When the final story of the Panama Canal treaties is written, an important chapter is likely to involve the visit here of Senate majority leader Robert C. Byrd (D-W. Va.) and six of his Democratic colleagues.

The senators. who complete their four-day trip Saturday, have not really heard any new arguments about whether the canal should be surrendered to eventual Panamanian control. Nor are they likely to give any immediate indication of how they will vote when the treaties face the required test of approval by two-thirds of the Senate.

The senators nevertheless will return to Washington with some clearly changes perceptions that could ultimately play an important role in the Carter administration's struggle for ratification of the pacts.

All seven admit insights into the emotions that the canal issue arouses among Panama's 1.7 million people and its effect on U.S. Latin American relations as well as the nature of the government here and its chief, Gen. Omar Torrijos.

The senators' visit could also have a major effect on events within Panama. Because of what they told Torrijos about the arguements being made against him by anti-treaty forces in the United States, there is a strong possibility that he may soon take steps to counter charges that his government is guilty of widespread human-rights violations.

In all this, the key figure is Bryd. If he moves from his present uncommitted stance to advocy of the treaties, his powers as majority leader could make him the man for whom the administration has been searching - an influential senator willing to take command of the pro-treaty forces.

The visit also was important for its potential effects on Byrd's traveling companions: Sens. James R. Sasser (Tenn.), Spark M. Matsunago (Hawaii), Walter D. Huddleston (Ky.), Donald W. Riegle Jr. (Mich.), Paul S. Sarbanes (Md.) and Howard M. Metsenbaum (Ohio).

All are moderate-to-liberal Democrats caught between their normal tendency toward loyalty to the administration and the knowledge that there is strong opposition to the treaties in their constituencies. If senators of their persuasion cannot be induced to take an affirmative stance, the treaties have little hope of approval.

That obviously was on their minds during their hectic schedule of conferences with the canal's U.S. administrators and military guardians and talks with Panamanians from all walks of life.

For the most part, however, their attention centerred on trying to take the measure of Torrijos, who personally escorted them on a barnstorming tour from the Atlantic to the Pacific and then sat down with the senators for a long private discussion at his ocean-side retreat outside the capital.

Foes of the treaties in the United States have portrayed Torrijos as an iron-dissent dictator who had ruthlessly supressed dissent with Panama and as a radical leftist intene on moving his country - and the canal - into the Communist orbit.

Several of the senators admitted privately, however, that their impression of the actual situation did not square with that image. They now seem to have a picture of a country where press and political activism are kept on a short leash but where the pinitive powers of dictatorship are exercise with moderation.

Still, the senators told Torrijos that while incidents of political imprisonment or exile have been relatively rare, his government's imagine on human rights questions is not good. They also told him that he could help his cause by easing up some of the reprewith the impression that he intends to take such steps soon.

The tour of the countryside also made clear to the senators that Torrijos, despite being a dictator, has great popular support and an uncanny knack for reaching out to the people.

Again and again, they saw him, minus the entourage of bodyguards that surround most Latin military dictators, olunge into adoring crowds to hug and kiss admirers or hunker down in the square of an Indian Village to engage in finger-pointing, semifirtations arguments with the local women about who is responsible for rising food prices.

Other question of his political sympathies. Torrijobs went to great lengths to assure the senators that, despite his occasionally radical rhetoric and his chuminess with Cuban President Fidel Castrol, he is not a Communist and never could be.

In fact, the senators reported, Torrijos said communism is so alien a concept to most Panamanians that he would be driven from office if he tried to steer the country in that direction. Conversely, he added if Panama ever came under Communist controls, he himself would refuse to live there.

As to what might happen if the treaties fails to pass the Senate, the visitors said Torrijos seemed to regard that as a possibility so tragic that he did not want to think about it.

Some people in his outrage said his feelings on that point were unwittingly underscored by an incident that occurred in the San Bias Islands. Some of the travel there was by dugout canoes, and, as Torijos and Byrd climbed into one, the slat serving as a seat collapsed under them.

"That's the first time that two governments have fallen at the same," Byrd laughed.