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1. Numerical Scattering Amplitudes with pySecDec

Author

Heinrich, G., Jones, S. P., Kerner, M., Magerya, V., Olsson, A., and Schlenk, J.

Subjects
High Energy Physics - Phenomenology
Abstract

We present a major update of the program pySecDec, a toolbox for the evaluation of dimensionally regulated parameter integrals. The new version enables the evaluation of multi-loop integrals as well as amplitudes in a highly distributed and flexible way, optionally on GPUs. The program has been optimised and runs up to an order of magnitude faster than the previous release. A new integration procedure that utilises construction-free median Quasi-Monte Carlo rules is implemented. The median lattice rules can outperform our previous component-by-component rules by a factor of 5 and remove the limitation on the maximum number of sampling points. The expansion by regions procedures have been extended to support Feynman integrals with numerators, and functions for automatically determining when and how analytic regulators should be introduced are now available. The new features and performance are illustrated with several examples., Comment: 31 pages, 13 figures; published version

Published
2023
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2. Event Generators for High-Energy Physics Experiments

Author

Campbell, J. M., Diefenthaler, M., Hobbs, T. J., Höche, S., Isaacson, J., Kling, F., Mrenna, S., Reuter, J., Alioli, S., Andersen, J. R., Andreopoulos, C., Ankowski, A. M., Aschenauer, E. C., Ashkenazi, A., Baker, M. D., Barrow, J. L., van Beekveld, M., Bewick, G., Bhattacharya, S., Bierlich, C., Bothmann, E., Bredt, P., Broggio, A., Buckley, A., Butter, A., Butterworth, J. M., Byrne, E. P., Calame, C. M. Carloni, Chakraborty, S., Chen, X., Chiesa, M., Childers, J. T., Cruz-Martinez, J., Currie, J., Darvishi, N., Dasgupta, M., Denner, A., Dreyer, F. A., Dytman, S., El-Menoufi, B. K., Engel, T., Ravasio, S. Ferrario, Figueroa, D., Flower, L., Forshaw, J. R., Frederix, R., Friedland, A., Frixione, S., Gallagher, H., Gallmeister, K., Gardiner, S., Gauld, R., Gaunt, J., Gavardi, A., Gehrmann, T., Ridder, A. Gehrmann-De, Gellersen, L., Giele, W., Gieseke, S., Giuli, F., Glover, E. W. N., Grazzini, M., Grohsjean, A., Gütschow, C., Hamilton, K., Han, T., Hatcher, R., Heinrich, G., Helenius, I., Hen, O., Hirschi, V., Höfer, M., Holguin, J., Huss, A., Ilten, P., Jadach, S., Jentsch, A., Jones, S. P., Ju, W., Kallweit, S., Karlberg, A., Katori, T., Kerner, M., Kilian, W., Kirchgaeßer, M. M., Klein, S., Knobbe, M., Krause, C., Krauss, F., Lang, J., Lang, J. -N., Lee, G., Li, S. W., Lim, M. A., Lindert, J. M., Lombardi, D., Lönnblad, L., Löschner, M., Lurkin, N., Ma, Y., Machado, P., Magerya, V., Maier, A., Majer, I., Maltoni, F., Marcoli, M., Marinelli, G., Masouminia, M. R., Mastrolia, P., Mattelaer, O., Mazzitelli, J., McFayden, J., Medves, R., Meinzinger, P., Mo, J., Monni, P. F., Montagna, G., Morgan, T., Mosel, U., Nachman, B., Nadolsky, P., Nagar, R., Nagy, Z., Napoletano, D., Nason, P., Neumann, T., Nevay, L. J., Nicrosini, O., Niehues, J., Niewczas, K., Ohl, T., Ossola, G., Pandey, V., Papadopoulou, A., Papaefstathiou, A., Paz, G., Pellen, M., Pelliccioli, G., Peraro, T., Piccinini, F., Pickering, L., Pires, J., Płaczek, W., Plätzer, S., Plehn, T., Pozzorini, S., Prestel, S., Preuss, C. T., Price, A. C., Quackenbush, S., Re, E., Reichelt, D., Reina, L., Reuschle, C., Richardson, P., Rocco, M., Rocco, N., Roda, M., Garcia, A. Rodriguez, Roiser, S., Rojo, J., Rottoli, L., Salam, G. P., Schönherr, M., Schuchmann, S., Schumann, S., Schürmann, R., Scyboz, L., Seymour, M. H., Siegert, F., Signer, A., Chahal, G. Singh, Siódmok, A., Sjöstrand, T., Skands, P., Smillie, J. M., Sobczyk, J. T., Soldin, D., Soper, D. E., Soto-Ontoso, A., Soyez, G., Stagnitto, G., Tena-Vidal, J., Tomalak, O., Tramontano, F., Trojanowski, S., Tu, Z., Uccirati, S., Ullrich, T., Ulrich, Y., Utheim, M., Valassi, A., Verbytskyi, A., Verheyen, R., Wagman, M., Walker, D., Webber, B. R., Weinstein, L., White, O., Whitehead, J., Wiesemann, M., Wilkinson, C., Williams, C., Winterhalder, R., Wret, C., Xie, K., Yang, T-Z., Yazgan, E., Zanderighi, G., Zanoli, S., and Zapp, K.

