If you're looking for a study of democracy in action at its best, stay out of New Mexico until after Tuesday's primary. From polygraphs to grand juries, from questionable land deals to suspect loans, the campaign has been a case study of the low road in American politics.

"This whole campaign has been one of rumor and innuendo," said an aide to one candidate.

The most serious fight is not between candidates but between former governor Jerry Apodaca, who is seeking the Democratic nomination for the U.S. Senate, and the Albuquerque Journal.

Last month, charging that the Journal had sought perjured testimony from a man who said Apodaca had accepted a payoff, the candidate called for a grand jury investigation of the paper's investigator.

The fight grows out of a suit filed against the newspaper several years ago by an Albuquerque lawyer who said the paper libeled him in a story by saying he had connections with organized crime. As part of the suit, Apodaca was implicated as an unwitting tool of organized crime, and Apodaca says that the paper, in gathering evidence for its defense, has sought to destroy him politically.

Although no charges have been proven against Apodaca, the issue has plagued his campaign. As a result he is the underdog in the race for the Senate nomination against New Mexico Attorney General Jeff Bingaman.

"This race isn't Apodaca and Jeff Bingaman, it's Apodaca and the Albuquerque Journal," said Chris Brown, Apodoca's campaign manager.

The winner of the primary will face Republican Sen. Harrison H. Schmitt in November.

It's in the primary races for gubernatorial nominations that the polygraphs and land deals are issues.

The likely Democratic nominee is Toney Anaya, a former attorney general and one-time assistant to incumbent Gov. Bruce King.

His opponent is Aubrey Dunn, a conservative former state senator who was running behind in the polls and decided to go on the attack. Among his allegations is that Anaya, while on King's staff, sold pardons to people.

King has been quietly supporting Dunn, so Anaya, to prove his innocence, took a lie detector test that he says confirms his side of the story. Dunn may now be even farther behind.

On the Republican side, the battle is between two former state senators, John Irick, the darling of the conservative Republican hierarchy, and Bill Sego, an aggressive campaigner who says he is more electable.

Sego has a wide lead in the polls and might have a lock on the race were it not for a ruling by a federal judge last fall that he and a business partner defrauded someone in a land swap some years ago.

The other knockdown race is for the Democratic nomination in New Mexico's third congressional district, newly created as a result of the 1980 census.

Among the candidates is Tom Udall, son of former interior secretary Stewart Udall and nephew of Rep. Morris K. Udall (D-Ariz.), but all the talk lately is about Bill Richardson.

Richardson burst on the political scene in 1980 by coming within 5,000 votes of defeating Rep. Manuel Lujan Jr. (R-N.M.). So Richardson, who was born in Mexico, looked like the favorite in the newly drawn district in northern New Mexico, which is heavily Hispanic.

But for the last few weeks, Richardson has been on the defensive.

For one, he had to deny charges by Tom Udall and another opponent, Lt. Gov. Roberto Mondragon, that he urged each to quit the race and promised support in 1984, when, he said, he would run for the Senate.

He also had to amend some campaign literature that said he was the late senator Hubert H. Humphrey's "top" foreign policy adviser. Ah, just "an" adviser, he now says.

He also is on the defensive about a $100,000 loan from a Santa Fe bank, for which the collateral is not clear. The Federal Election Commission is investigating. His lawyers blame Tom Udall for the complaint, and the race is now considered a tossup.

All in all, things are so out of hand in New Mexico that the Democratic state chairman went on television Thursday night calling for a cease-fire among the candidates. Apparently no one was listening.