{"title":"根据巴利茨基-科夫切戈夫方程的解析解研究 HERA 的质子结构函数 F2p","authors":"Ranjan Saikia, Pragyan Phukan, Jayanta Kumar Sarma","doi":"10.1088/1572-9494/ad260d","DOIUrl":null,"url":null,"abstract":"In this paper, the proton structure function <inline-formula>\n<tex-math>\n<?CDATA ${F}_{2}^{p}(x,{Q}^{2})$?>\n</tex-math>\n<mml:math overflow=\"scroll\"><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:math>\n<inline-graphic xlink:href=\"ctpad260dieqn3.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> at small-<italic toggle=\"yes\">x</italic> is investigated using an analytical solution to the Balitsky–Kovchegov (BK) equation. In the context of the color dipole description of deep inelastic scattering (DIS), the structure function <inline-formula>\n<tex-math>\n<?CDATA ${F}_{2}^{p}(x,{Q}^{2})$?>\n</tex-math>\n<mml:math overflow=\"scroll\"><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:math>\n<inline-graphic xlink:href=\"ctpad260dieqn4.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> is computed by applying the analytical expression for the scattering amplitude <italic toggle=\"yes\">N</italic>(<italic toggle=\"yes\">k</italic>, <italic toggle=\"yes\">Y</italic>) derived from the BK solution. At transverse momentum <italic toggle=\"yes\">k</italic> and total rapidity <italic toggle=\"yes\">Y</italic>, the scattering amplitude <italic toggle=\"yes\">N</italic>(<italic toggle=\"yes\">k</italic>, <italic toggle=\"yes\">Y</italic>) represents the propagation of the quark-antiquark dipole in the color dipole description of DIS. Using the BK solution we extracted the integrated gluon density <italic toggle=\"yes\">xg</italic>(<italic toggle=\"yes\">x</italic>, <italic toggle=\"yes\">Q</italic>\n<sup>2</sup>) and then compared our theoretical estimation with the LHAPDF global data fits, NNPDF3.1sx and CT18. Finally, we have investigated the behavior of <inline-formula>\n<tex-math>\n<?CDATA ${F}_{2}^{p}(x,{Q}^{2})$?>\n</tex-math>\n<mml:math overflow=\"scroll\"><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:math>\n<inline-graphic xlink:href=\"ctpad260dieqn5.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> in the kinematic region of 10<sup>−5</sup> ≤ <italic toggle=\"yes\">x</italic> ≤ 10<sup>−2</sup> and 2.5 GeV<sup>2</sup> ≤ <italic toggle=\"yes\">Q</italic>\n<sup>2</sup> ≤ 60 GeV<sup>2</sup>. Our predicted results for <inline-formula>\n<tex-math>\n<?CDATA ${F}_{2}^{p}(x,{Q}^{2})$?>\n</tex-math>\n<mml:math overflow=\"scroll\"><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:math>\n<inline-graphic xlink:href=\"ctpad260dieqn6.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> within the specified kinematic region are in good agreement with the recent high-precision data for <inline-formula>\n<tex-math>\n<?CDATA ${F}_{2}^{p}(x,{Q}^{2})$?>\n</tex-math>\n<mml:math overflow=\"scroll\"><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy=\"false\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\"false\">)</mml:mo></mml:math>\n<inline-graphic xlink:href=\"ctpad260dieqn7.gif\" xlink:type=\"simple\"></inline-graphic>\n</inline-formula> from HERA (H1 Collaboration) and the LHAPDF global parametrization group NNPDF3.1sx.","PeriodicalId":10641,"journal":{"name":"Communications in Theoretical Physics","volume":"52 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Investigation of proton structure function F2p at HERA in light of an analytical solution to the Balitsky–Kovchegov equation\",\"authors\":\"Ranjan Saikia, Pragyan Phukan, Jayanta Kumar Sarma\",\"doi\":\"10.1088/1572-9494/ad260d\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, the proton structure function <inline-formula>\\n<tex-math>\\n<?CDATA ${F}_{2}^{p}(x,{Q}^{2})$?>\\n</tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\\\"false\\\">)</mml:mo></mml:math>\\n<inline-graphic xlink:href=\\\"ctpad260dieqn3.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> at small-<italic toggle=\\\"yes\\\">x</italic> is investigated using an analytical solution to the Balitsky–Kovchegov (BK) equation. In the context of the color dipole description of deep inelastic scattering (DIS), the structure function <inline-formula>\\n<tex-math>\\n<?CDATA ${F}_{2}^{p}(x,{Q}^{2})$?>\\n</tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\\\"false\\\">)</mml:mo></mml:math>\\n<inline-graphic xlink:href=\\\"ctpad260dieqn4.