C' Mariani INFN Rome

1
March 6th, 2005 _at_XLth Rencontres de Moriond
New K2K Results

• C. Mariani (INFN Rome)
• for K2K collaboration

2
K2K Collaboration
250km
JAPAN High Energy Accelerator Research
Organization (KEK) / Institute for Cosmic Ray
Research (ICRR), Univ. of Tokyo / Kobe University
/ Kyoto University / Niigata University / Okayama
University / Tokyo University of Science / Tohoku
University KOREA Chonnam National University /
Dongshin University / Korea University / Seoul
National University U.S.A. Boston University /
University of California, Irvine / University of
Hawaii, Manoa / Massachusetts Institute of
Technology / State University of New York at
Stony Brook / University of Washington at
Seattle POLAND Warsaw University / Solton
Institute Since 2002 JAPAN Hiroshima
University / Osaka University U.S.A. Duke
University CANADA TRIUMF / University of
British Columbia ITALY Rome FRANCE Saclay
SPAIN Barcelona / Valencia SWITZERLAND Geneva
RUSSIA INR-Moscow
3
1. Introduction and history of K2K

• 1995
• Proposed to study neutrino oscillation for
  atmospheric neutrinos anomaly.
• 1999
• Started taking data.
• 2000
• Detected smaller number of neutrinos than the
  expectation at a distance of 250 km. Disfavored
  null oscillation at the 2s level.
• 2002
• Observed indications of neutrino oscillation. The
  probability of null oscillation is less than 1.
• 2004
• Confirm neutrino oscillation with both a deficit
  of nm and the distortion of the En spectrum.

4
2. K2K experiment
1 event/2days
1011 nm/2.2sec (/10m?10m)
106 nm/2.2sec (/40m?40m)
nm
12GeV protons
nt
p
SK
m
TargetHorn
100m
200m decay pipe
250km
p monitor
Near n detectors (ND)
m monitor
(monitor the beam center)

• Signal of n oscillation at K2K
• Reduction of nm events
• Distortion of nm energy spectrum

5
Neutrino beam and the directional control

• 1GeV neutrino beam by a dual horn system with
  250kA.

The beam direction monitored by muons
X center
?1 mrad
Y center
lt?1mrad
5 years
6
Accumulated POT (Protons On Target)
10.5x1019 POT, 8.91019 POT for Analysis
Accumulated POT (1018)
K2K-I
K2K-II
K2K-II
K2K-I
protons/pulse (1012)
Oct-Nov 04
Jan 03
7
Neutrino spectrum and the far/near ratio
Far/Near Ratio
nm energy spectrum _at_ K2K near detector
beam MC w/ PION Monitor
10-6
1.0
2.0
En (GeV)
En (GeV)
8
SK Events
Decay electron cut.
?500msec
?20MeV Deposited Energy
No Activity in Outer Detector Event Vertex in
Fiducial Volume More than 30MeV Deposited Energy
107 events
Analysis Time Window
?5msec
-0.2ltTSK-Tspill-TOFlt1.3msec
(BG 1.6 events within ?500ms
2.410-3 events in 1.5ms)
TDIFF. (ms)
9
3. Analysis Overview
KEK
Observation n, pm and qm
Measurement F(En), n int.
n interaction MC
Far/Near Ratio (beam MC with p mon.)
SK
Observation n and En rec.
Expectation n and En rec.
(sin22q, Dm2)
10
NEUT K2K Neutrino interaction MC

• CC quasi elastic (CCQE)
• CC (resonant) single p(CC-1p)
• DIS
• NC

s/E (10-38cm2/GeV)
En (GeV)
11
4. Near detector measurements

• 1KT Water Cherenkov Detector (1KT)
• Scintillating-fiber/Water sandwich Detector
  (SciFi)
• Lead Glass calorimeter (LG) before 2002
• Scintillators Bar Detector (SciBar) after 2003
• Muon Range Detector (MRD)

LG calorimeter
Muon range detector
12
4.1 1KT Flux measurement

• The same detector technology as Super-K.
• Sensitive to low energy neutrinos.

?Far/Near Ratio (by MC)110-6
M Fiducial mass MSK22,500Kton, MKT25ton e
efficiency eSK-I(II)77.0(78.2), eKT74.5
exp SK
13
4.2 SciBar neutrino interaction study

• Full Active Fine-Grained detector (target CH).
• Sensitive to a low momentum track.
• Identify CCQE events and other interactions
  (non-QE) separately.

