Efficient numerical evaluation of Feynman integrals

Zhao Li; Jian Wang; Qi-Shu Yan; Xiaoran Zhao

doi:10.1088/1674-1137/40/3/033103

Chinese Physics C> 2016, Vol. 40> Issue(3) : 033103 DOI: 10.1088/1674-1137/40/3/033103

Efficient numerical evaluation of Feynman integrals

Zhao Li ^1,2,, ,
Jian Wang ^3,, ,
Qi-Shu Yan ^4,5,, ,
Xiaoran Zhao ^1,4,,

1.
Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China
2.
State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China
3.
PRISMA Cluster of Excellence &
4.
School of Physics Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
5.
Center for High-Energy Physics, Peking University, Beijing 100871, China
6.
School of Physics Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Abstract
HTML
Reference
Related

PDF

Abstract：
Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with O(10^-3) accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass.
- sector decomposition ,
- quasi-Monte Carlo ,
- Higgs

References

[1]	S. Chatrchyan et al, Phys. Lett. B, 716: 30-61 (2012)
[2]	G. Aad et al, Phys. Lett. B, 716: 1-29 (2012)
[3]	C. Anzai, A. Hasselhuhn, M. Hschele et al, JHEP, 07: 140 (2015)
[4]	C. Anastasiou, C. Duhr, F. Dulat et al, Phys. Rev. Lett., 114(21): 212001 (2015)
[5]	D. de Florian and J. Mazzitelli, Phys. Rev. Lett., 111: 201801 (2013)
[6]	X. Chen, T. Gehrmann, E. Glover et al, Phys. Lett. B, 740: 147-150 (2015)
[7]	R. Boughezal, F. Caola, K. Melnikov et al, Phys. Rev. Lett., 115(8): 082003 (2015)
[8]	R. Boughezal, C. Focke, W. Giele et al, Phys. Lett. B, 748: 5-8 (2015)
[9]	O. Brein, A. Djouadi, and R. Harlander, Phys. Lett. B, 579: 149-156 (2004)
[10]	O. Brein, R. Harlander, M. Wiesemann et al, Eur. Phys. J. C, 72: 1868 (2012)
[11]	G. Ferrera, M. Grazzini, and F. Tramontano, Phys. Rev. Lett., 107: 152003 (2011)
[12]	G. Ferrera, M. Grazzini, and F. Tramontano, Phys. Lett. B, 740: 51-55 (2015)
[13]	T. Binoth and G. Heinrich, Nucl. Phys. B, 585: 741-759 (2000)
[14]	T. Binoth and G. Heinrich, Nucl. Phys. B, 680: 375-388 (2004)
[15]	G. Heinrich and V. A. Smirnov, Phys. Lett. B, 598: 55-66 (2004)
[16]	Z. Nagy and D. E. Soper, JHEP, 0309: 055 (2003)
[17]	Z. Nagy and D. E. Soper, Phys. Rev. D, 74: 093006 (2006)
[18]	T. Binoth, J. P. Guillet, G. Heinrich et al, JHEP, 10: 015 (2005)
[19]	C. Bogner and S. Weinzierl, Comput. Phys. Commun., 178: 596-610 (2008)
[20]	A. V. Smirnov, Comput. Phys. Commun., 185: 2090-2100 (2014)
[21]	S. Borowka, G. Heinrich, S. P. Jones et al, Comput. Phys. Commun., 196: 470-491 (2015)
[22]	G. P. Lepage, J. Comput. Phys., 27: 192 (1978)
[23]	C. Bogner and S. Weinzierl, Int. J. Mod. Phys. A, 25: 2585-2618 (2010)
[24]	G. Heinrich, Int. J. Mod. Phys. A, 23: 1457-1486 (2008)
[25]	T. Kaneko and T. Ueda, Comput. Phys. Commun., 181: 1352-1361 (2010)
[26]	T. Kaneko and T. Ueda, Sector Decomposition Via Computational Geometry, in Proceedings of 13th International Workshop on Advanced computing and analysis techniques in physics research (ACAT 2010), p. 082
[27]	C. Anastasiou, S. Beerli, and A. Daleo, JHEP, 0705: 071 (2007)
[28]	J. Dick, F. Y. Kuo, and I. H. Sloan, Acta Numerica, 22: 133-288 (2013)
[29]	F. Kuo, Journal of Complexity, 19(3): 301-320 (2003), oberwolfach Special Issue
[30]	J. Dick, Journal of Complexity, 20(4): 493-522 (2004)
[31]	K. A. Olive et al, Chin. Phys. C, 38: 090001 (2014)
[32]	T. Hahn, Comput. Phys. Commun., 168: 78-95 (2005)
[33]	T. Hahn and M. Perez-Victoria, Comput. Phys. Commun., 118: 153-165 (1999)

Access

Get Citation

Zhao Li, Jian Wang, Qi-Shu Yan and Xiaoran Zhao. Efficient numerical evaluation of Feynman integrals[J]. Chinese Physics C, 2016, 40(3): 033103. doi: 10.1088/1674-1137/40/3/033103

Zhao Li, Jian Wang, Qi-Shu Yan and Xiaoran Zhao. Efficient numerical evaluation of Feynman integrals[J]. Chinese Physics C, 2016, 40(3): 033103. doi: 10.1088/1674-1137/40/3/033103 shu

RIS(for EndNote,Reference Manager,ProCite)

BibTex

Txt

Milestone

Received: 2015-08-13
Revised: 2015-10-23

Fund

Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)

Article Metric

Article Views(3048)
PDF Downloads(52)
Cited by(0)

Policy on re-use

To reuse of Open Access content published by CPC, for content published under the terms of the Creative Commons Attribution 3.0 license (“CC CY”), the users don’t need to request permission to copy, distribute and display the final published version of the article and to create derivative works, subject to appropriate attribution.

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Efficient numerical evaluation of Feynman integrals

Corresponding author: Zhao Li,

Corresponding author: Jian Wang,

Corresponding author: Qi-Shu Yan,

Corresponding author: Xiaoran Zhao,

1. Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China

2. State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China

3. PRISMA Cluster of Excellence &

4. School of Physics Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

5. Center for High-Energy Physics, Peking University, Beijing 100871, China

6. School of Physics Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received Date: 2015-08-13

Accepted Date: 2015-10-23

Available Online: 2016-02-29

Fund Project: Supported by the Natural Science Foundation of China (11305179 11475180), Youth Innovation Promotion Association, CAS, IHEP Innovation (Y4545170Y2), State Key Lab for Electronics and Particle Detectors, Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y4KF061CJ1), Cluster of Excellence Precision Physics, Fundamental Interactions and Structure of Matter (PRISMA-EXC 1098)

Abstract: Feynman loop integrals are a key ingredient for the calculation of higher order radiation effects, and are responsible for reliable and accurate theoretical prediction. We improve the efficiency of numerical integration in sector decomposition by implementing a quasi-Monte Carlo method associated with the CUDA/GPU technique. For demonstration we present the results of several Feynman integrals up to two loops in both Euclidean and physical kinematic regions in comparison with those obtained from FIESTA3. It is shown that both planar and non-planar two-loop master integrals in the physical kinematic region can be evaluated in less than half a minute with O(10^-3) accuracy, which makes the direct numerical approach viable for precise investigation of higher order effects in multi-loop processes, e.g. the next-to-leading order QCD effect in Higgs pair production via gluon fusion with a finite top quark mass.

HTML

Reference (33)

Efficient numerical evaluation of Feynman integrals

Abstract：

References

Access

Article Metrics

Metrics

通讯作者: 陈斌, bchen63@163.com

Email This Article