Loopedia is a new database at loopedia.org for information on Feynman
integrals, intended to provide both bibliographic information as well as
results made available by the community. Its bibliometry is complementary to
that of SPIRES or arXiv in the sense that it admits searching for integrals by
graph-theoretical objects, e.g. its topology.Comment: 16 pages, lots of screenshot

Bogner, C.

Borowka, S.

Hahn, T.

Heinrich, G.

Jones, S. P.

Kerner, M.

Michel, M.

Panzer, E.

Papara, V.

von Manteuffel, A.

Computer Physics Communications

English

arXiv

C. Bogner

S. Borowka

T. Hahn

G. Heinrich

S.P. Jones

M. Kerner

A. von Manteuffel

M. Michel

E. Panzer

V. Papara

Crossref

Loopedia, a database for loop integrals

Loopedia is a new database at loopedia.org for Feynman integrals, providing both bibliographic information as well as results made available by the community. Its bibliometry is complementary to that of INSPIRE or arXiv, as it allows to search for integrals by graph-theoretical specifications, e.g. their topology

Bogner, C

Borowka, S

Hahn, T

Heinrich, G

Jones, SP

Kerner, M

Von Manteuffel, A

Michel, M

Panzer, Erik

Papara, V

Oxford University Research Archive

PoS(RADCOR2017)016Loopedia, a Database for Loop IntegralsC. BognerInstitut für Physik, Humboldt-Universität zu Berlin, D–10099 Berlin, GermanyS. BorowkaTheoretical Physics Department, CERN, Geneva, SwitzerlandT. Hahn∗Max-Planck-Institut für Physik, Föhringer Ring 6, D–80805 MunichE-mail: hahn@mpp.mpg.deG. HeinrichMax-Planck-Institut für Physik, Föhringer Ring 6, D–80805 MunichS.P. JonesMax-Planck-Institut für Physik, Föhringer Ring 6, D–80805 MunichM. KernerMax-Planck-Institut für Physik, Föhringer Ring 6, D–80805 MunichA. von ManteuffelDept. of Physics & Astronomy, Michigan State University, East Lansing, MI 48824, USAM. MichelCP3, Université Catholique de Louvain, B–1348 Louvain-la-Neuve, BelgiumE. PanzerAll Souls College, University of Oxford, OX1 4AL, Oxford, UKV. PaparaMax-Planck-Institut für Physik, Föhringer Ring 6, D–80805 MunichLoopedia is a new database at loopedia.org for Feynman integrals, providing both biblio-graphic information as well as results made available by the community. Its bibliometry is com-plementary to that of INSPIRE or arXiv, as it allows to search for integrals by graph-theoreticalspecifications, e.g. their topology.13th International Symposium on Radiative Corrections24–29 September, 2017St. Gilgen, Austria∗Speaker.c© Copyright owned by the author(s) under the terms of the Creative CommonsAttribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0). https://pos.sissa.it/PoS(RADCOR2017)016Loopedia T. Hahn1. IntroductionSearching and accessing bibliographic information in high-energy physics is generally solvedsatisfactorily through databases such as INSPIRE and arXiv. The search within these databases isindexed by ‘traditional’ metrics: author, title, year of publication, etc. However, for the practitionerin loop calculations it is not easy to find e.g. publications which refer to a particular loop integral,where the integral is specified in some graph-theoretical way, say by its topology.Loopedia [1] attempts to fill this gap, while not being limited to bibliographic information. Thedescription field of each record can hold any kind of textual information (e.g. URLs to software),and in addition arbitrary files can be uploaded, for example Fortran programs or Maple worksheets.2. Integrals and GraphsScalar Feynman loop integrals correspond to graphs and as such can be identified by a repre-sentation of the corresponding graph. A common choice is the edge (adjacency) list: each prop-agator (edge) is specified by the pair of vertices (nodes) it connects – external nodes need not bedistinguished to identify the topology. For example, the following two-loop box graph has the edgelist (e,0) (0,1) (0,2) (e,1) (1,3) (2,3) (2,4) (3,5) (e,4) (4,5) (e,5):e5e4e1e032The Nickel index [2, 3, 4] provides an alternative representation which is constructed as fol-lows: start at a vertex 0 and write down all vertices connected to 0 (e for external legs), then inserta ‘|’. Repeat the procedure for the other vertices but omit edges already included. For the two-loopbox graph above this procedure leads tovertex 0 1 2 3 4 5connected to e12 e[0]3 [0]34 [12]5 e[2]5 e[34]and hence its Nickel index is e12|e3|34|5|e5|e|.The Nickel index provides a compact identifier and has therefore been chosen as the basicobject by which integrals are indexed in Loopedia. Neither the edge list nor the Nickel index isunique, however, i.e. depending on the chosen labelling the same graph may have different edgelists/Nickel indices. Loopedia therefore canonicalizes all input.Besides this ‘bare’ Nickel index, which represents just the topology of the graph, Loopediaintroduces an augmented form, the colored Nickel index, CNickel for short, which additionallycaptures the configuration of masses and external q2. Loopedia color-codes them on the screen:1PoS(RADCOR2017)016Loopedia T. HahnNickelCNickel E1E2E3E4 P1P2P3P4P5P6P7For each ‘edge identifier’ of the Nickel (e or a digit), the coloring has a mass identifier:0 for zero,{z, n, s} for {any, non-zero, special} mass scale,1. . .9, a. . .y (not n, s) for a definite non-zero mass scale.The ‘s’ option is for cases like thresholds or pseudo-thresholds, and the exact meaning of ‘special’should be detailed in the description of the integral.The ‘definite’ identifiers also represent arbitrary scales (though not zero) but unlike the ‘zns’choices they express equality of scales within the graph, similar to named patterns in a computer-algebra system. The graph in the example above has several massive propagators/ legs, but all withthe same scale ‘1’.3. User GuideLoopedia is located at loopedia.org and when accessed, the Start Page is displayed. Oneenters a graph in the input field and/or chooses constraints for the search with the lower controlbars and then hits the button.The graph is entered via its edge list. The user has some freedom there: generally the input isunderstood as long as a pairing of vertices into propagators can reasonably be inferred from it. Thismeans that e.g. FeynArts [5] or QGRAF [6] notation can directly be pasted into the input form. Anedge list is internally converted to a Nickel index right away. Alternatively, the Nickel index canalso be entered directly.3.1 Browsing GraphsThe search results are displayed in Loopedia’s Graph Browser (Fig. 1). The matches areorganized such that the topology appears on the left-hand side and the configurations for whichinformation is available are on the right. Every graph icon is clickable.Clicking on one of the graph icons opens the single-graph display for that graph. For iconsin the left column it starts the Configuration Editor (Fig. 2), for icons in the right column it opensthe Record Display (Fig. 3). The Graph Browser is skipped and the Configuration Editor is startedimmediately if the search delivers no matches and an explicit graph was entered, to commenceadding a new record.3.2 Viewing Single GraphsThe navigation panel at the top has buttons to edit the configuration , the topology, to browse the configurations of the topology , and to return to the start page. Depending on the situation not all buttons may be active.2PoS(RADCOR2017)016Loopedia T. HahnFigure 1: The Loopedia Graph BrowserIn the main part of the page, a picture of the graph is shown underneath its various textualrepresentations (edge list, [C]Nickel index, database path). To the right the Configuration Chooseris displayed, with the defaults preset to the current values (if any).When editing a topology (bare Nickel index only) the page ends here, i.e. in order to proceedone needs to choose a configuration first. Otherwise