  In the present work we perform a systematic shell model study of Gamow-Teller
transition strength distributions in $sd$ shell nuclei using $ab~initio$
effective interactions. The $ab~initio$ effective interactions are based on
in-medium similarity renormalization group (IM-SRG) and coupled-cluster
effective interaction (CCEI) approaches. The aim of the present work is to test
the predictive power of $ab~initio$ effective interactions by using the
available experimental data of Gamow-Teller strength distributions in $sd$
shell nuclei. We perform calculations for $^{20}$Ne $\rightarrow$ $^{20}$F,
$^{23}$Na $\rightarrow$ $^{23}$Mg, $^{23}$Na $\rightarrow$ $^{23}$Ne, $^{24}$Mg
$\rightarrow$ $^{24}$Na, $^{24}$Mg $\rightarrow$ $^{24}$Al, $^{25}$Mg
$\rightarrow$ $^{25}$Al, $^{26}$Mg $\rightarrow$ $^{26}$Na, $^{26}$Mg
$\rightarrow$ $^{26}$Al, $^{26}$Si $\rightarrow$ $^{26}$Al, $^{27}$Al
$\rightarrow$ $^{27}$Si, $^{28}$Si $\rightarrow$ $^{28}$P, $^{31}$P
$\rightarrow$ $^{31}$Si, and $^{32}$S $\rightarrow$ $^{32}$P transitions. For
comparison we also show the results obtained by using the phenomenological USDB
Hamiltonian. The phenomenological USDB results of the Gamow-Teller
(GT$_+$/GT$_-$) strength distributions show reasonable agreements with the
experimental data in comparison to the $ab~initio$ interactions. We also
calculate the electron capture reaction rates for $^{23}$Na(e$^-$,
$\nu$)$^{23}$Ne and $^{25}$Mg(e$^-$, $\nu$)$^{25}$Na using $ab~initio$ and USDB
interactions.
