Stability of muon number in EAS calculations · 2008-02-28 · Stability of muon number in EAS calculations S. Ostapchenko University of Karlsruhe, Institute for Nuclear Technology

Stability of muon number in EAS calculations

S. Ostapchenko

University of Karlsruhe, Institute for Nuclear Technology

Nuclear Interactions Workshop

INT, University of Washington, Seattle, February 20-22 2008

�Avoid models as much as you can!�

�Important issues are INPUT OF REAL DATA ...�

A. Watson

• Muon production in air showers

• Relative importance of 'central' & peripheral hadronic collisions

- di�raction dissociation

• High energy interactions - model approach

• Model parameter freedom & impact on Nµ

• Experimental situation

1

Muon production in extensive air showers (EAS)

EAS development ⇐ high energy interactions

• backbone - hadron cascade

• guided by few interactions of initial (fastest secondary)

particle ⇒ main source of �uctuations

• many sub-cascades of secondaries ⇒ well averaged

Basic quantities:

• shower maximum position Xmax

- mainly sensitive to p−air interactions

• number of muons at ground Nµ

- mainly sensitive to π−air

• particle content of the hadronic cascade:

- mainly π±

- ∼ 10÷ 20% K±, K0

- ∼ 10÷ 20% N, N̄

Dete tion: extensive air showers (EAS)

e

1000

α E 0N (max)

6 km

1200

200

depth(g/cm )2

12 km0X

vertical shower

zenith angle of 40 deg.

sea level

sea level

shower size Ne

max

0ln

(E /A

)X

α

700

(Pryke, Auger Proje t)� parti les: , e and �� about 7 � 1010 harged parti les at Xmax in EAS withE0 = 1020 eV2

Hadronic cascade equations (neglecting particle decays):

dNa(E, z)

dz= −σa(E)Na(E, z) +

∑b

∫ 1

E/E0

dx

xσb(E/x) Nb(E/x, z)

dna/b(x,E/x)

dx

• σa(E) ≡ 1/λa(E) - inverse mean free pass (in g/cm2)

• z =∫∞H dh ρair(h) - depth (in g/cm2)

•dna/b(x,E)

dx - normalized (per event) spectrum of particles a produced in b−air interaction

Dominant contribution to Nµ - from pion cascading

Example: increase N chp−air by 100% (QGSJET)

or N chπ−air by 10% - comparable e�ects

(leading hadron energy kept unchanged!)

But: shape of meson spectra important

0.9

1

1.1

1017

1018

1019

1020

E0, eV

∆N

µ/N

µ (

1 G

eV)

Np-air+100%

Nπ-air+10%

3

Simpli�ed picture:

• only pion cascade

• scaling: σπ(E) = const, dnπ(x,E)/dx = f (x)

• muons produced by π± decays at �xed Edecπ

dNπ±(E, z)

dz= −σπ± Nπ±(E, z) + σπ±

[∫ 1

E/E0

dx

xNπ±(E/x, z)

dnπ±(x)

dx

]

Beginning of the cascade: Nπ±(E,Z) ∼dnπ±/p(x,E0)

dx

∣∣∣x=E/E0

∼ 1E (rapidity plato)

⇒[∫ 1

E/E0dxx Nπ±(E/x, z)

dnπ±(x)

dx

]∼ N ch

π−air - multiplicity of charged pions (E � E0)

Low energy pions produced more abundantly

⇒ deeper in the cascade (z � 1): Nπ±(E,Z) ∼ E−1−d

⇒[∫ 1

E/E0dxx Nπ±(E/x, z)

dnπ±(x)

dx

]∼∫ 1

E/E0dx xd

dnπ±(x)

dx

E.g., d ' 1 ⇒ [...] ∼ 〈xπ±〉 = 1− 〈xπ0〉

0

5

10

15

20

0 5 10 15 20 rapidity y

dN

/dy p + N at 1010 GeV → π+ (QGSJET)

20 GeV 40 PeV

4

⇒ Nµ depends on

• σinelπ−air

• N chπ−air

• forward spectra of secondaries

Experimental data:

• mainly at low energies

• mainly for pp

⇒ model-based extrapolation to pA (AA) & higher energies

Stability (instability) of Nµ - within a particular model approach!

