Precision Measurement of the Proton Flux with AMS Experiment

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Precision Measurement of the Proton Flux with AMS Experiment

AMS Days at CERN

Geneva, April 16

^th

2015

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2 V. Choutko Proton Flux AMS Days CERN

Introduc>on

Protons are the most abundant charged particles in cosmic rays.

Knowledge of the precise behavior of the proton spectrum is important in understanding the origin, acceleration, and

propagation of cosmic rays.

Recent important measurements of the proton flux in cosmic rays have reported different variations of the flux with energy.

In particular, the ATIC–2, CREAM, and PAMELA experiments showed deviations of the proton flux from a single power law.

Here we report on the precise measurement of the proton flux in primary cosmic rays in the rigidity range from 1 GV to 1.8 TV

based on 300 million events collected by the AMS.

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TRD TOF

Tracker

TOF RICH

ECAL L1

L2

L7-L8 L3-L4

L9

L5-L6

ToF (4 Layers)

Velocity and Direc>on Δβ/β

²

(Z=1) ≈ 4%

TRD, Tracker, RICH ,TOF, ECAL

Charge Magnitude Along Par>cle Trajectory

ΔZ (Z=1) ≈ 0.05-0.2

Tracker (9 Layers) + Magnet

Rigidity and Charge Sign

Bending Coordinate Resolu>on (Z=1) ≈ 10 µm MDR (Z=1) ≈ 2 TV

AMS Cosmic Ray Protons Measurement

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Charge

0.5 1 1.5 2 2.5

Events

10

5

10

6

10

7

10

8

10

9

P Data

10

9

11.4 ×

He Nuclei

AMS Data Sample

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Proton Selec>on

(I)   Downgoing Par>cle β > 0.3

(II)   Rigidity (R) Above Geomagne>c Cutoﬀ (R _C )

R > 1.2R

_C

[IGRF Magne>c Field]

(III) Charge |Z|~1 along Par>cle Trajectory:

For instance, for Inner Tracker 0.7 <|Z| <1.5

(IV)   Full Tracker Level arm (L1 to L9), Z>0

(V)  χ ² /NDF of the Par>cle Trajectory Fit < 10

Eﬃciency 98-‐99 %, Removes Bulk of Events with Large Scaiering and Wrongly Measured Rigidity

( VI) Reconstructed Mass > 0.5 GeV/c ²

Removes low rigidity π ’ s

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Residual Background

(I)   Protons from He and other Nuclei interacted on

very top of AMS:

0.5% @ 1GV and negligible (<0.1%) above 10 GV

(ΙΙ)  π’s from protons interacted on top of AMS:

Less than 0.1% in all rigidity range

(III)   Positrons and Electrons:

Less than 0.1% in all rigidity range

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Flux Measurement

Assuming flux over geomagnetic cutoff is isotropic

the differential in rigidity flux can be defined as

Rigidity 1-1800 GV

Effective Acceptance from MC, Verified with Data

Time ~63,000,000 sec , R>30 GV

Φ _i (R) =

N _i

T _i A _i ε _i ΔR _i

Trigger Efficiency from Data Bin width

Events Corrected for Bin to Bin Migration due to Tracker Rigidity Resolution

i=1,72

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Proton flux: (i) systematic errors on trigger efficiency

Trigger eﬃciency [4/4 TOF + VETO ] was measured using 1% prescaled event sample obtained with unbiased 3 out of 4 ToF coincidence

trigger. The error is dominated by the sta>s>cs available from the unbiased trigger.

LowerTOF (layers 3 and 4)

UpperTOF (layers 1 and 2)

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This systema>c error is negligible (less than 0.1%) below 100GV and reaches 1.5% at 1.8TV.

VETO

V. Choutko Proton Flux AMS Days CERN

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Rigidity[GV]

1 10 10

²

10

³

Tr ig g er E ff ic ie n cy

0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98 1

Data

MC Geant 4.9.6

Trigger Eﬃciency Measured from

Unbiased Trigger

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Proton ﬂux: (ii) systema>c errors on the acceptance and event selec>on

The effec>ve acceptance obtained with Geant4.9.6 simula>on was corrected for small differences between the data and the Monte Carlo samples related to the event reconstruc>on and selec>on. The typical systema>c error on the flux is 0.8% at 200GV.

The detector is mostly made of carbon and aluminum. The corresponding inelas>c cross sec>ons of p + C and p + Al are known to

within 10% at 1GV and 4% at 300GV, and 7%

at 1.8TV from model es>ma>ons.

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Acceptance Error due to Interac>ons

Knowledge of p+C(Al) inelastic σ is important to assess error on acceptance due to proton interactions. p+C(Al) inelas>c σ is known 4 to 10 % accuracy.

