They were shaggy and, to Ed Sullivan’s mind, under-shampooed, but the Rolling Stones cemented their arrival in the United States when they appeared on his variety show in October 1964, accompanied by screaming fans and aided by one Les Paul guitar in the hands of Keith Richards.

Guitar buffs have tracked the instrument for years. Eric Clapton is said to have played it. Jimmy Page was photographed with it. Bernie Marsden of Whitesnake owned it.

So it is perhaps no surprise that the 1959 Gibson — with its gleaming sunburst finish, mahogany body and maple top — would end up in the Metropolitan Museum of Art, the gift of a collector who this year generously donated 500 vintage guitars.

“These guitars are examples of outstanding artistry and craftsmanship as well as visually powerful tools of expression and distinction,” the museum said in a statement announcing the gift.

But in recent weeks, a representative for Mick Taylor, 76, a former guitarist for the Stones, surfaced to say that Taylor was surprised to learn that the guitar was in the museum.

Taylor’s account is that he purchased the guitar from a road manager for the Stones while playing with John Mayall, then brought it with him in 1969 when he joined the Stones for five years. His version has been recounted by music journalists, guitar aficionados and a Stones historian.