Decomposition of Feynman integrals by multivariate intersection numbers
Hjalte Frellesvig,Federico Gasparotto,Stefano Laporta,M. K. Mandal,Pierpaolo Mastrolia,Luca Mattiazzi,Sebastian Mizera +6 more
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In this paper, the authors present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master Integrals, employing multivariate intersection numbers.Abstract:
We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master integrals, employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers, and provide three different approaches for a direct decomposition of Feynman integrals, which we dub the straight decomposition, the bottom-up decomposition, and the top-down decomposition. These algorithms exploit the unitarity structure of Feynman integrals by computing intersection numbers supported on cuts, in various orders, thus showing the synthesis of the intersection-theory concepts with unitarity-based methods and integrand decomposition. We perform explicit computations to exemplify all of these approaches applied to Feynman integrals, paving a way towards potential applications to generic multi-loop integrals.read more
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Integral reduction with Kira 2.0 and finite field methods
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Virtual QCD corrections to gluon-initiated diphoton plus jet production at hadron colliders
Simon Badger,Christian Brønnum-Hansen,Dmitry Chicherin,Thomas Gehrmann,H. B. Hartanto,Johannes M. Henn,Matteo Marcoli,Ryan Moodie,Tiziano Peraro,Simone Zoia +9 more
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On the computation of intersection numbers for twisted cocycles
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Constructing canonical Feynman integrals with intersection theory
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References
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Generalized unitarity and one-loop amplitudes in N=4 super-Yang-Mills
TL;DR: For scalar box functions with at least one massless external leg, the authors showed that the coefficients can also be obtained from quadruple cuts, which are not useful in Minkowski signature.
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JaxoDraw: A graphical user interface for drawing Feynman diagrams
Daniele Binosi,L. Theußl +1 more
TL;DR: JaxoDraw is a Feynman graph plotting tool written in Java that has a complete graphical user interface that allows all actions to be carried out via mouse click-and-drag operations in a WYSIWYG fashion.
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Reducing full one-loop amplitudes to scalar integrals at the integrand level
TL;DR: In this article, the coefficients of the 4-, 3-, 2-and 1-point one-loop integrals of arbitrary scattering processes are derived from the amplitude of the wavelet.
Book
Computational Commutative Algebra 1
Martin Kreuzer,Lorenzo Robbiano +1 more
TL;DR: This book about Grbner bases and their applications contains 3 chapters, 20 sections, 44 tutorials, 165 exercises, and numerous further amusements to help you bridge the gap between theoretical computer algebra and actual computation.
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New results on $\nu_\mu \to \nu_\tau$ appearance with the OPERA experiment in the CNGS beam
N. Agafonova,R. Brugnera,K. Hakamata,N. Di Marco,D. A. Podgrudkov,L. Patrizii,K. Suzuki,Naotaka Naganawa,H. Shibuya,G. Giacomelli,Vitaliano Chiarella,P. del Amo Sanchez,A. Bertolin,Thomas Strauss,J. Marteau,A. Schembri,E. Miyashita,Shigeki Aoki,T. Omura,N. M. Okateva,N. G. Polukhina,M. T. Muciaccia,Tomoko Ariga,Hiroki Rokujo,M. Pozzato,A. Ben Dhahbi,C. S. Yoon,T. Matsuo,A. Minotti,Jiro Kawada,Y. Nakatsuka,A. Hollnagel,G. Grella,S. Dusini,G. Brunetti,Mario Stipčević,C. Jollet,K. Ozaki,B. Klicek,J. Yoshida,G. Mandrioli,Pierre Vilain,Alessandro Paoloni,L. Consiglio,S. Ogawa,F. Pupilli,T. Asada,D. Duchesneau,Marcos Dracos,A. Garfagnini,H. Ishida,S. Zemskova,Antonio Russo,Antonio Ereditato,A. Meregaglia,Osamu Sato,I. Kreslo,A. B. Aleksandrov,A. M. Guler,S. M. Stellacci,Hiroaki Kawahara,S. Tufanli,A. Di Crescenzo,Utku Kose,K. Kodama,E. Pennacchio,Amina Zghiche,B. Büttner,I. G. Park,P. Strolin,M. Roda,M. Kamiscioglu,B. D. Park,Caren Hagner,R. Rescigno,Chiara Sirignano,C. Goellnitz,P. Migliozzi,M. Tenti,G. De Lellis,C. Kamiscioglu,Motoaki Miyanishi,Satoru Takahashi,N. Mauri,T. Hayakawa,Torben Ferber,M. Hierholzer,M. Yoshimoto,I. Shakiryanova,Maximiliano Sioli,Tatsuhiro Naka,Salvatore Buontempo,N. I. Starkov,A.G. Olshevsky,Nicola D'Ambrosio,J. Ebert,M. Spinetti,F. Terranova,Gianfranca De Rosa,Alessandro Pastore,Ante Ljubičić,J. Favier,T. M. Roganova,R. A. Fini,I. Rostovtseva,T. Schcedrina,Björn Wonsak,Adele Lauria,Toshiyuki Nakano,Krešimir Jakovčić,G. Shoziyoev,C. Gustavino,B. Hosseini,D. Autiero,J. H. Kim,H. Pessard,Yoshihiro Sato,F. Grianti,T. Fukuda,O. G. Ryazhskaya,Cristiano Bozza,M. S. Vladimirov,L. Chaussard,A. Sheshukov,Katsumi Ishiguro,Kunihiro Morishima,S. Mikado,Yu. Zaitsev,Artem Chukanov,André Rubbia,C. Pistillo,A. Longhin,D. Di Ferdinando,Maria Cristina Montesi,P. Tolun,M. Nakamura,V. Tioukov,S. Simone,E. Medinaceli,Y. A. Gornushkin,J. Goldberg,K. Pretzl,J. L. Vuilleumier,M. Ishikawa,L. Votano,P. Monacelli,J. Lenkeit,V. Matveev,Taishi Katsuragawa,Kimio Niwa,Nobuko Kitagawa,W. Schmidt-Parzefall,Masahiro Komatsu,G. Sirri,L. Stanco,P. F. Loverre,A. Badertscher,T. Hara,M. De Serio,M. Chernyavskiy,D. Bender,Gaston Wilquet,S. Dmitrievski,A. M. Anokhina,T. Shiraishi,A. S. Malgin,Akitaka Ariga +166 more
TL;DR: The OPERA neutrino experiment is designed to perform the first observation of neutrinos oscillations in direct appearance mode in the $
u_\mu \to
u_ \tau$ channel, via the detection of the leptons created in charged current interactions.