In this article, we perform a sensitivity study of an un-binned angular analysis of the $Bto D^*ell u_ell$ decay, including the contributions from the right-handed current. We show that the angular observable can constrain very strongly the right-ha
nded current without the intervention of the yet unsolved $V_{cb}$ puzzle.
We study $bar{Q}Qbar{q}q$ and $bar{Q}qQbar{q}$ molecular states as mixed states in QCD sum rules. By calculating the two-point correlation functions of pure states of their corresponding currents, we review the mass and coupling constant predictions
of $J^{PC}=1^{++}$, $1^{--}$, $1^{-+}$ molecular states. By calculating the two-point mixed correlation functions of $bar{Q}Qbar{q}q$ and $bar{Q}qQbar{q}$ molecular currents, and we estimate the mass and coupling constants of the corresponding ``physical state that couples to both $bar{Q}Qbar{q}q$ and $bar{Q}qQbar{q}$ currents. Our results suggest that $1^{++}$ states are more likely mixing from $bar{Q}Qbar{q}q$ and $bar{Q}qQbar{q}$ components, while for $1^{--}$ and $1^{-+}$ states, there is less mixing between $bar{Q}Qbar{q}q$ and $bar{Q}qQbar{q}$. Our results suggest the $Y$ series of states have more complicated components.
We study $bar qq$-hybrid mixing for the light vector mesons and $bar qq$-glueball mixing for the light scalar mesons in Monte-Carlo based QCD Laplace sum rules. By calculating the two-point correlation function of a vector $bar qgamma_mu q$ (scalar
$bar q q$) current and a hybrid (glueball) current we are able to estimate the mass and the decay constants of the corresponding mixed physical state that couples to both currents. Our results do not support strong quark/gluonic mixing for either the $1^{--}$ or the $0^{++}$ states.
We use the Laplace/Borel sum rules (LSR) and the finite energy/local duality sum rules (FESR) to investigate the non-strange $udbar ubar d$ and hidden-strange $usbar ubar s$ tetraquark states with exotic quantum numbers $J^{PC}=0^{+-}$ . We systemati
cally construct all eight possible tetraquark currents in this channel without covariant derivative operator. Our analyses show that the $udbar ubar d$ systems have good behaviour of sum rule stability and expansion series convergence in both the LSR and FESR analyses, while the LSR for the $usbar ubar s$ states do not associate with convergent OPE series in the stability regions and only the FESR can provide valid results. We give the mass predictions $1.43pm0.09$ GeV and $1.54pm0.12$ GeV for the $udbar ubar d$ and $usbar ubar s$ tetraquark states, respectively. Our results indicate that the $0^{+-}$ isovector $usbar ubar s$ tetraquark may only decay via weak interaction mechanism, e.g. $X_{usbar{u}bar{s}}to Kpipi$, since its strong decays are forbidden by kinematics and the symmetry constraints on the exotic quantum numbers. It is predicted to be very narrow, if it does exist. The $0^{+-}$ isoscalar $usbar ubar s$ tetraquark is also predicted to be not very wide because its dominate decay mode $X_{usbar{u}bar{s}}tophipipi$ is in $P$-wave.
We calculate the complete form of the dimension-8 condensate contributions in the two-point correlator of the ($1^{-+}$,$0^{++}$) light hybrid current considering the operator mixing under renormalization. We find the inclusion these higher power cor
rections as well as the update of $langle g^3G^3rangle$ increase the QCD sum rule mass prediction for the $1^{-+}$ light hybrid. The obtained conservative mass range 1.72--2.60 GeV does not favor the $pi_1(1400)$ and the $pi_1(1600)$ to be pure hybrid states and suggests the $pi_1(2015)$ observed by E852 is more likely to have much of a hybrid constituent. We also study the $b_1pi$ and $rhopi$ decay patterns of the $1^{-+}$ light hybrid with light-cone QCD sum rules. We obtain a relatively large partial decay width of the $b_1pi$ mode, which is consistent with the predictions from the flux tube models and lattice QCD. More interestingly, using the tensor interpolating current we find the partial decay width of the $rhopi$ mode is small due to the absence of the leading twist contribution in the light-cone expansion of the correlation function.
We calculate the coefficients of the dimension-8 quark and gluon condensates in the current-current correlator of $1^{-+}$ light hybrid current $gbar{q}(x)gamma_{ u}iG_{mu u}(x)q{(x)}$. With inclusion of these higher-power corrections and updating th
e input parameters, we re-analyze the mass of the $1^{-+}$ light hybrid meson from Monte-Carlo based QCD sum rules. Considering the possible violation of factorization of higher dimensional condensates and variation of $langle g^3G^3rangle$, we obtain a conservative mass range 1.72--2.60,GeV, which favors $pi_{1}(2015)$ as a better hybrid candidate compared with $pi_{1}(1600)$ and $pi_{1}(1400)$.