5

'Central' & peripheral collisions:

relative importance for σinelh−air, K

inelh−air, N

chh−air?

What is 'central'?

• 'black disc' limit: σinel(b) ∼ 1 ⇒ σel/σtot ' 1/2

• experiment: σelpp/σ

totpp ' 1/4 @

√s = 1.8 TeV

Interaction pro�le & b-contributions to σinelp−air @ E0 = 106 GeV:

0

0.25

0.5

0.75

1

0 2 4 6 b, Fm

σin

el(b

)

p+14N (1 PeV) QGSJET-II

0

0.5

1

1.5

2

0 2 4 6 b, Fm

b σ

inel

(b)


6

b-dependence & b-contributions to K inelp−air @ E0 = 106 GeV:

0

0.2

0.4

0.6

0.8

0 2 4 6 b, Fm

Kin

el(b

)


average

0

0.5

1

1.5

0 2 4 6 b, Fm

b σ

inel

(b)

Kin

el(b

)


Model dependence - mainly due to the treatment of peripheral interactions

7

b-dependence & b-contributions to N chp−air @ E0 = 106 GeV:

0

25

50

75

100

0 2 4 6 b, Fm

Nch

(b)


average

0

50

100

150

0 2 4 6 b, Fm

b σ

inel

(b)

Nch

(b)


Knowledge of 'central' physics - insu�cient for EAS predictions

Peripheral contribution:

- decisive for cross sections & energy losses

- still of high importance for 〈Nch〉

8

Di�raction dissociation

multiple production projectile di�raction target di�raction double di�raction

rapidity gap

rapidity gap

rapidity gap

Leading proton spectrum & di�raction contributions

10-2

10-1

1

0.2 0.4 0.6 0.8 x

x dn

/dx

p+N (1 PeV) → p QGSJET II

9

High energy interactions: qualitative picture

Hadronic interactions - multiple scattering processes (parton cascades)

Di�erent projectile-target systems (pp, πp, pA, AA):

• di�erent initial conditions for parton evolution (x− and b− distributions)

• same interaction mechanism

(picture from R. Engel)

Single scattering:

• (a) 'soft' (all |q2| ∼ p2t < Q2

0, Q0 ∼ 1 GeV2) cascade

- large e�ective area (∆b2 ∼ 1/|q2|)- slow energy rise

⇒ dominant at relatively low energies

• (b) cascade of 'hard' partons (all |q2| � Q20)

- small e�ective area

- rapid energy rise

⇒ important at very high energies and small impact parameters

• (c) 'semi-hard' scattering (some |q2| > Q20)

- large e�ective area

- rapid energy rise

⇒ dominates at high energies and over a wide b-range

(a) (b) (c) (d)

10

General model strategy:

• describe 'elementary' interactions (parton cascades)

- scattering amplitude

- hadronization procedure (conversion of partons into hadrons)

• apply Reggeon approach to treat multiple scattering processes

• describe particle production as a superposition of a number of 'elementary' processes

Parton cascades start at low virtualities

⇒ phenomenological scheme:

• Q20 - cuto� between 'soft' and perturbative physics

• 'Soft' interactions (all |q2| - small ⇒ αs(q2) > 1):

- pQCD is inapplicable ⇒ Regge pole amplitude ('soft' Pomeron)

• 'Semi-hard' processes (|q2| > Q20 ⇒ αs(q

2)� 1)- 'soft' Pomeron for

∣∣p2t

∣∣ < Q20

- QCD parton ladder for∣∣p2t

∣∣ > Q20

11

General interaction ⇒ 'general Pomeron':

χPad(s, b) = χ

Psoftad (s, b) + χ

Pshad (s, b)

= +

soft Pomeron

QCD ladder

soft Pomeron

• particle production: perturbative parton cascade + string hadronization

Important: direct relation between the eikonal and inclusive jet cross section

2

∫d2b χ

Pshad (s, b) ≡ σjet

ad (s,Q20)

σjetad (s,Q2

0) =∑

I,J=q,q̄,g

∫p2t>Q

20

dp2t

∫dx+dx−

dσ2→2IJ (x+x−s, p2

t )

dp2t

× fI/a(x+,M 2

F ) fJ/d(x−,M 2

F )

12

Multiple scattering approach

General interaction - superposition of many 'elementary' processes; �nal states - Regge cuts

... ...σtotad = Im =

∑

Or

... ...σtotad = Im =

∑

Contribution with m inelastic and n elastic subprocesses (neglecting di�raction):

σ(m,n)ad (s) =

∫d2b

[2χP

ad(s, b)]n

n!