the page continues with the available recordsand the New Record Form (Fig. 4).3.3 Entering New RecordsTo enter a new record one must first navigate to a graph and a configuration as outlined above.The New Record Form is found beneath the available records.Upon successful submission the submitted record is displayed again for review, with controlsfor editing and deletion (Fig. 5). An e-mail is sent to the submitter’s address with an individualizedURL that allows to access the review page again for future editing.The submitted records are not visible publicly before they have been confirmed by a moderator.This is a safety measure we implemented currently to prevent situations like submitters deletingeach other’s records; this may change in the future. The moderators are notified together with thesubmitter and will usually make new records public in a timely manner.4. Internal structureLoopedia is realized as a bash script in a CGI environment which uses the Unix file system asdatabase and is indexed by the mlocate utility.The database contains (in the real filesystem sense) one directory for each bare Nickel in-dex, with subdirectories for the configuration index (the second part of the CNickel) of the same3PoS(RADCOR2017)016Loopedia T. HahnFigure 2: The Loopedia Configuration Editorgraph. Underneath comes another layer of subdirectories for the visibility (public, private,deleted), and below that, one directory for each record. The actual implementation inserts a fewmore directory layers for indexing and performance reasons so that the full database path becomesdb/L/`/p/Nickel/s/Config/Visibility/Recordwhere L, `, p, s are the number of loops, legs, propagators, and scales, respectively. The databaseroot ‘db’ is included in the path to be able to make anchored searches. Records have identifierssimilar to the maildir format in Unix, e.g. 1482239373.Z1Fv.Almost all graph-theoretical operations in Loopedia are taken care of by the Python libraryGraphState [4]. GraphState allows to supplement a graph with configurations, i.e. add extra integersto either the nodes or the edges. The colored Nickel index used by Loopedia implements a singleedge coloring which encodes masses and external q2.To draw the graph, a Python function translates the graph into Graphviz’s DOT language [7],from which neato produces an SVG image. SVG is an XML-based vector format rendered by allmodern browsers and scales well in the icon-size plaquettes of the Graph Browser.5. SummaryWe presented a new database which allows to search for bibliographic and other informationon loop integrals based on topology-related information. The intention of Loopedia is to collect theinformation available in the literature and to make it searchable by graph. It relies on the conceptthat the community will actively contribute to the database by submitting new integral information.4PoS(RADCOR2017)016Loopedia T. HahnFigure 3: The Loopedia Record DisplayThe database is hosted at the Max Planck Institute for Physics in Munich with broadband internetaccess and a daily backup at loopedia.org.References[1] C. Bogner et al., “Loopedia, a Database for Loop Integrals,” arXiv:1709.01266 [hep-ph].[2] J.F. Nagle, J. Math. Phys. 7 (1966) 1588.[3] B.G. Nickel, D.I. Meiron, G.A. Baker, Compilation of 2-pt and 4-pt graphs for continuous spinmodel, University of Guelph report, 1977.[4] D. Batkovich, Y. Kirienko, M. Kompaniets, S. Novikov, arXiv:1409.8227.The GraphState library is at https://pypi.python.org/pypi/GraphState.[5] J. Küblbeck, M. Böhm, A. Denner, Comput. Phys. Commun. 60 (1990) 165;T. Hahn, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260].[6] P. Nogueira, J. Comput. Phys. 105 (1993) 279[7] E.R. Gansner, S.C. North, Software - Practice and Experience 30 (2000) 1203, graphviz.org.5PoS(RADCOR2017)016Loopedia T. HahnFigure 4: The New Record FormFigure 5: The Loopedia Record Review6