Subjects
High Energy Physics - Phenomenology, High Energy Physics - Experiment
Abstract

We provide an overview of the status of Monte-Carlo event generators for high-energy particle physics. Guided by the experimental needs and requirements, we highlight areas of active development, and opportunities for future improvements. Particular emphasis is given to physics models and algorithms that are employed across a variety of experiments. These common themes in event generator development lead to a more comprehensive understanding of physics at the highest energies and intensities, and allow models to be tested against a wealth of data that have been accumulated over the past decades. A cohesive approach to event generator development will allow these models to be further improved and systematic uncertainties to be reduced, directly contributing to future experimental success. Event generators are part of a much larger ecosystem of computational tools. They typically involve a number of unknown model parameters that must be tuned to experimental data, while maintaining the integrity of the underlying physics models. Making both these data, and the analyses with which they have been obtained accessible to future users is an essential aspect of open science and data preservation. It ensures the consistency of physics models across a variety of experiments., Comment: 164 pages, 10 figures, contribution to Snowmass 2021

Published
2022

3. Expansion by regions with pySecDec

Author

Heinrich, G., Jahn, S., Jones, S. P., Kerner, M., Langer, F., Magerya, V., Poldaru, A., Schlenk, J., and Villa, E.

Subjects
High Energy Physics - Phenomenology
Abstract

We discuss the technique of expansion by regions from a geometric perspective, and its implementation within pySecDec, a toolbox for the evaluation of dimensionally regulated parameter integrals. The program offers an automated way to perform asymptotic expansions and provides a new mechanism for efficiently evaluating amplitudes, as well as individual integrals. The usage of the new features available within pySecDec is illustrated with several examples., Comment: 43 pages, 12 figures; replaced by version published in CPC

Published
2021
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4. Calculating Four-Loop Corrections in QCD

Author

Moch, S. and Magerya, V.

Subjects
High Energy Physics - Phenomenology
Abstract

We review the current status of perturbative corrections in QCD at four loops for scattering processes with space- and time-like kinematics at colliders, with specific focus on deep-inelastic scattering and electron-positron annihilation. The calculations build on the parametric reduction of loop and phase space integrals up to four-loop order using computer algebra programs such as FORM, designed for large scale computations., Comment: 13 pages LaTeX, 2 figures; based on the talk given by S.Moch at the DESY workshop "Antidifferentiation and the Calculation of Feynman Amplitudes", Zeuthen, Oct 04-09, 2020

Published
2021

5. Five-Particle Phase-Space Integrals in QCD

Author

Gituliar, O., Magerya, V., and Pikelner, A.