[−2χP

ad(s, b)]n

n!

13

Physical quantity - 'topological' cross sections (m inelastic processes):

σ(m)ad (s) =

∞∑n=0

σ(m,n)ad (s) =

∫d2b

[2χP

ad(s, b)]n

n!e−2χP

ad(s,b)

⇒ inelastic cross section:

σinelad (s) =

∞∑m=1

σ(m,)ad (s) =

∫d2b

[1− e−2χP

ad(s,b)]

Hadron-nucleus (nucleus-nucleus) scattering - Glauber approach:

• phase additivity

• nucleons distributed according to the ground state wave function

σinelaA (s) =

∫d2b

{1−

[1−

∫d2ζ TA(ζ)

(1− e−2χP

ad(s,|~b−~ζ|))]A}

TA(ζ) =∫dz ρA(~ζ, z) - nuclear pro�le function

Often used:

σinelaA (s) =

∫d2b

{1−

[1− σinel

ap (s) TA(b)]A}

- incorrect (nucleon size neglected)

14

Non-linear e�ects

Large s, small b, large A:

• many partons closely packed

•⇒ parton cascades overlap and interact with each other

•⇒ parton shadowing (slower rise of parton density)

• saturation (maximal possible density reached)

(picture from R. Engel)

Non-linear e�ects in QCD: interaction between parton ladders

...

...

...

...

15

Pomeron approach: non-linear e�ects ≡ Pomeron-Pomeron interactions

1

1 2

33

4

y ,b

y ,b

y ,b

y ,b y ,b

y ,b

y ,b

y ,b3

y ,b3

1

y ,b4

y ,b3

2

1

5

3

1 1

2 2

22

5

(a) (b) (c)

QGSJET II:

• all order re-summation of (non-loop) Pomeron 'nets'

• (parameter-free) A-enhancement of screening e�ects in hA (AA) collisions

• hadronic �nal states - unitarity cuts of multi-Pomeron diagrams

• preserves QCD factorization for inclusive jet cross section

σjetad (s,Q2

0) =∑

I,J=q,q̄,g

∫p2t>Q

20

dp2t

∫dx+dx−

dσ2→2IJ (x+x−s, p2

t )

dp2t

× f scrI/a(x

+,M 2F ) f scr

J/d(x−,M 2

F )

• but:∫d2b χ

Pshad (s, b) 6= σjet

ad (s,Q20) - due to non-factorizable contributions

16

Model parameter freedom and EAS muon content

Based on collaboration with J. Knapp

Main idea - produce few parameter sets of comparable quality

I Default version of QGSJET-II

II Increased low mass di�raction

2-component eikonal scheme: |a〉 = 1√2|1a〉 + 1√

2|2a〉

|ka〉 - di�ractive eigenstates for hadron a;couple to a Pomeron with di�erent strength λk/a

• default: λ1/p/λ2/p =4, λ1/π/λ2/π =4.7

• version II: λ1/p/λ2/p =7, λ1/π/λ2/π =9

σtotpp (s) = 2

∫d2b

1

4

2∑i,j=1

[1− e−λi/p λj/p χpp(s,b)

]σinelpp (s) =

∫d2b

1

4

2∑i,j=1

[1− e−2λi/p λj/p χpp(s,b)

]σs−diffrpp (s) = 2

∫d2b

1

4

2∑j=1

[e−λ1/p λj/p χpp(s,b) − e−λ2/p λj/p χpp(s,b)

]2

17

14

2∑i,j=1

[1− e−λi/p λj/p χpp(s,b)

]=

{1, b→ 0

χpp(s, b)− 12 (2− λ1/p λ2/p)2 χ2

pp(s, b) + ..., b→∞

Higher di�raction ⇒ cross sections reduced at high energies (inelastic screening)

Topological cross section (n inelastic sub-processes):

σ(n)ad (s) =

∫d2b

1

4

2∑i,j=1

[2λi/a λj/d χad(s, b)

]nn!