Loopedia is a new database at loopedia.org for information on Feynman integrals, intended to provide both bibliographic information as well as results made available by the community. Its bibliometry is complementary to that of INSPIRE or arXiv in the sense that it admits searching for integrals by graph-theoretical objects, e.g. its topology

Panzer, E

Oxford University Research Archive (ORA)

Loopedia is a new database at loopedia.org for Feynman integrals, providing both bibliographic information as well as results made available by the community. Its bibliometry is complementary to that of Inspire or arXiv, as it allows to search for integrals by graph-theoretical specifications, e.g. their topology

Jones, S P

von Manteuffel, A

CERN Document Server

Loopedia, a Database for Loop Integrals

Loopedia is a new database at loopedia.org for information on Feynman integrals, intended to provide both bibliographic information as well as results made available by the community. Its bibliometry is complementary to that of Inspire or arXiv in the sense that it admits searching for integrals by graph-theoretical objects, e.g. its topology.Loopedia is a new database at loopedia.org for information on Feynman integrals, intended to provide both bibliographic information as well as results made available by the community. Its bibliometry is complementary to that of SPIRES or arXiv in the sense that it admits searching for integrals by graph-theoretical objects, e.g. its topology

Jones, S.P.

Loopedia is a new database at loopedia.org for Feynman integrals, providing both bibliographic information as well as results made available by the community. Its bibliometry is complementary to that of Inspire or arXiv, as it allows to search for integrals by graph-theoretical specifications, e.g. their topology.Peer Reviewe

