Two-loop integrals for tt¯+jet production at hadron colliders in the leading colour approximation
A bstract We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for pp → t t ¯ j . We derive differential equations for the master integrals by solving the integration-by-parts identities over finite fields. Of the two...
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| Veröffentlicht in: | The journal of high energy physics 2024-07, Vol.2024 (7), p.73 |
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| container_title | The journal of high energy physics |
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| creator | Badger, Simon Becchetti, Matteo Giraudo, Nicolò Zoia, Simone |
| description | A
bstract
We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for
pp
→
t
t
¯
j
. We derive differential equations for the master integrals by solving the integration-by-parts identities over finite fields. Of the two systems of differential equations, one is presented in canonical ‘d log’ form, while the other is found to have an elliptic sector. For the elliptic topology we identify the relevant elliptic curve, and present the differential equations in a more general form which depends quadratically on
ε
and contains non-logarithmic one-forms in addition to the canonical d log’s. We solve the systems of differential equations numerically using generalised series expansions with the boundary terms obtained using the auxiliary mass flow method. A summary of all one-loop and two-loop planar topologies is presented including the list of alphabet letters for the ‘d log’ form systems and high-precision boundary values. |
| doi_str_mv | 10.1007/JHEP07(2024)073 |
| format | Article |
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bstract
We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for
pp
→
t
t
¯
j
. We derive differential equations for the master integrals by solving the integration-by-parts identities over finite fields. Of the two systems of differential equations, one is presented in canonical ‘d log’ form, while the other is found to have an elliptic sector. For the elliptic topology we identify the relevant elliptic curve, and present the differential equations in a more general form which depends quadratically on
ε
and contains non-logarithmic one-forms in addition to the canonical d log’s. We solve the systems of differential equations numerically using generalised series expansions with the boundary terms obtained using the auxiliary mass flow method. A summary of all one-loop and two-loop planar topologies is presented including the list of alphabet letters for the ‘d log’ form systems and high-precision boundary values.</description><identifier>EISSN: 1029-8479</identifier><identifier>DOI: 10.1007/JHEP07(2024)073</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Approximation ; Classical and Quantum Gravitation ; Color ; Curves ; Differential equations ; Elementary Particles ; Elliptic functions ; Fields (mathematics) ; Identities ; Integrals ; Kinematics ; Mass flow ; Physics ; Physics and Astronomy ; Quantum Field Theories ; Quantum Field Theory ; Quantum Physics ; Quarks ; Regular Article - Theoretical Physics ; Relativity Theory ; Series expansion ; String Theory ; Topology</subject><ispartof>The journal of high energy physics, 2024-07, Vol.2024 (7), p.73</ispartof><rights>The Author(s) 2024</rights><rights>The Author(s) 2024. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><orcidid>0009-0002-0160-4896 ; 0000-0002-6273-8145 ; 0000-0002-8089-9209 ; 0000-0003-1159-728X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/JHEP07(2024)073$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://doi.org/10.1007/JHEP07(2024)073$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>314,776,780,860,27901,27902,41096,42165,51551</link.rule.ids></links><search><creatorcontrib>Badger, Simon</creatorcontrib><creatorcontrib>Becchetti, Matteo</creatorcontrib><creatorcontrib>Giraudo, Nicolò</creatorcontrib><creatorcontrib>Zoia, Simone</creatorcontrib><title>Two-loop integrals for tt¯+jet production at hadron colliders in the leading colour approximation</title><title>The journal of high energy physics</title><addtitle>J. High Energ. Phys</addtitle><description>A
bstract
We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for
pp
→
t
t
¯
j
. We derive differential equations for the master integrals by solving the integration-by-parts identities over finite fields. Of the two systems of differential equations, one is presented in canonical ‘d log’ form, while the other is found to have an elliptic sector. For the elliptic topology we identify the relevant elliptic curve, and present the differential equations in a more general form which depends quadratically on
ε
and contains non-logarithmic one-forms in addition to the canonical d log’s. We solve the systems of differential equations numerically using generalised series expansions with the boundary terms obtained using the auxiliary mass flow method. A summary of all one-loop and two-loop planar topologies is presented including the list of alphabet letters for the ‘d log’ form systems and high-precision boundary values.