awk script always prints sum=0

I'm sorry if the question might be silly, but I am totally new to awk scripting. What I want to do is to calculate and print the usage of CPU and memory by the user "root". I wrote this bash script which executes an awk script:

#!/bin/bash

ps aux > processi.txt
echo Lancio script3.awk
awk -f script3.awk processi.txt

and the awk script is the following:

#!/usr/bin/awk

BEGIN{
print "Inizio script\n"
cpu=0
mem=0
}

/root/{
    printf("Cpu usata da root loop=%.1f, memoria=%.1f\n",$3,$4)

        cpu=cpu+$3
        mem=mem+$4
}

END{
printf("Cpu usata da root=%.1f, memoria=%.1f\n",$cpu,$mem)
print "\nFine script\n"
}

But the print from the END is 0, while in /root/ is correct. Any advice?