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Nucleon’s Axial-Vector Form Factor in the Hard-Wall AdS/QCD Model

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Abstract

The axial-vector form factor of the nucleons is considered in the framework of hard-wall model of holographic QCD. A new interaction term between the bulk gauge and matter fields was included into the interaction Lagrangian. We obtain the axial-vector form factor of nucleons in the boundary QCD from the bulk action using AdS/CFT correspondence. The momentum square dependence of the axial-vector form factor is analysed numerically.

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Notes

  1. See [14, 15, 18] for more details.

  2. This relation takes place only for the nucleons in ground states.

  3. Such a trick was used in [26], where different isocomponents of the same field in the isospin background had different quantization formulas of spectra because of isospin interaction with the background. Quantization formulas for the spectra of all isocomponents, which were obtained from the boundary condition at z = z IR , were reduced to the same one and the values of the infrared boundaries for the different isocomponents were reduced to the same z IR by introducing extra infrared boundary terms.

  4. It should be noted that, in [45] a choice of Γ matrices is different than here and the Γ5 in that work has a form \( {\Gamma }^{5}=-i\gamma ^{5}=\left (\begin {array}{cc} 0 & i \\ i & 0 \end {array}\right )\). This is a reason of distinction between the forms of the extra boundary term here and in [45].

  5. In the five dimensional theory Γz is the fifth component of the 5D ΓA vector and under rotations of the \(\left (z,x\right )\) plane it is transformed as z component of this vector. So, it can not be considered as a scalar matrix in five dimensional theory as was γ 5 in four dimensional theory. Consequently, the Lagrangian terms in (35) do not remain invariant under these rotations. So, this kind of interaction can not be considered as a physical one in the bulk theory. The interpretation ”a minimal-type coupling, which is absent in four dimensions, but exists in five dimensions” concerning these terms is not consistent with the holographic duality, since this duality establishes a correspondence between the interactions in four and five dimensions both of which are physical.

  6. In the exact isospin symmetry case the quark (and nucleon) masses are equal and G A is the same for all isospin states (for both nucleons). In the medium, when we deal with isospin asymmetry, it will be different for the different isospin states due to the mass splitting effect ([24–26]).

  7. Note that the values of G A presented in the tables, except the hard-wall results, were taken from the graphs in the corresponding reference and are the approximate values.

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Acknowledgments

S. Mamedov and B.B. Sirvanli thanks T. Aliev for useful discussions. S. Mamedov thanks S. Siwach for reading manuscript and useful comments. This work has been done under the grant 2221 - Fellowships for Visiting Scientists and Scientists on Sabbatical Leave of TUBITAK organization of Turkey.

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Authors and Affiliations

  1. Physics Department, Gazi University, Teknikokullar, Ankara, Turkey

    Shahin Mamedov & Berin Belma Sirvanli

  2. Institute for Physical Problems, Baku State University, Z.Khalilov 23, Baku, AZ-1148, Azerbaijan

    Shahin Mamedov & Narmin Huseynova

  3. Institute of Physics, Azerbaijan National Academy of Sciences, H.Javid ave. 33, AZ-1143, Baku, Azerbaijan

    Shahin Mamedov & Ibrahim Atayev

  4. Theoretical Physics Department, Physics Faculty, Baku State University, Z.Khalilov 23, Baku, AZ-1148, Azerbaijan

    Narmin Huseynova

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  1. Shahin Mamedov
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  2. Berin Belma Sirvanli
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Mamedov, S., Sirvanli, B.B., Atayev, I. et al. Nucleon’s Axial-Vector Form Factor in the Hard-Wall AdS/QCD Model. Int J Theor Phys 56, 1861–1874 (2017). https://doi.org/10.1007/s10773-017-3330-x

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