Two-loop conformal generators for leading-twist operators in QCD
A bstract QCD evolution equations in minimal subtraction schemes have a hidden symmetry: one can construct three operators that commute with the evolution kernel and form an SL(2) algebra, i.e. they satisfy (exactly) the SL(2) commutation relations. In this paper we find explicit expressions for the...
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creator | Braun, V.M. Manashov, A.N. Moch, S. Strohmaier, M. |
description | A
bstract
QCD evolution equations in minimal subtraction schemes have a hidden symmetry: one can construct three operators that commute with the evolution kernel and form an SL(2) algebra, i.e. they satisfy (exactly) the SL(2) commutation relations. In this paper we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer
d
= 4 − 2ϵ space-time dimensions at the intermediate stage. In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams. Quantum corrections to conformal generators in
d
= 4 − 2ϵ effectively correspond to the conformal symmetry breaking in the physical theory in four dimensions and the SL(2) commutation relations lead to nontrivial constraints on the renormalization group equations for composite operators. This approach is valid to all orders in perturbation theory and the result includes automatically all terms that can be identified as due to a nonvanishing QCD
β
-function (in the physical theory in four dimensions). Our result can be used to derive three-loop evolution equations for flavor-nonsinglet quark-antiquark operators including mixing with the operators containing total derivatives. These equations govern, e.g., the scale dependence of generalized hadron parton distributions and light-cone meson distribution amplitudes. |
doi_str_mv | 10.1007/JHEP03(2016)142 |
format | Article |
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bstract
QCD evolution equations in minimal subtraction schemes have a hidden symmetry: one can construct three operators that commute with the evolution kernel and form an SL(2) algebra, i.e. they satisfy (exactly) the SL(2) commutation relations. In this paper we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer
d
= 4 − 2ϵ space-time dimensions at the intermediate stage. In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams. Quantum corrections to conformal generators in
d
= 4 − 2ϵ effectively correspond to the conformal symmetry breaking in the physical theory in four dimensions and the SL(2) commutation relations lead to nontrivial constraints on the renormalization group equations for composite operators. This approach is valid to all orders in perturbation theory and the result includes automatically all terms that can be identified as due to a nonvanishing QCD
β
-function (in the physical theory in four dimensions). Our result can be used to derive three-loop evolution equations for flavor-nonsinglet quark-antiquark operators including mixing with the operators containing total derivatives. These equations govern, e.g., the scale dependence of generalized hadron parton distributions and light-cone meson distribution amplitudes.</description><identifier>ISSN: 1029-8479</identifier><identifier>EISSN: 1029-8479</identifier><identifier>DOI: 10.1007/JHEP03(2016)142</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Broken symmetry ; Classical and Quantum Gravitation ; Commutation ; Elementary Particles ; Evolution ; Generators ; High energy physics ; Mathematical analysis ; Operators (mathematics) ; Physics ; Physics and Astronomy ; Quantum chromodynamics ; Quantum Field Theories ; Quantum Field Theory ; Quantum Physics ; Regular Article - Theoretical Physics ; Relativity Theory ; String Theory ; Symmetry</subject><ispartof>The journal of high energy physics, 2016-03, Vol.2016 (3), p.1-41, Article 142</ispartof><rights>The Author(s) 2016</rights><rights>SISSA, Trieste, Italy 2016</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c384t-ff013fca533f94bf511fec62aac9b751a2baa72eb99abe943fd9e3736a22929f3</citedby><cites>FETCH-LOGICAL-c384t-ff013fca533f94bf511fec62aac9b751a2baa72eb99abe943fd9e3736a22929f3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/JHEP03(2016)142$$EPDF$$P50$$Gspringer$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://doi.org/10.1007/JHEP03(2016)142$$EHTML$$P50$$Gspringer$$Hfree_for_read</linktohtml><link.rule.ids>315,782,786,866,27931,27932,41127,42196,51583</link.rule.ids></links><search><creatorcontrib>Braun, V.M.</creatorcontrib><creatorcontrib>Manashov, A.N.</creatorcontrib><creatorcontrib>Moch, S.</creatorcontrib><creatorcontrib>Strohmaier, M.</creatorcontrib><title>Two-loop conformal generators for leading-twist operators in QCD</title><title>The journal of high energy physics</title><addtitle>J. High Energ. Phys</addtitle><description>A
bstract
QCD evolution equations in minimal subtraction schemes have a hidden symmetry: one can construct three operators that commute with the evolution kernel and form an SL(2) algebra, i.e. they satisfy (exactly) the SL(2) commutation relations. In this paper we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer
d
= 4 − 2ϵ space-time dimensions at the intermediate stage. In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams. Quantum corrections to conformal generators in
d
= 4 − 2ϵ effectively correspond to the conformal symmetry breaking in the physical theory in four dimensions and the SL(2) commutation relations lead to nontrivial constraints on the renormalization group equations for composite operators. This approach is valid to all orders in perturbation theory and the result includes automatically all terms that can be identified as due to a nonvanishing QCD
β
