You have given the answer yourself by saying that meditation does help in mental relaxation and in physical fitness ...
 
What happens to your productivity when you are not fit physically or mentally disturbed?
Does it go up or down?
 
I think you don't like the word meditation, sounds religious? So maybe you can replace it with relaxation.
 
WORK AND RELAXATION makes music together. They are the up and the down, the yin and the yang, the rhythm of a good life.
 
Over the past 30 years, a tremendous amount of research has been done on relaxation or meditation, and the findings are truly amazing. Relaxation (meditation) can lower blood pressure and cholesterol levels, help prevent heart disease, relieve or even prevent headaches, reduce pain, help control hypertension, help you sleep better and cure insomnia, alleviate panic attacks, improve your ability to come up with creative solutions to problems, increase your memory and ability to learn, improve your energy level, improve your self-esteem, reduce depression, improve your relationships and your health, and make you feel better in general.
 
But the kind of relaxation these folks studied was not what most of us mean when we say, “Yeah, I had a relaxing weekend.” They were studying a more concentrated, more profound form of relaxation, and you cannot get it watching TV. The relaxation that produces those results requires you to relax your mind as well as your body.
 
When you relax like that for twenty minutes once or twice a day, all kinds of good things happen to your body. It's extremely healthy and it feels good. It's psychologically healthy. It's the antidote to stress. People who relax like that have a less intense reaction to stressful situations, and they recover from them faster than people who don't.
 
That kind of change is healthy for your body and good for your relationships and for productivity at work as well, it's just more fun! Stress is unpleasant.
 
I could go on and on — the amount of research on this subject is extensive It works very well, and it's all you need. It's easy and enjoyable. It takes a little time, but it's worth it. This is something that not only has long-term benefits, but also feels good in the short-term.