Light cone sum rules for ${\gamma }^{*}N\to \Delta$ transition form factors

A theoretical framework is suggested for the calculation of ${\gamma }^{*}N\to \Delta$ transition form factors using the light-cone sum rule approach. Leading-order sum rules are derived and compared with the existing experimental data. We find that the transition form factors in a several GeV region are dominated by the soft contributions that can be thought of as overlap integrals of the valence components of the hadron wave functions. The minus components of the quark fields contribute significantly to the result, which can be reinterpreted as large contributions of the quark orbital angular momentum.

Figure 1

Structure of QCD factorization for baryon form factors.

Figure 2

Schematic structure of the light-cone sum rule for baryon form factors.

Figure 3

The average value $⟨x⟩$ of the momentum fraction $x_3$ in the sum rules (4.1, 4.2) as a function of the momentum transfer $Q^2$. The lower and the upper solid curves correspond to the first and the second sum rule in (4.1), respectively. The dashed curve corresponds to (4.2). The value of the threshold $x_0$ (3.16) is plotted by dots for comparison.

Figure 4

The Borel parameter dependence of the ratio $G_M/3G_{\mathrm{dipole}}$ where $G_{\mathrm{dipole}}=1/(1+Q^2/0.71{)}^2$. The magnetic form factor $G_M$ is defined in (2.4). The solid and the dashed curves correspond to the calculation using $M_B^2=2.5{\mathrm{GeV}}^2$ and $M_B^2=1.5{\mathrm{GeV}}^2$, respectively. In both cases the asymptotic nucleon distribution amplitudes of the leading and higher twists are used.

Figure 5

The ratio $G_M^{\mathrm{Ash}}/3G_{\mathrm{dipole}}$ where $G_{\mathrm{dipole}}=1/(1+Q^2/0.71{)}^2$. The form factor $G_M^{\mathrm{Ash}}$ is defined in (2.5). The solid and the dashed curves correspond to the calculation using the asymptotic and the QCD sum rules motivated nucleon distribution amplitudes of the leading and higher twists, respectively. The data points are from 82 (blue squares), 100 (red triangles), and 65, 101, 102, 103, 104 (red squares).

Figure 6

The ratio $G_M/3G_{\mathrm{dipole}}$ where $G_{\mathrm{dipole}}=1/(1+Q^2/0.71{)}^2$. The magnetic form factor $G_M$ is defined in (2.4). The identification of the curves and data points is the same as in Fig. 5.

Figure 7

The ratio $G_T/3G_{\mathrm{dipole}}$ where $G_{\mathrm{dipole}}=1/(1+Q^2/0.71{)}^2$. The form factor $G_T$ is defined in (2.5). The identification of the curves and data points is the same as in Fig. 5.

Figure 8

Separate contributions to the light-cone sum rule results (solid curves) for the ratio $G_M/3G_{\mathrm{dipole}}$ where $G_{\mathrm{dipole}}=1/(1+Q^2/0.71{)}^2$. The terms in $f_N$, ${\lambda }_1$ and ${\lambda }_2$ are shown by the dashed, dotted and dash-dotted curves, respectively. The results on the left panel correspond to the asymptotic distribution amplitudes and the ones on the right panel are obtained including a CZ-like model, see text.

Figure 9

The ratio $R_{\mathrm{EM}}(Q^2)=-G_E/G_M$ of the electric and the magnetic form factors, cf. (2.5). The solid and the dashed curves correspond to the calculation using the asymptotic and the QCD sum rules motivated nucleon distribution amplitudes of the leading and higher twists, respectively. The data points are from 105 (red triangles) and 65 (blue squares).

Figure 10

The ratio $R_{\mathrm{SM}}\sim -G_C/G_M$ of the quadrupole and the magnetic form factors, cf. (2.5). The solid and the dashed curves correspond to the calculation using the asymptotic and the QCD sum rules motivated nucleon distribution amplitudes of the leading and higher twists, respectively. The data points are from 105 (red triangles) and 65 (blue squares).