Ballsy move to call HR like that. Best move you could have made in your circumstances. It puts extra sets of eyes on them at work, making it that much more difficult to maintain contact and raises the stakes in risking getting caught. Most likely they get reprimanded and get separated by distance or separate shifts, depending on how they react, maybe one or both gets fired.
Next, have your wife handwrite a no contact letter to the other man stating how horribly ashamed she is of her behavior and how terrible she feels for risking her family, marriage, and husband, which mean more to her than anything in the world, and that if other man ever tries to contact her again, she will file harassment charges against him. This will help you gauge how much she wants to help you heal and how she feels about the other man. Making her handwrite it helps her to realize the severity of her betrayal and helps her get over the other man.
After that, ask your wife for the truth about the affair. It is hard to believe that they worked together, granted in a huge factory, but they had close contact, took breaks together, ate lunch together, presumably they were around other employees who knew them both and knew he was married, but no one ever made a comment in front of or to your wife that gave her any idea that he was or might be married. She was completely in the dark about this? It may be true, but it is not believable.
You can judge that you are getting the truth when it starts to make sense. Does it make sense to you that your wife did not know other man was married? If there are other things that don't make sense to you, push your wife for answers on those, too. Tell your wife that you might like her to take a polygraph if she insists on sticking to stories that are not believable. About 100% of cheaters lie about the affair, minimize how often they had sex, minimize their interest in pursuing the affair partner, and try to paint themselves in a favorable light. Cheaters lie. Assume all your wife's words are lies except those that are supported by her actions. Stop looking at your wife like you know her. You don't. At least for the past year or so, this is a person you don't know. Don't give her the same level of belief and trust that you used to give to that old wife who you knew. This is a new wife and a new marriage. Your old wife and old marriage are gone forever.
Next, tell your wife she must give you access to all communication devices and accounts, all passwords, and let you know her whereabouts 24/7 until she regains your trust.
Tell your wife that you cannot control her, you can only control yourself, what you are willing to accept in your marriage and what you are not, and how you react to her actions.
In general, demand respect for yourself. Do not let her tell you that your lack of attention caused her to cheat. You did nothing deceitful. You were honest with her. She lied and cheated on you. Even if you acknowledge that her complaints are valid, she could have told you how she felt and, if you still didn't change, she could have divorced you.
Add any other requirements you feel you need to heal. Sex? She was giving it to the other man. Has she been denying it to you? This is another way to gauge whether she is moving past the affair and back to the marriage or continuing to pine for the other man.
The things posted here are not unreasonable. They are things that we all expect of a marriage - remaining faithful, being open and honest, not keeping secrets.
If your wife doesn't want to meet your conditions, file for divorce. You will save yourself a lot of time, trouble, and needless pain just to end up in the same place in the end anyway, but at least you'll be able to respect yourself. Sometimes filing for divorce is the wakeup call that a cheater needs to see that the betrayed spouse is serious, especially if the betrayed spouse had been a bit of doormat.
There's a post on here that I liked so much I put it in my signature. It's a list of the correct behaviors that a cheating spouse should do if they really mean to fix things. Have her read it and see if she does them.
Krichali,I have to ditto that. It's a brilliant summary! I've read it several times now and plan to get my CW to read it and then discuss it. Mine is a quite hopeless case. But so are many on this site are.
Swerve, I feel your pain.You're getting a lot of good advice. Do not back down from your heartfelt feelings. Good luck!
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This kind of cosmic dumbassery occupies a temporal plane of ineptitude and lack of reason so profound a Zen master could spend a lifetime meditating upon its philosophical consequences.”
I was in a mood last night when I saw this and said, WTF. I found the site and read through it, and could not figure out why this was being posted.
Now I see why you did it.
L's wife is a hardcore serial cheater, and she doesn't even know why she is the way she is. All she wants is her man to take her back, but he's never going to because he has self control and too much self respect.
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Re: Having major trouble 
