Analytic results for two-loop master integrals for Bhabha scattering I

Abstract We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman...
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Gespeichert in:

Autor*in:	Henn, Johannes M. [verfasserIn] Smirnov, Vladimir A.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2013

Schlagwörter:	NLO Computations

Anmerkung:	© SISSA, Trieste, Italy 2013

Übergeordnetes Werk:	Enthalten in: Journal of high energy physics - Berlin : Springer, 1997, 2013(2013), 11 vom: 06. Nov.
Übergeordnetes Werk:	volume:2013 ; year:2013 ; number:11 ; day:06 ; month:11

Links:	Volltext

DOI / URN:	10.1007/JHEP11(2013)041

Katalog-ID:	SPR030432685

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520			\|a Abstract We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. The crucial point of this strategy is to use a new basis of the master integrals where all master integrals are pure functions of uniform weight. This allows to cast the differential equations into a simple canonical form, which can straightforwardly be integrated order by order in ϵ. The boundary conditions are also particularly transparent in this setup. We identify the class of functions relevant to this problem to all orders in ϵ. We present the results up to weight four for all except one integrals in terms of a subset of Goncharov polylogarithms, which one may call two-dimensional harmonic polylogarithms. For one integral, and more generally at higher weight, the solution is written in terms of Chen iterated integrals.
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allfields	10.1007/JHEP11(2013)041 doi (DE-627)SPR030432685 (SPR)JHEP11(2013)041-e DE-627 ger DE-627 rakwb eng Henn, Johannes M. verfasserin aut Analytic results for two-loop master integrals for Bhabha scattering I 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA, Trieste, Italy 2013 Abstract We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. The crucial point of this strategy is to use a new basis of the master integrals where all master integrals are pure functions of uniform weight. This allows to cast the differential equations into a simple canonical form, which can straightforwardly be integrated order by order in ϵ. The boundary conditions are also particularly transparent in this setup. We identify the class of functions relevant to this problem to all orders in ϵ. We present the results up to weight four for all except one integrals in terms of a subset of Goncharov polylogarithms, which one may call two-dimensional harmonic polylogarithms. For one integral, and more generally at higher weight, the solution is written in terms of Chen iterated integrals. NLO Computations (dpeaa)DE-He213 Smirnov, Vladimir A. aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2013(2013), 11 vom: 06. Nov. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2013 year:2013 number:11 day:06 month:11 https://dx.doi.org/10.1007/JHEP11(2013)041 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2013 2013 11 06 11
spelling	10.1007/JHEP11(2013)041 doi (DE-627)SPR030432685 (SPR)JHEP11(2013)041-e DE-627 ger DE-627 rakwb eng Henn, Johannes M. verfasserin aut Analytic results for two-loop master integrals for Bhabha scattering I 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA, Trieste, Italy 2013 Abstract We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. The crucial point of this strategy is to use a new basis of the master integrals where all master integrals are pure functions of uniform weight. This allows to cast the differential equations into a simple canonical form, which can straightforwardly be integrated order by order in ϵ. The boundary conditions are also particularly transparent in this setup. We identify the class of functions relevant to this problem to all orders in ϵ. We present the results up to weight four for all except one integrals in terms of a subset of Goncharov polylogarithms, which one may call two-dimensional harmonic polylogarithms. For one integral, and more generally at higher weight, the solution is written in terms of Chen iterated integrals. NLO Computations (dpeaa)DE-He213 Smirnov, Vladimir A. aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2013(2013), 11 vom: 06. Nov. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2013 year:2013 number:11 day:06 month:11 https://dx.doi.org/10.1007/JHEP11(2013)041 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2013 2013 11 06 11
allfields_unstemmed	10.1007/JHEP11(2013)041 doi (DE-627)SPR030432685 (SPR)JHEP11(2013)041-e DE-627 ger DE-627 rakwb eng Henn, Johannes M. verfasserin aut Analytic results for two-loop master integrals for Bhabha scattering I 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA, Trieste, Italy 2013 Abstract We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. The crucial point of this strategy is to use a new basis of the master integrals where all master integrals are pure functions of uniform weight. This allows to cast the differential equations into a simple canonical form, which can straightforwardly be integrated order by order in ϵ. The boundary conditions are also particularly transparent in this setup. We identify the class of functions relevant to this problem to all orders in ϵ. We present the results up to weight four for all except one integrals in terms of a subset of Goncharov polylogarithms, which one may call two-dimensional harmonic polylogarithms. For one integral, and more generally at higher weight, the solution is written in terms of Chen iterated integrals. NLO Computations (dpeaa)DE-He213 Smirnov, Vladimir A. aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2013(2013), 11 vom: 06. Nov. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2013 year:2013 number:11 day:06 month:11 https://dx.doi.org/10.1007/JHEP11(2013)041 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2013 2013 11 06 11
