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Deutsches Elektronen-Synchrotron
DESY, Zeuthen
Collaboration: DESY - RISC Linz
Advanced Summation Techniques and their Applications in Quantum Field
Theory
Mission :
Perturbative higher order calculations in Quantum Field Theories
rely on advanced analytic summation and integration techniques in
certain classes of sums and transcendental functions. Various probelms
lead to difference equations in Π-Σ
fields. The collaboration
between Deutsches Elektronen Synchrotron, DESY, Zeuthen and RISC at
Johannes Kepler University, Linz aims on further development of these
technologies, innovative search for new methods and the creation of efficient
tools based on Computer Algebra.
Beyond the application of these methods, algorithms and tools in Quantum
Field Theory, these methods may be of interest in other fields, such as
number theory (multiple zeta values, irrationality proofs, theory of
periods, new relations between sums), general summation and analytic
integration methods.
A cooperation contract between both institutions was signed
in February 2007. This contract has been prolonged for five years in February 2012.
Both sites also host nodes of the EU Network:
LHCPhenoNet.
Team :
DESY :
J. Blümlein,
S. Moch, T. Riemann; I. Bierenbaum (U. Hamburg), A. De Freitas,
A. Hasselhuhn, S. Klein (RWTH Aachen),
F. Wißbrock
RISC :
P. Paule, M. Kauers, C. Schneider; J. Ablinger (also DESY), C. Raab, M. Round, F. Stan (Paris)
Publications :
1. I. Bierenbaum, J. Blümlein, S. Klein, (DESY), C. Schneider (RISC),
Difference Equations in Massive Higher Order Calculations,
arXiv:0707.4659 [math-ph],DESY-07-111, SFB-CPP-07-041, Technical Report
No. 2007-19 SFB F013 (Austria), PoS ACAT2007:082, (2007).
2. S. Moch (DESY), C. Schneider (RISC),
Feynman integrals and difference equations,
arXiv::0709.1769 [math-ph],
DESY-07-138, SFB-CPP-07-050, Technical Report No. 2007-22
(Austria), PoS ACAT2007:083, (2007).
3. I. Bierenbaum, J. Blümlein, S. Klein, (DESY), C. Schneider (RISC)
Two-Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Productions to
O(ε),
arXiv::0208.0273 [hep-ph],
DESY-08-029, SFB-CPP-08-16, Technical Report No. 2008-04
(Austria), Nucl. Phys. B803 (2008) 1-41.
4. J. Blümlein (DESY), M. Kauers (RISC), S. Klein, (DESY), C.
Schneider (RISC)
From Moments to Functions in Quantum Chromodynamics,
arXiv::0902.4095 [hep-ph],
DESY-09-011, SFB-CPP-09-17, PoS (ACAT) 106 (2009).
5. J. Blümlein (DESY), M. Kauers (RISC), S. Klein, (DESY), C.
Schneider (RISC)
Determining the closed form of the
O(αs3) anomalous dimensions and Wilson
coefficients from
Mellin moments by means of computer algebra
arXiv::0902.4091 [hep-ph],
DESY-09-002, SFB-CPP-09-22, Comput. Phys. Commun. 190 (2009) 2143-2165.
6. J. Ablinger (RISC), J. Blümlein (DESY), S. Klein, (RWTH Aachen), C.
Schneider (RISC)
Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams
arXiv::1006.4797 [math-ph],
DESY-10-090, SFB-CPP-10-53, TTK-10-37, 110-115
Nucl.Phys.Proc.Suppl. 205-206 (2010) 110-115.
7. J. Ablinger (RISC), I. Bierenbaum (Valencia), J. Blümlein (DESY), A. Hasselhuhn
(DESY), S. Klein, (RWTH Aachen), C.
Schneider (RISC), F. Wißbrock (DESY)
Heavy Flavor DIS Wilson coefficients in the asymptotic regime
arXiv::1007.0375 [hep-ph],
DESY-10-093, SFB-CPP-10-58, TTK-10-38, Nucl.Phys.Proc.Suppl. 205-206 (2010) 242-249.
