3
 f_2=\frac{\sqrt{\frac{s-4 \text{mpsi}^2}{s-4 \text{me}^2}} \left(16 \text{ca} \text{cw} \text{EE}^2 g
   \text{gpsi} s^2 \sqrt{s \left(-4 \text{me}^2+4 \text{mpsi}^2+s\right)} \cos (\theta ) \text{mZ}^8-64
   \text{ca} \text{cw} \text{EE}^2 g \text{gpsi} \text{me}^2 s \sqrt{s \left(-4 \text{me}^2+4
   \text{mpsi}^2+s\right)} \cos (\theta ) \text{mZ}^8+8 \text{ca} \text{cw} \text{EE}^2 g \text{gpsi} s^4
   \cos (\theta ) \text{mZ}^6-32 \text{ca} \text{cw} \text{EE}^2 g \text{gpsi} \text{me}^2 s^3 \cos
   (\theta ) \text{mZ}^6+16 \text{ca} \text{cw} \text{EE}^2 g \text{gpsi} s^2 \sqrt{s \left(-4
   \text{me}^2+4 \text{mpsi}^2+s\right)} \Gamma ^2 \cos (\theta ) \text{mZ}^6-64 \text{ca} \text{cw}
   \text{EE}^2 g \text{gpsi} \text{me}^2 s \sqrt{s \left(-4 \text{me}^2+4 \text{mpsi}^2+s\right)} \Gamma
   ^2 \cos (\theta ) \text{mZ}^6-40 \text{ca} \text{cw} \text{EE}^2 g \text{gpsi} s^3 \sqrt{s \left(-4
   \text{me}^2+4 \text{mpsi}^2+s\right)} \cos (\theta ) \text{mZ}^6+160 \text{ca} \text{cw} \text{EE}^2 g
   \text{gpsi} \text{me}^2 s^2 \sqrt{s \left(-4 \text{me}^2+4 \text{mpsi}^2+s\right)} \cos (\theta )
   \text{mZ}^6-16 \text{ca} \text{cw} \text{EE}^2 g \text{gpsi} s^5 \cos (\theta ) \text{mZ}^4+64
   \text{ca} \text{cw} \text{EE}^2 g \text{gpsi} \text{me}^2 s^4 \cos (\theta ) \text{mZ}^4+8 \text{ca}
   \text{cw} \text{EE}^2 g \text{gpsi} s^4 \Gamma ^2 \cos (\theta ) \text{mZ}^4-32 \text{ca} \text{cw}
   \text{EE}^2 g \text{gpsi} \text{me}^2 s^3 \Gamma ^2 \cos (\theta ) \text{mZ}^4-8 \text{ca} \text{cw}
   \text{EE}^2 g \text{gpsi} s^3 \sqrt{s \left(-4 \text{me}^2+4 \text{mpsi}^2+s\right)} \Gamma ^2 \cos
   (\theta ) \text{mZ}^4+32 \text{ca} \text{cw} \text{EE}^2 g \text{gpsi} \text{me}^2 s^2 \sqrt{s \left(-4
   \text{me}^2+4 \text{mpsi}^2+s\right)} \Gamma ^2 \cos (\theta ) \text{mZ}^4+32 \text{ca} \text{cw}
   \text{EE}^2 g \text{gpsi} s^4 \sqrt{s \left(-4 \text{me}^2+4 \text{mpsi}^2+s\right)} \cos (\theta )
   \text{mZ}^4-128 \text{ca} \text{cw} \text{EE}^2 g \text{gpsi} \text{me}^2 s^3 \sqrt{s \left(-4
   \text{me}^2+4 \text{mpsi}^2+s\right)} \cos (\theta ) \text{mZ}^4-8 a \text{ca} \text{cv} g^2
