Role of QCD compositeness in the production of scalar and tensor mesons through single-photon annihilation $e^{+}{e}^{-}\to {\gamma }^{*}\to \gamma S(T)$

We study the exclusive production of scalar $S=0^{++}$ and tensor $T=2^{++}$ mesons through single-photon annihilation $e^{+}{e}^{-}\to {\gamma }^{*}\to \gamma S(T)$. Using QCD compositeness of the involved hadrons considered as quark-antiquark systems, the prediction for the scaling of the differential cross sections of these processes is $d\sigma /dt\sim 1/s^3$ at large $s$. We further derive the scaling of the ${\gamma }^{*}\to \gamma S$ and ${\gamma }^{*}\to \gamma T$ transition form factors: $F_{{\gamma }^{*}\gamma S}(s)\sim 1/s$ and $F_{{\gamma }^{*}\gamma T}(s)\sim 1/s^2$. Results for the respective cross sections of the scalar and tensor meson production are presented. Note, when scalar and tensor mesons are considered as tetraquark systems of two tightly bound color diquarks, corresponding to them transition form factors and differential cross sections have the same falloffs as in case of quark-antiquark picture. For other tetraquark or two-hadron molecules configurations the transition form factors $F_{{\gamma }^{*}\gamma S(T)}(s)$ and the differential cross section $d\sigma /dt$ have additional $1/s$ and $1/s^2$ falloffs, respectively.

Figure 1

The single-photon annihilation $e^{+}{e}^{-}\to {\gamma }^{*}\to \gamma S(T)$.

Figure 2

Form factors $F_{{\gamma }^{*}\gamma f_0(980)}(s)$ and $F_{{\gamma }^{*}\gamma a_0(980)}(s)$ at ${\mathrm{\Lambda }}_{f_0}=350\mathrm{MeV}$ and ${\mathrm{\Lambda }}_{a_0}=250\mathrm{MeV}$.

Figure 3

Form factors $F_{{\gamma }^{*}\gamma f_2(1270)}(s)$ and $F_{{\gamma }^{*}\gamma a_2(1320)}(s)$ at ${\mathrm{\Lambda }}_{f_2}=950\mathrm{MeV}$ and ${\mathrm{\Lambda }}_{a_2}=1000\mathrm{MeV}$.

Figure 4

$\sigma (e^{+}{e}^{-}\to {\gamma }^{*}\to \gamma f_0(980))$ and $\sigma (e^{+}{e}^{-}\to {\gamma }^{*}\to \gamma a_0(980))$ at ${\mathrm{\Lambda }}_{f_0}=350\mathrm{MeV}$ and ${\mathrm{\Lambda }}_{a_0}=250\mathrm{MeV}$. Data are taken from Ref. [8].

Figure 5

The integral cross section divided by two-photon decay width $\sigma (e^{+}{e}^{-}\to {\gamma }^{*}\to \gamma f_0)/\mathrm{\Gamma }(f_0\to \gamma \gamma )$ for $f_0=f_0(1370)$, $f_0(1500)$, and $f_0(1710)$ with ${\mathrm{\Lambda }}_{f_0}=350\mathrm{MeV}$.

Figure 6

The integral cross section divided by two-photon decay width $\sigma (e^{+}{e}^{-}\to {\gamma }^{*}\to \gamma a_0)/\mathrm{\Gamma }(a_0\to \gamma \gamma )$ for $a_0=a_0(1450)$ and $a_0(1950)$ with ${\mathrm{\Lambda }}_{a_0}=250\mathrm{MeV}$.

Figure 7

$\sigma (e^{+}{e}^{-}\to {\gamma }^{*}\to \gamma f_2(1270))$ and $\sigma (e^{+}{e}^{-}\to {\gamma }^{*}\to \gamma a_2(1320))$ at ${\mathrm{\Lambda }}_{f_2}=950\mathrm{MeV}$ and ${\mathrm{\Lambda }}_{a_2}=1000\mathrm{MeV}$.