Bogner, Christian

Borowka, Sophia

Hahn, Thomas

Heinrich, Gudrun

Kerner, Matthias

von Manteuffel, Andreas

Papara, Viktor

edoc Server  Dokumenten-Publikationsserver der Humboldt-Universität zu Berlin

1Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distributionof this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Published under licence by IOP Publishing Ltd1234567890 ‘’“”ACAT2017 IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 1085 (2018) 052003  doi :10.1088/1742-6596/1085/5/052003Loopedia, a Database for Loop IntegralsC. Bogner1, S. Borowka2, T. Hahn3, G. Heinrich3, S.P. Jones3,M. Kerner3, A. von Manteuffel4, M. Michel5, E. Panzer6,V. Papara31 Institut für Physik, Humboldt-Universität zu Berlin, D–10099 Berlin, Germany2 Theoretical Physics Department, CERN, Geneva, Switzerland3 Max-Planck-Institut für Physik, Föhringer Ring 6, D–80805 Munich4 Dept. of Physics & Astronomy, Michigan State University, East Lansing, MI 48824, USA5 CP3, Université Catholique de Louvain, B–1348 Louvain-la-Neuve, Belgium6 All Souls College, University of Oxford, OX1 4AL, Oxford, UKAbstract. Loopedia is a new database at loopedia.org for Feynman integrals, providingboth bibliographic information as well as results made available by the community. Itsbibliometry is complementary to that of Inspire or arXiv, as it allows to search for integralsby graph-theoretical specifications, e.g. their topology.1. IntroductionSearching and accessing bibliographic information in high-energy physics is generally solvedsatisfactorily through databases such as Inspire and arXiv. The search within these databasesis indexed by ‘traditional’ metrics: author, title, year of publication, etc. However, forthe practitioner in loop calculations it is not easy to find e.g. publications which refer toa particular loop integral, where the integral is specified in some graph-theoretical way, sayby its topology.Loopedia [1] attempts to fill this gap, while not being limited to bibliographic information.The description field of each record can hold any kind of textual information (e.g. URLs tosoftware), and in addition arbitrary files can be uploaded, for example Fortran programs orMaple worksheets.2. Integrals and GraphsScalar Feynman loop integrals correspond to graphs and as such can be identified by arepresentation of the corresponding graph. A common choice is the edge (adjacency) list:each propagator (edge) is specified by the pair of vertices (nodes) it connects – external nodesneed not be distinguished to identify the topology. For example, the following two-loop boxgraph has the edge list (e,0) (0,1) (0,2) (e,1) (1,3) (2,3) (2,4) (3,5) (e,4) (4,5) (e,5):21234567890 ‘’“”ACAT2017 IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 1085 (2018) 052003  doi :10.1088/1742-6596/1085/5/052003e5e4e1e032The Nickel index [2, 3, 4] provides an alternative representation which is constructed asfollows: start at a vertex 0 and write down all vertices connected to 0 (e for external legs),then insert a ‘|’. Repeat the procedure for the other vertices but omit edges already included.For the two-loop box graph above this procedure leads tovertex 0 1 2 3 4 5connected to e12 e[0]3 [0]34 [12]5 e[2]5 e[34]and hence its Nickel index is e12|e3|34|5|e5|e|.The Nickel index provides a compact identifier and has therefore been chosen as the basicobject by which integrals are indexed in Loopedia. Neither the edge list nor the Nickel indexis unique, however, i.e. depending on the chosen labelling the same graph may have differentedge lists/Nickel indices. Loopedia therefore canonicalizes all input.Besides this ‘bare’ Nickel index, which represents just the topology of the graph, Loopediaintroduces an augmented form, the colored Nickel index, CNickel for short, which additionallycaptures the configuration of masses and external q2. Loopedia color-codes them on the screen:NickelCNickel E1E2E3E4 P1P2P3P4P5P6P7For each ‘edge identifier’ of the Nickel (e or a digit), the coloring has a mass identifier:0 for zero,{z, n, s} for {any, non-zero, special} mass scale,1. . . 9, a. . . y (not n, s) for a definite non-zero mass scale.The ‘s’ option is for cases like thresholds or pseudo-thresholds, and the exact meaning of‘special’ should be detailed in the description of the integral.The ‘definite’ identifiers also represent arbitrary scales (though not zero) but unlike the‘zns’ choices they express equality of scales within the graph, similar to named patterns in acomputer-algebra system. The graph in the example above has several massive propagators/legs, but all with the same scale ‘1’.3. User GuideLoopedia is located at loopedia.org and when accessed, the Start Page is displayed. Oneenters a graph in the input field and/or chooses constraints for the search with the lowercontrol bars and then hits the button.31234567890 ‘’“”ACAT2017 IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 1085 (2018) 052003  doi :10.1088/1742-6596/1085/5/052003The graph is entered via its edge list. The user has some freedom there: generally the inputis understood as long as a pairing of vertices into propagators can reasonably be inferred fromit. This means that e.g. FeynArts [5] or QGRAF [6] notation can directly be pasted into theinput form. An edge list is internally converted to a Nickel index right away. Alternatively,the Nickel index can also be entered directly.Figure 1. The Loopedia Graph Browser3.1. Browsing GraphsThe search results are displayed in Loopedia’s Graph Browser (Fig. 1). The matches areorganized such that the topology appears on the left-hand side and the configurations forwhich information is available are on the right. Every graph icon is clickable.Clicking on one of the graph icons opens the single-graph display for that graph. For iconsin the left column it starts the Configuration Editor (Fig. 