Subjects
High Energy Physics - Phenomenology
Abstract

We present analytical expressions for the 31 five-particle phase-space master integrals in massless QCD as an $\epsilon$-series with coefficients being multiple zeta values of weight up to 12. In addition, we provide a computer code for the Monte-Carlo integration in higher dimensions, based on the RAMBO algorithm, that has been used to numerically cross-check the obtained results in 4, 6, and 8 dimensions., Comment: 11 pages, 2 tables; contribution to the proceedings of Loops and Legs in Quantum Field Theory, 29 April 2018 - 04 May 2018, St. Goar, Germany; based on arXiv:1803.09084

Published
2018

6. Event generators for high-energy physics experiments

Author

Campbell, J, Diefenthaler, M, Hobbs, T, Hoche, S, Isaacson, J, Kling, F, Mrenna, S, Reuter, J, Alioli, S, Andersen, J, Andreopoulos, C, Ankowski, A, Aschenauer, E, Ashkenazi, A, Baker, M, Barrow, J, van Beekveld, M, Bewick, G, Bhattacharya, S, Bierlich, C, Bothmann, E, Bredt, P, Broggio, A, Buckley, A, Butter, A, Butterworth, J, Byrne, E, Calame, C, Chakraborty, S, Chen, X, Chiesa, M, Childers, J, Cruz-Martinez, J, Currie, J, Darvishi, N, Dasgupta, M, Denner, A, Dreyer, F, Dytman, S, El-Menoufi, B, Engel, T, Ravasio, S, Figueroa, D, Flower, L, Forshaw, J, Frederix, R, Friedland, A, Frixione, S, Gallagher, H, Gallmeister, K, Gardiner, S, Gauld, R, Gaunt, J, Gavardi, A, Gehrmann, T, De Ridder, A, Gellersen, L, Giele, W, Gieseke, S, Giuli, F, Glover, E, Grazzini, M, Grohsjean, A, Gutschow, C, Hamilton, K, Han, T, Hatcher, R, Heinrich, G, Helenius, I, Hen, O, Hirschi, V, Hofer, M, Holguin, J, Huss, A, Ilten, P, Jadach, S, Jentsch, A, Jones, S, Ju, W, Kallweit, S, Karlberg, A, Katori, T, Kerner, M, Kilian, W, Kirchgaesser, M, Klein, S, Knobbe, M, Krause, C, Krauss, F, Lang, J, Lee, G, Li, S, Lim, M, Lindert, J, Lombardi, D, Lonnblad, L, Loschner, M, Lurkin, N, Ma, Y, Machado, P, Magerya, V, Maier, A, Majer, I, Maltoni, F, Marcoli, M, Marinelli, G, Masouminia, M, Mastrolia, P, Mattelaer, O, Mazzitelli, J, Mcfayden, J, Medves, R, Meinzinger, P, Mo, J, Monni, P, Montagna, G, Morgan, T, Mosel, U, Nachman, B, Nadolsky, P, Nagar, R, Nagy, Z, Napoletano, D, Nason, P, Neumann, T, Nevay, L, Nicrosini, O, Niehues, J, Niewczas, K, Ohl, T, Ossola, G, Pandey, V, Papadopoulou, A, Papaefstathiou, A, Paz, G, Pellen, M, Pelliccioli, G, Peraro, T, Piccinini, F, Pickering, L, Pires, J, Placzek, W, Platzer, S, Plehn, T, Pozzorini, S, Prestel, S, Preuss, C, Price, A, Quackenbush, S, Re, E, Reichelt, D, Reina, L, Reuschle, C, Richardson, P, Rocco, M, Rocco, N, Roda, M, Garcia, A, Roiser, S, Rojo, J, Rottoli, L, Salam, G, Schonherr, M, Schuchmann, S, Schumann, S, Schurmann, R, Scyboz, L, Seymour, M, Siegert, F, Signer, A, Chahal, G, Siodmok, A, Sjostrand, T, Skands, P, Smillie, J, Sobczyk, J, Soldin, D, Soper, D, Soto-Ontoso, A, Soyez, G, Stagnitto, G, Tena-Vidal, J, Tomalak, O, Tramontano, F, Trojanowski, S, Tu, Z, Uccirati, S, Ullrich, T, Ulrich, Y, Utheim, M, Valassi, A, Verbytskyi, A, Verheyen, R, Wagman, M, Walker, D, Webber, B, Weinstein, L, White, O, Whitehead, J, Wiesemann, M, Wilkinson, C, Williams, C, Winterhalder, R, Wret, C, Xie, K, Yang, T, Yazgan, E, Zanderighi, G, Zanoli, S, Zapp, K, Campbell J. M., Diefenthaler M., Hobbs T. J., Hoche S., Isaacson J., Kling F., Mrenna S., Reuter J., Alioli S., Andersen J. R., Andreopoulos C., Ankowski A. M., Aschenauer E. C., Ashkenazi A., Baker M. D., Barrow J. L., van Beekveld M., Bewick G., Bhattacharya S., Bierlich C., Bothmann E., Bredt P., Broggio A., Buckley A., Butter A., Butterworth J. M., Byrne E. P., Calame C. M. C., Chakraborty S., Chen X., Chiesa M., Childers J. T., Cruz-Martinez J., Currie J., Darvishi N., Dasgupta M., Denner A., Dreyer F. A., Dytman S., El-Menoufi B. K., Engel T., Ravasio S. F., Figueroa D., Flower L., Forshaw J. R., Frederix R., Friedland A., Frixione S., Gallagher H., Gallmeister K., Gardiner S., Gauld R., Gaunt J., Gavardi A., Gehrmann T., De Ridder A. G., Gellersen L., Giele W., Gieseke S., Giuli F., Glover E. W. N., Grazzini M., Grohsjean A., Gutschow C., Hamilton K., Han T., Hatcher R., Heinrich G., Helenius I., Hen O., Hirschi V., Hofer M., Holguin J., Huss A., Ilten P., Jadach S., Jentsch A., Jones S. P., Ju W., Kallweit S., Karlberg A., Katori T., Kerner M., Kilian W., Kirchgaesser M. M., Klein S., Knobbe M., Krause C., Krauss F., Lang J., Lang J. -N., Lee G., Li S. W., Lim M. A., Lindert J. M., Lombardi D., Lonnblad L., Loschner M., Lurkin N., Ma Y., Machado P., Magerya V., Maier A., Majer I., Maltoni F., Marcoli M., Marinelli G., Masouminia M. R., Mastrolia P., Mattelaer O., Mazzitelli J., McFayden J., Medves R., Meinzinger P., Mo J., Monni P. F., Montagna G., Morgan T., Mosel U., Nachman B., Nadolsky P., Nagar R., Nagy Z., Napoletano D., Nason P., Neumann T., Nevay L. J., Nicrosini O., Niehues J., Niewczas K., Ohl T., Ossola G., Pandey V., Papadopoulou A., Papaefstathiou A., Paz G., Pellen M., Pelliccioli G., Peraro T., Piccinini F., Pickering L., Pires J., Placzek W., Platzer S., Plehn T., Pozzorini S., Prestel S., Preuss C. T., Price A. C., Quackenbush S., Re E., Reichelt D., Reina L., Reuschle C., Richardson P., Rocco M., Rocco N., Roda M., Garcia A. R., Roiser S., Rojo J., Rottoli L., Salam G. P., Schonherr M., Schuchmann S., Schumann S., Schurmann R., Scyboz L., Seymour M. H., Siegert F., Signer A., Chahal G. S., Siodmok A., Sjostrand T., Skands P., Smillie J. M., Sobczyk J. T., Soldin D., Soper D. E., Soto-Ontoso A., Soyez G., Stagnitto