BEIJING — With the sentencing of Gu Kailai on Monday for the murder of a British businessman, China’s Communist Party leaders are trying to close the book on the deepest political crisis they have faced in two decades.

Now their attention turns to an even more vexing chapter of that process: What to do with Gu’s husband, the once-powerful, now-deposed regional Communist Party leader Bo Xilai.

Bo’s spectacular downfall and the murder mystery entangling his wife this year threw the country’s rulers into turmoil at a particularly sensitive time, ahead of a once-in-a-decade leadership transition in China.

Bo had been campaigning for promotion to China’s highest circle of power — a seat on the nine-member Standing Committee, which essentially controls every lever of power in the country. In pursuit of that goal, he had cultivated allies in the top levels of party leadership, becoming a somewhat polarizing figure. As a result, his fall exposed fissures between the party’s factions, including a clash between supporters of Bo and those backing his competitors.

The rare exposure of such divisions at the higher echelons of the Communist Party is a main reason that its leaders are eager to put the affair behind them.

The rifts go beyond personality and loyalty and involve deep philosophical differences. Bo represented a brash, left-wing, Maoist ideology that was in some ways the antithesis of the party’s market-driven factions. But the overriding goal of the party has remained self-preservation.

For that reason, many experts think that the party’s top officials are trying to resolve the scandal, including the fate of Bo and his former lieutenant Wang Lijun, before the leadership transition begins this fall.

But in doing so, the party faces a conundrum.

Punishment options

If Bo goes largely unpunished, the new leadership would inherit an unresolved and potentially destabilizing issue. Punishing Bo too heavily, on the other hand, would risk angering his ideological allies as well as his fellow “princelings” — influential figures who, like Bo, are the offspring of China’s revolutionary leaders. Either choice could exacerbate existing splits within the party.

That dilemma may be one reason that, conspicuously, Bo was never mentioned in the official coverage of his wife’s trial by state-run media, said Zhang Ming, a political science professor at Renmin University in Beijing.

Party leaders either plan to take a more lenient stance on Bo or have yet to make up their minds, Zhang said. Either way, distancing him from the lurid details of Gu’s sensational murder trial serves their purpose.

“The party certainly has tried to limit the influence of the scandal,” Zhang said.

In many ways, party leaders used Gu’s trial to test the waters and set the stage for their more difficult undertaking with Bo, said Cheng Li, an expert on Chinese leadership at the Brookings Institution.

Since Bo is still a Communist Party member, China’s leaders could punish him politically through party channels, something that could happen quickly. They could also pursue criminal charges against him — a prospect that could take more time and involve much more serious consequences for Bo, a former party chief in Chongqing.