WHAT IS THIS new China connection? Is it as substantial and helpful as the administration was proclaiming while Vice Premier Teng Hsiao-ping was here? Several new developments impel us to ask. One is the revelation that Jimmy Carter never asked Peking for a pledge not to use force to regain Taiwan. The other is the performance of Mr. Teng.

Why was a no-force pledge not sought? The administration seems to have felt that since a request was certain to be refused -- and since Taiwan's security did not depend on it anyway -- it would only make trouble to ask. There was evidently a disposition on the part of both the militant Brzezinski wing and the moderate Vance wing not to jostle normalization, which both wanted for their own foreign-policy reasons and which Jimmy Carter wanted for political considerations as well.

But surely Taiwan was owed at least the Americans' best effort to extract the strongest guarantee. The lapse suggests an almost indecent yearning, if not an irresponsible haste. How revealing that Jimmy Carter, when queried about it at a news conference, dissembled. We do not say Taiwan's security is the worse off as a result. On the contrary, the disclosure is sure to strengthen Congress' determination to write language asserting the American interest in the security of Taiwan. Mr. Carter himself, playing catch-up, now asserts that the United States might even go to war to protect the island. But to be afraid to ask .... What must the Chinese have thought when they saw the Carter administration tiptoeing so?

That question, it seems to us, is relevant to the way Mr. Teng conducted himself when he left. The very next day he attacked the United States for bungling in Iran and "for allowing the Soviet Union to place a lot of pawns on the world's chessboard." It is hard to know what to make of this. Either Mr. Teng was deeply disappointed in his talks here, in which case the administration's claim to have made history with him is absurd. Or he was led to believe that such attacks would serve the useful purpose of spurring the United States to greater anti-Soviet exertions -- one wonders in this connection how he interpreted being received for his first American meal in Zbigniew Brzezinski's home.

The question is not academic. Mr. Teng is obsessed by neighboring Vietnam's march into Cambodia. This may well be the reason he suddenly accelerated China's drive toward normalization last fall. Having massed forces on Vietnam's border, he is threatening unspecified "prudent... sanctions." Unquestionably, China has a problem. But so does the United States. For Mr. Teng, by coming to Washington as this crisis flowered, did a very clever thing.

If the United States, notwithstanding its last-minute warnings, essentially stands still while China moves against Vietnam, this country will appear as a co-conspirator to the Soviet Union -- at a moment when the overwhelming American interest lies in moving toward a SALT agreement. Alternatively, if the United States steps back, it will appear to many, in Washington as well as Peking, as unreliable and weak. Either way, Peking becomes the arbiter of American policy to an unacceptable degree.

Underneath these considerations lies a deeper reason for queasiness. It is the impression that Jimmy Carter has still not gotten on top of the basic ideological split between Secretary of State Vance, with his first-things-first emphasis on SALT, and National Security Adviser Brzezinski, whose readiness to challenge the Kremlin can take on a gratuitous edge. In the China case, Mr. Carter's advisers took different approaches. Demonstrably, he did not demand from them a fully thought-out and worked-out policy before proceeding.

In brief, the capital's liberals, presumably including Mr. Vance, are scared by how close the United States has gotten to a regime with, it seems, only anti-Sovietism on its mind -- although Mr. Brzezinski appears to revel in it. Many conservatives are troubled by the looseness evident in the treatment of Taiwan. Jimmy Carter looks foolish for the questionable management of two critical Washington triangles, Moscow-Peking-Washington and Carter-Vance-Brzezinski. He leaves a lot of anxious Americans and foreigners alike right back where they were in mid-1978, wondering just who's in charge.