CCQE Candidate
2 track events
CCQE
n
p
non-QE
m
Dqp qobs -qCCQE
p
m
25?
Dqp (degree)
14
Neutrino energy reconstruction
15
A hint of K2K forward m deficit.

• K2K observed forward m deficit.
• A source is non-QE events.
• For CC-1p,
• Suppression of q2/0.1GeV2 at q2lt0.1GeV2 may
  exist.
• (0.1GeV2 value comes from fitting 2 track nonQE
  sample in SciBar)
• For CC-coherent p,
• The coherent p may not exist.
• We do not identify which process causes the
  effect. The MC CC-1p (coherent p) model is
  corrected phenomenologically.
• Oscillation analysis is insensitive to the choice.

Preliminary
q2rec
q2rec (GeV/c)2
(Data-MC)/MC
SciBar non-QE Events
q2rec (GeV/c)2
16
4.3 Near Detector Spectrum Measurements

• 1KT
• Fully Contained 1 ring m (FC1Rm) sample.
• SciBar
• 1 track, 2 track QE (Dqp25?), 2 track nQE
  (Dqpgt25?) where one track is m.
• SciFi
• 1 track, 2 track QE (Dqp25?), 2 track nQE
  (Dqpgt30?) where one track is m.
• After applying the low q2 suppression of nQE
  observed in SciBar, the angular distributions of
  all other samples are reasonably reproduced.

17
1KT m momentum and angular distributions.with
measured spectrum
flux measurement
low q2 corr.
1Kt m-like sample Quasi elastic Single pion
20
0
90
qm (deg.)
18
4.4 Near Detectors combined measurements

• (pm,qm) for 1track, 2trackQE and 2track nQE
  samples ? F(En), nQE/QE
• Fitting parameters
• F(En), nQE/QE ratio
• Detector uncertainties on the energy scale and
  the track counting efficiency.
• The change of track counting efficiency by
  nuclear effect uncertainties proton
  re-scattering and p interactions in a nucleus
• Strategy
• Measure F(En) in the more relevant region of
  qm?20? for 1KT and qm?10? for SciFi and SciBar.
• Apply a low q2 correction factor to the CC-1p
  model (or coherent p).
• Measure nQE/QE ratio for the entire qm range.

19
En QE (MC) nQE(MC)
MC templates
0-0.5 GeV
KT data
qm (MeV/c)
0.5-0.75GeV
0.75-1.0GeV
1.0-1.5GeV
Pm (MeV/c)

• n flux FKEK(En) (8 bins)
• n interaction (nQE/QE)

20
Flux measurements

• c2638.1 for 609 d.o.f
• F1 ( En lt 500) 0.78 ? 0.36
• F2 ( 500? En lt 750) 1.01 ? 0.09
• F3 ( 750? En lt1000) 1.12 ? 0.07
• F4 (1000? En lt1500) 1.00
• F5 (1500? En lt2000) 0.90 ? 0.04
• F6 (2000? En lt2500) 1.07 ? 0.06
• F7 (2500? En lt3000) 1.33 ? 0.17
• F8 (3000? En ) 1.04 ? 0.18
• nQE/QE 1.02 ? 0.10
• The nQE/QE error of 10 is assigned based on the
  sensitivity of thefitted nonQE/QE value by
  varying the fit criteria.
• qgt10?(20 ?) cut nQE/QE0.95 ?0.04
• standard(CC-1p low q2 corr.) nQE/QE1.02 ?0.03
• No coherent pnQE/QE1.06 ?0.03

F(En) at KEK
preliminary
En
21
SciFi (K2K-IIa with measured spectrum)
qm 1trk
Pm 1trk
flux measurement
Pm 2trk QE
qm 2trk QE
Pm 2trk non-QE
qm 2trk non-QE
10
0
2
(GeV/c)
0
40
(degree)
22
SciBar (with measured flux)
qm 1trk
Pm 1trk
flux measurement
Pm 2trk QE
qm 2trk QE
qm 2trk nQE
Pm 2trk nQE
10
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5. Super-K oscillation analysis

