Hat notation

You could also try \textsuperscript{$\wedge$} which yields:

To put this into context, (\textsuperscript{$\wedge$}N225), will yield:

The question wasn't "should it be done?" But, for the same reason men climb mountains, "could it be done?" The answer, with the scalerel package, is yes. Thus, we introduce \reallywidehat [EDITED to add phantom rule below argument, so that baseline of result matches baseline of original argument. RE-EDITED to \ensuremath on the \widthof calculation (thanks to Thruston)]

See also my answer at Serious problem with \widebar for a related approach.

NEW ANSWER WITH stackengine

This answer is an improvement because it handles vertical space much better than the earlier solution.

\documentclass{article}
\usepackage{scalerel,stackengine}
\stackMath
\newcommand\reallywidehat[1]{%
\savestack{\tmpbox}{\stretchto{%
  \scaleto{%
    \scalerel*[\widthof{\ensuremath{#1}}]{\kern-.6pt\bigwedge\kern-.6pt}%
    {\rule[-\textheight/2]{1ex}{\textheight}}%WIDTH-LIMITED BIG WEDGE
  }{\textheight}% 
}{0.5ex}}%
\stackon[1pt]{#1}{\tmpbox}%
}
\parskip 1ex
\begin{document}

$\reallywidehat{zbcdefghijklm}$

$\reallywidehat{zbcdefghijk}$

$\reallywidehat{zbcdefghi}$

$\reallywidehat{zbcdefg}$

$\reallywidehat{zbcde}$

$\reallywidehat{zbc}$

$\reallywidehat{zb}$

$x\cdot\reallywidehat{a_1+a_2}\cdot y$

\end{document}

ALTERNATE ANSWER USING \mathchar"0362 (the \widehat accent) RATHER THAN \bigwedge

EDITED to use \mathchar"0362 rather than the normal carat accent (\mathchar"305E)

A comment requested this alternate form, which is perhaps superior to the given form above.

\documentclass{article}
\usepackage{scalerel,stackengine}
\stackMath
\newcommand\reallywidehat[1]{%
\savestack{\tmpbox}{\stretchto{%
  \scaleto{%
    \scalerel*[\widthof{\ensuremath{#1}}]{\kern.1pt\mathchar"0362\kern.1pt}%
    {\rule{0ex}{\textheight}}%WIDTH-LIMITED CIRCUMFLEX
  }{\textheight}% 
}{2.4ex}}%
\stackon[-6.9pt]{#1}{\tmpbox}%
}
\parskip 1ex
\begin{document}

$\reallywidehat{zbcdefghijklm}$

$\reallywidehat{zbcdefghijk}$

$\reallywidehat{zbcdefghi}$

$\reallywidehat{zbcdefg}$

$\reallywidehat{zbcde}$

$\reallywidehat{zbc}$

$\reallywidehat{zb}$

$x\cdot\reallywidehat{a_1+a_2}\cdot y$

$\widehat{zb}$ is actual widehat

\end{document}

EARLIER ANSWER WITH array

\documentclass{article}
\usepackage{scalerel}

\newcommand\reallywidehat[1]{\arraycolsep=0pt\relax%
\begin{array}{c}
\stretchto{
  \scaleto{
    \scalerel*[\widthof{\ensuremath{#1}}]{\kern-.5pt\bigwedge\kern-.5pt}
    {\rule[-\textheight/2]{1ex}{\textheight}} %WIDTH-LIMITED BIG WEDGE
  }{\textheight} % 
}{0.5ex}\\           % THIS SQUEEZES THE WEDGE TO 0.5ex HEIGHT
#1\\                 % THIS STACKS THE WEDGE ATOP THE ARGUMENT
\rule{-1ex}{0ex}
\end{array}
}

\begin{document}

$\reallywidehat{zbcdefghijklm}$

$\reallywidehat{zbcdefghijk}$

$\reallywidehat{zbcdefghi}$

$\reallywidehat{zbcdefg}$

$\reallywidehat{zbcde}$

$\reallywidehat{zbc}$

$\reallywidehat{zb}$

$x\cdot\reallywidehat{a_1+a_2}\cdot y$

\end{document}