{"id":28926,"date":"2024-03-10T07:51:33","date_gmt":"2024-03-10T08:51:33","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%85%d8%b4%d8%a7%d8%b1%da%a9%d8%aa-%d8%ba%db%8c%d8%b1%d9%82%d8%a7%d8%a8%d9%84-%d9%81%d8%a7%da%a9%d8%aa%d9%88%d8%b1%d8%b3%d8%a7%d8%b2%db%8c-%d9%85%d8%b1%d8%aa%d8%a8\/"},"modified":"2024-03-10T07:51:39","modified_gmt":"2024-03-10T08:51:39","slug":"%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%85%d8%b4%d8%a7%d8%b1%da%a9%d8%aa-%d8%ba%db%8c%d8%b1%d9%82%d8%a7%d8%a8%d9%84-%d9%81%d8%a7%da%a9%d8%aa%d9%88%d8%b1%d8%b3%d8%a7%d8%b2%db%8c-%d9%85%d8%b1%d8%aa%d8%a8","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d9%85%d8%b4%d8%a7%d8%b1%da%a9%d8%aa-%d8%ba%db%8c%d8%b1%d9%82%d8%a7%d8%a8%d9%84-%d9%81%d8%a7%da%a9%d8%aa%d9%88%d8%b1%d8%b3%d8%a7%d8%b2%db%8c-%d9%85%d8%b1%d8%aa%d8%a8\/","title":{"rendered":"\u0645\u0642\u0627\u0644\u0647 \u0645\u0634\u0627\u0631\u06a9\u062a \u063a\u06cc\u0631\u0642\u0627\u0628\u0644 \u0641\u0627\u06a9\u062a\u0648\u0631\u0633\u0627\u0632\u06cc \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0628\u0647 \u0639\u0646\u0627\u0635\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u0645\u0644\u06af\u0631 \u062a\u06a9 \u062c\u0631\u0645\u06cc \u0633\u0647 \u062d\u0644\u0642\u0647 A_{Qg}^{(3)} \u0648 \u0394A_{Qg}^{(3)}"},"content":{"rendered":"\n\n\n\n\n\n\n\n\n\n\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\nThe non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $\u0394A_{Qg}^{(3)}$<\/td>\n<\/tr>\n
\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0645\u0642\u0627\u0644\u0647 \u0645\u0634\u0627\u0631\u06a9\u062a \u063a\u06cc\u0631\u0642\u0627\u0628\u0644 \u0641\u0627\u06a9\u062a\u0648\u0631\u0633\u0627\u0632\u06cc \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0628\u0647 \u0639\u0646\u0627\u0635\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u0645\u0644\u06af\u0631 \u062a\u06a9 \u062c\u0631\u0645\u06cc \u0633\u0647 \u062d\u0644\u0642\u0647 A_{Qg}^{(3)} \u0648 \u0394A_{Qg}^{(3)}<\/td>\n<\/tr>\n
\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\nJ. Ablinger, A. Behring, J. Bl\u00fcmlein, A. De Freitas, A. von Manteuffel, C. Schneider, K. Sch\u00f6nwald<\/td>\n<\/tr>\n
\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 <\/td>\n\u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n<\/tr>\n
\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647: <\/td>\nPDF<\/td>\n<\/tr>\n
\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n14<\/td>\n<\/tr>\n
\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a <\/td>\nHigh Energy Physics – Phenomenology,\u0641\u06cc\u0632\u06cc\u06a9 \u0627\u0646\u0631\u0698\u06cc \u0628\u0627\u0644\u0627 – \u067e\u062f\u06cc\u062f\u0627\u0631\u0634\u0646\u0627\u0633\u06cc ,<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a <\/td>\nSubmitted 1 March, 2024; originally announced March 2024. , Report number: DO–TH 23\/15. DESY 24–027, RISC Report series 24–02, ZU-TH 13\/24, CERN-TH-2024-30<\/td>\n<\/tr>\n
\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n\u0627\u0631\u0633\u0627\u0644 1 \u0645\u0627\u0631\u0633 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u0634\u0645\u0627\u0631\u0647 \u06af\u0632\u0627\u0631\u0634: \u0627\u0646\u062c\u0627\u0645-23\/15.DESY 24–027 \u060c \u06af\u0632\u0627\u0631\u0634 RISC \u0633\u0631\u06cc 24–02 \u060c Zu-Th 13\/24 \u060c Cern-TH-2024-30<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n

