American military leaders believe that long-standing differences between the Arabs and Kurds in northern Iraq will lead to violence if all U.S. troops leave that area by Dec. 31, as planned, according to a new study by the Rand Corp.

“Without significant U.S. involvement — and perhaps even with it, given enough time — Arab and Kurdish participants will eventually have a dispute that leads to violence, which will cause the mechanism to degrade or collapse,” according to the Defense Department-funded study for the U.S. command in Iraq that Rand released last week.

The study concludes in part that “unless and until [Iraqi] politicians succeed in addressing the strategic challenges that destabilize the region, a U.S. military presence will be needed in northern Iraq to prevent such a breakdown.”

This reminder of trouble in northern Iraq arrives as Shiite and Sunni elements are continuing to commit violent acts against each other in the southern part of the country, illustrating the problems facing the Baghdad government as it wrestles with the political impact of seeking a residual U.S. combat force to remain in the country after year’s end.

According to the Rand study, conflicts dividing the Arabs, Kurds, Turkmens and other elements of the northern population reflect Iraq’s most complex and contentious political challenges.

They involve disputes over provincial boundaries that go back to the Saddam Hussein regime, when the dictator tried to subdue Kurdish opposition by forced relocation of Arabs into the area.

Complicating today’s situation was the movement of Kurds back into the area after the U.S.-led invasion of 2003, and Kurds taking military control of even more territory.

There also are deep questions over the status of Kirkuk, the largest city in the area, where a census, long delayed, was supposed to determine who could vote in a referendum on the city’s future. Arabs and Turkmens questioned participation of newly arrived Kurds, and the issue has yet to be resolved.

Increasing the city’s importance is the fact it “sits directly on top of the largest oil fields in the region — making the territory a very lucrative asset,” according to the study. Since the boundary issues remain, there exists a dispute over whether petroleum from these fields comes under the jurisdiction of the Kurdish regional government or that of the central government in Baghdad.

Finally, and perhaps most important today, is the question of area security. There, too, the study finds matters “exacerbated by the existence of parallel Kurdish and Iraqi security institutions.” The two Kurdish political parties have their own military, police and intelligence services. Their soldiers, referred to as the pesh merga, though nominally under Kurdish government control, are in reality affiliated with their separate political parties.

The Arabs, Turkmens and other groups object to Kurdish soldiers trying to provide security in their areas. While some attempts have been made to integrate the pesh merga into the Iraqi army — about 30,000 soldiers are considered to have done so — the Kurds continue to keep others as permanent militia.

The glue that holds matters together is a series of confidence-building measures that stand to collapse because U.S. military participation is vital at almost every level, according to the study. Begun in 2009 at the joint request of Iraqi Prime Minister Nouri al-Maliki and Massoud Barzani, president of the semiautonomous Kurdish region, the so-called U.S.-Arab-Kurdish measures were designed to provide security in the area and “create a process by which the ISF [Iraqi Security Forces] and the pesh merga can build trust at an operational level in locations where they might otherwise be at odds,” the study said.

For example, U.S. military trainers work with both Iraqi and Kurdish forces in the region. U.S. troops participate in joint Kurd-Iraqi patrols and checkpoints in three of the most tense governates: Nineveh, Kirkuk and Diyala.

An American officer rides herd on each governate’s combined coordination center, where forces jointly plan operations and deployments in disputed areas. Finally, an American colonel is the U.S. representative on the Senior Working Group that oversees all activities.

The combined Kurdish-Iraqi-American force, known as the Nineveh Golden Lions, is considered an elite unit. Its members have their own insignia, shared quarters and joint operations. U.S. Ambassador to Iraq James Jeffrey told Congress in February that the force was an “extraordinarily successful . . . important tactical tool in the field to suppress possible violence or possible disputes.”

State Department officials have discussed taking over some of these roles if the U.S. military departs as planned. But the Rand study says that while a foreign service officer could handle a coordination-center oversight position, “U.S. diplomats would be ill-suited to join Kurdish and Iraqi security forces on armed patrols or at checkpoints, where disagreements on operations and tactics are most likely to lead to violence.”

Meanwhile, adding to U.S. concerns, the joint two-year agreement between Maliki and Barzani that led to the establishment of the joint force is set to expire in December. With the prospect of no U.S. troops on the scene to act as arbiters, the study expresses doubts that expansion and perhaps even continuation of the joint program will be “a viable option.”