G., Tena-Vidal J., Tomalak O., Tramontano F., Trojanowski S., Tu Z., Uccirati S., Ullrich T., Ulrich Y., Utheim M., Valassi A., Verbytskyi A., Verheyen R., Wagman M., Walker D., Webber B. R., Weinstein L., White O., Whitehead J., Wiesemann M., Wilkinson C., Williams C., Winterhalder R., Wret C., Xie K., Yang T. -Z., Yazgan E., Zanderighi G., Zanoli S., Zapp K., Campbell, J, Diefenthaler, M, Hobbs, T, Hoche, S, Isaacson, J, Kling, F, Mrenna, S, Reuter, J, Alioli, S, Andersen, J, Andreopoulos, C, Ankowski, A, Aschenauer, E, Ashkenazi, A, Baker, M, Barrow, J, van Beekveld, M, Bewick, G, Bhattacharya, S, Bierlich, C, Bothmann, E, Bredt, P, Broggio, A, Buckley, A, Butter, A, Butterworth, J, Byrne, E, Calame, C, Chakraborty, S, Chen, X, Chiesa, M, Childers, J, Cruz-Martinez, J, Currie, J, Darvishi, N, Dasgupta, M, Denner, A, Dreyer, F, Dytman, S, El-Menoufi, B, Engel, T, Ravasio, S, Figueroa, D, Flower, L, Forshaw, J, Frederix, R, Friedland, A, Frixione, S, Gallagher, H, Gallmeister, K, Gardiner, S, Gauld, R, Gaunt, J, Gavardi, A, Gehrmann, T, De Ridder, A, Gellersen, L, Giele, W, Gieseke, S, Giuli, F, Glover, E, Grazzini, M, Grohsjean, A, Gutschow, C, Hamilton, K, Han, T, Hatcher, R, Heinrich, G, Helenius, I, Hen, O, Hirschi, V, Hofer, M, Holguin, J, Huss, A, Ilten, P, Jadach, S, Jentsch, A, Jones, S, Ju, W, Kallweit, S, Karlberg, A, Katori, T, Kerner, M, Kilian, W, Kirchgaesser, M, Klein, S, Knobbe, M, Krause, C, Krauss, F, Lang, J, Lee, G, Li, S, Lim, M, Lindert, J, Lombardi, D, Lonnblad, L, Loschner, M, Lurkin, N, Ma, Y, Machado, P, Magerya, V, Maier, A, Majer, I, Maltoni, F, Marcoli, M, Marinelli, G, Masouminia, M, Mastrolia, P, Mattelaer, O, Mazzitelli, J, Mcfayden, J, Medves, R, Meinzinger, P, Mo, J, Monni, P, Montagna, G, Morgan, T, Mosel, U, Nachman, B, Nadolsky, P, Nagar, R, Nagy, Z, Napoletano, D, Nason, P, Neumann, T, Nevay, L, Nicrosini, O, Niehues, J, Niewczas, K, Ohl, T, Ossola, G, Pandey, V, Papadopoulou, A, Papaefstathiou, A, Paz, G, Pellen, M, Pelliccioli, G, Peraro, T, Piccinini, F, Pickering, L, Pires, J, Placzek, W, Platzer, S, Plehn, T, Pozzorini, S, Prestel, S, Preuss, C, Price, A, Quackenbush, S, Re, E, Reichelt, D, Reina, L, Reuschle, C, Richardson, P, Rocco, M, Rocco, N, Roda, M, Garcia, A, Roiser, S, Rojo, J, Rottoli, L, Salam, G, Schonherr, M, Schuchmann, S, Schumann, S, Schurmann, R, Scyboz, L, Seymour, M, Siegert, F, Signer, A, Chahal, G, Siodmok, A, Sjostrand, T, Skands, P, Smillie, J, Sobczyk, J, Soldin, D, Soper, D, Soto-Ontoso, A, Soyez, G, Stagnitto, G, Tena-Vidal, J, Tomalak, O, Tramontano, F, Trojanowski, S, Tu, Z, Uccirati, S, Ullrich, T, Ulrich, Y, Utheim, M, Valassi, A, Verbytskyi, A, Verheyen, R, Wagman, M, Walker, D, Webber, B, Weinstein, L, White, O, Whitehead, J, Wiesemann, M, Wilkinson, C, Williams, C, Winterhalder, R, Wret, C, Xie, K, Yang, T, Yazgan, E, Zanderighi, G, Zanoli, S, Zapp, K, Campbell