The non-first-order-factorizable contributions (The terms ‘first-order-factorizable contributions’ and ‘non-first-order-factorizable contributions’ have been introduced and discussed in Refs. \\cite{Behring:2023rlq,Ablinger:2023ahe}. They describe the factorization behaviour of the difference- or differential equations for a subset of master integrals of a given problem.) to the unpolarized and polarized massive operator matrix elements to three-loop order, $A_{Qg}^{(3)}$ and $\u0394A_{Qg}^{(3)}$, are calculated in the single-mass case. For the $_2F_1$-related master integrals of the problem, we use a semi-analytic method based on series expansions and utilize the first-order differential equations for the master integrals which does not need a special basis of the master integrals. Due to the singularity structure of this basis a part of the integrals has to be computed to $O(\\varepsilon^5)$ in the dimensional parameter. The solutions have to be matched at a series of thresholds and pseudo-thresholds in the region of the Bjorken variable $x \\in ]0,\\infty[$ using highly precise series expansions to obtain the imaginary part of the physical amplitude for $x \\in ]0,1]$ at a high relative accuracy. We compare the present results both with previous analytic results, the results for fixed Mellin moments, and a prediction in the small-$x$ region. We also derive expansions in the region of small and large values of $x$. With this paper, all three-loop single-mass unpolarized and polarized operator matrix elements are calculated.<\/p>\n

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  • \r\n\t\t\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627 \u0645\u06cc \u0628\u0627\u0634\u062f. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.\r\n\t\t<\/li>\r\n\t\t
  • \r\n\t\t\u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.\r\n\t\t<\/li>\r\n\t<\/td>\r\n\t\r\n\t\r\n<\/tr>\r\n<\/table>\r\n\r\n\r\n\n","protected":false},"excerpt":{"rendered":"

    \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc The non-first-order-factorizable contributions to the three-loop single-mass operator matrix elements $A_{Qg}^{(3)}$ and $\u0394A_{Qg}^{(3)}$ \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 […]<\/p>\n","protected":false},"featured_media":27,"comment_status":"open","ping_status":"closed","template":"","meta":{"pmpro_default_level":"","site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}}},"product_cat":[15,21],"product_tag":[319,320],"class_list":{"0":"post-28926","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-15","7":"product_cat-21","8":"product_tag-high-energy-physics-phenomenology","9":"product_tag-320","10":"pmpro-has-access","11":"desktop-align-left","12":"tablet-align-left","13":"mobile-align-left","15":"first","16":"instock","17":"shipping-taxable","18":"purchasable","19":"product-type-variable"},"yoast_head":"\n\u0645\u0642\u0627\u0644\u0647 \u0645\u0634\u0627\u0631\u06a9\u062a \u063a\u06cc\u0631\u0642\u0627\u0628\u0644 \u0641\u0627\u06a9\u062a\u0648\u0631\u0633\u0627\u0632\u06cc \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0628\u0647 \u0639\u0646\u0627\u0635\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u0645\u0644\u06af\u0631 \u062a\u06a9 \u062c\u0631\u0645\u06cc \u0633\u0647 \u062d\u0644\u0642\u0647 A_{Qg}^{(3)} \u0648 \u0394A_{Qg}^{(3)} - \u0641\u0631\u0648\u0634\u06af\u0627\u0647 \u0627\u06a9\u0633\u067e\u0631\u0633<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/express24.ir\/d\/product\/\u0645\u0642\u0627\u0644\u0647-\u0645\u0634\u0627\u0631\u06a9\u062a-\u063a\u06cc\u0631\u0642\u0627\u0628\u0644-\u0641\u0627\u06a9\u062a\u0648\u0631\u0633\u0627\u0632\u06cc-\u0645\u0631\u062a\u0628\/\" \/>\n<meta property=\"og:locale\" content=\"fa_IR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0645\u0642\u0627\u0644\u0647 \u0645\u0634\u0627\u0631\u06a9\u062a \u063a\u06cc\u0631\u0642\u0627\u0628\u0644 \u0641\u0627\u06a9\u062a\u0648\u0631\u0633\u0627\u0632\u06cc \u0645\u0631\u062a\u0628\u0647 \u0627\u0648\u0644 \u0628\u0647 \u0639\u0646\u0627\u0635\u0631 \u0645\u0627\u062a\u0631\u06cc\u0633 \u0639\u0645\u0644\u06af\u0631 \u062a\u06a9 \u062c\u0631\u0645\u06cc \u0633\u0647 \u062d\u0644\u0642\u0647 A_{Qg}^{(3)} \u0648 \u0394A_{Qg}^{(3)} - 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