You wouldn't think that typesetting the Cabibbo-Kobayashi-Maskawa (CKM) matrix's unitarity and normalisation relations would be hard, would you? Well, depending on how anal retentive you are it's either just a case of whacking in the right subscript indices or it's a minor voyage of discovery into how LaTeX doesn't always know best. When it comes to math typesetting I'm quite picky, so you can safely assume that I consider this to be a nice example of the latter!
First, lets try it the näive way. Put this in your LaTeX source, using \usepackage{amsmath} in the document preamble:
\begin{subequations}
\label{eq:CKMUnitarityRelations}
\begin{equation}
V_{ud}V_{ub}^{*} + V_{cd}V_{cb}^{*} + V_{td}V_{tb}^{*} &= 0 \qquad (db) \label{eq:CKMRelnDB} \\
V_{us}V_{ub}^{*} + V_{cs}V_{cb}^{*} + V_{ts}V_{tb}^{*} &= 0 \qquad (ds) \label{eq:CKMRelnDS} \\
V_{ud}V_{us}^{*} + V_{cd}V_{cs}^{*} + V_{td}V_{ts}^{*} &= 0 \qquad (sb) \label{eq:CKMRelnSB}
\end{equation}
%
\noindent and
%
\begin{equation}
V_{ud}V_{td}^{*} + V_{us}V_{ts}^{*} + V_{ub}V_{tb}^{*} &= 0 \qquad (ut) \label{eq:CKMRelnUT} \\
V_{cd}V_{td}^{*} + V_{cs}V_{ts}^{*} + V_{cb}V_{tb}^{*} &= 0 \qquad (ct) \label{eq:CKMRelnCT} \\
V_{ud}V_{cd}^{*} + V_{us}V_{cs}^{*} + V_{ub}V_{cb}^{*} &= 0 \qquad (uc) \label{eq:CKMRelnUC} \\
\end{equation}
\end{subequations}
Here I've divided the relations first into those between rows and then between columns, using the amsmath package to do the subequation labelling, alignment around the equals sign and so on. Here's the output:
Now I don't know about you, but the unequal (math mode) spacing of the flavour indices, the variations in subscript height between conjugated and unconjugated V's and the different widths of the terms look pretty scrappy to me. Let's try to fix these little visual quirks.
Now a more careful approach, using the maybemath, amsmath and hepnicenames packages. This time, we need to put a bunch of definitions in the preamble or in a personal style/package/class:
\usepackage{amsmath,maybemath,hepnicenames}
\DeclareRobustCommand{\mymath}[1]{\ensuremath{\maybebmsf{#1}}}
\DeclareRobustCommand{\CkmElementConj}[2]{\mymath{V_{{#1}{#2}}^{*}}\xspace}
\DeclareRobustCommand{\CkmElement}[2]{\mymath{V_{{#1}{#2}}^{\phantom{*}}}\xspace}
\DeclareRobustCommand{\Vud}{\CkmElement{\Pup}{\Pdown}}
\DeclareRobustCommand{\Vus}{\CkmElement{\Pup}{\Pstrange}}
\DeclareRobustCommand{\Vub}{\CkmElement{\Pup}{\Pbottom}}
\DeclareRobustCommand{\Vcd}{\CkmElement{\Pcharm}{\Pdown}}
\DeclareRobustCommand{\Vcs}{\CkmElement{\Pcharm}{\Pstrange}}
\DeclareRobustCommand{\Vcb}{\CkmElement{\Pcharm}{\Pbottom}}
\DeclareRobustCommand{\Vtd}{\CkmElement{\Ptop}{\Pdown}}
\DeclareRobustCommand{\Vts}{\CkmElement{\Ptop}{\Pstrange}}
\DeclareRobustCommand{\Vtb}{\CkmElement{\Ptop}{\Pbottom}}
\DeclareRobustCommand{\VudConj}{\CkmElementConj{\Pup}{\Pdown}}
\DeclareRobustCommand{\VusConj}{\CkmElementConj{\Pup}{\Pstrange}}
\DeclareRobustCommand{\VubConj}{\CkmElementConj{\Pup}{\Pbottom}}
\DeclareRobustCommand{\VcdConj}{\CkmElementConj{\Pcharm}{\Pdown}}
\DeclareRobustCommand{\VcsConj}{\CkmElementConj{\Pcharm}{\Pstrange}}
\DeclareRobustCommand{\VcbConj}{\CkmElementConj{\Pcharm}{\Pbottom}}
\DeclareRobustCommand{\VtdConj}{\CkmElementConj{\Ptop}{\Pdown}}
\DeclareRobustCommand{\VtsConj}{\CkmElementConj{\Ptop}{\Pstrange}}
\DeclareRobustCommand{\VtbConj}{\CkmElementConj{\Ptop}{\Pbottom}}
%% CKM element pairing for unitarity relations
\newlength{\CKMPairWidth}
\settowidth{\CKMPairWidth}{\Vtd\VtbConj}
\DeclareRobustCommand{\@Vbox}[1]{\makebox[\CKMPairWidth]{#1}}
\DeclareRobustCommand{\VCkmPair}[2]{\ensuremath{\@Vbox{{#1}{#2}}}}
These definitions are mostly for compactness. The definitions of the
CKM elements and conjugates include a superscript phantom
asterisk to make the two take up the same vertical space, and the
\VCkmPair macro fixes each term to be the same width.
The flavour indices are implemented using the quark macros from
my hepnicenames package (in the hepnames
set) to do the particle symbols via commands like \Pcharm.
Here's the output:
Now the equations themselves are written as follows,
\begin{subequations}
\label{eq:CKMUnitarityRelations}
\begin{align}
\VCkmPair{\Vud}{\VubConj} + \VCkmPair{\Vcd}{\VcbConj} +
\VCkmPair{\Vtd}{\VtbConj} &= 0 \qquad (\Pdown\Pbottom) \label{eq:CKMRelnDB} \\
\VCkmPair{\Vus}{\VubConj} + \VCkmPair{\Vcs}{\VcbConj} +
\VCkmPair{\Vts}{\VtbConj} &= 0 \qquad (\Pdown\Pstrange) \label{eq:CKMRelnDS} \\
\VCkmPair{\Vud}{\VusConj} + \VCkmPair{\Vcd}{\VcsConj} +
\VCkmPair{\Vtd}{\VtsConj} &= 0 \qquad (\Pstrange\Pbottom) \label{eq:CKMRelnSB}
\end{align}
%
\noindent and
%
\begin{align}
\VCkmPair{\Vud}{\VtdConj} + \VCkmPair{\Vus}{\VtsConj} +
\VCkmPair{\Vub}{\VtbConj} &= 0 \qquad (\Pup\Ptop) \label{eq:CKMRelnUT} \\
\VCkmPair{\Vcd}{\VtdConj} + \VCkmPair{\Vcs}{\VtsConj} +
\VCkmPair{\Vcb}{\VtbConj} &= 0 \qquad (\Pcharm\Ptop) \label{eq:CKMRelnCT} \\
\VCkmPair{\Vud}{\VcdConj} + \VCkmPair{\Vus}{\VcsConj} +
\VCkmPair{\Vub}{\VcbConj} &= 0 \qquad (\Pup\Pcharm) \label{eq:CKMRelnUC}
\end{align}
\end{subequations}
This approach produces the following output:
Not bad, eh? And that, as they say, is that.