allfieldsGer	10.1007/JHEP11(2013)041 doi (DE-627)SPR030432685 (SPR)JHEP11(2013)041-e DE-627 ger DE-627 rakwb eng Henn, Johannes M. verfasserin aut Analytic results for two-loop master integrals for Bhabha scattering I 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA, Trieste, Italy 2013 Abstract We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. The crucial point of this strategy is to use a new basis of the master integrals where all master integrals are pure functions of uniform weight. This allows to cast the differential equations into a simple canonical form, which can straightforwardly be integrated order by order in ϵ. The boundary conditions are also particularly transparent in this setup. We identify the class of functions relevant to this problem to all orders in ϵ. We present the results up to weight four for all except one integrals in terms of a subset of Goncharov polylogarithms, which one may call two-dimensional harmonic polylogarithms. For one integral, and more generally at higher weight, the solution is written in terms of Chen iterated integrals. NLO Computations (dpeaa)DE-He213 Smirnov, Vladimir A. aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2013(2013), 11 vom: 06. Nov. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2013 year:2013 number:11 day:06 month:11 https://dx.doi.org/10.1007/JHEP11(2013)041 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2013 2013 11 06 11
allfieldsSound	10.1007/JHEP11(2013)041 doi (DE-627)SPR030432685 (SPR)JHEP11(2013)041-e DE-627 ger DE-627 rakwb eng Henn, Johannes M. verfasserin aut Analytic results for two-loop master integrals for Bhabha scattering I 2013 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © SISSA, Trieste, Italy 2013 Abstract We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. The crucial point of this strategy is to use a new basis of the master integrals where all master integrals are pure functions of uniform weight. This allows to cast the differential equations into a simple canonical form, which can straightforwardly be integrated order by order in ϵ. The boundary conditions are also particularly transparent in this setup. We identify the class of functions relevant to this problem to all orders in ϵ. We present the results up to weight four for all except one integrals in terms of a subset of Goncharov polylogarithms, which one may call two-dimensional harmonic polylogarithms. For one integral, and more generally at higher weight, the solution is written in terms of Chen iterated integrals. NLO Computations (dpeaa)DE-He213 Smirnov, Vladimir A. aut Enthalten in Journal of high energy physics Berlin : Springer, 1997 2013(2013), 11 vom: 06. Nov. (DE-627)320910571 (DE-600)2027350-2 1029-8479 nnns volume:2013 year:2013 number:11 day:06 month:11 https://dx.doi.org/10.1007/JHEP11(2013)041 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_20 GBV_ILN_40 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_105 GBV_ILN_110 GBV_ILN_150 GBV_ILN_161 GBV_ILN_293 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2064 GBV_ILN_2068 GBV_ILN_2106 GBV_ILN_2108 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4307 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4338 AR 2013 2013 11 06 11
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author	Henn, Johannes M.
spellingShingle	Henn, Johannes M. misc NLO Computations Analytic results for two-loop master integrals for Bhabha scattering I
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topic_title	Analytic results for two-loop master integrals for Bhabha scattering I NLO Computations (dpeaa)DE-He213
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title	Analytic results for two-loop master integrals for Bhabha scattering I
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title_full	Analytic results for two-loop master integrals for Bhabha scattering I
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title_sort	analytic results for two-loop master integrals for bhabha scattering i
title_auth	Analytic results for two-loop master integrals for Bhabha scattering I
abstract	Abstract We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. The crucial point of this strategy is to use a new basis of the master integrals where all master integrals are pure functions of uniform weight. This allows to cast the differential equations into a simple canonical form, which can straightforwardly be integrated order by order in ϵ. The boundary conditions are also particularly transparent in this setup. We identify the class of functions relevant to this problem to all orders in ϵ. We present the results up to weight four for all except one integrals in terms of a subset of Goncharov polylogarithms, which one may call two-dimensional harmonic polylogarithms. For one integral, and more generally at higher weight, the solution is written in terms of Chen iterated integrals. © SISSA, Trieste, Italy 2013
abstractGer	Abstract We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. The crucial point of this strategy is to use a new basis of the master integrals where all master integrals are pure functions of uniform weight. This allows to cast the differential equations into a simple canonical form, which can straightforwardly be integrated order by order in ϵ. The boundary conditions are also particularly transparent in this setup. We identify the class of functions relevant to this problem to all orders in ϵ. We present the results up to weight four for all except one integrals in terms of a subset of Goncharov polylogarithms, which one may call two-dimensional harmonic polylogarithms. For one integral, and more generally at higher weight, the solution is written in terms of Chen iterated integrals. © SISSA, Trieste, Italy 2013
abstract_unstemmed	Abstract We evaluate analytically the master integrals for one of two types of planar families contributing to massive two-loop Bhabha scattering in QED. As in our previous paper, we apply a recently suggested new strategy to solve differential equations for master integrals for families of Feynman integrals. The crucial point of this strategy is to use a new basis of the master integrals where all master integrals are pure functions of uniform weight. This allows to cast the differential equations into a simple canonical form, which can straightforwardly be integrated order by order in ϵ. The boundary conditions are also particularly transparent in this setup. We identify the class of functions relevant to this problem to all orders in ϵ. We present the results up to weight four for all except one integrals in terms of a subset of Goncharov polylogarithms, which one may call two-dimensional harmonic polylogarithms. For one integral, and more generally at higher weight, the solution is written in terms of Chen iterated integrals. © SISSA, Trieste, Italy 2013
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title_short	Analytic results for two-loop master integrals for Bhabha scattering I
url	https://dx.doi.org/10.1007/JHEP11(2013)041
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Analytic results for two-loop master integrals for Bhabha scattering I

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