• Total Number of events
• Enrec spectrum shape of FC-1ring-m events
• Systematic error term

f x Systematic error parameters
Normalization, Flux, and nQE/QE ratio are in fx
Near Detector measurements, Pion Monitor
constraint, beam MC estimation, and Super-K
systematic uncertainties.
24
K2K-SK events
(56)
for Enrec
Updated from the previous analysis
25
KS probability0.08
SK Events
Toy MC
Expected shape (No Oscillation)
EnrecGeV
CC-QE assumption
107
150.9
V Nuclear potential
26
6. Results

• Best fit values.
• sin22q 1.51
• Dm2 eV2 2.19?10-3
• Best fit values in the physical region.
• sin22q 1.00
• Dm2 eV2 2.79?10-3
• DlogL0.75

A toy MC
Dm2
12.6
2.79
sin22q1.51 can occur due to a a statistical
fluctuation with 12.6.
sin22q
1.51
1.00
27
Data are consistent with the oscillation.

• NSKobs107
• NSKexp (best fit)150.9

preliminary
Dm2eV2
Best Fit KS prob.36
sin22q
EnrecGeV
Based on DlnL
28
Log Likelihood difference from the minimum.
DlnL
DlnL
- 68 - 90 - 99
- 68 - 90 - 99
sin22q
Dm2eV2

• Dm2lt(1.873.58)10-3 eV2 at sin22q1.0 (90 C.L.)

29
nm disappearance versus En shape distortion
En shape
NSK (nm)
Dm2eV2
Dm2eV2
sin22q
sin22q
Both disappearance of nm and the distortion of En
spectrum have the consistent result.
30
K2K-I vs K2K-II
31
Null oscillation probability
The null oscillation probabilities are calculated
based on DlnL.
The value is changed from the previous one.
Disappearance of nm and distortion of the energy
spectrum as expected in neutrino oscillation.
K2K confirms neutrino oscillation discovered in
Super-K atmospheric neutrinos.
32
8. Summary

• With 8.91019 POT, K2K has confirmed neutrino
  oscillations at 4.0s (hep-ex/0411038).
• Disappearance of nm 3.0s
• Distortion of En spectrum 2.6s

Dm2eV2
K2K new results
0.006
- 68 - 90 - 99
preliminary
0.004
0.002
0.0 0.2 0.4 0.6 0.8 1.0
sin22q
33
Backup slide
34
Additional Error on nonQE

• nonQE value depends on fitting condition.
• Small angle cut 0.979
• CC1p re-weighting 1.056
• No coherent p 1.093
• CC1p re-weighting factor / 0.03 (1s)
• (SciBar only fit) / 4
• In total, 10 uncertainty exists.
• Fitting error is 5
• ? add 10 to nonQE error.

8
Official value
3.5
35
7. Other Physics in K2K (K2K-I data only)
nm H2O?NC1p0
nm?ne search
1KT
90CL limit
90CL sensitivity
Dm2eV2
not NC1p0
Mgg(MeV)
sin22qme
0.065?0.001?0.007
PRL 93 (2004) 051801
0.064 (our MC)
36
NEUT K2K Neutrino interaction MC

• CC quasi elastic (CCQE)
• Smith and Moniz with MA1.1GeV
• CC (resonance) single p(CC-1p)
• Rein and Sehgals with MA1.1GeV
• DIS
• GRV94 JETSET with Bodek and Yang correction.
• CC coherent p
• ReinSehgal with the cross section rescale by J.
  Marteau
• NC
• Nuclear Effects

s/E (10-38cm2/GeV)
En (GeV)
37
Overall normalization error on Nsk for Nov99
Errors
Take errors not considered in matrix
Central Value 76.05evts
KT dominated by FV error SK also.
5.34
38
Null oscillation DlnL
preliminary
The null oscillation probabilities are calculated
based on DlnL.
The value is changed from the previous one.
Disappearance of nm and distortion of the energy
spectrum as expected in neutrino oscillation.
K2K confirmed neutrino oscillation discovered in
Super-K atmospheric neutrinos.
39
The change of NSKexp in K2K-I (Bugs)

• The detector position
• 295m ? 294m -1
• MC difference between KT and SK
• KT MA(QE)1.1 s (NCel)KT1.1s(NCel)SK
• SK MA(QE)1.0 ? Efficiency change! -1
• NSKexp Change 2