Rigidity [GV]

1 10 10² 10³

p+C inelastic cross section [mb]

200 220 240 260 280

GEANT 4-09-06

GEANT 4-09-06 Uncertainty NA61 (2012)

Denisov (1973) Bellettini (1965)

σqe

Carroll (1979) + Bowen (1958) Letaw (1983)

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Using scaled by ±10% cross sections MC samples allowed to evaluate acceptance error.

The corresponding systematic error is 1% at 1GV, 0.6% from 10 to 300GV, and 0.8% at 1.8TV.

Rigidity [GV]

1 10 10² 10³

p+Al inelastic cross section [mb]

380 400 420 440 460 480 500 520

540 GEANT 4-09-06

GEANT 4-09-06 Uncertainty Denisov (1973)

Bellettini (1965) Carroll (1979) Letaw (1983) MiniBoone (2009)

Acceptance Error due to Interac>ons

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Proton Flux: (iii) systema>c errors on background contamina>on

The background contribu>ons from protons which originated in the interac>ons of nuclei at the top of AMS, no>ceable

only below 2GV, are

subtracted from the ﬂux and the uncertain>es are

accounted for in the systema>c errors.

nuclei

proton

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Proton ﬂux: (iv) systema>c errors on geomagne>c cutoﬀ

The cutoﬀ was calculated by backtracing par>cles from the top of AMS out to 50 Earth’s radii. A safety factor of 1.2 is then applied. It was varied from 1.0 to 1.4 and the resul>ng proton ﬂuxes showed a systema>c uncertainty of 2% at 1GV and negligible above 2GV.

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We have also veriﬁed that using the most recent IGRF model and the IGRF model with external non-‐symmetric magne>c ﬁelds does not introduce observable

changes in the ﬂux values nor in the systema>c errors.

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Proton ﬂux: (v) systema>c errors on unfolding

Among many unfolding procedures, we selected two. The small diﬀerences between the two procedures (< 0.5%) are accounted as a systema>c error.

We have checked the sensi>vity of the results to the binning by:

1.  increasing the bin width by factors of 2 and 4

2.  reducing the bin width by factors of 2 and 4.

The resul>ng uncertainty is well within the assigned systema>c errors.

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Proton ﬂux: (vi) systema>c errors on the rigidity resolu>on func>on

The rigidity resolu>on func>on was veriﬁed with data from both the ISS and the 400 GeV proton beam. For this the residuals between the hit coordinates measured in tracker

layers L1 and L9 and those obtained from the track ﬁt from only the inner tracker L2 to L8 were compared between data and

simula>on.

In order to addi>onally validate the alignment of the external layers the diﬀerence between the rigidity measured using the informa>on from L1 to L8 and from L2 to L9 was

compared between data and the simula>on.

L1

L5 L6 L3

L4

L7 L8

L9

L2

MAG N ET

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-1 ] [ GV 4001

Rigidity1 -

-0.02 -0.01 0 0.01 0.02

Events

10 102

103

104

105

106

a)

400 GeV/c TestBeam Data

400 GeV/c Simulation

The resolution function for 400 GeV/c protons measured in the test beam compared with Monte Carlo simulated events.

The corresponding unfolding errors were obtained by varying the width of the Gaussian core of the resolu>on func>on by 5% and the amplitude of the non-‐

Gaussian tails by ∼ 20% and found to be 1% below 200GV and 3% at 1.8TV.

Proton ﬂux: (vi) systema>c errors on the rigidity resolu>on func>on (cont’d)

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Proton ﬂux: (vii) systema>c errors on the absolute rigidity scale (1/Δ)

1) Residual tracker misalignment:

From the 400GeV/c test beam data it was measured to be less then 1/(300TV). For the ISS data this error was es>mated by comparing the E/R ra>o for electron and positron events, where E is the energy measured with the ECAL and R is the rigidity measured with the tracker. It was found to be 1/(26TV), limited by the current high energy positron sta>s>cs and corresponds to ﬂux error 2.5% @1 TV.

18 Rigidity

Energy

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

Bin Events

10 102

E>30 GeV e+

E>30 GeV, Scaled e-

e-

E +

e+

E

e-

(E/R)

+ - (E/R)e

∆ = 1

e-

E +

e+

E

e-

(E/R)

+ - (E/R)e

∆ = 1

e-

E +

e+

E

e-

(E/R)

+ - (E/R)e

∆ = 1

e-

E +

e+

E

e-

(E/R)

+ - (E/R)e

∆ = 1

1/Δ∼0 and σ(1/Δ)=1/26 TV

^-‐1

Normalized

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Proton ﬂux: (vii) systema>c errors on the absolute rigidity scale

2) Magne>c ﬁeld:

Mapping measurement (0.25%) and temperature correc>ons (0.1%).

Taken in quadrature and weighted by the measured ﬂux rigidity

dependence, this amounts to less than 0.5% systema>c error on the ﬂux.