e−2λi/a λj/d χad(s,b)

⇒ larger multiplicity �uctuations

III Higher Q20-cuto� (4 GeV2 instead of 2.5 GeV2)

�Semi-hard� component reduced; saturation may be reached at a higher scale

IV Baryon "junction" suppressed ⇒ less inelastic interaction

Energy-momentum sharing between 2n string ends:

N (n)a (x1, ..., x2n) ∼

2n∏i=1

x−αRi

(1−

2n∑k=1

xk

)αlead

• without �junction� mechanism: αlead = αqqq̄q = αR − 2αB

• �junction�: αlead = αlead(n) = 1− 2αB +(

2n − 3

)(1− αR)

V Less "valence" string ends ( αR=0.7 instead of 0.5), no "junction", higher string tension

18

Structure functions: version V - slightly steeper ⇒ faster increase of σtot, Nch

0

0.5

1

1.5 F2(

x,Q

2 )

Q2=2.7 GeV2Q2=2.7 GeV2Q2=2.7 GeV2 Q2=4.0 GeV2Q2=4.0 GeV2Q2=4.0 GeV2Q2=4.0 GeV2 Q2=6.0 GeV2Q2=6.0 GeV2Q2=6.0 GeV2Q2=6.0 GeV2

0

0.5

1

1.5

10-5

10-3

10-1

x

F2(

x,Q

2 )

Q2=8.0 GeV2Q2=8.0 GeV2Q2=8.0 GeV2Q2=8.0 GeV2

10-5

10-3

10-1

x


10-5

10-3

10-1

x


19

3-Pomeron coupling: slightly smaller in version V

⇒ smaller screening, smaller di�raction, faster increase of σtot, Nch

0

0.02

0.04 x P F2D(

3)

Q2=2.7 GeV2

β=0.0030Q2=4.0 GeV2

β=0.0044Q2=6.0 GeV2

β=0.0066Q2=8.0 GeV2

β=0.0088

0

0.02

0.04 x P F2D(

3)

Q2=2.7 GeV2

β=0.0067Q2=4.0 GeV2

β=0.0099Q2=6.0 GeV2

β=0.0148Q2=8.0 GeV2

β=0.0196

0

0.02

0.04

10-4

10-2

xP

x P F2D(

3)

Q2=2.7 GeV2

β=0.0218

10-4

10-2

xP

Q2=4.0 GeV2

β=0.0320

10-4

10-2

xP

Q2=6.0 GeV2

β=0.0472

10-4

10-2

xP

Q2=8.0 GeV2

β=0.0620

20

σtot:

• suppressed in version II - stronger inelastic screening

• suppressed in version III - �semi-hard� contribution reduced by higher cuto�, saturation reached

at higher Q2

• faster energy rise in version V - steeper PDFs, smaller screening

0

50

100

150

200

102

103

104

105

c.m. energy (GeV)

tota

l cro

ss s

ectio

n

p+p

π+p

K+p

Dashed lines - version Ia: reduced di�raction for pions & kaons

21

Forward spectra: better described in version II due to higher di�raction

10-1

1

0.2 0.4 0.6 0.8 1long. momentum fraction x

x E dn/dx p+p at 100 GeV → p

10-1

1


x E dn/dx p+p at 100 GeV → p

10-5

10-4

10-3

10-2

10-1

1


x E dn/dx p+p at 100 GeV → π+

10-5

10-4

10-3

10-2

10-1

1


x E dn/dx p+p at 100 GeV → π-

4

5

6789

10

20

30

0 0.2 0.4 0.6 0.8 1long. momentum fraction x

x dσ

/dx π++p at 13.7 GeV → π+

10-1

1

10

0 0.2 0.4 0.6 0.8 1long. momentum fraction x

x dσ

/dx π++p at 13.7 GeV → π-

22

Multiplicity: general agreement within 10%

0

0.2

0.4

0.6

0.8

-4 -2 0 2 4 rapidity y

dn/dy p+p at 100 GeV → π+

0

0.2

0.4

0.6


dn/dy p+p at 100 GeV → π-

0

0.2

0.4

0.6

0.8


dn/dy π++p at 100 GeV → π+

0

0.2

0.4

0.6


dn/dy π++p at 100 GeV → π-

0

1

2

3

-5 -2.5 0 2.5 5 pseudorapidity eta

dn/de

ta p+p at 100+100 GeV → C

NSD

0

2

4

6

-5 -2.5 0 2.5 5 pseudorapidity eta

dn/de

ta p+p at 900+900 GeV → C

23

Multiplicity distribution: too broad in version II -

asymmetric eigenstates enhance �uctuations

10-6

10-5

10-4

10-3

10-2

10-1

0 20 40 60 80 multiplicity n

P(n

)

p+p at 100+100 GeV → C

| η| < 2.5

NSD

More discrimination possibilities o�ered by RHIC data

24

Hadron-air cross sections:

• the same trends as for hadron-proton

• reduced di�erences

0

200

400

600

104

106

108

1010

E0, GeV

inel

astic

cro

ss s

ectio

n, m

b

p - 14N

π - 14N

K - 14N

25

Inelasticity:

• at high energies smallest in version II - large di�raction

• suppressed in version III at high energies due to higher Q0-cuto�

• version IV (baryon �junction� mechanism turned o�) - moderate e�ect

• less �valence� string ends in version V - large e�ect at low energies

0.4

0.5

0.6

0.7

0.8

104

106

108

1010

E0, GeV

inel

asti

city p - 14N

0.4

0.5

0.6

0.7

0.8

104

106

108

1010

E0, GeV i

nel

asti

city π - 14N

26

Multiplicity:

• slower rising in version III (higher Q0-cuto�) - semi-hard contribution reduced

• fast energy rise in version V - due to steeper PDFs, smaller screening, modi�ed hadronization

(smaller string mass cuto�)

• other versions - similar to each other

0.6

0.8

1

1.2

1.4

104

106

108

1010

E0, GeV

Nch

rat

io (

rela

tiv

e to

th

e d

efau

lt)

p - 14N

0.6

0.8

1

1.2

1.4

104

106

108

1010

E0, GeV N

ch r

atio

(re

lati

ve

to t

he

def

ault

)

π - 14N

27

Muon number (Eµ>1 GeV) at ground:

• smallest Nµ in version II (high di�raction)

- smaller σinel

- smaller Nch

- smaller inelasticity

• next goes version III (high Q0-cuto�) - same reasons

• other versions - close to the default

• e.g., version V ('softer' string ends):

- higher multiplicity

- but softer pion spectra

• smaller di�raction for π & K:

- higher inelasticity

- but higher 〈π0〉

0.8

0.9

1

1.1

1.2

1016

1017

1018

1019

1020

E0, eV

muo

n (1

GeV

) nu

mbe

r ra

tio

28

It appeared to be impossible to enlarge Nµ in the chosen scheme

Other lessons:

• most e�cient way to modify Nµ - via the 'peripheral' (large b) contribution

• in particular, di�raction has the largest in�uence on EAS characteristics:

• but - constraint by data

• alternative way - change the transition from pp to πp, pA & πA

In the discussed approach - include 'Pomeron loop' contributions (in progress):

• provide additional screening corrections in peripheral collisions

•⇒ result in smaller 3-Pomeron coupling

• but negligible in 'central' collisions ⇒ higher multiplicity & inelasticity in hA, AA

• still: no drastic e�ect expected

Alternative approaches - reduce the 'peripheral' contribution:

• e.g., via a quick parton density saturation at large b (CGC)

(a) (b) (c) (d)

29

Experimental situation

HiRes-Mia & AGASA - same energy range but contradictory results

• ρµ(600 m) in Mia ∼ ρµ(Fe / QGSJET)• ρµ(600 m) in AGASA ∼ ρµ(p / QGSJET)

Cosmi ray omposition using muons� hadrons (superposition model):hN�i = A N0 � (E=A)� ; � � 0:87� photons: muon-poor showers (E < 1018eV)however: situation un lear at higher energies� HiRes-MIA data:

0.1 1

0.1

1

��

��

��+

ρ µ

��+

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

QGSJet IronQGSJet Proton

sys.

sys. + stat.