2), for icons in the right columnit opens the Record Display (Fig. 3). The Graph Browser is skipped and the ConfigurationEditor is started immediately if the search delivers no matches and an explicit graph wasentered, to commence adding a new record.3.2. Viewing Single GraphsThe navigation panel at the top has buttons to edit the configuration , the topology, to browse the configurations of the topology , and to return to the startpage . Depending on the situation not all buttons may be active.In the main part of the page, a picture of the graph is shown underneath its various textualrepresentations (edge list, [C]Nickel index, database path). To the right the ConfigurationChooser is displayed, with the defaults preset to the current values (if any).41234567890 ‘’“”ACAT2017 IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 1085 (2018) 052003  doi :10.1088/1742-6596/1085/5/052003Figure 2. The Loopedia Configuration EditorWhen editing a topology (bare Nickel index only) the page ends here, i.e. in order toproceed one needs to choose a configuration first. Otherwise the page continues with theavailable records and the New Record Form (Fig. 4).3.3. Entering New RecordsTo enter a new record one must first navigate to a graph and a configuration as outlinedabove. The New Record Form is found beneath the available records.Upon successful submission the submitted record is displayed again for review, withcontrols for editing and deletion (Fig. 5). An e-mail is sent to the submitter’s address withan individualized URL that allows to access the review page again for future editing.The submitted records are not visible publicly before they have been confirmed by amoderator. This is a safety measure we implemented currently to prevent situations likesubmitters deleting each other’s records; this may change in the future. The moderators arenotified together with the submitter and will usually make new records public in a timelymanner.4. Internal structureLoopedia is realized as a bash script in a CGI environment which uses the Unix file systemas database and is indexed by the mlocate utility.The database contains (in the real filesystem sense) one directory for each bare Nickel index,with subdirectories for the configuration index (the second part of the CNickel) of the same51234567890 ‘’“”ACAT2017 IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 1085 (2018) 052003  doi :10.1088/1742-6596/1085/5/052003Figure 3. The Loopedia Record Displaygraph. Underneath comes another layer of subdirectories for the visibility (public, private,deleted), and below that, one directory for each record. The actual implementation insertsa few more directory layers for indexing and performance reasons so that the full databasepath becomesdb/L/`/p/Nickel/s/Config/Visibility/Recordwhere L, `, p, s are the number of loops, legs, propagators, and scales, respectively. Thedatabase root ‘db’ is included in the path to be able to make anchored searches. Recordshave identifiers similar to the maildir format in Unix, e.g. 1482239373.Z1Fv. (Maildir storeseach incoming e-mail in a separate file, whose name includes a timestamp, to avoid raceconditions. For the same reason, we store each record in a separate folder.)Almost all graph-theoretical operations in Loopedia are taken care of by the Pythonlibrary GraphState [4]. GraphState allows to supplement a graph with configurations, i.e. addextra integers to either the nodes or the edges. The colored Nickel index used by Loopediaimplements a single edge coloring which encodes masses and external q2.To draw the graph, a Python function translates the graph into Graphviz’s DOT language[7], from which neato produces an SVG image. SVG is an XML-based vector format renderedby all modern browsers and scales well in the icon-size plaquettes of the Graph Browser.5. SummaryWe presented a new database which allows to search for bibliographic and other informationon loop integrals based on topology-related information. The intention of Loopedia is tocollect the information available in the literature and to make it searchable by graph. It relies61234567890 ‘’“”ACAT2017 IOP PublishingIOP Conf. Series: Journal of Physics: Conf. Series 1085 (2018) 052003  doi :10.1088/1742-6596/1085/5/052003Figure 4. The New Record FormFigure 5. The Loopedia Record Reviewon the concept that the community will actively contribute to the database by submittingnew integral information. The database is hosted at the Max Planck Institute for Physics inMunich with broadband internet access and a daily backup at loopedia.org.[1] C. Bogner et al., “Loopedia, a Database for Loop Integrals,” arXiv:1709.01266 [hep-ph].[2] J.F. Nagle, J. Math. Phys. 7 (1966) 1588.[3] B.G. Nickel, D.I. Meiron, G.A. Baker, Compilation of 2-pt and 4-pt graphs for continuous spin model,University of Guelph report, 1977.[4] D. Batkovich, Y. Kirienko, M. Kompaniets, S. Novikov, arXiv:1409.8227.The GraphState library is at https://pypi.python.org/pypi/GraphState.[5] J. Küblbeck, M. Böhm, A. Denner, Comput. Phys. Commun. 60 (1990) 165;T. Hahn, Comput. Phys. Commun. 140 (2001) 418 [hep-ph/0012260].[6] P. Nogueira, J. Comput. Phys. 105 (1993) 279[7] E.R. Gansner, S.C. North, Software - Practice and Experience 30 (2000) 1203, graphviz.org.

Journal of Physics Conference Series

ORA - Oxford University Research Archive

https://edoc.hu-berlin.de/bitstream/18452/25435/4/JPCS_1085_5_052003.pdf

Loopedia, a Database for Loop Integrals

Abstract

Similar works

Full text

Available Versions

Crossref

Oxford University Research Archive

Oxford University Research Archive

Oxford University Research Archive (ORA)

CERN Document Server

Oxford University Research Archive (ORA)

CERN Document Server

edoc Server Dokumenten-Publikationsserver der Humboldt-Universität zu Berlin

ORA - Oxford University Research Archive