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White left the World Cup squad for personal reasons.
England said in a statement that the player is not expected to come back for the rest of the tournament.
It asked that the player's privacy be respected.
He did not play for the Three Lions as they finished top of Group B.
He didn't play in the first two games against Iran and the United States because of illness and missed the win against Wales on Tuesday night.
Following the news, the Gunners said on social media: "We're all with you, Ben".
White, who has spent most of his career in central defence, was included in the England squad for the World Cup after an impressive season in the right-back position.
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