H. Kubo

2. introduction updating muon flux simulation for MUMON/emulsion
motivation
further understanding of MUMON response
check validity of our tuning in high momentum region
goals
flux tuning compatible with 13a neutrino flux tuning (TN-217)
error estimation in the same manner as neutrino flux
comparison with emulsion measurement in 2010/2014
including anti-nu mode (-250kA)

3. list of systematic error sources (1)
same or similar method as TN-217 neutrino flux tuning study
special error treatment for muon flux
source
sub-source
estimation method
meson
NA61 data error
variation of 500 thrown set (incl. A-scaling errors)
NA61 p-q binning
diff. from BMPT fitting inside NA61 region
out of NA61 region
diff. b/w FLUKA and BMPT fitting
BMPT extrapolation
500 thrown BMPT parameters, outside NA61 only
momentum scaling
diff. from alternative multi-data tuning
pion to pion
tuning size itself + conservative 50% for out side region
baryon
sec. proton data
variation of 500 thrown set
leading baryon
diff. among tuning methods (p-only, w/ nS data)
non-primary
with and w/o preliminary tuning
x-sec
prod. cross section
500 thrown quasi-elastic cross sections
horn
abs. horn current
difference by +-5kA variation
skin effect
with and w/o skin effect
material
horn water
with and w/o horn water layer (1mm)
dump thickness
+ 1s dump material thickness/density variation

4. list of systematic error sources (2)
same or similar method as TN-217 neutrino flux tuning study
special error treatment for muon flux
source
sub-source
estimation method
p beam
beam position of emulsion shots
consistency b/w SSEMX and OTRX
+ SSEM optics Y fit precision
beam divergence
difference from wide beam sample (conservative)
beam width
1s variation (X:0.12mm, Y:0.98mm)
POT normalization
2.6%
alignment
target alignment
1mrad (X, Y)
horn alignment
checked similar as neutrino study  negligible
un-tuned
interaction in He gas
conservative 100 % errors (GCALOR region)
stat.
MC statistics
simple calc.

5. 11.2 % 11.3 % 11.0 % TOTAL source sub-source 13a 250kA 13a -250kA
meson
multiplicity
NA61
2.7 %
2.4 %
2.5 %
NA61 binning
0.7 %
0.4 %
2.6 %
out of NA61
1.1 %
2.1 %
3.3 %
BMPT fitting
1.6 %
3.1 %
6.5 %
momentum scaling
0.3 %
1.0 %
pion interaction
0.5 %
nucleon prod.
1.3 %
1.2 %
2.2%
prod. xsec
8.5 %
7.6 %
proton beam
beam opt.+ pos.
< 1%
POT norm.
alignment
target alignment
0.9 %
< 2%
horn current
abs. current
4.5 %
4.0 %
0 %
skin effect
< 1 %
2.0 %
untuned
He interaction
1.5 %
4.7 %
material
horn water
dump thickness
statistic
MC stat. error
0.8 %
TOTAL
11.2 %
11.3 %
11.0 %

6. MC error table (11b: previous tuning)
source
flux error
(250kA)
Pion production
9.0 %
Kaon production
1.3 %
dump interaction
0.7 %
nucleon production
3.6 %
prod. cross section
9.1 %
proton beam
2.8 %
target alignment
0.5 %
horn current
horn skin effect
2.0 %
minor interaction modes
1.2 %
MC statistics
0.3 %
total
14.3 %

7. - = 250kA – 0kA subtraction 250kA : horn focused + unfocused regionqp qp
250kA
0kA -
Pp[GeV/c]
Pp[GeV/c] qp
250kA : horn focused unfocused region
0kA : unfocused region only
subtraction :
horn focused region only
better prediction?
250kA - 0kA =
Pp[GeV/c]

8. TOTAL 11.2 % 11.3 % 11.0 % 13.1 % 14.8 % source sub-source 250kA
meson
multiplicity
NA61
2.7 %
2.4 %
2.5 %
2.8 %
2.6 %
NA61 binning
0.7 %
0.4 %
0.1 %
out of NA61
1.1 %
2.1 %
3.3 %
1.4 %
BMPT fitting
1.6 %
3.1 %
6.5 %
0.5 %
1.5 %
mom. scaling
0.3 %
1.0 %
0.2 %
pion interaction
nucleon prod.
1.3 %
1.2 %
2.2 %
prod. xsec
8.5 %
7.6 %
10.2 %
10.4 %
proton beam
beam opt.+ pos.
< 1%
POT norm.
alignment
target alignment
0.9 %
< 2%
1.7 %
horn current
abs. current
4.5 %
4.0 %
0 %
5.9 %
6.8 %
skin effect
< 1 %
2.0 %
untuned
He interaction
4.7 %
0.6 %
material
horn water
3.4 %
dump thickness
4.6 %
statistic
MC stat. error
0.8 %
TOTAL
11.2 %
11.3 %
11.0 %
13.1 %
14.8 %

