Ahmed - unless the sandy soils are very acidic or water logged (which I doubt in your case), they will tend to contain less organic matter than more medium or fine textured soils under the same climate/management. This is because organic matter can become occluded (or hidden) and protected from degradation by soil organisms though its association with fine clay particles. So organic matter turnover is higher and accumulation lower is sandy soils than in fine soils (this is made worse in climates that encourage microbial degradation). Also if the soil has been under agriculture for a long time, organic matter content will decline as rate of turnover and loss is higher than inpuuts from residues, There are some classic long term experiments in the UK that demonstrate these effects over decades of monitoring - search for Broadbalk and Woburn (more sandy site) experiments.
There may be many reasons for low total organic carbon in loamy sandy soils where you mentioned empty farm and no vegetation:
1. Less or meagre crop residues on the soil surface, Therefore, increasing attention should be given to cropping systems in such soil where residues are allowed to remain on the soil surface following harvest, such as in conservation tillage or zero tillage.
2. Less microbial biomass. Loamy sandy soils devoid of vegetation has less microbial biomass. The size of the microbial biomass carbon may account for 2% of the total soil C.
3. Less below ground soil components, Below ground compounds such as roots are mostly absent or their contribution is negligible to organic matter in such types of soil.
4. In loamy sandy soil most of the organic matter are stable humus, a major part can not be extracted and termed as residual fraction.
5. Contribution from animals and waste product of animals is less towards organic matter in such soils.
6. The other factors may be excessive tillage, imbalanced fertilizer use, severe soil degradation and prevalence of tropical, sub-tropical, arid and semi-arid climatic conditions.
You have some very good responses already. I would just add that the soil texture- not sure if you meant a loamy sand, or sandy loam (?) is separate from the soil organic fraction. Soil organic matter is typically 58% soil carbon. The less organic additions you have from microorganisms, root exudates, or management, the lower your SOM and SOC will be. Higher loss of soil carbon (respiration) with increases in temperature and may be a concern with global warming.
In case of loamy sand soils, say regions in punjab, have very low organic carbon around .25-.35% and even with intensive cultivation and higher inputs, the organic carbon content seems to be stabilized and do no show trend of increase
In punjab soils, the higher productivity is due to higher inputs, relatively higher solar radiation and comparatively lower temperatures