latqcdtools.physics.runningCoupling
=============

`CA(Nc) -> float`
 
    Casimir operator of adjoint representation of SU(Nc).

    Args:
        Nc (int): Number of colors.

    Returns:
        float : CA 
    
`CF(Nc) -> float`
 
    Casimir operator of defining representation of SU(Nc).

    Args:
        Nc (int): Number of colors.

    Returns:
        float : CF 
    
`b0(Nf, Nc=3) -> float`
 
    Universal one-loop beta coefficient for SU(Nc), expansion in g.  

    Args:
        Nf (int): Number of active quark flavors. 
        Nc (int): Number of colors.

    Returns:
        float : b0 
    
`b1(Nf, Nc=3) -> float`
 
    Universal two-loop beta coefficient for SU(Nc), expansion in g. 

    Args:
        Nf (int): Number of active quark flavors.
        Nc (int): Number of colors.

    Returns:
        float : b1 
    
`b2_dimreg_MSbar(Nf, Nc=3) -> float`
 
    Three-loop beta coefficient for SU(Nc) using dimensional regularization in MS-bar scheme. 

    Args:
        Nf (int): Number of active quark flavors.
        Nc (int): Number of colors.

    Returns:
        float : b2_MS-bar (dim reg) 
    
`b3_dimreg_MSbar(Nf, Nc=3) -> float`
 
    Four-loop beta coefficient for SU(Nc) using dimensional regularization in MS-bar scheme. 

    Args:
        Nf (int): Number of active quark flavors.
        Nc (int): Number of colors.

    Returns:
        float : b3_MS-bar (dim reg) 
    
`beta_func(beta, Nf=3) -> float`
 
    QCD asymptotic scaling relation to two loops.

    Args:
        beta (float-like)
        Nf (int, optional): Number of active quark flavors. Defaults to 3.

    Returns:
        float: f_as(beta)