^{1,2}

^{,*}

^{1}

^{,†}

^{1}

^{,‡}

^{3}.

The structure functions

The idea of the present work is to investigate the leading

We are interested in the electromagnetic deep inelastic scattering (DIS) of a charged lepton from a vector meson. The DIS cross section is given by the contraction of a leptonic tensor,

In this work we focus on the structure functions associated with unpolarized vector mesons.

The polarized structure functions

At this point it is convenient to define the Bjorken parameter

We use the notation of

Let us briefly explain how different contributions behave in Eq.

In addition, we should comment on the different parametric regions in terms of

For finite values of

The work is organized as follows. In Sec.

DIS processes of charged leptons from scalar and vector mesons in the D3D7-brane system have been studied in several papers

Firstly, we give a brief description of the D3D7-brane system. Let us consider

For

It is possible to induce excitations in the transverse directions to the D7-brane. These are two types of scalar excitations

Some features of D7-brane fluctuations on the

Beyond the quadratic order, the interaction Lagrangian for these modes has been derived in reference

Up to this point we have described the D3D7-brane system presented in

For unpolarized vector mesons we shall study only the contributions to the

The FCS amplitude can be derived by using the gauge/string theory duality, by studying a four-point interaction with vector modes on the D7-brane and graviphotons related to current insertion on the boundary as external states. This gauge field arises from a particular decomposition of the graviton mode in ten dimensions:

The structure functions have been calculated in this context by considering a single intermediate hadron state in

These results are valid for DIS from mesons considered in the context of the D3D7-brane system. However, it is important to keep in mind that

The nonplanar

Feynman-Witten diagram associated to the DIS process with two intermediate hadron states. The momentum and the twist of each field are indicated, while the solutions are given in section

We want to study the

Since the lowest

The next step is to consider the exchange of

In the IR region, the relevant interaction includes two type II modes (one associated to the

For the UV vertex we have to consider the interaction between the

The diagram we need to calculate is shown in Fig.

In order to calculate the diagram we need the

Finally, we redefine the D7-brane fields as

We now derive the FCS amplitude related to the one-point function

For more details we refer the reader to Ref.

We expect qualitatively similar results to hold in the context of different Dp-brane models.

We have obtained the

This is similar to what happens for the glueball in the IR deformed version of

The physical implication of this result is that, at strong coupling, for the above energy range DIS is dominated by a two-hadron final state. From the viewpoint of the FCS process it corresponds, through the optical theorem, to a situation where there are two intermediate hadron states. The structure functions

It is important to consider the moments of the structure functions defined as

Several moments of these structure functions have been calculated in Ref.

There is a mistake in Table 5 of Ref.

In order to investigate this point we have carried out the best fit of the structure

Results of the first moments of

Comparison of our results for the first moments of the structure function

Figure

See for example Refs.

From Table

In addition, there are two very important aspects related to

In order to properly account for unitarity corrections in the holographic string theoretical dual picture one should be able to calculate a string worldsheet genus expansion of the four-point superstring theory scattering amplitude, which is at present an extremely difficult task. The string theory genus expansion of the scattering amplitude contains the sum of all massive string theory states propagating in the

On the other hand, fortunately at low

N. K. acknowledges kind hospitality at the Institut de Physique Théorique, CEA Saclay, and at the Institute for Theoretical Physics, University of Amsterdam, during the completion of this work. G. M. acknowledges kind hospitality at the International Center for Theoretical Physics, Trieste, where part of this work has been done. This work has been supported by the National Scientific Research Council of Argentina (CONICET), the National Agency for the Promotion of Science and Technology of Argentina (ANPCyT-FONCyT) Grants No. PICT-2015-1525 and No. PICT-2017-1647, and the CONICET Grant PIP-UE Búsqueda de nueva física.

Scalar spherical harmonics on the 3-sphere belong to the

In our case of interest, i.e., the UV vertex of the diagram shown in Fig.