8. J. Ablinger (RISC), J. Blümlein (DESY), S. Klein, (RWTH Aachen), C.
Schneider (RISC), F. Wißbrock (DESY)
The
O(αs3)
Massive Operator Matrix Elements of
O(nf)
for the Structure Function
F2(x,Q2)
and Transversity.
arXiv::1008.3347 [hep-ph],
DESY-10-109, TTK-10-46, SFB-CPP-10-077, Nucl.Phys. B844 (2011) 26-54.
9. J. Blümlein (DESY), S. Klein, (RWTH Aachen), C.
Schneider (RISC), F. Stan (RISC)
A Symbolic Summation Approach to Feynman Integral Calculus
arXiv:1011.2656 [cs.SC], DESY-10-185, TTK-10-49, SFB-CPP-10-107,
J. Symb. Comput. (2011) in print.
10. J. Ablinger (RISC), J. Blümlein (DESY), C.Schneider (RISC)
Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
11.
J. Ablinger (RISC), J. Blümlein (DESY), S. Klein (RWTH Aachen), C.Schneider (RISC), F. Wißbrock (DESY)
3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion Lines.
DESY 11-104, DO-TH 11/17, LPN 11-35, SFB/CPP-11-34, TTK--11--21
12. J. Ablinger (RISC), J. Blümlein (DESY), A. Hasselhuhn (DESY), S. Klein (RWTH), C. Schneider
(RISC), F. Wißbrock (DESY)
New Heavy Flavor Contributions to the DIS Structure Function F2(x,Q2) at
O(αs3)
arXiv:1105.6063 [math-ph], DESY 10--065, DO--TH 12/05, SFB/CPP-12-09, LPN 12--036,
13. J. Blümlein (DESY), A. Hasselhuhn (DESY), C. Schneider (RISC)
Evaluation of Multi-Sums for Large Scale Problems
arXiv:1105.6063 [math-ph], DESY 10--247, DO--TH 12/06, SFB/CPP-12-13, LPN 12--038,
Related Theses :
1. S. Klein (DESY), Diploma Thesis:
"Heavy Flavor Coefficient Functions in
Deep-Inelastic
Scattering at O(αs2) and Large Virtualities", Potsdam
University, October 2006
(.pdf)
Heraeus-Prize 2007
2. J. Ablinger (RISC), Diploma Thesis:
"A Computer Algebra Toolbox for
Harmonic Sums
Related to Particle Physics", Johannes Kepler University Linz, February 2009, 2] arXiv:1011.1176 [math-ph]
(.pdf)
3. S. Klein (DESY), PhD-Thesis:
"Mellin Moments of Heavy Flavor
Contributions to F2(x,Q2) at NNLO", Dortmund
University, September 2009, arxiv:0910.3101 [hep-ph]
(.pdf)
German Physical Society Dissertation Prize
2011
4. F. Wißbrock (DESY), Diploma-Thesis:
"O(αs3 TF2 NF)
Contributions to the Heavy Flavor Wilson Coefficients of
the Structure Function F2(x,Q2) at Q2 >> m2", Free University Berlin, June
2010, arxiv:1010.4251 [hep-ph]
(.pdf)
5. F. Stan (RISC), PhD-Thesis:
"Algorithms for Special Functions:
Computer Algebra and Analytical Aspects", Johannes Kepler University Linz,
July 2010
(.pdf)
6. J. Ablinger (RISC), PhD-Thesis:
"Computer Algebra Algorithms for Special
Functions in Particle Physics", Johannes Kepler University Linz,
April 2012
(.pdf)
News and Press:
February 2012: Contract DESY-RISC prolongated until 2017
October 2009: prestigious START-Preis awarded to Manuel Kauers
February 2007: Collaboration Contract RISC-DESY signed
Disclaimer
Johannes Bluemlein,
Last modified: Sat Apr 14 10:08:00 CEST 2007
Mission :
Perturbative higher order calculations in Quantum Field Theories rely on advanced analytic summation and integration techniques in certain classes of sums and transcendental functions. Various probelms lead to difference equations in Π-Σ fields. The collaboration between Deutsches Elektronen Synchrotron, DESY, Zeuthen and RISC at Johannes Kepler University, Linz aims on further development of these technologies, innovative search for new methods and the creation of efficient tools based on Computer Algebra. Beyond the application of these methods, algorithms and tools in Quantum Field Theory, these methods may be of interest in other fields, such as number theory (multiple zeta values, irrationality proofs, theory of periods, new relations between sums), general summation and analytic integration methods. A cooperation contract between both institutions was signed in February 2007. This contract has been prolonged for five years in February 2012.Both sites also host nodes of the EU Network: LHCPhenoNet.
