By Jody Godoy and Jonathan Stempel NEW YORK (Reuters) -Former Republican U.S. vice presidential candidate and Alaska Governor Sarah Palin went to trial against the New York Times on Thursday, in a highly anticipated defamation case that could test long-standing protections for American news media. Palin, 57, is suing over a 2017 editorial that incorrectly linked her political rhetoric to a 2011 Arizona mass shooting that left six dead and U.S. Representative Gabby Giffords seriously wounded, and which the newspaper later corrected. In his opening statement, Palin’s lawyer, Shane Vogt, told jur…