Chanel balance is broken
It's tough to make out what you have from these photos. What I can see is the knife lock shoe, which, while damaged, looks similar to our 15-014.
Assuming this is correct then there is a good chance that you have our Series 751. Right now that's my tentative guess; your next step should be to remove an undamaged version of your balance (knife shoe and all) and carefully compare it to our Series 751. Note the design of the channel, shoe, and everything else and let me know if they differ in any way. We have other options.
I measured the track size is 44", on side of track, there is "19TG", which seems model number.
What size shall I buy?
If the stamp on your old balance is 19TG, then the length should be 20", not 44". That's a huge disparity. I highly recommend that you check the size just to be 100% sure. Make sure you're only measuring the balance itself, not the jamb liner in which it's installed.
You're welcome! Please let me know if we can be of any further assistance.