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In General Formula (X), 

Xa$_{1 }$ represents a hydrogen atom, a methyl group, a trif› luoromethyl group, or a hydroxymethyl group. 

T represents a single bond or a divalent linking group. 

Rx$_{1 }$ to Rx$_{3 }$ each independently represent a straight-chain or branched alkyl group, or a monocyclic or polycyclic cycloalkyl group. Here, two of Rx$_{1 }$ to Rx$_{3 }$ may bond with each other to form a monocyclic or polycyclic cycloalkyl group. 

Examples of the divalent linking group as T include an alkylene group, a -(COO-Rt)- group, and a -(O-Rt)› group. Here, Rt represents an alkylene group or a cycloalky› lene group. 

Tis preferably a single bond or a -(COO-Rt)- group. Here, Rt is preferably an alkylene group having 1 to 5 carbon atoms, and a ----CH$_{2}$ - group or a -(CH$_{2}$ ) 3 - group are more preferable. 

The alkyl group as Rx$_{1 }$to Rx$_{3 }$ is preferably an alkyl group having 1 to 4 carbon atoms such as a methyl group, an ethyl group, an n-propyl group, an isopropyl group, an n-butyl group, an isobutyl group, or at-butyl group. 

The cycloalkyl group as Rx$_{1 }$ to Rx$_{3 }$ is preferably a monocyclic cycloalkyl group such as a cyclopentyl group or cyclohexyl group, or a polycyclic cycloalkyl group such as a norbornyl group, a tetracyclodecanyl group, a tetracy- clododecanyl group, or an adamantyl group. 

As the cycloalkyl group which may be formed by two of Rx$_{1 }$ to Rx$_{3 }$ bonding with each other to form, a monocyclic cycloalkyl group such as a cyclopentyl group or cyclohexyl group, or a polycyclic cycloalkyl group such as a norbornyl group, a tetracyclodecanyl group, a tetracyclododecanyl group, or an adamantyl group is preferable. 

In particular, Rx$_{1 }$ is a methyl group or an ethyl group, and an aspect in which Rx$_{2 }$ and Rx$_{3 }$ bond with each other to form the cycloalkyl group described above is preferable. 

Specific examples are given below of the acid-decompos› able repeating unit; however, the present invention is not limited thereto. 

(In the formulae, Rx is H, CH$_{3}$ , CF$_{3}$ , CH$_{2}$OH, Rxa, and Rxb are respectively alkyl groups having 1 to 4 carbon atoms) 

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