
1) BΥNeˤĤ. Cosmosfull M.C餺
	ϲĤʤǡꤷޤ
	(ϥ֥åɤʷ׻)
	
	㤨С1ryޤξ硥򤤤ʤϲˤĤʤȡ
	ϲɤ餮ʿѲΤ顤
	eventȤ⡤ޤäƱȥ󥸥
	֤ơۤȤɼѤˤϤʤޤ

	ǡŻҤˤʤäʳǲϲˤĤʤȤ
	ͤޤȡεޤǤεΥɤ餮
	ȡŻФˤɤΤ褦˥ͥ륮ʬ뤫ɤ餮
	ޤǤ⤽θ,ŻҤɤΤ褦ȯã뤫
	ɤ餮ޤ

	ǡ⤦γҤΥͥ륮ʬޤ
	ϲˤĤʤΤԤĤȤΤͤޤޤ
	ԤäƤȡfull M.CˤʤΤǡʬɤ餮
	ޤǺʬΤԤĤȤȤˤʤޤ
	ͤȤơʬȻפΤϿƤΥͥ륮Er=1/100Ǥ
	(⤦礭ͤǤ⤴ޤϤǤ礦)ޤ	
	ͤùߤɤ餮礭ΤǡɬŻҤ
	ʤäʳǲϲˤĤʤȤɬפǤ

	ƤơγҤΥͥ륮ʬȡʤˤ
        10MeVȤ100MeVȤŻҤޤϡϲ
	ˤĤʤȤƤ⡤ϲ٤ⰭʤΤȡ
	ȸƤ٤褦ʡʤΤǡΤƤ뤳Ȥˤޤ
	ɤΥͥ륮ʲʤ餹Ƥ뤫ǤEt=1GeVʲʤ
	ƤΤɸǤ(Ϥäȹ⤹ʤȻפäƤޤ)

	Ǥϡ100 GeVŻҤ䥬ͤƥϥ֥åɤˡ
	NeȤɤʤ뤫?
	ϲˤĤʤΤ100 x Er = 1 GeVޤԤġ
	1GeVʲϼΤƤΤǡNe0ȤФޤ(γ
	󤬤ä)ޤȤNeˤEr礭뤫
	(٤~1/20ɤ餮ޤȤʤʤ) Et
	뤫⿮ǤNeޤȤݾ
	Ǥʤΰˤʤޤ

	ϥ֥åɤˡϤɤΥͥ륮ʤ¿?  
	ȯã̵뤷Ƥ褤γҤΥͥ륮Ϥ褽Ƥ10^-4Ǥäơ	
	Et x 10 ^4 =10 TeVʾ ŻҤ䥬ʤ顤ϥ֥åɤˡ
	"¿"(ʲ褦˰¿ϤǤʤ)ƻȤȸȤˤʤޤ

	1ryϥɥξϤȤŻҤˤʤΤϤʤƤΥͥ륮
	ʬ줿ʳʤΤȡγҤ٤ȯΤǡ Er
	1ȤɤǤ⡤TeVʲ˥ϥ֥åɤˡŬѤΤ
	Ǥ

	10TeVʲΥɬFull M.CǤ롥η׻ʤ
	ϤޤäʤϥEt=100MeVޤȤС
	10TeV->1TeVȤ뤳ȤϽ褽CosmosǤEt=1 GeV
	ϸꡥ

2) 10 TeVʾʤ顤ϥ֥åɤˡǵ᤿ꤷƤ褤?
	դɬפʤΤϡBβϲ1ȯãꤷ
	뤳ȤǤޤ1GeVʾŻҤϲˤĤʤΤǡ
	(1GeVʾγҤ϶ι꤫鸫СΤ)
	̤1η׻ǽФΡȲᤷƤ褤Ȥˤʤޤ
	(ޥγ1GeVŻҤɤΤ餤äƹߤäƤ뤫
	1ʬФޤ?)
	
	̾BβǤϥƥ롦ͥ륮Ec=76MeVȤǷ׻
	Ԥ褦Ǥͤǡ嵭Υϥ֥åɤʷ׻ȡ
	1 Full M.C(Emin~1MeV)礦ɤǤϡԤäȹ礤ޤ
	(Full M.Cˤϥƥ롦ͥ륮ȤǰϤʤȤ
	)