Zurich,1997 CERN, 2010

B in G au ss

1200 800

400 In 12 years the field has remained the same to <1%

3D field map (120,000 locations) Measured at CERN

in May 2010

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Break Down of Systema>c Errors @ 200GV

Source Error (%) Trigger 0.2

Acceptance 1.1 -‐ Selec>on 0.85 -‐ Interac>ons 0.6 -‐ Geomagne>c Cutoﬀ [<2 GeV] 0

Unfolding & Rigidity Resolu>on 0.95 Rigidity Scale 0.7

-‐ Residual tracker misalignment 0.55 -‐ Magne>c ﬁeld accuracy 0.45

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Four Examples of Independent

Veriﬁca>on of Systema>c Errors on

•  Acceptance

•   Time Stability

•  Rigidity Scale

•   Unfolding

V. Choutko Proton Flux AMS Days CERN 21

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Veriﬁca>on of the Systema>c Error Assigned to Acceptance

θ

°

6 8 10 12 14 16 18 20

Flux Ratio

0.96 0.97 0.98 0.99 1 1.01 1.02 1.03 1.04

Data

Systematic Uncertainty Range

The variation of the flux ratio above 30 GV [Max GeoMag Cutoff] versus the angle θ to the AMS Z axis.

1.01

0.99

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Veriﬁca>on of the Stability of Detector Performance

Date

Flux Ratio

0.97 0.98 0.99 1 1.01 1.02

1.03 b)

Data

09/11 01/12 05/12 09/12 01/13 05/13 09/13

The variation of the (monthly) flux ratio above 45GV

[Above Solar modulation Time Dependent Effects] vs time.

1.01

0.99

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Veriﬁca>on of the Systema>c Error Assigned to the Rigidity Scale

Rigidity [GV]

100 200 300 400 500 600 1000

Flux Ratio

0.85 0.9 0.95 1 1.05

1.1

1.15 c)

Data

The variation of the flux ratio vs the rigidity for different Tracker Layer 1 (L1) entry regions

0.98 1.02

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Flux obtained using the rigidity measured by only the inner tracker (2-8) is in good agreement with the flux measured using the full lever arm (1-9), specifically at -High rigidities (100 to 300GV) where the unfolding effects and resolution functions of the inner tracker (300 GV MDR) and the full lever arm one (2 TV MDR) are very different.

-Low rigidities (1 to 10GV) where the unfolding effects and the tails in the resolution functions of the inner tracker and full lever arm are also very different due to multiple and nuclear scattering.

1

2 3-4 5-6 7-8

9

1.01

0.99 Veriﬁca>on of the Systema>c Error of

Unfolding, Acceptance and Rigidity Resolu>on

1.00 1.02

0.98

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Rigidity [GV]

1 10 10² 10³

Error [%]

1 2 3 4 5 6 7

AV_Error Stat AV_Error Trig AV_Error Acc AV_Error Unf AV_Error Scale AV_Error Full

Sta>s>cal Trigger Acceptance

Unfolding Rigidity Scale

Total

2 1.5

4

1.3 Flux Errors Breakdown

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Rigidity [GV]

1 10 10

²

10

³

] 1.7 GV -1 sec -1 sr -2 [m 2.7 R ~ × Flux 0

2 4 6 8 10 12 14

10

3

×

AMS-02

a)

Proton Flux

300 Million Events

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) [GeV]

Kinetic Energy (E

K

1 10 10

²

10

³

10

⁴

] 1.7 GeV -1 sec -1 sr -2 [m 2.7 K E × Flux

⁰

2 4 6 8 10 12 14

103

×

AMS-02 ATIC-2 BESS-Polar CREAM PAMELA

b)

Proton Flux Comparison with Earlier

Measurements

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Proton Flux Fit with the Model

]

1.7

GV

-1

sec

-1

sr

-2

[m

2.7

R~ × Flux ⁸

9 10 11 12 13 14

10

3

×

AMS-02

Fit to Eq. (3)

Eq. (3) with Δ

γ

=0

Rigidity [GV]

10 10

²

10

³

\\\

Fit to Model χ² /NDF=25/26 Fit to Model with Δγ=0

(sys)

-0.003 +0.004

(fit)

-0.002 +0.002

= -2.849 γ

(sys)

-0.030 +0.046

(fit)

-0.021 +0.032

= 0.133 γ

∆

(sys) [GV]

-28

(fit)+66 -44

= 336+68

R0

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Model Independent Spectral Index Rigidity Dependence

Rigidity [GV]

10 10² 10³

Spectral Index

-2.9 -2.85 -2.8 -2.75 -2.7 -2.65 -2.6 -2.55

-2.5 b)

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Precision Measurement of the Proton Flux with AMS Experiment