   \text{gpsi}^2 s^3 \sqrt{s \left(-4 \text{me}^2+4 \text{mpsi}^2+s\right)} \sqrt{\text{mZ}^4+\left(\Gamma
   ^2-2 s\right) \text{mZ}^2+s^2} \cos (\theta ) \text{mZ}^4+32 a \text{ca} \text{cv} g^2 \text{gpsi}^2
   \text{me}^2 s^2 \sqrt{s \left(-4 \text{me}^2+4 \text{mpsi}^2+s\right)} \sqrt{\text{mZ}^4+\left(\Gamma
   ^2-2 s\right) \text{mZ}^2+s^2} \cos (\theta ) \text{mZ}^4+8 \text{ca} \text{cw} \text{EE}^2 g
   \text{gpsi} s^6 \cos (\theta ) \text{mZ}^2-32 \text{ca} \text{cw} \text{EE}^2 g \text{gpsi} \text{me}^2
   s^5 \cos (\theta ) \text{mZ}^2-8 \text{ca} \text{cw} \text{EE}^2 g \text{gpsi} s^5 \sqrt{s \left(-4
   \text{me}^2+4 \text{mpsi}^2+s\right)} \cos (\theta ) \text{mZ}^2+32 \text{ca} \text{cw} \text{EE}^2 g
   \text{gpsi} \text{me}^2 s^4 \sqrt{s \left(-4 \text{me}^2+4 \text{mpsi}^2+s\right)} \cos (\theta )
   \text{mZ}^2-8 a \text{ca} \text{cv} g^2 \text{gpsi}^2 s^5 \sqrt{\text{mZ}^4+\left(\Gamma ^2-2 s\right)
   \text{mZ}^2+s^2} \cos (\theta ) \text{mZ}^2+32 a \text{ca} \text{cv} g^2 \text{gpsi}^2 \text{me}^2 s^4
   \sqrt{\text{mZ}^4+\left(\Gamma ^2-2 s\right) \text{mZ}^2+s^2} \cos (\theta ) \text{mZ}^2+8 a \text{ca}
   \text{cv} g^2 \text{gpsi}^2 s^4 \sqrt{s \left(-4 \text{me}^2+4 \text{mpsi}^2+s\right)}
   \sqrt{\text{mZ}^4+\left(\Gamma ^2-2 s\right) \text{mZ}^2+s^2} \cos (\theta ) \text{mZ}^2-32 a \text{ca}
   \text{cv} g^2 \text{gpsi}^2 \text{me}^2 s^3 \sqrt{s \left(-4 \text{me}^2+4 \text{mpsi}^2+s\right)}
   \sqrt{\text{mZ}^4+\left(\Gamma ^2-2 s\right) \text{mZ}^2+s^2} \cos (\theta ) \text{mZ}^2\right) \theta
   \left(s-4 \text{mpsi}^2\right)}{256 \text{cw}^2 \text{mZ}^4 \pi ^2 s^3 \left(\text{mZ}^4+\left(\Gamma
   ^2-2 s\right) \text{mZ}^2+s^2\right)^{3/2}}
2
  • 6
    Let me guess: This was generated by some computer algebra system, Maple perhaps? – Harald Hanche-Olsen Apr 13 '19 at 20:13
  • 4
    I don't think breaking the equation into separate lines will help with the readability. It's a mess. Go back to maple and try to find a better output. Or start by finding where the fraction switches, and print the numerator and denominator separately. – Teepeemm Apr 13 '19 at 20:34
5