Team :
DESY : J. Blümlein, S. Moch, T. Riemann; I. Bierenbaum (U. Hamburg), A. De Freitas, A. Hasselhuhn, S. Klein (RWTH Aachen), F. WißbrockRISC : P. Paule, M. Kauers, C. Schneider; J. Ablinger (also DESY), C. Raab, M. Round, F. Stan (Paris)
Publications :
1. I. Bierenbaum, J. Blümlein, S. Klein, (DESY), C. Schneider (RISC),Difference Equations in Massive Higher Order Calculations,
arXiv:0707.4659 [math-ph],DESY-07-111, SFB-CPP-07-041, Technical Report No. 2007-19 SFB F013 (Austria), PoS ACAT2007:082, (2007).
2. S. Moch (DESY), C. Schneider (RISC),
Feynman integrals and difference equations,
arXiv::0709.1769 [math-ph], DESY-07-138, SFB-CPP-07-050, Technical Report No. 2007-22 (Austria), PoS ACAT2007:083, (2007).
3. I. Bierenbaum, J. Blümlein, S. Klein, (DESY), C. Schneider (RISC)
Two-Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Productions to O(ε),
arXiv::0208.0273 [hep-ph], DESY-08-029, SFB-CPP-08-16, Technical Report No. 2008-04 (Austria), Nucl. Phys. B803 (2008) 1-41.
4. J. Blümlein (DESY), M. Kauers (RISC), S. Klein, (DESY), C. Schneider (RISC)
From Moments to Functions in Quantum Chromodynamics,
arXiv::0902.4095 [hep-ph], DESY-09-011, SFB-CPP-09-17, PoS (ACAT) 106 (2009).
5. J. Blümlein (DESY), M. Kauers (RISC), S. Klein, (DESY), C. Schneider (RISC)
Determining the closed form of the O(αs3) anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra
arXiv::0902.4091 [hep-ph], DESY-09-002, SFB-CPP-09-22, Comput. Phys. Commun. 190 (2009) 2143-2165.
6. J. Ablinger (RISC), J. Blümlein (DESY), S. Klein, (RWTH Aachen), C. Schneider (RISC)
Modern Summation Methods and the Computation of 2- and 3-loop Feynman Diagrams
arXiv::1006.4797 [math-ph], DESY-10-090, SFB-CPP-10-53, TTK-10-37, 110-115 Nucl.Phys.Proc.Suppl. 205-206 (2010) 110-115.
7. J. Ablinger (RISC), I. Bierenbaum (Valencia), J. Blümlein (DESY), A. Hasselhuhn (DESY), S. Klein, (RWTH Aachen), C. Schneider (RISC), F. Wißbrock (DESY)
Heavy Flavor DIS Wilson coefficients in the asymptotic regime
arXiv::1007.0375 [hep-ph], DESY-10-093, SFB-CPP-10-58, TTK-10-38, Nucl.Phys.Proc.Suppl. 205-206 (2010) 242-249.
