On the measurement of the proton-air cross section using ...Ralf Ulrich ([email protected]) On...

On the measurement of the proton-air crosssection using air shower data

Ralf UlrichJ. Blumer, R. Engel, F. Schussler, M. Unger

KIT, Forschungszentrum Karlsruhe

Aspen 2007

Introduction

Analysis methods

Unaccompanied hadrons

Frequency attenuation

Distribution of Xmax

RMStailshape

Sources of systematic uncertainties

Cosmic ray composition

Methodical

Air shower fluctuations

Hadronic interaction models

Ralf Ulrich ([email protected]) On the measurement of the proton-air cross section using air shower data 1 / 25

Overview

(Energy/eV)10

log10 11 12 13 14 15 16 17 18 19

Cro

ss s

ecti

on

(p

roto

n-a

ir)

[m

b]

250

300

350

400

450

500

550

600

650

700

Mielke et al. 1994Aglietta et al. 1999

Baltrusaitis et al. 1984Honda et al. 1999

Knurenko et al. 1999

Nam et al. 1975Siohan et al. 1978Belov et al.

QGSJET01

EPOS

NEXUS3

SIBYLL2.1

QGSJETII.3

Energy [GeV]210 310 410 510 610 710 810 910 1010

[GeV]ppsEquivalent c.m. energy 10 210 310 410 510

Tevatron (p-p)

LHC (p-p)

LHC (C-C)


Contributions to total cross section


First interaction and fluctuations in air showers

primary particleatmospheric boundary

ground level

fluctu

atio

ns

(flu

ctu

ations)

flu

ctu

ati

on

s

(fluctuations)


Air shower profile fluctuations

0 200 400 600 800 1000 1200 1400 1600 1800 2000

6N

/ 1

0

2000

4000

6000

610×

electrons eV19protons, 10

0 200 400 600 800 1000 1200 1400 1600 1800 2000

6N

/ 1

0

10

20

30

10×

muons

]-2slant depth [gcm0 200 400 600 800 1000 1200 1400 1600 1800 2000

(N)

10

RM

S o

f lo

g

0.0

0.1

0.2

0.3 minimum of shower fluctuations

all simulations performed with CONEXRalf Ulrich ([email protected]) On the measurement of the proton-air cross section using air shower data 5 / 25

Air shower profile development (extended Heitler model)

n=1

n=2

n=3

charged neutral

primary

inel

π π

π+ -

o

n(charged)n(neutral) = 2

1 Xmax ∝ λinel + λe.m. · ln( E0

nmult Ec)

Oppenheimer, Heitler, Matthews (2005)


High energy hadronic interaction models

total / EmaxE0 0.2 0.4 0.6 0.8 1

pro

bab

ility

0

0.01

0.02

0.03

0.04

0.05

0.06

eV19EPOS, protons at 10eV19QGSJET, protons at 10

eV19QGSJETII, protons at 10eV19SIBYLL, protons at 10eV19NEXUS, protons at 10

total / Ee.m.E0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

pro

bab

ility

-410

-310

-210

-110

eV19EPOS, protons at 10

eV19QGSJET, protons at 10eV19QGSJETII, protons at 10

eV19SIBYLL, protons at 10

eV19NEXUS, protons at 10

(multiplicity)10

log1 1.5 2 2.5 3 3.5

pro

bab

ility

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08eV19EPOS, protons at 10

eV19QGSJET, protons at 10

eV19QGSJETII, protons at 10

eV19SIBYLL, protons at 10

eV19NEXUS, protons at 10dP

dXmax

∼ P(nmult)⊗P(ninel)⊗P(re.m.)⊗ . . .


HE models

macroscopic parameters

microscopic parameters

model

cross section multiplicity elasticity . . .

