optimization_mass

<mass_function> パラメーターは7個で、a,b,c,d,f,g,h x は (a-b) を意味する u, d, t, b, c, s, ele, muon, tau 8種類の粒子について、

m_u/m_t = ups = ((x)Exp[(x)/3]Sinh[c/3 - cd] + (x)Sinh[cd] - cExp[(x)/3]Cosh[c/3 - cd] + cCosh[cd])/((x)Exp[(x)/3] Sinh[c - cd] + (-x)* Sinh[2c/3 - cd] - cExp[(x)/3] Cosh[c - cd] + cCosh[2c/3 - c*d])/(2.2/173000) // Simplify

  → PDFのp22,式(60)
  /(2.2/173000)は、実験値で得られたm_u/m_tである。
  
  charms = ((x)*Exp[(x)/3]*Sinh[2 c/3 - c*d] + (-x)*Sinh[c/3 - c*d] - 
 c*Exp[(x)/3]*Cosh[2 c/3 - c*d] + 
 c*Cosh[c/3 - c*d])/((x)*Exp[(x)/3] Sinh[c - c*d] + (-x)*
  Sinh[2*c/3 - c*d] - c*Exp[(x)/3] Cosh[c - c*d] + 
 c*Cosh[2*c/3 - c*d])/(1275/173000)
 
 downs = ((a - b)^2 - c^2)/((a - f)^2 - 
 c^2) Sqrt[(f*(-Exp[-2*b/3] + 1))/(b*(-Exp[-2*f/3] + 
    1))] ((a - f)*Exp[(a - f)/3]*Sinh[c/3 - c*d] + (a - f)*
   Sinh[c*d] - c*Exp[(a - f)/3]*Cosh[c/3 - c*d] + 
  c*Cosh[-c*d])/((a - b)*Exp[(a - b)/3] Sinh[c - c*d] + (-a + b)*
   Sinh[2*c/3 - c*d] - c*Exp[(a - b)/3] Cosh[c - c*d] + 
  c*Cosh[2*c/3 - c*d])/(4.7/173000)
  
  stranges = ((a - b)^2 - c^2)/((a - f)^2 - 
 c^2) Sqrt[(f*(-Exp[-2*b/3] + 1))/(b*(-Exp[-2*f/3] + 
    1))] ((a - f)*Exp[(a - f)/3]*Sinh[2 c/3 - c*d] + (-a + f)*
   Sinh[c/3 - c*d] - c*Exp[(a - f)/3]*Cosh[2 c/3 - c*d] + 
  c*Cosh[c/3 - c*d])/((a - b)*
   Exp[(a - b)/3] Sinh[c - c*d] + (-a + b)*Sinh[2*c/3 - c*d] - 
  c*Exp[(a - b)/3] Cosh[c - c*d] + c*Cosh[2*c/3 - c*d])/(95/
 173000)
 
 botoms = ((a - b)^2 - c^2)/((a - f)^2 - 
 c^2) Sqrt[(f*(-Exp[-2*b/3] + 1))/(b*(-Exp[-2*f/3] + 
    1))] ((a - f)*Exp[(a - f)/3]*Sinh[c - c*d] + (-a + f)*
   Sinh[2 c/3 - c*d] - c*Exp[(a - f)/3]*Cosh[c - c*d] + 
  c*Cosh[2 c/3 - c*d])/((a - b)*
   Exp[(a - b)/3] Sinh[c - c*d] + (-a + b)*Sinh[2*c/3 - c*d] - 
  c*Exp[(a - b)/3] Cosh[c - c*d] + c*Cosh[2*c/3 - c*d])/(41.8/
 1730)
 
 electrons = ((a - b)^2 - c^2)/((g - h)^2 - c^2)*

Sqrt[(g*(Exp[2a/3] - 1))/(a(Exp[2g/3] - 1))] Sqrt[(h*(-Exp[-2b/3] + 1))/(b(-Exp[-2h/3] + 1))] ((g - h) Exp[(g - h)/3]Sinh[c/3 - cd] + (g - h)Sinh[cd] - cExp[(g - h)/3]Cosh[c/3 - cd] + cCosh[-cd])/((a - b)Exp[(a - b)/3] Sinh[c - cd] + (-a + b) Sinh[2c/3 - cd] - cExp[(a - b)/3] Cosh[c - cd] + cCosh[2c/3 - c*d])/(0.510999/173000)

  muons = ((a - b)^2 - c^2)/((g - h)^2 - c^2)*

Sqrt[(g*(Exp[2a/3] - 1))/(a(Exp[2g/3] - 1))] Sqrt[(h*(-Exp[-2b/3] + 1))/(b(-Exp[-2h/3] + 1))] ((g - h) Exp[(g - h)/3]Sinh[2c/3 - cd] + (-g + h)Sinh[c/3 - cd] - cExp[(g - h)/3]Cosh[2c/3 - cd] + cCosh[c/3 - cd])/((a - b) Exp[(a - b)/3] Sinh[c - cd] + (-a + b)Sinh[2c/3 - cd] - cExp[(a - b)/3] Cosh[c - cd] + cCosh[2c/3 - c*d])/(105.65/ 173000)

 tauons = ((a - b)^2 - c^2)/((g - h)^2 - c^2)*

Sqrt[(g*(Exp[2a/3] - 1))/(a(Exp[2g/3] - 1))] Sqrt[(h*(-Exp[-2b/3] + 1))/(b(-Exp[-2h/3] + 1))] ((g - h) Exp[(g - h)/3]Sinh[c - cd] + (-g + h)Sinh[2c/3 - cd] - cExp[(g - h)/3]Cosh[c - cd] + cCosh[2c/3 - cd])/((a - b) Exp[(a - b)/3] Sinh[c - cd] + (-a + b)Sinh[2c/3 - cd] - cExp[(a - b)/3] Cosh[c - cd] + cCosh[2c/3 - c*d])/(1776.86/ 173000)