I'm looking for 20 to zero degree synthetic sleeping bag.
Your temp ratings are confusing. A +15/+20 degree bag is considered for 3-season use. A +10 to zero degree and below are generally used for winter.
If you are looking for an all-in-one bag, then you will struggle to find something that will keep you warm in winter, yet allow you to vent in the 40+ degree summer nights without a weight penalty-- unless you are willing to consider quilts instead of bags? I have a +20 degree FF down bag, and I wouldn't even consider taking the bag on my winter backpacking trips that can see temps in the single digits and below.
Furthermore you are going to struggle to find a lightweight, zero degree synthetic bag, just because synthetic bags, and if fact some down bags, at this rating are not light.
I think for better suggestions you need to state what conditions this bag is going to be used for and then we can give you more substantial advise.