J. M., Diefenthaler M., Hobbs T. J., Hoche S., Isaacson J., Kling F., Mrenna S., Reuter J., Alioli S., Andersen J. R., Andreopoulos C., Ankowski A. M., Aschenauer E. C., Ashkenazi A., Baker M. D., Barrow J. L., van Beekveld M., Bewick G., Bhattacharya S., Bierlich C., Bothmann E., Bredt P., Broggio A., Buckley A., Butter A., Butterworth J. M., Byrne E. P., Calame C. M. C., Chakraborty S., Chen X., Chiesa M., Childers J. T., Cruz-Martinez J., Currie J., Darvishi N., Dasgupta M., Denner A., Dreyer F. A., Dytman S., El-Menoufi B. K., Engel T., Ravasio S. F., Figueroa D., Flower L., Forshaw J. R., Frederix R., Friedland A., Frixione S., Gallagher H., Gallmeister K., Gardiner S., Gauld R., Gaunt J., Gavardi A., Gehrmann T., De Ridder A. G., Gellersen L., Giele W., Gieseke S., Giuli F., Glover E. W. N., Grazzini M., Grohsjean A., Gutschow C., Hamilton K., Han T., Hatcher R., Heinrich G., Helenius I., Hen O., Hirschi V., Hofer M., Holguin J., Huss A., Ilten P., Jadach S., Jentsch A., Jones S. P., Ju W., Kallweit S., Karlberg A., Katori T., Kerner M., Kilian W., Kirchgaesser M. M., Klein S., Knobbe M., Krause C., Krauss F., Lang J., Lang J. -N., Lee G., Li S. W., Lim M. A., Lindert J. M., Lombardi D., Lonnblad L., Loschner M., Lurkin N., Ma Y., Machado P., Magerya V., Maier A., Majer I., Maltoni F., Marcoli M., Marinelli G., Masouminia M. R., Mastrolia P., Mattelaer O., Mazzitelli J., McFayden J., Medves R., Meinzinger P., Mo J., Monni P. F., Montagna G., Morgan T., Mosel U., Nachman B., Nadolsky P., Nagar R., Nagy Z., Napoletano D., Nason P., Neumann T., Nevay L. J., Nicrosini O., Niehues J., Niewczas K., Ohl T., Ossola G., Pandey V., Papadopoulou A., Papaefstathiou A., Paz G., Pellen M., Pelliccioli G., Peraro T., Piccinini F., Pickering L., Pires J., Placzek W., Platzer S., Plehn T., Pozzorini S., Prestel S., Preuss C. T., Price A. C., Quackenbush S., Re E., Reichelt D., Reina L., Reuschle C., Richardson P., Rocco M., Rocco N., Roda M., Garcia A. R., Roiser S., Rojo J., Rottoli L., Salam G. P., Schonherr M., Schuchmann S., Schumann S., Schurmann R., Scyboz L., Seymour M. H., Siegert F., Signer A., Chahal G. S., Siodmok A., Sjostrand T., Skands P., Smillie J. M., Sobczyk J. T., Soldin D., Soper D. E., Soto-Ontoso A., Soyez G., Stagnitto G., Tena-Vidal J., Tomalak O., Tramontano F., Trojanowski S., Tu Z., Uccirati S., Ullrich T., Ulrich Y., Utheim M., Valassi A., Verbytskyi A., Verheyen R., Wagman M., Walker D., Webber B. R., Weinstein L., White O., Whitehead J., Wiesemann M., Wilkinson C., Williams C., Winterhalder R., Wret C., Xie K., Yang T. -Z., Yazgan E., Zanderighi G., Zanoli S., and Zapp K.