294m
295m
40
CC-1p suppression versus coherent p
41
Systematic Bias without the MC correction.
ND (SciBar) measurement
DATA MC w/ CC-1p suppression MC template
Default MC
Oscillation Results
MC w/o low q2 correction sin22q1.00 Dm22.65
10-3 eV2 Prob.(null oscillation)0.0049 Correc
ted MC for low q2 sin22q1.00 Dm22.7310-3eV2
Prob.(null oscillation)0.011
Toy MC
systematic bias
There is a small bias in nQE/QE and the low
energy flux.
nQE/QE
flux
42
Oscillation result with a default MC
Without low q2 MC correction
The result w/o low q2 MC correction gives the
better (biased) measurement due to the more low
energy flux and the smaller nQE/QE.
43
K2K-I vs K2K-II

• Best fit values.
• sin22q 1.08, 1.51
• Dm2 eV2 2.73?10-3, 2.19?10-3
• Best fit values in the physical region.
• sin22q 1.00, 1.00
• Dm2 eV2 2.86?10-3 , 2.79?10-3
• DlogL0.02, 0.75
• KSK2K-I K2K-II 77

44
Enrec for K2K-I and K2K-II
K2K-I
K2K-II
45
K2K-I vs K2K-II
46

• 1KT sys error summary and the change.
• SciBar sys. error

47
1KT sys. error

• Systematic error
• Fiducial updated -4.0 (lt- 4.0)
  Smys analysis
• Escale updated -0.3
• FADC (scale) updated -0.8
• FADC(cut position) -1.5 (New)
  Shaomins analysis
• Background -0.5
• Multi-event -0.7
• Event rate(New) -2.0
• Profile (New) -0.3
• KT origin -4.9 (Prev.
  4.4)
• SK efficiency -3.0
• CT norm. -0.3 for K2K-II 0.6
  for K2K-I
• Far/Near 5.6 -7.3

48
SciBar Systematic Error (2track/1track)

• Detector oriented
• Vertex Matching Efficiency 2.7
  -1.0
• Threshold Effect (-15) 0.7
• Xtalk Effect (2/4/6) 1.1
  -1.1
• Finding Efficiency
  0.9 -4.3
• Total (Detector)
  3.1 -4.5

• Nuclear Effect
• Proton Re-scattering
  2.9 -2.6
• Pion Absorption
  1.7 -1.7
• Pion inelastic scattering
  2.3 -2.9
• Total (Nuclear)
  4.1 -4.2

• Total
  5.1 -6.2

49
SciBar Systematic Error (2track QE/2track nQE)

• Detector oriented
• Angle resolution
  1.0
• X-talk Effect
  2.2 -2.9
• Momentum scale (-2.7) 1.5
  -4.3
• Total (Detector)
  2.8 -5.2

• Nuclear Effect
• Proton Re-scattering
  2.9 -2.8
• Pion Absorption
  -5.4
• Pion inelastic scattering
  0.3 -4.7
• Total (Nuclear Effect)
  2.9 -7.7

• Total
  4.0 -9.3

50
Track finding Efficiency
2nd Track Efficiency (MC)
MC true 2nd Track (NHITX/Y?3Hit)
Detected! ( 1. Could Find 2nd Track
2. Rec.track overlap
with more than 1 true Hit)
1.0
Overall Eff. 59.0 gt20Hit 85.3
gt40Hit 91.1
0.8
0.6
Finding Efficiency
0.4
0.2
(This can be improved!)
0 20 40 60 80 100 120 140
(NHIT)
Evaluated DATA/MC w/ Eye scan.
51
Eye scan Result
Eye scanners (M.Hasegawa ,K.Hiraide
Y.Takubo,S.Yamamoto)
? Data (Eye) ? MC (Eye)
Integrated bin (gt40Hits)
1.35 0.93 0.97 1.01 1.00 0.96 0.98 0.98
52
Systematic error (Finding Eff.)
Compared
DATA
2Track/1Track (default MC) vs 2Track/1Track
(MC )
MC
Entry lt5 5 - 9 10 -14 15
-19 20 - 24 25 - 29 30 - 34 35 - 39 40
(each bin MC) 0 265 2257
3824 3976 3654 3027 2406
8009 27418 DATA/ MC 0 1.35
0.93 0.97 1.01 1.00 0.96
0.98 0.98
0 0.54 0.10 0.06 0.05 0.04
0.03 0.03 0.02 (stat.err)
Total 0 358 2108 3719
4034 3659 3017 2364 7849
27034 0 143
226 229 199 146 91
72 160 475
2track/1track 0.5032 (27418/54106) ? 0.496
/- 0.013 (27034/54490)
Systematic Error (Track finding Eff.) 0.9 ,
-4.3
53
Same as previous one except binning size is 125/2
nsec that is a half of intervals of two bunches.
54
Residual of K2K-SK event timing relative to
neutrino beam bunches. Timing correlation is
clearly seen and a sigma is obtained as about
30nsec.
55
Number of observed events (F.C. in fid. vol.) as
a function of integrated CT
56
Number of observed events (F.C. in all inner
volume) as a function of integrated CT
57
Results (without small angle)