. . .

diffraction

. . .

parton distribution fragmentation

→ all macroscopic parameters are correlated


Composition - impact on Xmax

]-2 [gcmmaxX

600 700 800 900 1000 1100 1200

frac

tio

n

-410

-310

-210

-110proton (58%)helium (30%)iron (10%)gamma (2%)sum

Uncertain composition above ∼ 1015.5eV impacts all air shower observables

SIBYLL 1019eV



atmospheric boundary

ground level

hadron calorimeter

satellite

ballone

anti-coincidence array

protons

experimental results from: Nam et al. (1975), Siohan et al. (1978), Mielke et al. (1994), . . .




ground level

hadron calorimeter

satellite

ballone

anti-coincidence array

protons heavier primaries

experimental results from: Nam et al. (1975), Siohan et al. (1978), Mielke et al. (1994), . . .


Unaccompanied hadrons - cross section

φ(X ) = 1λ · e−X/λ

Top of atmosphere

φtop = φ(Xtop = 0gcm−2) by satellites, orφtop = φ(Xtop ∼ 5gcm−2) ballones

Bottom of atmosphere

φbottom = φ(Xground) measured by calorimeter

Flux attenuation

λprod = ∆X/ log(φtop/φbottom) with ∆X = Xbottom − Xtop

σprod = σtot − σel − σq−el − σdiffr



→ Attenuation of shower cascades in the atmosphere

ground level

air shower ground array


same energy proton showers

Ne

constant Nµ ⇒ equal E0 constant Ne ⇒ same distance to Xmax

experimental results from: Honda et al. (1993), Hara et al. (1999), Aglietta et al. (1999), ...




ground level




Ne Ne

deeply penetra

ting






ground level




Ne

deeply penetra

ting

Ne Ne




Frequency attenuation - examples

AGASA like experiment (Xobs=920gcm−2, ∆(Ne )Ne

= 0.05,∆(Nµ)

Nµ

= 0.1)

(toy detector simulation, Φ ∼E−2.7, 0◦

< θ < 60◦, protons only)

)θsec(1.05 1.1 1.15 1.2 1.25 1.3

freq

uen

cy

[ar

bit

rary

un

its]

310

) binµ/Ne

frequency of events in (N-2=87.7138gcmΛexponential attenuation,

hist_0Entries 3390Mean 889.2RMS 58

]-2 [gcm1-XobsX600 700 800 900 1000 1100 1200 1300 1400

entr

ies

0

50

100

150

200

250

hist_0Entries 3390Mean 889.2RMS 58

/deg < 21θ 0 < /deg < 29θ 21 < /deg < 36θ 29 < /deg < 42θ 36 <

>1GeV)) < 6.25µ

(Eµ

(N10

6.05 < log

>1MeV)) < 8.4e

(Ee

(N10

8.2 < log

→ observed attenuation is only partly due to cross section

compare for example Alvarez-Muniz et al. (2002)


Ne sensitivity

]-2(attenuation) [gcmΛ

0 20 40 60 80 100 120

(p

roto

n-a

ir)

[m

b]

tot

σ

0

200

400

600

800

1000

1200

1400 qgsjetqgsjetIIsibyll

Energy reconstruction/selection accurate (E0 = 10EeV), ∆(Ne )Ne

= 0.05, Xobs=920gcm−2


Ne sensitivity

]-2(attenuation) [gcmΛ

0 20 40 60 80 100 120

(p

roto

n-a

ir)

[m

b]

tot

σ

0

200

400

600

800

1000

1200

1400 qgsjetqgsjetIIsibyll

Energy reconstruction/selection accurate (E0 = 10EeV), ∆(Ne )Ne

= 0.05, Xobs=920gcm−2

∆Λ ∼ 5gcm−2 ⇒ ∆σ ∼ 300mb


Xmax distribution: tail and fluctuations

]-2 [gcmmaxX

600 700 800 900 1000 1100 1200

frac

tio

n

-410

-310

-210

-110

))Λtail (exp(-X/

RMSλint = k · Λobs = <M>

σint

all detector effectsand fluctuations arecontained in k

RMS

Walker & Watson (Havera Park, 1982)Linsley (1985)

tail

Baltrusaitis et al. (Fly’s eye, 1984)Knurenko et al. (Yakutsk, 1999)