</description><subject>Approximation</subject><subject>Classical and Quantum Gravitation</subject><subject>Color</subject><subject>Curves</subject><subject>Differential equations</subject><subject>Elementary Particles</subject><subject>Elliptic functions</subject><subject>Fields (mathematics)</subject><subject>Identities</subject><subject>Integrals</subject><subject>Kinematics</subject><subject>Mass flow</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum Field Theories</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Quarks</subject><subject>Regular Article - Theoretical Physics</subject><subject>Relativity Theory</subject><subject>Series expansion</subject><subject>String Theory</subject><subject>Topology</subject><issn>1029-8479</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>BENPR</sourceid><recordid>eNpFkEFLxDAQhYMguK6evQa8KFKdSdqmOcqyusqCHtZzSZp0t0ttapqi_8r_4C8zZQVPMzDvvXl8hFwg3CKAuHteLV9BXDFg6TUIfkRmCEwmRSrkCTkdhj0AZihhRvTm0yWtcz1tumC3XrUDrZ2nIfx83-xtoL13ZqxC4zqqAt0p4-NWubZtjPVDdNGws7S1yjTddjq40VPVR9tX864m3xk5rmOsPf-bc_L2sNwsVsn65fFpcb9OeszSkKCSlaoLlQtQGYg0Nzo1BZOG8dwIhpyDyeoqR651rbVALZjOFCpAjgqRz8nlITf-_hjtEMp97NLFlyUHUaCUBWNRBQfV0PvY2Pp_FUI50SsP9MqJXhnp8V8sdWY7</recordid><startdate>20240709</startdate><enddate>20240709</enddate><creator>Badger, Simon</creator><creator>Becchetti, Matteo</creator><creator>Giraudo, Nicolò</creator><creator>Zoia, Simone</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>8FE</scope><scope>8FG</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><orcidid>https://orcid.org/0009-0002-0160-4896</orcidid><orcidid>https://orcid.org/0000-0002-6273-8145</orcidid><orcidid>https://orcid.org/0000-0002-8089-9209</orcidid><orcidid>https://orcid.org/0000-0003-1159-728X</orcidid></search><sort><creationdate>20240709</creationdate><title>Two-loop integrals for tt¯+jet production at hadron colliders in the leading colour approximation</title><author>Badger, Simon ; Becchetti, Matteo ; Giraudo, Nicolò ; Zoia, Simone</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-p154t-1a9caf8a670a50746db4d829d236d721330d5fc613bbfbb71b72b5a1a0131a113</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Approximation</topic><topic>Classical and Quantum Gravitation</topic><topic>Color</topic><topic>Curves</topic><topic>Differential equations</topic><topic>Elementary Particles</topic><topic>Elliptic functions</topic><topic>Fields (mathematics)</topic><topic>Identities</topic><topic>Integrals</topic><topic>Kinematics</topic><topic>Mass flow</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum Field Theories</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Quarks</topic><topic>Regular Article - Theoretical Physics</topic><topic>Relativity Theory</topic><topic>Series expansion</topic><topic>String Theory</topic><topic>Topology</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Badger, Simon</creatorcontrib><creatorcontrib>Becchetti, Matteo</creatorcontrib><creatorcontrib>Giraudo, Nicolò</creatorcontrib><creatorcontrib>Zoia, Simone</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central UK/Ireland</collection><collection>Advanced Technologies & Aerospace Collection</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>Advanced Technologies & Aerospace Database</collection><collection>ProQuest Advanced Technologies & Aerospace Collection</collection><collection>Publicly Available Content Database</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>ProQuest Central China</collection><jtitle>The journal of high energy physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Badger, Simon</au><au>Becchetti, Matteo</au><au>Giraudo, Nicolò</au><au>Zoia, Simone</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Two-loop integrals for tt¯+jet production at hadron colliders in the leading colour approximation</atitle><jtitle>The journal of high energy physics</jtitle><stitle>J. High Energ. Phys</stitle><date>2024-07-09</date><risdate>2024</risdate><volume>2024</volume><issue>7</issue><spage>73</spage><pages>73-</pages><eissn>1029-8479</eissn><abstract>A
bstract
We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for
pp
→
t
t
¯
j
. We derive differential equations for the master integrals by solving the integration-by-parts identities over finite fields. Of the two systems of differential equations, one is presented in canonical ‘d log’ form, while the other is found to have an elliptic sector. For the elliptic topology we identify the relevant elliptic curve, and present the differential equations in a more general form which depends quadratically on
ε
and contains non-logarithmic one-forms in addition to the canonical d log’s. We solve the systems of differential equations numerically using generalised series expansions with the boundary terms obtained using the auxiliary mass flow method. A summary of all one-loop and two-loop planar topologies is presented including the list of alphabet letters for the ‘d log’ form systems and high-precision boundary values.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/JHEP07(2024)073</doi><orcidid>https://orcid.org/0009-0002-0160-4896</orcidid><orcidid>https://orcid.org/0000-0002-6273-8145</orcidid><orcidid>https://orcid.org/0000-0002-8089-9209</orcidid><orcidid>https://orcid.org/0000-0003-1159-728X</orcidid><oa>free_for_read</oa></addata></record> |
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| source | DOAJ Directory of Open Access Journals; EZB-FREE-00999 freely available EZB journals; Alma/SFX Local Collection; Springer Nature OA Free Journals |
| subjects | Approximation Classical and Quantum Gravitation Color Curves Differential equations Elementary Particles Elliptic functions Fields (mathematics) Identities Integrals Kinematics Mass flow Physics Physics and Astronomy Quantum Field Theories Quantum Field Theory Quantum Physics Quarks Regular Article - Theoretical Physics Relativity Theory Series expansion String Theory Topology |
| title | Two-loop integrals for tt¯+jet production at hadron colliders in the leading colour approximation |
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