Decoupling of the structure functions in momentum space based on the Laplace transformation
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914809155420160 |
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| author | Boroun, G. R. Ha, Phuoc |
| author_facet | Boroun, G. R. Ha, Phuoc |
| contents | Using Laplace transform techniques, we describe the determination of the longitudinal structure function $F_{L}(x,Q^2)$, at the leading-order approximation in momentum space, from the structure function $F_{2}(x,Q^2)$ and its derivative with respect to ${\ln}Q^2$ in a kinematical region of low values of the Bjorken variable $x$. Since the $x$ dependence of $F_2(x,Q^2)$ and its evolution with $Q^2$ are determined much better by the data than $F_L(x,Q^2)$, this method provides both a direct check on $F_L(x,Q^2)$ where measured, and a way of extending $F_L(x,Q^2)$ into regions of $x$ and $Q^2$ where there are currently no data. In our calculations, we ultilize the Block-Durand-Ha parametrization for the structure function $F_{2}(x,Q^2)$ [M. M. Block, L. Durand and P. Ha, Phys.Rev.D {\bf89}, 094027 (2014)]. We find that the Laplace transform method in momentum space provides correct behaviors of the extracted longitudinal structure function $F_{L}(x,Q^2)$ and that our obtained results are in line with data from the H1 Collaboration and other results for $F_{L}(x,Q^2)$ obtained using Mellin transform method. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_08560 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decoupling of the structure functions in momentum space based on the Laplace transformation Boroun, G. R. Ha, Phuoc High Energy Physics - Phenomenology Using Laplace transform techniques, we describe the determination of the longitudinal structure function $F_{L}(x,Q^2)$, at the leading-order approximation in momentum space, from the structure function $F_{2}(x,Q^2)$ and its derivative with respect to ${\ln}Q^2$ in a kinematical region of low values of the Bjorken variable $x$. Since the $x$ dependence of $F_2(x,Q^2)$ and its evolution with $Q^2$ are determined much better by the data than $F_L(x,Q^2)$, this method provides both a direct check on $F_L(x,Q^2)$ where measured, and a way of extending $F_L(x,Q^2)$ into regions of $x$ and $Q^2$ where there are currently no data. In our calculations, we ultilize the Block-Durand-Ha parametrization for the structure function $F_{2}(x,Q^2)$ [M. M. Block, L. Durand and P. Ha, Phys.Rev.D {\bf89}, 094027 (2014)]. We find that the Laplace transform method in momentum space provides correct behaviors of the extracted longitudinal structure function $F_{L}(x,Q^2)$ and that our obtained results are in line with data from the H1 Collaboration and other results for $F_{L}(x,Q^2)$ obtained using Mellin transform method. |
| title | Decoupling of the structure functions in momentum space based on the Laplace transformation |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2403.08560 |