Abstract

We provide an overview of the status of Monte-Carlo event generators for high-energy particle physics. Guided by the experimental needs and requirements, we highlight areas of active development, and opportunities for future improvements. Particular emphasis is given to physics models and algorithms that are employed across a variety of experiments. These common themes in event generator development lead to a more comprehensive understanding of physics at the highest energies and intensities, and allow models to be tested against a wealth of data that have been accumulated over the past decades. A cohesive approach to event generator development will allow these models to be further improved and systematic uncertainties to be reduced, directly contributing to future experimental success. Event generators are part of a much larger ecosystem of computational tools. They typically involve a number of unknown model parameters that must be tuned to experimental data, while maintaining the integrity of the underlying physics models. Making both these data, and the analyses with which they have been obtained accessible to future users is an essential aspect of open science and data preservation. It ensures the consistency of physics models across a variety of experiments.

Published
2024

7. Fuchsia: a tool for reducing differential equations for Feynman master integrals to epsilon form

Author

Gituliar, O. and Magerya, V.

Subjects
High Energy Physics - Phenomenology, Mathematical Physics, Mathematics - Classical Analysis and ODEs
Abstract

We present $\text{Fuchsia}$ $-$ an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients $\partial_x\,\mathbf{f}(x,\epsilon) = \mathbb{A}(x,\epsilon)\,\mathbf{f}(x,\epsilon)$ finds a basis transformation $\mathbb{T}(x,\epsilon)$, i.e., $\mathbf{f}(x,\epsilon) = \mathbb{T}(x,\epsilon)\,\mathbf{g}(x,\epsilon)$, such that the system turns into the epsilon form: $\partial_x\, \mathbf{g}(x,\epsilon) = \epsilon\,\mathbb{S}(x)\,\mathbf{g}(x,\epsilon)$, where $\mathbb{S}(x)$ is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator $\epsilon$. That makes the construction of the transformation $\mathbb{T}(x,\epsilon)$ crucial for obtaining solutions of the initial equations. In principle, $\text{Fuchsia}$ can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals., Comment: 20 pages

Published
2017
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8. Fuchsia and master integrals for splitting functions from differential equations in QCD

Author

Gituliar, O. and Magerya, V.

Subjects
High Energy Physics - Phenomenology
Abstract

We report on the recent progress in reducing differential equations for Feynman master integrals to canonical form with the help of a method proposed by Roman Lee. For the first time, we present Fuchsia --- our open-source implementation of the Lee algorithm written in Python using mathematical routines of a free computer algebra system SageMath. We demonstrate Fuchsia by reducing differential equations for NLO contributions to splitting functions in QCD, which contain both loops and legs integrals., Comment: 7 pages; Contribution to Loops and Legs in Quantum Field Theory 2016; *.m files with examples

Published
2016

10. Machine learning and LHC event generation

Author

Butter, A., Plehn, T., Schumann, S., Badger, S., Caron, S., Cranmer, K., Di Bello, F.A., Dreyer, E., Forte, S., Ganguly, S., Gonçalves, D., Gross, E., Heimel, T., Heinrich, G., Heinrich, L., Held, A., Höche, S., Howard, J.N., Ilten, P., Isaacson, J., Janßen, T., Jones, S, Kado, M., Kagan, M., Kasieczka, G., Kling, F., Kraml, S., Krause, C., Krauss, F., Kröninger, K., Barman, R.K., Luchmann, M., Magerya, V., Maitre, D., Malaescu, B., Maltoni, F., Martini, T., Mattelaer, O., Nachman, B., Pitz, S., Rojo, J., Schwartz, M., Shih, D., Siegert, F., Stegeman, R., Stienen, B.P.J., Thaler, J., Verheyen, Rob, Whiteson, D., Winterhalder, R., Zupan, J., Butter, A., Plehn, T., Schumann, S., Badger, S., Caron, S., Cranmer, K., Di Bello, F.A., Dreyer, E., Forte, S., Ganguly, S., Gonçalves, D., Gross, E., Heimel, T., Heinrich, G., Heinrich, L., Held, A., Höche, S., Howard, J.N., Ilten, P., Isaacson, J., Janßen, T., Jones, S, Kado, M., Kagan, M., Kasieczka, G., Kling, F., Kraml, S., Krause, C., Krauss, F., Kröninger, K., Barman, R.K., Luchmann, M., Magerya, V., Maitre, D., Malaescu, B., Maltoni, F., Martini, T., Mattelaer, O., Nachman, B., Pitz, S., Rojo, J., Schwartz, M., Shih, D., Siegert, F., Stegeman, R., Stienen, B.P.J., Thaler, J., Verheyen, Rob, Whiteson, D., Winterhalder, R., and Zupan, J.

