muonGENASѥƥޥƥå


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

Τ˥ȥ饤Ȥθʸ񤬽ФƤΤǤҤȤȡ
ʲΤ褦ˤ¿Ω


1)muѥ᥿饤ˤNeȤΤǤϤʤ
 	 --> 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>ϤʤɤGaussʬۤ򤹤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








 






