Runner is on first base. Ball is hit to second baseman who fields the ball with his bare hand and maintains control of it. The second baseman then touches the runner advancing to 2nd base with his glove hand that does not have the ball in it, but the ball is still in his bare hand. Is the runner out even though he was not physically touched by the ball?

Does the fielder have to physically touch the runner with the ball in order to get the tag out? I couldn't find anything in the rules specific to this situation.

Runner is not out by definition of a legal touch. SSUSA 1.46 legal touch. Runner must be tagged by hand holding ball or glove holding ball, not hold in one and tag with other