Hints:

1. The condition for cancellation of tadpoles can be formulated as vanishing of 1-point functions $$ \langle \phi(x)\rangle_{J=0}~=~0\qquad\text{and}\qquad\langle \chi(x)\rangle_{J=0}~=~0,$$ cf. e.g. my Phys.SE answer here.

2. The first condition is automatic satisfied due to a $U(1)$-symmetry of the complex field $\phi$.

3. The second condition can be made to hold by adding a 1-vertex interaction term $Y\chi$ to the Lagrangian density, cf. Ref. 1.

References:

1. M. Srednicki, QFT; chapter 9. A prepublication draft PDF file is available here.

Hints:

1. The condition for cancellation of tadpoles can be formulated as vanishing of 1-point functions $$ \langle \phi(x)\rangle_{J=0}~=~0\qquad\text{and}\qquad\langle \chi(x)\rangle_{J=0}~=~0,$$ cf. e.g. my Phys.SE answer here.

2. The first condition is automatic satisfied due to a $U(1)$-symmetry of the complex field $\phi$.

3. The second condition can be made to hold by adding a 1-vertex interaction term $Y\chi$ to the Lagrangian density, cf. Ref. 1.

References:

1. M. Srednicki, QFT, 2007; chapter 9. A prepublication draft PDF file is available here.

Hints:

1. The condition for cancellation of tadpoles can be formulated as vanishing of 1-point functions $$ \langle \phi(x)\rangle_{J=0}~=~0\qquad\text{and}\qquad\langle \chi(x)\rangle_{J=0}~=~0,$$ cf. e.g. my Phys.SE answer here.

2. The first condition is automatic satisfied due to a $U(1)$-symmetry of the complex field $\phi$.

3. The second condition can be made to hold by adding a 1-vertex interaction term $Y\chi$ in the Lagrangian density, cf. Ref. 1.

References:

1. M. Srednicki, QFT; chapter 9. A prepublication draft PDF file is available here.

Hints:

1. The condition for cancellation of tadpoles can be formulated as vanishing of 1-point functions $$ \langle \phi(x)\rangle_{J=0}~=~0\qquad\text{and}\qquad\langle \chi(x)\rangle_{J=0}~=~0,$$ cf. e.g. my Phys.SE answer here.

2. The first condition is automatic satisfied due to a $U(1)$-symmetry of the complex field $\phi$.

3. The second condition can be made to hold by adding a 1-vertex interaction term $Y\chi$ to the Lagrangian density, cf. Ref. 1.

References:

1. M. Srednicki, QFT; chapter 9. A prepublication draft PDF file is available here.