%%----------------------------------------------------------------------------%%
%%---------------------------- Personal Macros -------------------------------%%
%%----------------------------------------------------------------------------%%

%% A central location to add your favorite macros.

%% A few examples to get you started.
\newcommand{\uv}[1]{\ensuremath{\mathbf{\hat{#1}}}}
\newcommand{\bo}{\ensuremath{\mathbf{\Omega}}}
\newcommand{\eref}[1]{Eq.~\ref{#1}}
\newcommand{\fref}[1]{Fig.~\ref{#1}}
\newcommand{\tref}[1]{Table~\ref{#1}}

%%-------------------------------- defs.tex ----------------------------------%%

\newcommand{\TODO}[1]{\textcolor{blue}{\textit{\textbf{TODO:}\ #1}}}

\newcommand{\ie}{\textit{i.e.}\xspace}
\newcommand{\eg}{\textit{e.g.}\xspace}
\newcommand{\cf}{\textit{cf.}\xspace}
\newcommand{\apriori}{\textit{a priori}\xspace}
\WithSuffix\newcommand\apriori*{\textit{a-priori}\xspace}
\newcommand{\aposteriori}{\textit{a posteriori}\xspace}
\newcommand{\adhoc}{\textit{ad hoc}\xspace}
\newcommand{\etal}{\textit{et al.}\xspace}
\newcommand{\perse}{\textit{per se}\xspace}
\newcommand{\etc}{\textit{etc.}\xspace}
\newcommand{\viz}{\textit{viz.}\xspace}
\newcommand{\via}{\textit{via}\xspace}
\newcommand{\qua}{\textit{qua}\xspace}
\newcommand{\viceversa}{\textit{vice versa}\xspace}

\newcommand{\mathspace}{\ \ }
\newcommand{\mathtext}[1]{\mathspace\text{#1}\mathspace}

\newcommand{\fm}{\ensuremath{\mathrm{fm}}}
\newcommand{\fmi}{\ensuremath{\mathrm{fm}^{-1}}}

\newcommand{\vecr}{\mathbf{r}}
\newcommand{\vecx}{\mathbf{x}}
\newcommand{\vecy}{\mathbf{y}}
\newcommand{\vecz}{\mathbf{z}}
\newcommand{\vecn}{\mathbf{n}}
\newcommand{\vecm}{\mathbf{m}}
\newcommand{\vecp}{\mathbf{p}}
\newcommand{\veck}{\mathbf{k}}
\newcommand{\vecq}{\mathbf{q}}
\newcommand{\vece}{\mathbf{e}}
\newcommand{\veca}{\mathbf{a}}
\newcommand{\vecb}{\mathbf{b}}
\newcommand{\vecu}{\mathbf{u}}
\newcommand{\vecv}{\mathbf{v}}

\newcommand{\vecR}{\mathbf{R}}
\newcommand{\vecP}{\mathbf{P}}
\newcommand{\vecK}{\mathbf{K}}
\newcommand{\vecX}{\mathbf{X}}
\newcommand{\vecY}{\mathbf{Y}}
\newcommand{\vecZ}{\mathbf{Z}}

\newcommand{\vZero}{\mathbf{0}}
\newcommand{\vNabla}{\boldsymbol{\nabla}}
\newcommand{\vtheta}{\boldsymbol{\theta}}
\newcommand{\vsigma}{\boldsymbol{\sigma}}

\newcommand{\vdelta}{\delta^{(3)}}

\newcommand{\dd}{\mathrm{d}}

\newcommand{\dx}[1]{\frac{\dd}{\dd #1}}
\newcommand{\dq}[1]{\!\!\frac{\mathrm{d}^3#1}{(2\pi)^3}}

\newcommand{\dqd}[1]{\!\!\frac{\mathrm{d}^d#1}{(2\pi)^d}}

\newcommand{\dn}[1]{\!\frac{\mathrm{d}#1_0}{2\pi}}
\newcommand{\dm}[1]{\!\frac{\mathrm{d}#1}{2\pi}}

\newcommand{\dfq}[1]{\!\!\frac{\mathrm{d}^4#1}{(2\pi)^4}}

\newcommand{\ddq}{\dq{q}}
\newcommand{\ddr}{\mathrm{d}^3r}

\newcommand{\del}[1]{\frac{\partial}{\partial #1}}
\newcommand{\deli}[2]{\frac{\partial^{#2}}{\partial #1^{#2}}}

\newcommand{\gsim}{\gtrsim}
\newcommand{\lsim}{\lesssim}

\newcommand{\ii}{\mathrm{i}}
\newcommand{\ee}{\mathrm{e}}
\newcommand{\vD}{\boldsymbol{D}}
\newcommand{\vcalD}{\boldsymbol{\cal D}}
\newcommand{\hc}{\mathrm{h.c.}}
\newcommand{\OO}{\mathcal{O}}
\newcommand{\ZZ}{\mathbb{Z}}
\newcommand{\RR}{\mathbb{R}}
\newcommand{\CC}{\mathbb{C}}
\newcommand{\YY}{Y}
\newcommand{\YYY}{\scalebox{1.33}{\ensuremath{\mathcal{Y}}}}
\newcommand{\HH}{\mathcal{H}}

\newcommand{\eps}{\varepsilon}
\newcommand{\one}{\mathbbm{1}}
\newcommand{\leviciv}{\epsilon}