9. why not improved?
0kA error is not so large, especially for dominant errors of horn on samples
less cancellation
even if the correlation is perfect, fractional error size would be kept
250kA
0kA
250kA-0kA
perfect correlation case
abs. flux
96000
22000
74000
abs. error
~10560
~2420
~8140
frac. error
~11%
~11 %

10. summary finished systematic error estimation for 13a tuned muon flux
total flux error ~ 11%
reduced from 11b tuning : 14.3%
dominant error : production cross section
if the cross section treatment is updated
(use NA61 result for primary p+C interactions)
250kA flux error will be 7.5%
250kA, -250kA, 0kA : similar error sizes
subtraction : no improvement on total flux error
may be meaningful on momentum distribution study

11. backup

12. NA61 pion coverage (250kA) Secondary p+ Secondary p-
4.2mm Gaussian beam
FLUKA2011simulation
mu, e > 50MeV/c
emulsion position, |Y|<12.5cm
horns 250kA
Secondary p+
Secondary p- q q
P[GeV/c]
P[GeV/c]
76% of total primary interactions
6% of total primary interactions
NA coverage : 91.1%
NA coverage : 47.9%
NA coverage : 85.6%
NA coverage : 33.7%

13. NA61 mult. + A scaling uncertainty
use 500 sets of thrown Data(NA61)/FLUKA ratios
same scheme as TN-217
mean/RMS of total flux (250kA)= 2.7%
2.7% uncertainty
emulsion position, |Y|<12.5cm, P>50Mev/c, horns 250kA
250kA

14. NA61 + A scaling uncertainty
horn current
RMS/Mean
= sys. error
250kA
2.7%
-250kA
2.4%
0kA
2.5%
2011 tuning
NA61 uncertainty
(250kA)
4.2%(Pi)
0.2% (K)
smaller error size than 11b case (based on NA )

15. out of NA61 phase space smaller error size than 2011 case (250kA)
horn current
NA61+FLUKA
7ch mean flux
[/cm2/1012POT]
NA61+BMPT
difference
= sys. error
250kA
9.68 x 104
9.57 x 104
1.1 %
-250kA
6.34 x 104
6.21 x 104
2.1 %
0kA
2.27 x 104
2.20 x 104
3.3 %
2011 tuning
9.72 x 104
9.92 x 104
smaller error size than 2011 case (250kA)
0kA,-250kA sample have larger uncertainties
because they have more out-of-NA61 component

16. Horn current uncertainty
absolute horn current : 5kA (2%) uncertainty
flux uncertainty 4.5% /
flux uncertainty 3.7% /

17. momentum scaling error
emulsion position, |Y|<12.5cm, P>50Mev/c
horn current
default tertiary
(NA61 only)
7ch mean flux
[/cm2/1012POT]
alter. tertiary
(multi-data)
difference
= sys. error
250kA
9.68 x 104
9.65 x 104
0.3 %
-250kA
6.34 x 104
6.33 x 104
0kA
2.27 x 104
2.25 x 104
1.0 %
250kA

18. skin effect Horn 1 main region inner conductor size: r1=27mm, r2 =30mm
δ=∞
δ=6.34mm
current density
current distribution
B-field

19. horn skin effect horn current no skin effect 7ch mean flux
emulsion position, |Y|<12.5cm, P>50Mev/c
horn current
no skin effect
7ch mean flux
[/cm2/1012POT]
w/ skin effect
difference
= sys. error
250kA
9.68 x 104
9.70 x 104
0.2 %
-250kA
not yet done
250kA

20. dump thickness uncertainty
density
(original)
(1 sigma shifted)
Dump graphite
1.707
1.716
(+0.009)
Dump Fe
7.87
7.92
(+0.05 **)
Dump concrete
2.300
2.323
(+0.023)
** including
uncertainty of thickness
increased density of dump materials by + 1sigma
take difference as systematic error size

21. dump thickness uncertainty
emulsion position, |Y|<12.5cm, P>50Mev/c
horn current
normal dump
7ch mean flux
[/cm2/1012POT]
1sigma dens dump
difference
= sys. error
250kA
9.68 x 104
9.48 x 104
2.1 %
-250kA
6.34 x 104
6.15 x 104
3.1 %
0kA
2.27 x 104
0.2 % **
** within statistical uncertainty
parent pion momentum
250kA
dense
normal
threshold
shifts
Pp [GeV/c]

22. horn water uncertainty
emulsion position, |Y|<12.5cm, P>50Mev/c
horn current
no water
7ch mean flux
[/cm2/1012POT]
with 1mm water
difference
= sys. error
250kA
9.68 x 104
9.53 x 104
1.5 %
-250kA
6.34 x 104
6.22 x 104
2.0 %
0kA
2.27 x 104
2.28 x 104
0.5 % **
** within statistical uncertainty
250kA

