Semileptonic form factors of ${\mathrm{\Xi }}_c\to \mathrm{\Xi }$ in QCD sum rules

There exists a significant deviation between the most recent lattice quantum chromodynamics (QCD) simulation and experimental measurement by Belle for ${\mathrm{\Xi }}_c^0\to {\mathrm{\Xi }}^{-}{\ell }^{+}{\nu }_{\ell }$. In this work, we investigate the ${\mathrm{\Xi }}_c\to \mathrm{\Xi }$ form factors in QCD sum rules. To this end, the two-point correlation functions of ${\mathrm{\Xi }}_c$ and $\mathrm{\Xi }$, and the three-point correlation functions of ${\mathrm{\Xi }}_c\to \mathrm{\Xi }$ are calculated. At the QCD level, contributions from up to dimension-6 four-quark operators are considered, and the leading order results of the Wilson coefficients are obtained. For the form factors, relatively stable Borel windows can be found. Our form factors are comparable with those of lattice QCD, except for $f_{\perp }$. The obtained form factors are then used to predict the branching ratios of ${\mathrm{\Xi }}_c\to \mathrm{\Xi }{\ell }^{+}{\nu }_{\ell }$, and our predictions are consistent with the most recent data of ALICE and Belle, and those of lattice QCD within error. Given that the branching ratios only contain limited information, we suggest the experimentalists directly measure the form factors of ${\mathrm{\Xi }}_c\to \mathrm{\Xi }$.

Figure 1

All the diagrams considered for the two-point correlation function of ${\mathrm{\Xi }}_c$ at the QCD level.

Figure 2

All “independent” diagrams considered for the two-point correlation function of $\mathrm{\Xi }$ at the QCD level. Here “independent” means that equivalent diagrams are not shown here.

Figure 3

All the diagrams considered for the three-point correlation functions of ${\mathrm{\Xi }}_c\to \mathrm{\Xi }$ at the QCD level.

Figure 4

The pole residues of ${\mathrm{\Xi }}_c$ and $\mathrm{\Xi }$ as functions of the Borel parameter $T_{+}^2$. The blue and red curves correspond to the $\overline{\mathrm{MS}}$ scheme and the pole mass scheme, respectively. The extreme points on these curves correspond to the experimental value of the baryon mass. The $s_{+}$ and $T_{+}^2$ corresponding to these extreme points can be found in Table 1.

Figure 5

The helicity form factors $f_{+,\perp ,0}(q^2)$ as functions of the Borel parameter $T_2^2$. The blue dots and red squares respectively correspond to the results obtained using the $\overline{\mathrm{MS}}$ scheme and the pole mass scheme. $q^2=0.0,-0.1,\dots ,-0.5{\mathrm{GeV}}^2$ are considered.

Figure 6

Same as Fig. 5, but for $g_{+,\perp ,0}$.

Figure 7

Our helicity form factors are compared with those of lattice QCD in Ref. [12]. All our form factors have been multiplied by a minus sign.