Where does the white space comes from (tikzmark)?

Question

I am coming from this answer of mine:

https://tex.stackexchange.com/a/394628/120578

The code is:

\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{calc}
%opening
\title{}
\author{}
\def\tikzmark#1{\begin{tikzpicture}[remember picture]\node(#1){};\end{tikzpicture}}


\makeatletter
\renewcommand\vec[1]{\ifdefined\xsh\relax\else\pgfmathsetmacro\xs{\f@size/3}\def\xsh{\xs pt}\fi\ifdefined\ysh\relax\else\pgfmathsetmacro\ys{\f@size/1.3}\xdef\ysh{\ys pt}\fi\tikzmark{VecStart}#1\tikzmark{VecStop}\begin{tikzpicture}[remember picture,overlay]\draw[->,>=stealth]($(VecStart)+(\xsh,\ysh)$)--($(VecStop)+(-\xsh,\ysh)$);\end{tikzpicture}\let\xsh=\undefined\let\ysh=\undefined}
\makeatother
\begin{document}

$\vec{AB}$

\xdef\xsh{5pt}
\xdef\ysh{14pt}
$$\displaystyle\int\vec{\displaystyle\frac{AB}{3}}dx$$

\end{document}

As you can see in the picture:

there is white space before and after the tikzmark.

Where did that space came from? If I change my tikzmark to:

\def\tikzmark#1{\tikz[remember picture]\node(#1){};}

I get exactly the same result.

A boundy of 50 will be offered after the acception of the answer (I want an explanation for the spaces and how can be avoided... I don't really care for other methods of the same result. Just want to understand where these spaces came from).

Answer 1

By using \coordinate instead of \node you take up no space. I also checked to see if the \hbox{} created by tikz had any effect, but couldn't tell by eye.

\documentclass[a4paper,10pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{calc}
%opening
\title{}
\author{}
\def\tikzmark#1{\begin{tikzpicture}[remember picture]\coordinate(#1);\end{tikzpicture}}


\makeatletter
\renewcommand\vec[1]{\ifdefined\xsh\relax
  \else
    \pgfmathsetmacro\xs{\f@size/3}%
    \def\xsh{\xs pt}%
  \fi
  \ifdefined\ysh\relax
  \else
    \pgfmathsetmacro\ys{\f@size/1.3}%
    \xdef\ysh{\ys pt}%
  \fi
  \tikzmark{VecStart}#1\tikzmark{VecStop}%
  \begin{tikzpicture}[remember picture,overlay]
    \draw[->,>=stealth]($(VecStart)+(\xsh,\ysh)$)--($(VecStop)+(-\xsh,\ysh)$);
  \end{tikzpicture}%
  \let\xsh=\undefined
  \let\ysh=\undefined}
\makeatother
\begin{document}

$\vec{AB}$

\xdef\xsh{0pt}%
\xdef\ysh{14pt}%
$$\displaystyle\int\vec{\displaystyle\frac{AB}{3}}dx$$
$$\displaystyle\int\null\frac{AB}{3}\null dx$$
$$\displaystyle\int\frac{AB}{3} dx$$

\end{document}