• 1kt q gt 20deg., SciFi and SciBar q gt 10deg.
• In each En bin, fitted flux is consistent each
  other.

58
CC1p suppression factor tuning
SciBar 2track nonQE
qm

• By using SciBar 2track-nonQE and fitted flux, I
  looked for the best value of CC1p suppression.
• Suppression factor
• q2/A (q2gtA)
• Scan A value and calculate c2 of q distribution.

CC1p q2/0.10
(DataMC)/MC Agree quite well
Calculate c2
A0.10 / 0.03
A
59
Results (CC1p re-weighted)

• CC1p re-weighting factor q2/0.10 (q2lt0.10)
• Flux is fixed
• nonQE value 0.979(q cut) ? 1.056(this result)
  (8)

60
Results (no coherent p) for comparison

• Coherent p production removed.
• Flux is fixed.
• nonQE value 1.093(this results)
• (CC1p re-weighting 1.056 3.5 difference)

61
Results (no cut, no re-weighting)for comparison

• Flux is consistent with q cut results.
• nonQE is significantly small, and c2 is bad.
• nonQE 0.856, c2 / dof 773.8 / 595 1.30

62
Flux v.s. fitting condition

• Fitted flux from q cut, CC1p re-weighting and no
  coherent are consistent each other.

63
NonQE v.s. CC1p re-weighting factor (SciBar only
fit)

• CC1p re-weighting factor / 0.03 (1s)
• ? nonQE
  / 4

SciBar Only Fit
64
Likelihood for Oscillation analysis
f x Systematic error parameters
Poisson prob. for FC events
of observed events
of expected events
65
Likelihood for Normalization
i energy bin j Interaction mode
Data/MC for of events in KT
of interaction in MC
SK efficiency
flux
nQE/QE
Far/Near
66
Likelihood for Spectrum Shape
SK efficiency
SK Energy Scale
flux
Far/Near
nQE/QE
Nj (Erec,Etrue) Event fraction in MC
N Normalization factor
67
Likelihood for Systematic parameters
neutrino flux, nQE/QE,NC
Far/Near Ratio
SK efficiency
Overall Normalization
SK Energy Scale
Systematic parameters for n flux are common for
SK-Ib and SK-II
of free parameter in fit 25 ? 33
34 (fnQE ? fCC-nQE, fNC)
68
Reconstructed vertex distribution for r2 vs Z
K2K-1
K2K-2
69
Visible energy distribution for F.C. events in
the fiducial volume in data (closed circle), M.C.
expectation with no oscillation (solid
histogram), oscillated with sin22q1.0,Dm22.010-
3eV2 (dashed histogram), and oscillated with
sin22q1.0,Dm23.010-3eV2 (dotted histogram).
70
Visible energy distribution for F.C. events in
the fiducial volume in data (closed circle), M.C.
expectation with no oscillation (solid
histogram), oscillated with sin22q1.0,Dm22.010-
3eV2 (dashed histogram), and oscillated with
sin22q1.0,Dm23.010-3eV2 (dotted histogram).
71
Visible energy distribution for F.C. events in
the fiducial volume in data (closed circle), M.C.
expectation with no oscillation (solid
histogram), oscillated with sin22q1.0,Dm22.010-
3eV2 (dashed histogram), and oscillated with
sin22q1.0,Dm23.010-3eV2 (dotted histogram).
72
Reconstructed muon momentum distribution for F.C.
1ring mu-like events in the fiducial volume in
data (closed circle), M.C. expectation with no
oscillation (solid histogram), oscillated with
sin22q1.0,Dm22.010-3eV2 (dashed histogram),
and oscillated with sin22q1.0,Dm23.010-3eV2
(dotted histogram).
73
Reconstructed muon momentum distribution for F.C.
1ring mu-like events in the fiducial volume in