	Ǥ3Full M.CEc=76MeVΥϥ֥åɷ׻礦Ȥ
	Ϲ礤ޤγҿϥ˿ľʿ̤ǿȤ
	Υ줿˹ߤäƤγҤηФΥ(ȥå󥰥)ϡ
	濴νΥȥå󥰥꤫ʤĹʤäƤ뤫Ǥ
	θ̤ϡʬ褦ˡ3Ǥϥ1
	᤯ȯãȸȤǤޤִοʥն
	γҿ1꾯ʤʤȤ̤˸ޤ
	Ne(max)θ~20%ˤڤ֤Τǡ1ͤ򤽤Τޤ޻Ȥ
	ȤǤʤȤˤʤޤ
	
	ǥϥ֥åɤʷ׻3ͤ˹碌ˤϡɬ
	ȤȤˤʤޤޤϥΤ碌
	ȡEcä礭ͤˤɬפ롤ȤȤˤʤޤ
	Ne(max) ~(E0/Ec)ʤΤǡ~20%ˤϡEc~91MeVȤʤ
	ʤȤˤʤޤȡնϹ礦
	¾Ǥϥϥ֥åɷ׻Ne䤿˾ʤȤȤˤʤ
	ޤäơΰǹ碌ˤϡǯˤä
	ͤɬפФƤޤ

	󥺥졼ϤˤդΤȤ˵ĤƤ(ȥå
	󥰥˲ݤпƤΥͥ륮ˤʤ뤫ȤΩ줫
	ͻΤǤ)76MeVȤΤ᤮81MeV̤ˤʤȤʤ	
	ȤäƤޤ(CosmosEc76MeV,ߤdefault81MeVˤʤä
	ϥǤ)

        ****************************************
	ߤCosmosǤϤΤ褦ϰڤƤʤΤǡϥ֥åɤ
	׻ФNeͤˤϽʬդɬפǤޤΤη׻
	Ec=76MeVǹԤ줿ȤˤդƲ
        ***************************************

3) ŻҤä򤷤ƤΤǤϡ20~30ǯΥ٥Ǥ¬ˤϥߥ塼(ޤ¿
  ϥϥɥ̵)Ƥޤ餬ɤΤ褦¬ȯã
  ¬Ƥ뤫ȤʤȤʤȤˤʤޤ٥åȤǤϱ򤪤
  θ̤ѶŪѤƤΤǡʤǤ
  ˴ؤƤ⡤GENASβޤˤ񤤤褦ˡ	
  ϥޥʼ(Ĥ)1֤λŻǤ 
	ǤդΥͥ륮,٤ǥŻҡߥ塼
	٥åȤθдäƤΥΥͥ륮
	׻ơϤ롼롥(ɤ餮Τ
	θM.C롼Ǥ)
	full M.CǤäƤѤʤǡ®롼Ǥ
	EpicsǤ˺롥(ȯ̤ϥͥ륮礭ʤ
	㤷ʤ̤EpicsäƤޤ)ͥ륮ϥߥ塼
	󥰥ԡǴơγҿѴƤΤɤ

	дǤιʤ(ΤɤǤȯ̤ΰ㤤
		ۥȥޥؤθ̤ΰ㤤
		ʣγҤ褿Υߥ󥰤ʤɤ̤
		ǹθ)

        ******************
	¸ȤбϤ٤ơ󥰥ԡбطˤΤǡɤΤ褦
	󥰥ԡ¬Τ(٤ξ)ϤäꤷƤְ㤦
	˥եå20%ѤäƤޤΤաޤǤ
	󥰥ԡΰ֤ʤɤ⡤٤ϤȿǤʤ
	եåϵޤʤ
	******************

	 ^^^^^^^^^^^^^^^^^^^	
	˴ؤGENASǤ
		ߥ塼äƤʤޤŻҤޤȤƥ쥹ݥ󥹤
	׻Ƥ롥(NeߤäƤ顤ˤϥޤδͿ줳줢Τǡ
	򤳤ߤˤ쥹ݥ󥹤׻Ƥ롼äǤ
	ʤΤʤޤŻҤʬɤ)
	ͥ륮η׻Landau-Vavilov-Gaussianɤ餮äƤʤ
        ^^^^^^^^^^^^^^^^^^
4)ɤɤɤ

	10TeVʲFull M.C3)θд쥹ݥ󥹤³дǤ
	ߤη׻ѥ餹СϤޤäǽΰǤ
	Τˤ3)Υ롼ޤ˺٤Ǥ

      1000TeVȤʤȡ10000Υ٥Full M.CΤϥɥΤǡ
	ϤꡤGENASɤ٤Ǥ礦ޤ1TeV̤ǤGENASȤ
	褦ˤ뿴յǤäɤǤ礦10TeVʲfull of
	fluctuationΥGENASΤ褦ˡǺƸΤϤʤʤ
	ѤȤΤäȤδۤǤ