\newcommand{\rot}{\mathrm{rot}}
\newcommand{\diag}{\mathrm{diag}}

\newcommand{\Laplace}{\Delta}

\newcommand{\EulerGamma}{C_E}

\newcommand{\Rp}{\mathrm{Re}}
\newcommand{\Ip}{\mathrm{Im}}

\newcommand{\Si}{\mathrm{Si}}
\newcommand{\Ci}{\mathrm{Ci}}
\newcommand{\Li}{\mathrm{Li}}
\newcommand{\LiTwo}{\mathrm{Li}_2}

\newcommand{\mean}[1]{\langle #1\rangle}

\newcommand{\sgn}{\mathrm{sgn}}

\newcommand{\vectornorm}[1]{{\|#1\|}}

\newcommand{\conj}[1]{\overline{#1}}
\newcommand{\abs}[1]{\left|#1\right|}

\newcommand{\CG}[6]{\ensuremath{C^{#5#6}_{#1#2,#3#4}}}

\newcommand{\ThreeJ}[6]{\left(\!\!%
\begin{array}{CCC}%
{#1} & {#3} & {#5} \\%
{#2} & {#4} & {#6}%
\end{array}%
\!\!\right)%
}

\newcommand{\SixJ}[6]{\left\{\!\!%
\begin{array}{CCC}%
{#1} & {#2} & {#3}\\[0.2em]%
{#4} & {#5} & {#6}%
\end{array}%
\!\!\right\}%
}

\newcommand{\couple}[3]{\left({#1}{#2}\right)\!{#3}}

\newcommand{\EB}{-E_B}
\newcommand{\EBp}{E_B}
\newcommand{\EBm}{\EB}

\newcommand{\LL}{\mathcal{L}}

\newcommand{\MN}{M_N}
\newcommand{\Md}{M_d}
\newcommand{\Mpi}{M_\pi}
\newcommand{\ec}{e}

\newcommand{\Mhi}{M_{\text{hi}}}
\newcommand{\Mlo}{M_{\text{lo}}}

\newcommand*\rvec[1]%
{\ensuremath{\overset{\smash{\raisebox{-1.5pt}{\tiny$\rightarrow$}}}{#1}}}
\newcommand*\lvec[1]%
{\ensuremath{\overset{\smash{\raisebox{-1.5pt}{\tiny$\leftarrow$}}}{#1}}}

\newcommand{\vDright}{\rvec{\vD}}
\newcommand{\vDleft}{\lvec{\vD}}

\newcommand{\vk}{\mathbf{k}}
\newcommand{\vp}{\mathbf{p}}
\newcommand{\vq}{\mathbf{q}}
\newcommand{\vx}{\mathbf{x}}
\newcommand{\vy}{\mathbf{y}}
\newcommand{\vz}{\mathbf{z}}
\newcommand{\vA}{\mathbf{A}}
\newcommand{\vj}{\mathbf{j}}
\newcommand{\vP}{\mathbf{P}}
\newcommand{\vK}{\mathbf{K}}
\newcommand{\vX}{\mathbf{X}}
\newcommand{\vB}{\mathbf{B}}

\newcommand{\dqn}{\dn{q}}

\newcommand{\keV}{\ensuremath{\mathrm{keV}}}
\newcommand{\MeV}{\ensuremath{\mathrm{MeV}}}

\newcommand{\atanh}{\mathrm{atanh}}

\newcommand{\tr}{\mathrm{tr}}
\newcommand{\Tr}{\mathrm{Tr}}

\newcommand{\LO}{\text{LO}\xspace}
\newcommand{\NLO}{\text{NLO}\xspace}
\newcommand{\NNLO}{\text{N$^2$LO}\xspace}
\newcommand{\NNNLO}{\text{N$^3$LO}\xspace}

\newcommand{\skrowspace}{0.5em}

\NewEnviron{subalign}[1][]{%
\begin{subequations}\begin{align}
  \BODY
\end{align}\label{#1}\end{subequations}
}

\NewEnviron{spliteq}{%
\begin{equation}\begin{split}
 \BODY
\end{split}\end{equation}
}

\NewEnviron{mleq}{%
\begin{equation}
 \BODY
\end{equation}
}

\newcommand{\ph}{{\phantom{0}}}

\newcommand{\cS}{\mathcal{S}}

\newcommand{\psia}{\psi_{\text{Lo}}}
\newcommand{\psib}{\psi_{\text{Hi}}}
\newcommand{\psiinf}{\psi_{\infty}}
\newcommand{\Om}{\OO}
\newcommand{\Vn}{V_{C,nL}^t}
\newcommand{\Vd}{\Delta V}
\newcommand{\keteta}{\xi}
\renewcommand{\vec}[1]{\mathbf{#1}}

\newcommand{\anc}{A}

\newcommand{\Dil}[2]{D_{#1,#2}}

\newcommand{\maxplus}{\mathbin{\stackrel{\text{max}}{+}}}
\newcommand{\minplus}{\mathbin{\stackrel{\text{min}}{+}}}

\newcommand{\inner}[2]{\langle#1,#2\rangle}
\newcommand{\maxinner}[2]{\inner{#1}{#2}_{\text{max}}}

\newcommand{\dvrsum}[2]{\sum\limits_{#1={-}#2/2}^{#2/2-1}}

\newcommand{\cdd}{{\cdot\cdot}}

\newtheorem{lemma}{Lemma}

\newcommand\abssym[1]{\left|#1\right|}
\newcommand\normsym[1]{\left\Vert#1\right\Vert}
\newcommand\norm[1]{\|#1\|}
\newcommand\parenth[1]{\left(#1\right)}

\newcommand{\Jostf}{\mathcal{F}}

\newcommand{\ny}[1]{\textcolor{gray}{NY: #1}}

\newcommand{\braketmatrix}[3]{\left \langle #1 \middle| #2 \middle| #3 \right \rangle}
