After befriends John F. Kennedy, Frank Sinatra recorded a special version of "High Hopes" as a JFK campaign jingle. Associated Press The Mafia detested the administration of John F. Kennedy as Attorney General Robert F. Kennedy raised the number of mob convictions from 35 in 1960 to 288 in 1963.

But there may be a much deeper connection between the Kennedys and the mob, and legendary entertainer Frank Sinatra reportedly served as a key intermediary and whipping boy in one case.

According to "The Dark Side of Camelot" by Seymour Hersh, Joseph P. Kennedy, Sr. (JFK's father) set up a meeting with Chicago mob boss Sam Giancana to obtain Giancana's support for Jack Kennedy's run for the White House — thereby combining the sway of Chicago crime syndicate with that of Mayor Richard J. Daley's Democratic machine.

Hersh also reported, along with others, that Giancana also helped funnel cash to buy votes and endorsements for the West Virginia Democratic primary election in May 1960.

The new book "The Kennedy Half-Century: The Presidency, Assassination, and Lasting Legacy of John F. Kennedy" by University of Virginia professor Larry Sabato highlights the connection by citing the story that Joseph Kennedy asked for Giancana's help over a dispute with another mobster, Frank Costello, and offered "the president's ear" in return.

Sabato also writes that "when JFK began having an affair with a black-haired beauty named Judith Campbell while he was still a U.S. senator, Giancana slept with her as well, reportedly so that he would eventually have a direct link to the White House."

It turns out, according to Sabato, that Sinatra introduced Senator Kennedy to Judy Campbell and also "served as the go-between for the West Virginia primary shenanigans."

After JFK reached the White House, however, the mob boss was not welcome near the president's ear. And Sinatra was the one that ultimately paid for it.

From "The Kennedy Half-Century":

When the Kennedys turned on Giancana once they were in the White House, Sinatra had to work hard to deflect the mobster's wrath at Sinatra on account of the Kennedys' unfaithfulness. In atonement, the singer played at Giancana's club, the Villa Venice, with his "Rat Pack" of fellow entertainers, for eight nights in a row.

Sabato notes that "Sinatra worked his way back into Giancana's good graces, but the Kennedys never did."

Here's The Rat Pack playing "Chicago" at the Villa Venice in 1962: