Abstract
The main purpose of particle physics is the explanation of the fundamental mechanism for the interaction of the elementary particles. On the experimental side the investigations take mainly place at the big accelerators at CERN (Geneva) or FERMILAB (Chicago). On the other hand it it essential to develop theoretical models which describe the fundamental interactions and which, of course, have to be confronted with the experiment.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
F. J. Yndurain, “Relativistic quantum mechanics and introduction to field theory,” Berlin, Germany: Springer (1996) 332 p. (Text and monographs in physics)
K. G. Chetyrkin, J. H. Kuhn and A. Kwiatkowski, “QCD corrections to the e+ e- cross-section and the Z boson decay rate: Concepts and results,” Phys. Rept. 277 (1996) 189.
R. V. Harlander and M. Steinhauser, “rhad: A program for the evaluation of the hadronic R-ratio in the perturbative regime of QCD,” Comput. Phys. Commun. 153 (2003) 244 [arXiv:hep-ph/0212294].
K. G. Chetyrkin and A. Khodjamirian, “Strange quark mass from pseudoscalar sum rule with O(alpha(s)**4) accuracy,” Eur. Phys. J. C 46 (2006) 721 [arXiv:hep-ph/0512295].
M. Tentyukov, D. Fliegner, M. Frank, A. Onischenko, A. Retey, H. M. Staudenmaier and J. A. M. Vermaseren, “ParFORM: Parallel Version of the Symbolic Manipulation Program FORM,” arXiv:cs.sc/0407066; M. Tentyukov, H. M. Staudenmaier and J. A. M. Vermaseren, “ParFORM: Recent development,” Nucl. Instrum. Meth. A 559 (2006) 224. H. M. Staudenmaier, M. Steinhauser, M. Tentyukov, J. A. M. Vermaseren, “ParFORM,” Computeralgebra Rundbriefe 39 (2006) 19. See also http://www-ttp.physik.uni-karlsruhe.de/∼parform.
FORM version 3.0 is described in: J. A. M. Vermaseren, “New features of FORM,” arXiv:math-ph/0010025; for recent developments, see also: M. Tentyukov and J. A. M. Vermaseren, “Extension of the functionality of the symbolic program FORM by external software,” arXiv:cs.sc/0604052; FORM can be obtained from the distribution site at http://www.nikhef.nl/∼form.
M. Tentyukov and J. A. M. Vermaseren, “The multithreaded version of FORM,” arXiv:hep-ph/0702279.
S. Laporta and E. Remiddi, “The analytical value of the electron (g-2) at order alpha 3 in QED,” