Relation between concentration of sugar in syrup VS its spoil rate My mother recently created a Centella asiatica vegetable juice.    

She states that we should add some sugar (e.g. 2 tea-spoons for 1.5 liter of vegetable water) to reduce the spoil rate of the juice.     

I disagree because I feel that the concentration rate is too low for that - it would increase the spoil rate instead.   However, it bases on just my feeling.

My assumption :- 

I believe water, sugar and honey can be stored almost forever, but syrup has relatively short storage time.        

There has to be some figures of sugar concentration (e.g. X gram of sugar per 1 liter of water) that make the spoilage rate maximum (parabola?), right?

Question :-

How is the relation between sugar concentration and spoil rate?
How much it can be applied to vegetable juice?     

Please also provide some graph/reference/research to support your answer because the belief will impact the rest of my life.     

Edit:
Here is what I interpret Juliana Karasawa Souza's answer :-
For a clear direct response for your question: yes, there is a correlation between sugar concentration and spoil rate. The correlation is actually between any kind of solute and spoil rate, so that's the reason for using salt and sugar as agents for preserving foods. 

The technical name is "water availability" and the maths behind that is "free water equivalent". That's because bacteria and other microorganisms need what we call "free water" to grow and reproduce - if the water is "bound" to other components like sugar or salt, they cannot be used for growing. 

The minimal concentration of sugar is 65% weight by weight if it is a simple solution of sugar in water (a.k.a. simple syrup)

If you want to use less sugar, you have to include other chemicals (called preservative agents) to prevent spoilage and bacterial growth. 

Here is the easiest to digest information I could find for how to do the calculation, without getting into many technical details on the chemical properties