8. J. Ablinger (RISC), J. Blümlein (DESY), S. Klein, (RWTH Aachen), C. Schneider (RISC), F. Wißbrock (DESY)
The O(αs3) Massive Operator Matrix Elements of O(nf) for the Structure Function F2(x,Q2) and Transversity.
arXiv::1008.3347 [hep-ph], DESY-10-109, TTK-10-46, SFB-CPP-10-077, Nucl.Phys. B844 (2011) 26-54.
9. J. Blümlein (DESY), S. Klein, (RWTH Aachen), C. Schneider (RISC), F. Stan (RISC)
A Symbolic Summation Approach to Feynman Integral Calculus
arXiv:1011.2656 [cs.SC], DESY-10-185, TTK-10-49, SFB-CPP-10-107, J. Symb. Comput. (2011) in print.
10. J. Ablinger (RISC), J. Blümlein (DESY), C.Schneider (RISC)
Harmonic Sums and Polylogarithms Generated by Cyclotomic Polynomials
11. J. Ablinger (RISC), J. Blümlein (DESY), S. Klein (RWTH Aachen), C.Schneider (RISC), F. Wißbrock (DESY)
3-Loop Heavy Flavor Corrections to DIS with two Massive Fermion Lines.
DESY 11-104, DO-TH 11/17, LPN 11-35, SFB/CPP-11-34, TTK--11--21
12. J. Ablinger (RISC), J. Blümlein (DESY), A. Hasselhuhn (DESY), S. Klein (RWTH), C. Schneider (RISC), F. Wißbrock (DESY)
New Heavy Flavor Contributions to the DIS Structure Function F2(x,Q2) at O(αs3)
arXiv:1105.6063 [math-ph], DESY 10--065, DO--TH 12/05, SFB/CPP-12-09, LPN 12--036,
13. J. Blümlein (DESY), A. Hasselhuhn (DESY), C. Schneider (RISC)
Evaluation of Multi-Sums for Large Scale Problems
arXiv:1105.6063 [math-ph], DESY 10--247, DO--TH 12/06, SFB/CPP-12-13, LPN 12--038,
Related Theses :
1. S. Klein (DESY), Diploma Thesis:"Heavy Flavor Coefficient Functions in Deep-Inelastic Scattering at O(αs2) and Large Virtualities", Potsdam University, October 2006 (.pdf)
Heraeus-Prize 2007
2. J. Ablinger (RISC), Diploma Thesis:
"A Computer Algebra Toolbox for Harmonic Sums Related to Particle Physics", Johannes Kepler University Linz, February 2009, 2] arXiv:1011.1176 [math-ph] (.pdf)
3. S. Klein (DESY), PhD-Thesis:
"Mellin Moments of Heavy Flavor Contributions to F2(x,Q2) at NNLO", Dortmund University, September 2009, arxiv:0910.3101 [hep-ph] (.pdf)
German Physical Society Dissertation Prize 2011
4. F. Wißbrock (DESY), Diploma-Thesis:
"O(αs3 TF2 NF) Contributions to the Heavy Flavor Wilson Coefficients of the Structure Function F2(x,Q2) at Q2 >> m2", Free University Berlin, June 2010, arxiv:1010.4251 [hep-ph] (.pdf)
5. F. Stan (RISC), PhD-Thesis:
"Algorithms for Special Functions: Computer Algebra and Analytical Aspects", Johannes Kepler University Linz, July 2010 (.pdf)
6. J. Ablinger (RISC), PhD-Thesis:
"Computer Algebra Algorithms for Special Functions in Particle Physics", Johannes Kepler University Linz, April 2012 (.pdf)
News and Press:
February 2012: Contract DESY-RISC prolongated until 2017October 2009: prestigious START-Preis awarded to Manuel Kauers
February 2007: Collaboration Contract RISC-DESY signed
Disclaimer
Johannes Bluemlein, Last modified: Sat Apr 14 10:08:00 CEST 2007