An independent, three-member panel is overseeing the five-day arbitration hearing, which is not open to the public, will shape DP World Tour fields when a decision is released.
The hearing centres around the DP World Tour's conflicting release regulations and its ability to enforce those rules upon members who chose to compete in LIV Golf events.
DP World Tour media officer Scott Crockett, in a briefing with reporters two weeks ago, said the panel would deliver their verdict "several weeks" after the hearing has taken place.
"Will we appeal if we lose? Will they appeal if they lose? Will their players still be able to play on the tour if they are appealing? Unfortunately, the simple and honest answer to all of that is we don't know," said Crockett.
DP World Tour members who competed in the inaugural LIV Golf event last June despite not receiving permission received three-event suspensions and fines.
Ian Poulter, Adrian Otaegui and Justin Harding challenged their suspension and won a stay from a British court last July that allowed them to compete in the Scottish Open.
The 13 players who are named as appellants for the hearing include Poulter, Otaegui, Harding, Patrick Reed, Lee Westwood, Graeme McDowell, Martin Kaymer, Sam Horsfield, Richard Bland, Shaun Norris, Laurie Canter, Wade Ormsby and Bernd Wiesberger.
There were originally 16 golfers who were involved but Sergio Garcia, Charl Schwartzel and Branden Grace all withdrew their names from the hearing case.
The PGA Tour, in a decision released moments after play in the lucrative breakaway series' inaugural event last June, suspended members who played the LIV Golf event and said anyone else who makes the jump will face the same fate.
The $255 million LIV series is being bankrolled by Saudi Arabia's Public Investment Fund, which critics say is a vehicle for the country to try to improve its image in the face of criticism of its human rights record.