Xmax sensitivity

]-2) [gcmmax

(XΛ

40 50 60 70 80 90 100 110 120

(p

roto

n-a

ir)

[m

b]

tot

σ

0

200

400

600

800

1000

1200

1400

]-2) [gcmmax

RMS(X

40 50 60 70 80 90 100 110 120

(p

roto

n-a

ir)

[m

b]

tot

σ

0

200

400

600

800

1000

1200

1400qgsjet

qgsjetII

sibyll

Xmax-resolution is 30gcm−2. Energy reconstruction is accurate (E0 = 10EeV).


Deconvolution of Xmax-distribution

Xmax = X1 + ∆X

-2 / gcmmaxX600 700 800 900 1000 1100 1200 1300 1400

pro

bab

ility

-510

-410

-310

-210

-110

-2 / gcm1X0 100 200 300 400 500 600 700

pro

bab

ility

-510

-410

-310

-210

-110

-2 X /gcm∆600 700 800 900 1000 1100 1200 1300

pro

bab

ility

-510

-410

-310

-210

-110

⊗=

PXmax(Xmax) =

∫∞

0

dX1 PX1(X1) · P∆X (∆X |X1; HEM)

method proposed by Belov et al. (HiRes)


Independence of ∆X -distribution from X1

QGSJET01, protons 1018eV (∼200.000 profiles):

-2 X / gcm∆600 700 800 900 1000 1100 1200 1300

Pro

bab

ility

-610

-510

-410

-310

-210 < 13 (n=53876)2/gcmfirst

0< X

< 39 (n=70785)2/gcmfirst

13< X

< 78 (n=52277)2/gcmfirst

39< X

< 533 (n=38958)2/gcmfirst

78< X

X1 and ∆X are independent parameters P∆X (∆X |X1) = P∆X (∆X )

(confirmed for NEXUS3, SIBYLL2.1, QGSJETII.3, QGSJET01 for protons at 1018eV and 1019eV)


Dependence on HE model

sibyll_0.5Entries 9800Mean 766.6RMS 54.6

]-2 X [gcm∆600 650 700 750 800 850 900 950 1000 1050 1100

X∆d

n /

d

-410

-310

-210

sibyll_0.5Entries 9800Mean 766.6RMS 54.6

QGSJETII, factor=0.5 QGSJETII, factor=0.6 QGSJETII, factor=0.7 QGSJETII, factor=0.8 QGSJETII, factor=0.9 QGSJETII, factor=1.0 QGSJETII, factor=1.2 QGSJETII, factor=1.4 QGSJETII, factor=1.6 QGSJETII, factor=1.8 QGSJETII, factor=2.0

→ similar dependence on multiplicity expected

P∆X is a function of σ and other correlated HE model parameters (multiplicity,...)

CONEX, QGSJETII, 10 EeV


∆X -distribution for different HE-models

-2 X / gcm∆600 650 700 750 800 850 900 950 1000 1050 1100

pro

bab

ility

-610

-510

-410

-310

-210 qgsjetsibyllnexusqgsjetII

Position of maximum shifts up to ∼ 60gcm−2

Exponential slope after maximum changes up to a factor of ∼ 1.36

→ Model-dependence


Sensitivity of deconvolution

[mb]modelσ - modifiedσ-500 -400 -300 -200 -100 0 100 200 300 400 500

[

mb

]tr

ue

σ -

re

cσ

-500

-400

-300

-200

-100

0

100

200

300

400

500 (QGSJET)max

X(QGSJET), X∆

(QGSJETII)max

X(QGSJETII), X∆

E0 = 1019eVRalf Ulrich ([email protected]) On the measurement of the proton-air cross section using air shower data 21 / 25