First, the source needs to be broken up inserting line breaks at suitable places so you can get some idea of the total structure of the formula. An editor that will show you matching parentheses and highlight text according to chosen patterns is a great help here.

It turns out that the formula is a fraction in which most of the text is a parenthesised expression in the denumerator. That needs to be taken out, named, and typeset explicitly. I chose to call this expression Ξ.

Also, there are lots of unnecessary \left\right pairs. I deleted those. Further, I replaced \text by the more appropriate \mathrm. I ended up with the following code. It's a complete, compilable latex document. It still has multiple issues that need to be dealt with before you have a readable output. Most importantly, all the multicharacter variable names need some spacing around them. Use \, for that.

\documentclass{article}
\usepackage{mathtools,amsfonts}
\allowdisplaybreaks[1]
\begin{document}
\begin{equation} 
  f_2=\frac{
    \sqrt{\frac{s-4 \mathrm{mpsi}^2}{s-4 \mathrm{me}^2}}
    \Xi \theta  (s-4 \mathrm{mpsi}^2)}
  {256 \mathrm{cw}^2 \mathrm{mZ}^4 \pi ^2 s^3
    (\mathrm{mZ}^4
    +(\Gamma ^2-2 s) \mathrm{mZ}^2+s^2)^{3/2}}
\end{equation}
where
\begin{align*}
  \Xi&=16 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g
     \mathrm{gpsi} s^2
     \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
     \cos (\theta ) \mathrm{mZ}^8
  \\&
  -64 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g \mathrm{gpsi} \mathrm{me}^2 s
  \sqrt{s (-4 \mathrm{me}^2 +4 \mathrm{mpsi}^2+s)} \cos (\theta ) \mathrm{mZ}^8
  +8 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g \mathrm{gpsi} s^4
  \cos (\theta ) \mathrm{mZ}^6
  \\&
  -32 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g \mathrm{gpsi} \mathrm{me}^2 s^3 \cos
  (\theta ) \mathrm{mZ}^6
  \\&
  +16 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g \mathrm{gpsi} s^2
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \Gamma ^2 \cos (\theta ) \mathrm{mZ}^6
  \\&
  -64 \mathrm{ca} \mathrm{cw}
  \mathrm{EE}^2 g \mathrm{gpsi} \mathrm{me}^2 s
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \Gamma ^2 \cos (\theta ) \mathrm{mZ}^6
  \\&
  -40 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2
  g \mathrm{gpsi} s^3
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \cos (\theta ) \mathrm{mZ}^6
  \\&
  +160 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g
  \mathrm{gpsi} \mathrm{me}^2 s^2
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)} \cos (\theta )
  \mathrm{mZ}^6
  \\&
  -16 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2
  g \mathrm{gpsi} s^5 \cos (\theta ) \mathrm{mZ}^4
  \\&
  +64 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g \mathrm{gpsi} \mathrm{me}^2 s^4
  \cos (\theta ) \mathrm{mZ}^4
  \\&
  +8 \mathrm{ca}
  \mathrm{cw} \mathrm{EE}^2 g \mathrm{gpsi} s^4 \Gamma ^2 \cos (\theta ) \mathrm{mZ}^4
  \\&
  -32 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g \mathrm{gpsi} \mathrm{me}^2
  s^3 \Gamma ^2 \cos (\theta ) \mathrm{mZ}^4
  \\&
  -8 \mathrm{ca} \mathrm{cw}   \mathrm{EE}^2 g \mathrm{gpsi} s^3
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \Gamma ^2 \cos (\theta ) \mathrm{mZ}^4
  \\&
  +32 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2
  g \mathrm{gpsi} \mathrm{me}^2 s^2
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \Gamma ^2 \cos (\theta ) \mathrm{mZ}^4
  \\&
  +32 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g \mathrm{gpsi} s^4
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \cos (\theta ) \mathrm{mZ}^4
  \\&
  -128 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2
  g \mathrm{gpsi} \mathrm{me}^2 s^3
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \cos (\theta ) \mathrm{mZ}^4
  \\&
  -8 a \mathrm{ca} \mathrm{cv} g^2 \mathrm{gpsi}^2 s^3
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \sqrt{\mathrm{mZ}^4+(\Gamma ^2-2 s) \mathrm{mZ}^2+s^2}
  \cos (\theta ) \mathrm{mZ}^4
  \\&
  +32 a \mathrm{ca} \mathrm{cv} g^2 \mathrm{gpsi}^2
  \mathrm{me}^2 s^2
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \sqrt{\mathrm{mZ}^4+(\Gamma ^2-2 s) \mathrm{mZ}^2+s^2}
  \cos (\theta ) \mathrm{mZ}^4
  \\&
  +8 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g
  \mathrm{gpsi} s^6 \cos (\theta ) \mathrm{mZ}^2
  -32 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g \mathrm{gpsi} \mathrm{me}^2
  s^5 \cos (\theta ) \mathrm{mZ}^2
  \\&
  -8 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g \mathrm{gpsi} s^5
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \cos (\theta ) \mathrm{mZ}^2
  \\&
  +32 \mathrm{ca} \mathrm{cw} \mathrm{EE}^2 g
  \mathrm{gpsi} \mathrm{me}^2 s^4
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)} \cos (\theta )
  \mathrm{mZ}^2
  \\&
  -8 a \mathrm{ca} \mathrm{cv} g^2 \mathrm{gpsi}^2 s^5
  \sqrt{\mathrm{mZ}^4+(\Gamma ^2-2 s)
  \mathrm{mZ}^2+s^2} \cos (\theta ) \mathrm{mZ}^2
  \\&
  +32 a \mathrm{ca} \mathrm{cv} g^2 \mathrm{gpsi}^2 \mathrm{me}^2 s^4
  \sqrt{\mathrm{mZ}^4+(\Gamma ^2-2 s) \mathrm{mZ}^2+s^2}
  \cos (\theta ) \mathrm{mZ}^2
  \\&
  +8 a \mathrm{ca}
  \mathrm{cv} g^2 \mathrm{gpsi}^2 s^4
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \sqrt{\mathrm{mZ}^4+(\Gamma ^2-2 s) \mathrm{mZ}^2+s^2}
  \cos (\theta ) \mathrm{mZ}^2
  \\&
  -32 a \mathrm{ca}
  \mathrm{cv} g^2 \mathrm{gpsi}^2 \mathrm{me}^2 s^3
  \sqrt{s (-4 \mathrm{me}^2+4 \mathrm{mpsi}^2+s)}
  \sqrt{\mathrm{mZ}^4+(\Gamma ^2-2 s) \mathrm{mZ}^2+s^2}
  \cos (\theta ) \mathrm{mZ}^2
\end{align*}
\end{document}
5

