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Is there other examples of using zk-SNARK for supporting "private transactions" except Zerocoin or Zchach ? (For example, is it possible to use zk-SNARK for health data ? or any other use cases in which the data privacy is important ?)

The only example I found was related to the "payment use case" such as Zerocash . Does it mean zk-SNARK use case in blockchain is limited to use it only in the payment use case ?

Is there other research papers on using zk-SNARK for supporting data privacy and private transactions in the blockchain except payment use case?

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The main feature of ZK-SNARKs is to "cryptographically verify the correctness of a computation". In extreme, this means that you could offload lot of smart contract computation from the chain, but be sure that the computation was executed as agreed.

Usecases for this are unlimited. And they are getting in reach for Ethereum thanks to libraries like ZoKrates.

If you wish to see a concrete example outside of the zcash schema, take a look at Plasma Ignis for ZKSNARK driven Plasma Subchain: https://medium.com/plasma-ignis/presenting-ignis-plasma-of-fire-502fab5a6f17

If you wish a good introduction to ZKSNARKs, I can recommend https://blog.decentriq.ch/zk-snarks-primer-part-one/

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We are seeing the emergence of a plethora of applications of zk-SNARKS in Blockchain ever since ZK Rollups have become an active area of research. ZK Rollups have been implemented for reducing the gas fee from transactions. It has been applied for various decentralised finance based exchanges such as Loopring. zk-SNARKS are also adopted in the Zether implementation for anonymous payment in Ethereum. AZTEC protocol has used zk-SNARKS for building privacy preserving smart contracts.

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