Precision Measurement of the Proton Flux with AMS Experiment

Precision Measurement of the Proton Flux with AMS Experiment

AMS Days at CERN

Geneva, April 16th 2015

V. Choutko/M.I.T.

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.

TRD

TOFTracker

TOFRICH

ECAL

L1

L2

L7-L8

L3-L4

L9

L5-L6 ToF (4 Layers) Velocity and Direc>on Δβ/β2 (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


Charge0.5 1 1.5 2 2.5

Events

510

610

710

810

910Data P910×11.4

He Nuclei

AMS Data Sample

Proton Selec>on

(I)  Downgoing Par>cle β > 0.3

(II)  Rigidity (R) Above Geomagne>c Cutoff (RC ) R > 1.2RC [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)  χ2/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/c2 Removes low rigidity π’s


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


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

Φi(R) = Ni

Ti Ai εi ΔRi

Trigger Efficiency from Data

Bin width


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

i=1,72

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)

8

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


Rigidity[GV]1 10 210 310

Trig

ger E

fficie

ncy

0.8

0.82

0.84

0.86

0.88

0.9

0.92

0.94

0.96

0.98

1Data

MC Geant 4.9.6

Trigger Efficiency Measured from Unbiased Trigger

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.



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 10 210 310

p+C

inelas

tic cr

oss s

ectio

n [mb

]

200

220

240

260

280

GEANT 4-09-06GEANT 4-09-06 UncertaintyNA61 (2012)Denisov (1973)Bellettini (1965)

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


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.


p+Al

inelas

tic cr

oss s

ectio

n [mb

]

380

400

420

440

460

480

500

520

540 GEANT 4-09-06GEANT 4-09-06 UncertaintyDenisov (1973)Bellettini (1965)Carroll (1979)Letaw (1983)MiniBoone (2009)

Acceptance Error due to Interac>ons

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


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.

14

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.


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.


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

MA

GN

ET


17

]-1 [ GV4001 - Rigidity

1

-0.02 -0.01 0 0.01 0.02

Even

ts

10

210

310

410

510

610a)

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)


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

RigidityEnergy

0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4

BinEvent

s

10

210

E>30 GeV+e E>30 GeV, Scaled-e

-eE + +eE-e(E/R) - +e(E/R)

= ∆1

-eE + +eE-e(E/R) - +e(E/R)

= ∆1

-eE + +eE-e(E/R) - +e(E/R)

= ∆1

-eE + +eE-e(E/R) - +e(E/R)

= ∆1

1/Δ∼0 and σ(1/Δ)=1/26 TV-‐1

Normalized


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

auss

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 19


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


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

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


°θ

6 8 10 12 14 16 18 20

Flu

x R

ati

o

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

Verifica>on of the Stability of Detector Performance


Date

Flu

x R

atio

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

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


Rigidity [GV]

100 200 300 400 500 600 1000

Flu

x R

ati

o

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

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.

25

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




Erro

r [%

]

1

2

3

4

5

6

7

AV_Error StatAV_Error TrigAV_Error AccAV_Error UnfAV_Error ScaleAV_Error Full

Sta>s>cal Trigger Acceptance

Unfolding

Rigidity Scale

Total

2 1.5

4

1.3

Flux Errors Breakdown


Rigidity [GV]

1 10 210 310

]1.7

GV

-1se

c-1

sr-2

[m

2.7 R~ ×Fl

ux

0

2

4

6

8

10

12

14

310×

AMS-02a)

Proton Flux

300 Million Events


) [GeV]K

Kinetic Energy (E

1 10 210 310 410

]1.7

GeV

-1se

c-1

sr-2

[m

2.7 K E×

Flux

0

2

4

6

8

10

12

14

310×

AMS-02ATIC-2BESS-PolarCREAMPAMELA

b)

Proton Flux Comparison with Earlier Measurements

Proton Flux Fit with the Model


]1.7

GV

-1se

c-1

sr-2 [m2.7 R~ ×

Flux

8

9

1011

12

13

14310×

AMS-02Fit to Eq. (3) Eq. (3) with Δγ=0

Rigidity [GV] 10 210 310

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

(sys)-0.003+0.004(fit)

-0.002+0.002 = -2.849γ

(sys)-0.030+0.046(fit)

-0.021+0.032 = 0.133γ∆

(sys) [GV]-28+66(fit)-44

+68 = 3360R

Model Independent Spectral Index Rigidity Dependence


Rigidity [GV] 10 210 310

Spec

tral In

dex

-2.9-2.85-2.8

-2.75-2.7

-2.65-2.6

-2.55-2.5 b)

310×

The spectral index varies with rigidity. In particular, the spectral index is progressively hardening with rigidity above ∼100 GV.

Spectral Index = d[log(Φ)]/d[log(R)]

Conclusion •  Precision measurement of proton flux with AMS is done from 1 GV to 1.8 TV based on 300 million events

•  The detailed varia>on of the flux spectral index is presented

•  The spectral index is progressively hardening at high rigidi>es


Precision Measurement of the Proton Flux with AMS Experiment

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