E ( 10 eV)18

(600

m)

(m

)

-2

β = 0.73 0.03 (0.02)

) more muons than in any QCD-based model10

-1

1

10

1 10 102

S(600) (m-2)

ρ µ(6

00)

(Eµ

≥ 1 G

eV

) (m

-2)

shaded: AGASA result

QGSJET, Proton

QGSJET, Iron

SIBYLL, Proton

SIBYLL, IronFig. 12. Comparison of experimental �� vs S0(600) or � h relation with that from COR-SIKA simulation.energies of 2 GeV is expe ted to be smaller than that at Akeno of 1 GeV abouta fa tor 1:2 � 1:5 [37℄. Therefore su h an agreement of the extrapolation of theabsolute values from both experiments is well understood. The important result,however, is the agreement of the slopes of the N� vs. Ne relation of both experimentsin quite di�erent energy regions.Sin e in the higher energy region, Ne an not be determined by AGASA, the ��(600)vs. S0(600) relation is used. The result at se � = 1:09 [26℄ is expressed as��(600) = (0:16� 0:01) � S0(600)0:82�0:03: (18)Taking into a ount the relation S0(600) / E0 / N0:9e , the above equation oin ideswith Eq. 17 in the overlapping energy region [26℄. Therefore the slope seems not to hange from 1014:5 eV to 1019 eV. If we take the absolute values of SIBYLL model asused in Dawson et al. [17℄ (refer to Fig. 4 of their paper), the omposition be omesheavier than iron below 1017 eV. This on lusion demonstrates that it is importantto ompare the experimental results with simulations in as wide energy range aspossible. 24

30

ρµ(400 m) in KASCADE-Grande: up to 1018 eV

• bounded by p / Fe (QGSJET-II-02)

•⇒ not much space for higher Nµ

31

32

Extra slides

Pomeron �loops�:

• small at low parton density (∼ G2)

• suppressed at high density:

∼∑∞

n1=0(−χP

dP(s0ey1 ,b1))n1

n1! = e−χPdP(s0e

y1 ,b1)

...

... ...

...

mm

n

1 2

2n1

2

1y ,b

y ,b

1

2Still a �nite correction at large b:

• of importance for σtot, σdiffr

• will lead to smaller 3P-coupling

•⇒ smaller nuclear screening

33

Comparison with RHIC (Brahms Collab.)

0

200

400

600

800

-5 -2.5 0 2.5 5pseudorapidity eta

dn/d

eta Au+Au 200 GeV c.m. → C

0-5%

5-10%

10-20%

20-30%

30-40%40-50%

• inclusive spectra - expressed via PDFs of free hadrons

• eikonal - expressed via 'parton distributions' probed during interaction:

p p

p...

(x, Q )2 (x, Q )2

34

• special role of (anti-) baryons (P. Grieder, 1973):

(anti-)nucleon share 1% (A) & 40% (B)

(don't decay⇒ increase number of 'generations')

35

Good-Walker scheme for di�raction

Low mass di�raction - 2-component eikonal scheme: |a〉 = 1√2|1a〉 + 1√

2|2a〉

|ka〉 - di�ractive eigenstates for hadron a;couple to a Pomeron with di�erent strength λk/a (λk/a + λk/a = 2)

σinelpp (s) =

∫d2b

1

4

2∑i,j=1

[1− e−2λi/p λj/p χ

Ppp(s,b)

]σs−diffrpp (s) = 2

∫d2b

1

4

2∑j=1

[e−λ1/p λj/p χ

Ppp(s,b) − e−λ2/p λj/p χ

Ppp(s,b)

]2

1

4

2∑i,j=1

[1− e−2λi/p λj/p χ

Ppp(s,b)

]=

{1, b→ 0

2χPpp(s, b)− 2 (2− λ1/p λ2/p)

2 (χPpp(s, b))

2 + ..., b→∞

Higher di�raction ⇒ cross sections reduced at high energies (inelastic screening)

Topological cross section (n inelastic sub-processes):

σ(n)ad (s) =

∫d2b

1

4

2∑i,j=1

[2λi/a λj/d χad(s, b)

]nn!

e−2λi/a λj/d χad(s,b)

⇒ larger multiplicity �uctuations in non-di�ractive collisions

Hadron-nucleus scattering (parameter-free) - stronger inelastic screening (A-enhancement)

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Documents

Stability of muon number in EAS calculations · 2008-02-28 · Stability of muon number in EAS calculations S. Ostapchenko University of Karlsruhe, Institute for Nuclear Technology