	פʤΤϸдΥ쥹ݥ󥹤ʤΤǡϥ֥åɤNeʤɤ
	ĤޤȤɤǤ⤤ȤиǤп
	ߤʤΤǡ10ܰäNeǤ⡤Neʤ顤ŻҤ
	(ߥ塼)дˤΤ褦ʥ쥹ݥ󥹤ФȤ
	бطΤʬɤ϶ǡ
	Ϥꡤ3NeȤäƤΤ
	ɤȤѤϤʤΰ̣ǤϤޤ
	ϥ֥åɡǯҤΤǽλŻ⡥
	Ҥʬ(1ryΥͥ륮ˤäѤʤ
	뤤ϡ¸ʬȤ)Ȥϥϥ֥åɤʥ
	ȯơɤ餮ѻޤθΥץ
	know howΤǡGENASβɤϴñߥ塼˴ؤƤ
	٤know howѤƤޤ

	Zhang᤬ޥʸȤGENASβɤ餹ȤäƤ
	ɤ⤽εۤʤΤǡϤܤïʤȥ
	ͤ

ʬĹʤäΤǡˤǤߤᡥ
¿ȯthreshold顤⥨ͥ륮ޤ
ӤƻȤfashonableɤɤäΤǡCosmosؤȤ߹ߤߤƤޤ
𤦤ԡ
Ϸ̿աCorsikaȤäƤͤءCorsikaΤäƤ뤫ꡤ 90GeVʲGheisha
ȤɤȤäƤޤGheishaä˻ꤹCosmosǤȤ褦ˤʤäƤޤ
defaultǤϤޤGheishaϥͥ륮¸Ų٤¸ʤɤʤäɤǤ
ΤؤΤʤǻȤȡˤäƤϤȤǤʤ̤ǤΤǡդɬפǤ




=========================================================================

2)ޤϥ1ryξ򤻤롥

ˤϡ򲿤餫ˡǵʲơ
ʤ٤ɤ餮ξʤˤ롥ʿѤ
ε§򸫤줬狼ä顤
ε§˽ȯɤ餮
Ĥä롼й®ȯ롼
ȸˡǤ롥

1ryξˤϥߥ塼ʬˤϤʤ
פΤǡphoto hadron production offΤޤޤǤ


äơĴ٤ʬϥޤŻҤǤ롥

ޤǤˡϡ
ֳ֤ߤ¬Ǥδ¬ͤѤ
ܶſ(COG)·ƵʲǤ롥
ǡɤ餮ϸʤʤ롥
ɬפʵ§Ūʥ֤ϵʲȤʿѤ
֤Ǥ롥 ( t^a exp(- bt^c)Τ褦
֤ɤեåȤ; linear exponential)
ɤ餮η׻ɬפʤΤ
1)ʿѤΥ֤¬ͤɤΤ褦
ɤ餤Ǥ뤫ʬ۷ log-gauss뤤
	2log-gaussʤɤɤեåȤ?
2)COGʬ۷Ǥ롥⤿֤ linear
exponentialä

ܶ㤨1MeVʾγҤˤĤƵ
Ȥơ¾ɬפˤʤΤϡ(ʲ)
ǤΥͥ륮ڥȥǤ롥

ƿɽѥ᡼Ȥơ1
ǽФƤ롤
ѥ᡼ȤƻȤȡޤǤǤ

3ȤƤlateral ʬۤƤ
˺ƤϤʤʤ


嵭Τ褦̤ɽƼѥ᡼1ryͥ륮
¸ʬСۤܤϴǤ롥


10TeVʲfull M.CǤ٤Ƥ롥

10TeVʾϡfull M.CHybridȯƱ	
ԤHybridͤ˲򤫤С3ͤˤʤ뤫
§򸫤ͥ륮ι⤤ϡfull M.C
פԤΤϺʤΤǡHybridǥ
ꡤ嵭ε§ŬѤ롥












muonGENASѥƥޥƥå
Τ˥ȥ饤Ȥθʸ񤬽ФƤΤǤҤȤȡ
ʲΤ褦ˤ¿Ω




׷:
1ryμࡤEnergy E0, (sec theta or cos theta) ¬(depth) xcore distantce RͿ줿ߥ塼θĿ̩٤狼ꡤ(ͥ륮) ֤ץ󥰤Ǥ뤳ȡ

