A "water right" is a person's right to use water, which is in a watercourse, stream, lake, and sometimes the ground.
Arkansas follows the "reasonable use" theory of water use by riparian--landowners whose property borders a watercourse, stream, or lake. Landowners may beneficially use water as long as they do not cause unreasonable damage to fellow riparians. Household use is given the highest priority, and use of over 1 acre-foot of water per year requires registration through the Commission or your local conservation district.
Groundwater is also subject to the reasonable use doctrine and to some regulation under the Arkansas Groundwater Protection and Management Act, which provides for the establishment of "critical groundwater areas."
For drainage, the "common enemy doctrine" applies, allowing a landowner to prevent damage to property by runoff without causing damage to neighbors.
Based on the legal analysis in Arkansas courts, the ONLY way you would be able to retain any rights at all to the water in an underground stream is to either be granted an easement to the source by the purchaser or by drilling into the stream from offsite.
And no farmer who purchases such land would do so without the water rights accompanying the sale.