Abstract

Contains fulltext : 292775.pdf (Publisher’s version ) (Open Access)

Published
2023

11. Expansion by regions with pySecDec

Author

Heinrich, G., primary, Jahn, S., additional, Jones, S.P., additional, Kerner, M., additional, Langer, F., additional, Magerya, V., additional, Põldaru, A., additional, Schlenk, J., additional, and Villa, E., additional

Published
2022
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12. Expansion by regions with pySecDec

Author

Heinrich, Gudrun, Jähnig, Sonja C, Jones, S P, Kerner, Matthias, Langer, F, Magerya, V, Põldaru, A, Schlenk, J, Villa, E, and University of Zurich

Subjects
High Energy Physics - Phenomenology, High Energy Physics - Phenomenology (hep-ph), 530 Physics, Hardware and Architecture, General Physics and Astronomy, FOS: Physical sciences, 10192 Physics Institute
Abstract

We discuss the technique of expansion by regions from a geometric perspective, and its implementation within pySecDec, a toolbox for the evaluation of dimensionally regulated parameter integrals. The program offers an automated way to perform asymptotic expansions and provides a new mechanism for efficiently evaluating amplitudes, as well as individual integrals. The usage of the new features available within pySecDec is illustrated with several examples., Comment: 43 pages, 12 figures; replaced by version published in CPC

Published
2021
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13. Calculating Four-Loop Corrections in QCD

Author

Moch, Sven-Olaf and Magerya, V.

Subjects
phase space, computer: algebra, perturbation theory: correction, kinematics, deep inelastic scattering, quantum chromodynamics, scattering, High Energy Physics::Experiment, parametric, electron positron: annihilation
Abstract

We review the current status of perturbative corrections in QCD at four loops for scattering processes with space- and time-like kinematics at colliders, with specific focus on deep-inelastic scattering and electron-positron annihilation. The calculations build on the parametric reduction of loop and phase space integrals up to four-loop order using computer algebra programs such as FORM, designed for large scale computations.

Published
2021
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15. $\color{fuchsia}{Fuchsia}$: a tool for reducing differential equations for Feynman master integrals to epsilon form

Author

Gituliar, O. and Magerya, V.

Subjects
Feynman, Feynman graph, differential equations, master integral, singularity
Abstract

We present $\color{fuchsia}{Fuchsia}$ $-$ an implementation of the Lee algorithm, which for a given system of ordinary differential equations with rational coefficients $\partial_x\,\mathbf{f}(x,\epsilon) = \mathbb{A}(x,\epsilon)\,\mathbf{f}(x,\epsilon)$ finds a basis transformation $\mathbb{T}(x,\epsilon)$, i.e., $\mathbf{f}(x,\epsilon) = \mathbb{T}(x,\epsilon)\,\mathbf{g}(x,\epsilon)$, such that the system turns into the epsilon form: $\partial_x\, \mathbf{g}(x,\epsilon) = \epsilon\,\mathbb{S}(x)\,\mathbf{g}(x,\epsilon)$, where $\mathbb{S}(x)$ is a Fuchsian matrix. A system of this form can be trivially solved in terms of polylogarithms as a Laurent series in the dimensional regulator $\epsilon$. That makes the construction of the transformation $\mathbb{T}(x,\epsilon)$ crucial for obtaining solutions of the initial equations. In principle, $\color{fuchsia}{Fuchsia}$ can deal with any regular systems, however its primary task is to reduce differential equations for Feynman master integrals. It ensures that solutions contain only regular singularities due to the properties of Feynman integrals.

Published
2017
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