23. production cross section
use NA x-sec and errors for p>20GeV/c
use NA x-sec and errors for only p>30GeV/c
use quasi-elastic x-sec as errors for all region
horn current
RMS of 500 samples
method A
method B
method C
250kA
2.1 %
2.5 %
8.5 %
-250kA
1.9 %
2.2 %
7.6 %
0kA
0.8 %
1.2 %
2.7 %

24. pion to pion interaction
emulsion position, |Y|<12.5cm, P>50Mev/c
horn current
w/o pipi tuning
7ch mean flux
[/cm2/1012POT]
with pipi tuning
difference
= sys. error
250kA
9.67 x 104
0.0 %
-250kA
6.33 x 104
0kA
2.27 x 104
pion to pion interactions
inside the HARP region
less affect muon flux

25. pion to pion interaction
assigned 50% conservative errors for only pion to pion interactions outside the HARP tuning region
horn current
pipi tuning
7ch mean flux
[/cm2/1012POT]
no-tuning region
50% reduced
difference
= sys. error
250kA
9.67 x 104
9.64 x 104
0.3 %
-250kA
6.33 x 104
6.31 x 104
0.4 %
0kA
2.27 x 104
2.26 x 104
0.5 %

26. reproduced BMPT/FLUKA ratios
pi+ official
pi+ repro.
Mark updated fitting code in the repository
thank you
I got similar BMPT fitting results
pi+ repro.
BMPT only

27. NA61 binning inside the NA61 region, BMPT reproduces data well
7ch mean flux [/cm2/1012POT]
emulsion position, |Y|<12.5cm, P>50Mev/c
Horn
BMPT+NA61
(official)
BMPT + NA61
(reproduced)
BMPT only
difference
250 kA
9.58 x 104
9.51 x 104
- 0.7 %
0 kA
2.20 x 104
2.14 x 104
- 2.6 %
-250 kA
6.21 x 104
6.22 x 104
6.19 x 104
- 0.4 %
inside the NA61 region, BMPT reproduces data well
BMPT can work as a kind of smoothing
 effect from NA61 bin-size can be estimated
assign differences as systematic uncertainty sizes
largely reduced from the previous tuning
11b tuning, 250kA case : 5.0%

28. errors on BMPT parameters
I included this error source in the previous(11b) muon flux tuning
concerns
if the model is proper and fitting is fairly done, fitting error for NA61 region reflects error size of NA61 data
 double counting?
using only outside region would be reasonable
new BMPT fitting parameters on NA data have
larger errors than previous one  I don’t know the cause

29. BMPT parameter errors outside NA61 region only 500 throws -250kA 250kA

30. pbeam position of the emulsion shots
from SSEM fit
[mm]
OTR
(low light yield)
MUMON (Si) [cm]
250kA X
0.08
-1.68 Y
0.29
-0.39
-250kA
1.37, 1.46
+-0.38
-0.36, -0.20
-1.81, -1.74
0.15, 0.03
0.17, 0.19
-1.27, -1.30
0kA
1.87, 1.68,
1.72, 2.16
0.16, -0.08
0.04, 0.44
3.17, 1.37,
4.41, 0.48
0.14, 0.10,
0.04, 0.38
0.31, 0.22
0.26, 0.40
6.20, 3.02,
5.17, 4.34
OTR light yield is under the threshold
SSEM X : OTR X inconsistent by 1.4~1.8mm
SSEM Y : consistent w/ OTR Y , large errors

31. pbeam position of the shots
tested shift [mm]
7ch mean flux
[/cm2/1012POT]
pbeam shifted
diff.
250kA
X 1.82, Y 1.38
9.68 x 104
9.69 x 104
0.1 %
-250kA
X 1.42, Y 1.38
6.34 x 104
6.36 x 104
0.3 %
0kA
X 1.86, Y 1.38
2.27 x 104
0.0 %
negligible effect on total flux
profile center shift (~3cm) occurs
250kA

32. alignment target position target tilt horn 1 tilt horn 2,3 alignment
relative position to beam center is important
integrated in proton beam error
target tilt
1mrad in both direction (X,Y)
estimated using same method as TN-217
horn 1 tilt
0.2mrad (X,Y)
 confirmed to be negligible
horn 2,3 alignment
already found to be negligible from the previous(11b) tuning study

33. target alignment horn current target tilt 7ch mean flux [/cm2/1012POT]
difference
= sys. error
250kA
9.68 x 104
X + 1mrad
9.72 x 104
+ 0.4 %
Y + 1mrad
9.76 x 104
+ 0.8 %
-250kA
6.34 x 104
6.30 x 104 %
6.28 x 104
- 1.0 %
0kA
2.27 x 104
- 0.1 % **
2.26 x 104
- 0.4 % **
** within statistical uncertainty

34. secondary baryon *integrated in meson multiplicity throwing 250kA
estimation method
secondary proton data *
0.1 %
0.2 %
throwing Data/FLUKA
according to the data error
leading baryon
1.3 %
1.2 %
2.2 %
difference among alterative
tuning methods
non-primary
0.0 %
difference from preliminary
out-target baryon tuning
total