Working on building my first solo recurve. After a few test shots, my string is tracking to the left side of the limb left-of-center toward the same side as the arrow shelf. How to I get my string to track more closely to center-line? Would I do this by filing down the limbtip string grooves more on one side?

Photo included for context and reference, but please keep in mind, the bow is still rough and not in a polished finished state yet, but the photo shows how it's tracking left of center. I haven't filed in the string groove at the limb center yet either.

I'm thinking I can maybe remedy this by filing down the left limbtip string groove more? Not 100% certain though and wanted to check with TradGang first. Thanks in advance. 

Also, the limbs appear to be straight, so I don't think it's twisting, it seems more related to the string grooves.

First off this looks pretty bad. The groove on the weak side already deeper than the other. Is you form new and the first bow off of it. Did you work off a center line laying the Limb out. How's the other end look.
Most times you start out leaving the tips wide and file deeper on one side or the other to get the limbs pulling straight then even up the tips as needed. If the other end looks good then your lay out may be off. Or if the form is new check it for being square and straight.

The other end is doing the exact same, left of center. Should I file more on the right side limbtip string groove?

Even for rough stringing, you need to get the notches square and the same length. Secondly, you should file the belly side of those notches at more of an angle, or round them into the belly in a Y shape...

look at this photo...



You are on the right track deepening the notch on the weak side, but they need to be much closer to the same before you do it. I like to have the tip overlays on before doing my fine tuning....

i have some video i did on tip overlays and adjustments if you like.   Kirk

 

Being your first recurve you are going to find these are much more sensitive to perfect alignment than deep core long bows, and perfect alignment starts with making sure you have everything exactly 90 degrees to the riser block and limb pads if its a TD bow. If your form has a twist in it, or the limbs that are mounted on a riser block are not exactly 90 degrees, you are building a twist into it from the start, and it will be a nightmare to try and get tracking straight.

Even if you use a string or a straight edge to find exact center of the limb tips, they will not track straight if everything isn't evenly 90 degrees from the butts and fades, to the hook.  Limb pads and the limbs need to be carefully checked prior to shaping width profile... On a one piece bow having a flat bench, or piece of granite with zero twist in it to check the limbs from tip to tip for 90 degree uniformity.

https://photos.app.goo.gl/LSwR5rkJjefeic2C6

For more help....You could start out by showing us photos of the bow unstrung and your bow forms you used to build it.    Kirk

Thank you SO much for the advice. I remarked my center line and adjusted my string grooves to be precise and equal. It's now coming back to dead center-line with every shot and let down. I can see now that I can't rough in the string grooves at all, and that they need to be precise from the get go to avoid these mishaps and worries. All is good now. SO THANKFUL! It's shooting like a gem!