-function (in the physical theory in four dimensions). Our result can be used to derive three-loop evolution equations for flavor-nonsinglet quark-antiquark operators including mixing with the operators containing total derivatives. These equations govern, e.g., the scale dependence of generalized hadron parton distributions and light-cone meson distribution amplitudes.</description><subject>Broken symmetry</subject><subject>Classical and Quantum Gravitation</subject><subject>Commutation</subject><subject>Elementary Particles</subject><subject>Evolution</subject><subject>Generators</subject><subject>High energy physics</subject><subject>Mathematical analysis</subject><subject>Operators (mathematics)</subject><subject>Physics</subject><subject>Physics and Astronomy</subject><subject>Quantum chromodynamics</subject><subject>Quantum Field Theories</subject><subject>Quantum Field Theory</subject><subject>Quantum Physics</subject><subject>Regular Article - Theoretical Physics</subject><subject>Relativity Theory</subject><subject>String Theory</subject><subject>Symmetry</subject><issn>1029-8479</issn><issn>1029-8479</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><sourceid>C6C</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><recordid>eNp1kNFLwzAQh4MoOKfPvhZ8mQ91d0nbNG_KNp0yUGE-hzRLRkfX1KRj-N_bUYUh-HTH3fc7jo-Qa4Q7BODjl_nsDdiIAma3mNATMkCgIs4TLk6P-nNyEcIGAFMUMCD3y72LK-eaSLvaOr9VVbQ2tfGqdT5E3SSqjFqV9Tpu92VoI9f87so6ep9ML8mZVVUwVz91SD4eZ8vJPF68Pj1PHhaxZnnSxtYCMqtVypgVSWFTRGt0RpXSouApKlooxakphFCFEQmzK2EYZ5miVFBh2ZCM-ruNd587E1q5LYM2VaVq43ZBYg45oshy2qE3f9CN2_m6-04i5ykHLjh01LintHcheGNl48ut8l8SQR6Myt6oPBiVndEuAX0idGS9Nv7o7j-Rb8aYd7M</recordid><startdate>20160301</startdate><enddate>20160301</enddate><creator>Braun, V.M.</creator><creator>Manashov, A.N.</creator><creator>Moch, S.</creator><creator>Strohmaier, M.</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</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><scope>7U5</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope></search><sort><creationdate>20160301</creationdate><title>Two-loop conformal generators for leading-twist operators in QCD</title><author>Braun, V.M. ; Manashov, A.N. ; Moch, S. ; Strohmaier, M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c384t-ff013fca533f94bf511fec62aac9b751a2baa72eb99abe943fd9e3736a22929f3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Broken symmetry</topic><topic>Classical and Quantum Gravitation</topic><topic>Commutation</topic><topic>Elementary Particles</topic><topic>Evolution</topic><topic>Generators</topic><topic>High energy physics</topic><topic>Mathematical analysis</topic><topic>Operators (mathematics)</topic><topic>Physics</topic><topic>Physics and Astronomy</topic><topic>Quantum chromodynamics</topic><topic>Quantum Field Theories</topic><topic>Quantum Field Theory</topic><topic>Quantum Physics</topic><topic>Regular Article - Theoretical Physics</topic><topic>Relativity Theory</topic><topic>String Theory</topic><topic>Symmetry</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Braun, V.M.</creatorcontrib><creatorcontrib>Manashov, A.N.</creatorcontrib><creatorcontrib>Moch, S.</creatorcontrib><creatorcontrib>Strohmaier, M.</creatorcontrib><collection>Springer Nature OA Free Journals</collection><collection>CrossRef</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>Access via ProQuest (Open Access)</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><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>The journal of high energy physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Braun, V.M.</au><au>Manashov, A.N.</au><au>Moch, S.</au><au>Strohmaier, M.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Two-loop conformal generators for leading-twist operators in QCD</atitle><jtitle>The journal of high energy physics</jtitle><stitle>J. High Energ. Phys</stitle><date>2016-03-01</date><risdate>2016</risdate><volume>2016</volume><issue>3</issue><spage>1</spage><epage>41</epage><pages>1-41</pages><artnum>142</artnum><issn>1029-8479</issn><eissn>1029-8479</eissn><abstract>A
bstract
QCD evolution equations in minimal subtraction schemes have a hidden symmetry: one can construct three operators that commute with the evolution kernel and form an SL(2) algebra, i.e. they satisfy (exactly) the SL(2) commutation relations. In this paper we find explicit expressions for these operators to two-loop accuracy going over to QCD in non-integer
d
= 4 − 2ϵ space-time dimensions at the intermediate stage. In this way conformal symmetry of QCD is restored on quantum level at the specially chosen (critical) value of the coupling, and at the same time the theory is regularized allowing one to use the standard renormalization procedure for the relevant Feynman diagrams. Quantum corrections to conformal generators in
d
= 4 − 2ϵ effectively correspond to the conformal symmetry breaking in the physical theory in four dimensions and the SL(2) commutation relations lead to nontrivial constraints on the renormalization group equations for composite operators. This approach is valid to all orders in perturbation theory and the result includes automatically all terms that can be identified as due to a nonvanishing QCD
β
-function (in the physical theory in four dimensions). Our result can be used to derive three-loop evolution equations for flavor-nonsinglet quark-antiquark operators including mixing with the operators containing total derivatives. These equations govern, e.g., the scale dependence of generalized hadron parton distributions and light-cone meson distribution amplitudes.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/JHEP03(2016)142</doi><tpages>41</tpages><oa>free_for_read</oa></addata></record> |
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subjects | Broken symmetry Classical and Quantum Gravitation Commutation Elementary Particles Evolution Generators High energy physics Mathematical analysis Operators (mathematics) Physics Physics and Astronomy Quantum chromodynamics Quantum Field Theories Quantum Field Theory Quantum Physics Regular Article - Theoretical Physics Relativity Theory String Theory Symmetry |
title | Two-loop conformal generators for leading-twist operators in QCD |
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