1)muѥ᥿饤ˤNeȤΤɤʤ
 	 --> E0, COG(ASȥ󥸥Center of Gravity)ɤ
	     ѥ᡼Ǥ롥

   Nmuʿ<Nmu>Υȥ󥸥ϰʲΤ褦ʴؿɤɽ롥

Ϥޤܰ¤ǡߥ졼ǳɬפꡥ



 Nmu(z) = a z^m  exp(-b z^n)

where  z = x/xm;  x is depth
       xm   = 66.7log10(E0/TeV) + 625 (g/cm^2)
       a = Nm exp(b)
       Nm = 29 E0^0.8 cos^0.61
       b=3.7
       m = bn
       n =0.606E0^0.0417

sec <=1.5̤ޤgood. sec=2Ǥɬפ⡥

  x>150 g/cm^2餫ʤɤȤʤ뤬x>500餤
ɸˤʤ顤sec > 1.5ޤɤĤ뤫⡥
sec  ~ 2Ǥ
	b=9.5
	xm=  ( 66.7log10(E0/TeV) + 600) *0.55
        n  =0.606E0^0.0417 * 0.55
٤˷Ѥɬפ????
heavyλE0ɬפ(뤤ϡheavy˻Ҥ
ʬƤ顤protonμȤ)

ƤʿѤ<Nmu>Ϸޤ뤬ɤ餮ɤ뤫
Nmu/<Nmu>ɤGaussʬۤ򤹤롥Gaussʬۤ
sigmañsamplingƤ⡤showerȯãȤؤʤ
ᡥ

  Nmu/<Nmu>COGؤȡ depth > 400Ǥ

define    <<Nmu>> = < Nmu/<Nmu> >

Ȥ
          <<Nmu>> = (COG/ A)^B
ɤǤ롣ơɤ餮
<<Nmu>>濴ȤgaussʬۤɤǤʬ롥
 (<<Nmu>>0.7 ~ 1.5餤ޤѲ롥)
A, Bsec, E0, depthʤɤδˤؿǡ
	 A ~ 320 ١
	 B ~ 0.22 ~ 0.35
      Gauss ʬۤsigma ~ 0.3
Ȥʤ롥A, Bsigma򤦤ޤѥ᥿饤
1)1ry, E0, sec, depth <Nmu>ᡤ
2) <<Nmu>>COG,A, Bʤɤ롥
3) sigma<<Nmu>> Nmu/<Nmu>sample롥
4) <Nmu>ʬäƤΤǡNmuޤ롥Ȥʤ롥
	ǥȯãȽʬؤΤNmusampling
	ǽ

-------1ʽλ


; ưͥ륮50 MeVʲmuϤۤȤɤʤ¿100MeVʾ塥
	ơд̤ȴ롥ޤǤ
	energy depositΥͥ륮¸⤳ΰǤϾʤ
	Ǥޤϥͥ륮ʬۤˤĤƤܤĤ֤롥

 Rmu:
<Rmu>ᡤCOGȤؤߤ롥
  <Rmu>  ~ exp(-COG/B)

B ~ 700  (¬꤬ǤϾ(depth=200 g/cm^2 -> 440)
	Ǥ礭ʤ(deth =1000 g/cm2-> 790).

def X=R/<Rmu>ʬۤGaussǤʤ

 A x^n exp(-bx^m)

ɤǤ롥AϥΡޥꥼ󥷥Ƿɤ
 Ȥ n, b, mΥƥޥƥåɵᡥ
 n = 0.4 ~2   b ~3  m ~0.5
ˤʤä X > 0.1 ǤϤۤȤɥ˥С
ʷˤʤΤǡx>0.1  X<0.1ʬ⡥
(X<0.1ȤΤϡ褽30m ʲ).











ʬ; T(nsec)

 R Ȥؤɬס

<T>g (gϴʿѤΰ̣)
 <T>g  ~A R^B   (R in m)
ɤǤ롥 A = A(COG) = 0.01,  B=B(COG) ~ 1.7٤

def X=T/<T>gɽؿϤʤʤʪǡñʤΤĤʤ
᤿Τϡ
def Y=log10(X)ʬۤȤꡤ2ĤGauss­ȤΤǤ롥

 dN/dY  = Gauss1(Y) + Gauss2(Y) (1normalize)

 Gauss(Y) = A exp(-( (Y-<Y>)/S)^2/2)

<Y> = <Y>(R)1,2˶̡
  A=A(R),  S=S(R)12̤η
R¸礭ܰ¤Ȥơ

<Y> = 0.5 x log10(R) - 1.4 .

( as R 10 -->1000 )ܰ¤Ȥ
A1 = 0.6 --> 1.0
S1 = 0.9 --> 0.4
A2 = 1.4 ---> 1.0
S2 = 0.9 --> 0.4
A1 =  0.6  ~ 1
Ȥä꤫