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> is computed by applying the analytical expression for the scattering amplitude <italic toggle=\\\"yes\\\">N</italic>(<italic toggle=\\\"yes\\\">k</italic>, <italic toggle=\\\"yes\\\">Y</italic>) derived from the BK solution. At transverse momentum <italic toggle=\\\"yes\\\">k</italic> and total rapidity <italic toggle=\\\"yes\\\">Y</italic>, the scattering amplitude <italic toggle=\\\"yes\\\">N</italic>(<italic toggle=\\\"yes\\\">k</italic>, <italic toggle=\\\"yes\\\">Y</italic>) represents the propagation of the quark-antiquark dipole in the color dipole description of DIS. Using the BK solution we extracted the integrated gluon density <italic toggle=\\\"yes\\\">xg</italic>(<italic toggle=\\\"yes\\\">x</italic>, <italic toggle=\\\"yes\\\">Q</italic>\\n<sup>2</sup>) and then compared our theoretical estimation with the LHAPDF global data fits, NNPDF3.1sx and CT18. Finally, we have investigated the behavior of <inline-formula>\\n<tex-math>\\n<?CDATA ${F}_{2}^{p}(x,{Q}^{2})$?>\\n</tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\\\"false\\\">)</mml:mo></mml:math>\\n<inline-graphic xlink:href=\\\"ctpad260dieqn5.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> in the kinematic region of 10<sup>−5</sup> ≤ <italic toggle=\\\"yes\\\">x</italic> ≤ 10<sup>−2</sup> and 2.5 GeV<sup>2</sup> ≤ <italic toggle=\\\"yes\\\">Q</italic>\\n<sup>2</sup> ≤ 60 GeV<sup>2</sup>. Our predicted results for <inline-formula>\\n<tex-math>\\n<?CDATA ${F}_{2}^{p}(x,{Q}^{2})$?>\\n</tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\\\"false\\\">)</mml:mo></mml:math>\\n<inline-graphic xlink:href=\\\"ctpad260dieqn6.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> within the specified kinematic region are in good agreement with the recent high-precision data for <inline-formula>\\n<tex-math>\\n<?CDATA ${F}_{2}^{p}(x,{Q}^{2})$?>\\n</tex-math>\\n<mml:math overflow=\\\"scroll\\\"><mml:msubsup><mml:mrow><mml:mi>F</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msubsup><mml:mo stretchy=\\\"false\\\">(</mml:mo><mml:mi>x</mml:mi><mml:mo>,</mml:mo><mml:msup><mml:mrow><mml:mi>Q</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mo stretchy=\\\"false\\\">)</mml:mo></mml:math>\\n<inline-graphic xlink:href=\\\"ctpad260dieqn7.gif\\\" xlink:type=\\\"simple\\\"></inline-graphic>\\n</inline-formula> from HERA (H1 Collaboration) and the LHAPDF global parametrization group NNPDF3.1sx.\",\"PeriodicalId\":10641,\"journal\":{\"name\":\"Communications in Theoretical Physics\",\"volume\":\"52 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2024-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Theoretical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1088/1572-9494/ad260d\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"PHYSICS, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Theoretical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1088/1572-9494/ad260d","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
摘要
本文利用巴利茨基-科夫切戈夫（BK）方程的解析解研究了小x处的质子结构函数F2p(x,Q2)。在深非弹性散射（DIS）的色偶极子描述背景下，结构函数 F2p(x,Q2) 是通过应用 BK 解法导出的散射振幅 N(k, Y) 分析表达式来计算的。在横动量 k 和总快速 Y 下，散射振幅 N(k, Y) 代表了 DIS 色彩偶极子描述中夸克-反夸克偶极子的传播。利用 BK 解决方案，我们提取了集成胶子密度 xg(x, Q2)，然后将我们的理论估计与 LHAPDF 全局数据拟合、NNPDF3.1sx 和 CT18 进行了比较。最后，我们研究了F2p(x,Q2)在10-5 ≤ x ≤ 10-2和2.5 GeV2 ≤ Q2 ≤ 60 GeV2运动学区域的行为。在指定的运动学区域内，我们对F2p(x,Q2)的预测结果与HERA（H1合作）和LHAPDF全局参数组NNPDF3.1sx最近的F2p(x,Q2)高精度数据非常吻合。
Investigation of proton structure function F2p at HERA in light of an analytical solution to the Balitsky–Kovchegov equation
In this paper, the proton structure function F2p(x,Q2) at small-x is investigated using an analytical solution to the Balitsky–Kovchegov (BK) equation. In the context of the color dipole description of deep inelastic scattering (DIS), the structure function F2p(x,Q2) is computed by applying the analytical expression for the scattering amplitude N(k, Y) derived from the BK solution. At transverse momentum k and total rapidity Y, the scattering amplitude N(k, Y) represents the propagation of the quark-antiquark dipole in the color dipole description of DIS. Using the BK solution we extracted the integrated gluon density xg(x, Q2) and then compared our theoretical estimation with the LHAPDF global data fits, NNPDF3.1sx and CT18. Finally, we have investigated the behavior of F2p(x,Q2) in the kinematic region of 10−5 ≤ x ≤ 10−2 and 2.5 GeV2 ≤ Q2 ≤ 60 GeV2. Our predicted results for F2p(x,Q2) within the specified kinematic region are in good agreement with the recent high-precision data for F2p(x,Q2) from HERA (H1 Collaboration) and the LHAPDF global parametrization group NNPDF3.1sx.
期刊介绍：
Communications in Theoretical Physics is devoted to reporting important new developments in the area of theoretical physics. Papers cover the fields of:
mathematical physics
quantum physics and quantum information
particle physics and quantum field theory
nuclear physics
gravitation theory, astrophysics and cosmology
atomic, molecular, optics (AMO) and plasma physics, chemical physics
statistical physics, soft matter and biophysics
condensed matter theory
others
Certain new interdisciplinary subjects are also incorporated.
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