Jodi Arias back in court Tuesday for death penalty argument

(CBS/AP) PHOENIX - As she awaits a decision by prosecutors on the future of her murder case, Jodi Arias and her attorneys are returning to court Tuesday to ask the judge to throw out the jury's finding that made her eligible for the death penalty.

TIMELINE: Jodi Arias murder case

PICTURES: Slain boyfriend of Jodi Arias

According to CBS affiliate KPHO, defense attorneys Kirk Nurmi and Jennifer Willmott and prosecutor Juan Martinez are scheduled to be at the morning hearing to discuss the penalty phase and a possible retrial.

Arias was convicted of first-degree murder May 8 in the stabbing and shooting death of Travis Alexander in his suburban Phoenix home. About two weeks later, the same jury failed to reach a unanimous decision on whether to sentence Arias to life in prison or death.

Her case is now in limbo as prosecutors decide whether to put on another penalty phase with a new jury in pursuit of the death penalty - or simply take the death penalty off the table, a move that would either see Arias spend the rest of her life behind bars or be eligible for release after 25 years. That decision would be up to the judge.

The oral arguments Tuesday focus on a determination by the Arias jury that she killed her one-time lover in an "especially cruel" manner. The determination meant that Arias was eligible for the death penalty.

Arias, 33, admitted she killed Alexander, but claimed it was self-defense after he attacked her. Prosecutors argued it was premeditated murder carried out in a jealous rage after the victim wanted to end their affair and planned a trip to Mexico with another woman.

Complete coverage of the Jodi Arias case on Crimesider