${\gamma }^{*}N\to N(1710)$ transition at high momentum transfer

In a relativistic quark model we study the structure of the $N(1710)$ resonance, and the ${\gamma }^{*}N\to N(1710)$ reaction focusing on the high momentum transfer region, where the valence quark degrees of freedom are expected to be dominant. The $N(1710)$ resonance, a state with spin 1/2 and positive parity ($J^P={\frac{1}{2}}^{+}$), can possibly be interpreted as the second radial excitation of the nucleon, after the Roper, $N(1440)$. We calculate the ${\gamma }^{*}N\to N(1710)$ helicity amplitudes, and predict that they are almost identical to those of the ${\gamma }^{*}N\to N(1440)$ reaction in the high momentum transfer region. Thus, future measurement of the helicity amplitudes for the ${\gamma }^{*}N\to N(1710)$ reaction can give a significant hint on the internal structure of the $N(1710)$ state.

Figure 1

${\gamma }^{*}N\to N(1710)$ transition form factors (solid line) compared with those for the Roper, ${\gamma }^{*}N\to N(1440)$ (dashed line). Data for the Roper are from CLAS [34].

Figure 2

${\gamma }^{*}N\to N(1710)$ helicity amplitudes at the resonance rest frame (solid line). Results are compared with those for the ${\gamma }^{*}N\to N(1440)$ amplitudes (dashed line), and the equivalent amplitude for the nucleon $N(939)$ (dotted line). See the text for the explanation on the equivalent nucleon case.