Sensitivity of deconvolution

[mb]modelσ - modifiedσ-500 -400 -300 -200 -100 0 100 200 300 400 500

[

mb

]tr

ue

σ -

re

cσ

-500

-400

-300

-200

-100

0

100

200

300

400

500 (QGSJET)max

X(QGSJET), X∆

(QGSJETII)max

X(QGSJETII), X∆

(SIBYLL)max

X(QGSJET), X∆(QGSJETII)

max X(QGSJET), X∆

model uncertainty band

E0 = 1019eVRalf Ulrich ([email protected]) On the measurement of the proton-air cross section using air shower data 21 / 25

Summary

measuring σp−air means measuring EAS fluctuations

assuming CR primary interaction length the only source of EASfluctuations is not enough. At least needed:

Additional HE interaction characteristics (multiplicity,...)

The first few interactions at still extreme energy

diffraction

Meaningful estimate of uncertainty needs: HE model dependence and CRcomposition x

Future

→ better understanding of fluctuations

→ measurement of composition

→ new experiments (fluorescence/cherenkov, muons, ...)


Final rating

method HE-model composition fluctuationsunaccompanied hadrons ⊙ ⊙ ⊕frequency attenuation ⊖ ⊖ ⊖⊖Xmax RMS ⊖ ⊖⊖ ⊖Xmax tail ⊖ ⊙ (⊕) ⊖Xmax deconvolution ⊖⊖ ⊖ ⊙


Final - ’conservative’ picture

(Energy/eV)10

log10 11 12 13 14 15 16 17 18 19

Cro

ss s

ecti

on

(p

roto

n-a

ir)

[m

b]

250

300

350

400

450

500

550

600

650

700

Mielke et al. 1994

Nam et al. 1975

Siohan et al. 1978

QGSJET01

EPOS

NEXUS3

SIBYLL2.1

QGSJETII.3

Energy [GeV]210 310 410 510 610 710 810 910 1010


Tevatron (p-p)

LHC (p-p)

LHC (C-C)

lower limits


Final - ’progressive’ picture

(Energy/eV)10

log10 11 12 13 14 15 16 17 18 19

Cro

ss s

ecti

on

(p

roto

n-a

ir)

[m

b]

250

300

350

400

450

500

550

600

650

700

Mielke et al. 1994

Baltrusaitis et al. 1984

Nam et al. 1975

Siohan et al. 1978

QGSJET01

EPOS

NEXUS3

SIBYLL2.1

QGSJETII.3

Energy [GeV]210 310 410 510 610 710 810 910 1010


Tevatron (p-p)

LHC (p-p)

LHC (C-C)

HE

mo

del

⇒ weak constraints on HE interaction models

98% confidence limit


Changing composition - data

Energy [eV]10

1710

1810

1910

20

]2>

[g/c

mm

ax<

X

500

550

600

650

700

750

800

850

900

950

1000

QGSJET01SIBYLL 2.1

DPMJET 2.55

HiRes-MIA

HiRes

Yakutsk 2001

Fly’s Eye

Yakutsk 1993

proton

iron

-ray

γ


Composition - model by Hillas


Equal intensity cut

)θsec(1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

inte

nsi

ty

[arb

itra

ry u

nit

s]

-910

-810

-710

-610) < 8.25

ch(N

10 8 < log

) < 8.5ch

(N10

8.25 < log

) < 8.75ch

(N10

8.5 < log

) < 9ch

(N10

8.75 < log

constant intensity → same primary energy (isotropic flux)

relates shower size Nch at different zenith angle with primary energy


Equal intensity cut

)θsec(1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

inte

nsi

ty

[arb

itra

ry u

nit

s]

-910

-810

-710

-610) < 8.25

ch(N

10 8 < log

) < 8.5ch

(N10

8.25 < log

) < 8.75ch

(N10

8.5 < log

) < 9ch

(N10

8.75 < log

constant intensity

constant intensity → same primary energy (isotropic flux)

relates shower size Nch at different zenith angle with primary energy


On the measurement of the proton-air cross section using ...Ralf Ulrich ([email protected]) On...

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