There are a lot of repeated items in your equation. I suggest you do something like the following, which (a) eliminates all left and \right sizing directives (this is necessary because \left and \right disallow line breaks) and expresses f_2 as the product and ratio of less-complex items. The repeated items are treated as new variables named \psi, \phi, \kappa, and \lambda; you're obviously free to come up with more descriptive variable names.

enter image description here

\documentclass{article}
\usepackage{mathtools}
\newcommand\vn[1]{\mathrm{\,#1}}
\begin{document}
\noindent
Put
$\psi=\sqrt{\smash[b]{s (-4 \vn{me}^2+4 \vn{mpsi}^2+s)}}$,
$\phi=\sqrt{\smash[b]{\vn{mZ}^4 +(\Gamma^2-2 s) \vn{mZ}^2+s^2}}$,
$\kappa= \vn{ca} \vn{cw} \vn{EE}^2\, g \vn{gpsi}\cos\theta$, and
$\lambda=\vn{ca} \vn{cv}\, g^2 \vn{gpsi}^2\cos\theta$.
Then 
\begin{align*}
f_2 &=u\cdot v\cdot \theta(s-4 \vn{mpsi}^2)/w, \\
\shortintertext{where}
u &= \biggl(\frac{s-4 \vn{mpsi}^2}{s-4 \vn{me}^2}\biggr)^{\!1/2} \\
v &=\begin{aligned}[t]
    &16  \kappa s^2 \psi  \vn{mZ}^8
     -64 \kappa \vn{me}^2 s \psi  \vn{mZ}^8
  \\&+8  \kappa s^4 \vn{mZ}^6
     -32 \kappa \vn{me}^2 s^3  \vn{mZ}^6
  \\&+16 \kappa s^2 \psi \Gamma^2  \vn{mZ}^6
     -64 \kappa \vn{me}^2 s \psi \Gamma^2  \vn{mZ}^6
  \\&-40 \kappa s^3 \psi  \vn{mZ}^6
     +160\kappa \vn{me}^2 s^2 \psi  \vn{mZ}^6
  \\&-16 \kappa s^5  \vn{mZ}^4
     +64 \kappa \vn{me}^2 s^4  \vn{mZ}^4
  \\&+8  \kappa s^4 \Gamma^2  \vn{mZ}^4
     -32 \kappa \vn{me}^2 s^3 \Gamma^2  \vn{mZ}^4
  \\&-8  \kappa s^3 \psi \Gamma^2  \vn{mZ}^4
     +32 \kappa \vn{me}^2 s^2 \psi \Gamma^2  \vn{mZ}^4
  \\&+32 \kappa s^4 \psi  \vn{mZ}^4
     -128\kappa \vn{me}^2 s^3 \psi  \vn{mZ}^4
  \\&+8  \kappa s^6  \vn{mZ}^2
     -32 \kappa \vn{me}^2 s^5  \vn{mZ}^2
  \\&-8  \kappa s^5 \psi  \vn{mZ}^2
     +32 \kappa \vn{me}^2 s^4 \psi  \vn{mZ}^2
  \\&-8 a\lambda s^3 \psi \phi  \vn{mZ}^4
     +32a\lambda \vn{me}^2 s^2 \psi \phi  \vn{mZ}^4
  \\&-8 a\lambda s^5 \phi  \vn{mZ}^2
     +32a\lambda \vn{me}^2 s^4 \psi   \vn{mZ}^2
  \\&+8 a\lambda s^4 \psi \phi   \vn{mZ}^2
     -32a\lambda \vn{me}^2 s^3 \psi \phi  \vn{mZ}^2   
  \end{aligned}\\
\shortintertext{and}
 w &=256 \vn{cw}^2 \vn{mZ}^4 \pi^2 s^3 \phi^3/\cos^3\theta
 \end{align*}
\end{document}

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