^{*}

^{†}

^{‡}

^{3}.

We show in this paper that, in a

There is a long-standing deviation between the standard model (SM) prediction and the experimental measurement for

There exist various NP scenarios to explain the muon

In our previous work

The paper is organized as follows. In Sec.

In the 2HDM, the

As in our previous work

Taking all these constraints into account, we will adopt the perturbativity criteria

Mass regions allowed in the (

We should emphasize that, except for the custodial symmetry that protects

The

In this paper, we generalize the previously studied texture of the up-quark Yukawa coupling to

In this case, for

In our scenario, the two crucial elements for addressing the muon

(a) Typical two-loop Barr-Zee-type diagrams with the top (

As for the new sets of two-loop Barr-Zee-type diagrams discussed in Ref.

Based on these observations, we will only consider the two-loop Barr-Zee-type diagrams shown in Fig.

Dependence of

It is worth mentioning that the recent lattice QCD calculations

It should also be mentioned that the two-loop Barr-Zee-type diagrams shown in Fig.

In this section, we analyze the tight constraints from the

The low-energy effective Hamiltonian for the inclusive

Following Ref.

Adopting the overall normalization of the SM contribution, the low-energy effective Hamiltonian for

A prominent constraint from the

Normalizing to the SM contribution, we can express

We now proceed to analyze the combined constraints from the branching ratio

Allowed parameter space in the (

Finally, let us discuss briefly the compatibility of our scenario with the direct collider constraints. In a framework similar to what is considered here, it has been found that the neutral and charged Higgs bosons with masses being as light as 200 GeV are still compatible with the current LHC constraints

In this paper, we have demonstrated that in the

This work is supported by the National Natural Science Foundation of China (Grants No. 11675061, No. 11775092, No. 11521064, and No. 11435003). X. L. is also supported in part by the self-determined research funds of CCNU from the college’s basic research and operation of MOE (CCNU18TS029).

In this Appendix, we collect the relevant expressions for the oblique parameters

Following Refs.

The amplitude for the typical two-loop Barr-Zee-type diagrams shown in Fig.

The amplitude for the new sets of two-loop Barr-Zee-type diagrams shown in Fig.

The well-known one-loop amplitudes generated by the neutral and charged Higgs boson propagators are given by

For the inclusive

For the