data (closed circle), M.C. expectation with no
oscillation (solid histogram), oscillated with
sin22q1.0,Dm22.010-3eV2 (dashed histogram),
and oscillated with sin22q1.0,Dm23.010-3eV2
(dotted histogram).
74
Reconstructed muon momentum distribution for F.C.
1ring mu-like events in the fiducial volume in
data (closed circle), M.C. expectation with no
oscillation (solid histogram), oscillated with
sin22q1.0,Dm22.010-3eV2 (dashed histogram),
and oscillated with sin22q1.0,Dm23.010-3eV2
(dotted histogram).
75
The distribution of the reconstructed direction
of muons relative to the direction from KEK to SK
for F.C. 1ring mu-like events in the fiducial
volume in data (closed circle), M.C. expectation
with no oscillation (solid histogram), oscillated
with sin22q1.0,Dm22.010-3eV2 (dashed
histogram), and oscillated with
sin22q1.0,Dm23.010-3eV2 (dotted histogram).
76
The distribution of the reconstructed direction
of muons relative to the direction from KEK to SK
for F.C. 1ring mu-like events in the fiducial
volume in data (closed circle), M.C. expectation
with no oscillation (solid histogram), oscillated
with sin22q1.0,Dm22.010-3eV2 (dashed
histogram), and oscillated with
sin22q1.0,Dm23.010-3eV2 (dotted histogram).
77
The distribution of the reconstructed direction
of muons relative to the direction from KEK to SK
for F.C. 1ring mu-like events in the fiducial
volume in data (closed circle), M.C. expectation
with no oscillation (solid histogram), oscillated
with sin22q1.0,Dm22.010-3eV2 (dashed
histogram), and oscillated with
sin22q1.0,Dm23.010-3eV2 (dotted histogram).
78
Reconstructed neutrino energy distribution for
F.C. 1ring mu-like events in the fiducial volume
in data (closed circle), M.C. expectation with no
oscillation (solid histogram), oscillated with
sin22q1.0,Dm22.010-3eV2 (dashed histogram),
and oscillated with sin22q1.0,Dm23.010-3eV2
(dotted histogram).
79
Reconstructed neutrino energy distribution for
F.C. 1ring mu-like events in the fiducial volume
in data (closed circle), M.C. expectation with no
oscillation (solid histogram), oscillated with
sin22q1.0,Dm22.010-3eV2 (dashed histogram),
and oscillated with sin22q1.0,Dm23.010-3eV2
(dotted histogram)
80
Reconstructed neutrino energy distribution for
F.C. 1ring mu-like events in the fiducial volume
in data (closed circle), M.C. expectation with no
oscillation (solid histogram), oscillated with
sin22q1.0,Dm22.010-3eV2 (dashed histogram),
and oscillated with sin22q1.0,Dm23.010-3eV2
(dotted histogram).
81
Summary of SK-2 absolute energy calibration

• Data agree with MC within /-1.9
• Time variation /-0.9 total uncertainty
  /- 2.1

82
Ring-counting likelihood for SK-2 m-like events
sub-GeV Plt400MeV/c
sub-GeV Pgt400MeV/c
multi-GeV
83
PID distributions for SK-2
multi-GeV (Evisgt1330MeV)
sub-GeV (Evislt1330MeV)
84
Systematic error on spectrum
K2K-1 ring counting PID vertex E scale
0.-0.5 1.9 1.1 2.0
0.5-1.0 2.1 0.5 2.0
1.-1.5 2.5 0.7 2.0
1.5-2.0 5.9 0.6 2.0
2.0-2.5 5.9 0.7 2.0
2.5- 5.9 0.7 2.0
2.7
K2K-2 ring counting PID vertex E scale
0.-0.5 2.6 2.5 2.0
0.5-1.0 2.2 0.9 2.0
1.-1.5 7.9 0.6 2.0
1.5-2.0 7.5 0.5 2.0
2.0-2.5 7.1 0.5 2.0
2.5- 7.1 0.5 2.0
2.1