A group of heavyweight republican senators is using a legal argument to try to convince President Donald Trump to exit the Paris climate agreement, but according to the experts whose papers they relied on, their interpretation is all wrong.

The 22 senators, including Senate Majority Leader Mitch McConnell and Senate Environment and Public Works Committee Chairman John Barrasso, sent a letter to Trump Thursday arguing that if the U.S. doesn't "make a clean break" from the Paris Agreement, it could make it impossible for Trump to rescind the Clean Power Plan.

"They wrote the letter to frighten the administration with the prospect of litigation," said Michael Burger, the executive director of the Sabin Center for Climate Change Law at Columbia University, "but the legal arguments are fundamentally wrong."

The senators' claim focuses on Section 115 of the Clean Air Act, which authorizes the EPA to require states to address emissions that endanger other countries, provided those countries offer the U.S. reciprocal protections.

"Because of existing provisions within the Clean Air Act and others embedded in the Paris Agreement, remaining in it would subject the United States to significant litigation risk that could upend your Administration's ability to fulfill its goal of rescinding the Clean Power Plan," the senators wrote.

But the Clean Power Plan is based on an entirely different part of the Clean Air Act—section 111, which requires emissions standards for power plants that have "the best system of emission reduction." How to define what the "best system" lies at the heart of the litigation over the Clean Power Plan. As Burger explains in a recent blog post, section 115 is not mentioned in the Clean Power Plan at all. The success or failure of efforts to overturn the Clean Power Plan will rest on attorneys' ability to argue based on section 111, he said.

President Trump met Thursday with NATO leaders in Brussels and is wrapping up his first foreign trip as president. Secretary of State Rex Tillerson said earlier this week that once the administration returns from the trip, Trump will make a decision on the Paris Agreement. The administration has heard arguments from both sides, including over 200 investors calling for the U.S. to stay in the agreement. White House advisors have been caught in their own tug-of-war over what to do about the accord.

In January, Burger and a number of co-authors published a paper that examined the ways in which section 115 could be used to address international climate change in the wake of the Paris Agreement. The paper argued that section 115 "grants the EPA and states broad latitude to address international air pollution comprehensively" and that it could be used "to establish an economy-wide, market-based approach for reducing GHG emissions."

But nowhere in the paper does it say that Section 115 provides any binding, legal authority that would require such regulation. "Nobody has ever made that argument," Burger said. "We don't make that argument in the paper, and I am not of the view that that's a particularly strong argument on the merits."

In the letter to Trump, the GOP senators wrote, "Leading environmental attorneys have been candid that they intend to use the Paris Agreement and the existing endangerment finding to force EPA to regulate under Section 115 of the Clean Air Act."

Then they cite David Bookbinder, the former chief counsel of the Sierra Club, as stating that together the Paris Agreement and Section 115 are the "silver bullet de jour of the enviros."

According to Bookbinder, the senators got just part of that right. "Section 115 is the silver bullet de jour," he said, "but silver bullets are magical thinking. You want to have them, but they don't really exist, and the only thing they kill are werewolves."

Like Burger, Bookbinder sees no legal authority to use Section 115 to argue against changing or rescinding the Clean Power Plan.

In addition to McConnell and Barrasso, the letter was signed by Sens. James Inhofe (Okla.), John Cornyn (Texas), Roy Blunt (Mo.), Roger Wicker (Miss.) Michael Enzi (Wyo.), Michael Crapo (Idaho), Jim Risch (Idaho), Thad Cochran (Miss.), M. Michael Rounds (S.D.), Rand Paul (Ky.), John Boozman (Ark.), Richard Shelby (Ala.), Luther Strange (Ala.), Orrin Hatch (Utah), Mike Lee (Utah), Ted Cruz (Texas), David Perdue (Ga.), Thom Tillis (N.C.), Tim Scott (S.C.) and Pat Roberts (Kan.).

Elsewhere in the Republican party, a small but growing group of legislators has adopted a more progressive stance on climate change. The bipartisan Climate Solutions Caucus now has 40 members from the House—20 from each party—and earlier this year, a group of Republican legislators introduced a House bill that called for climate action that could help the economy.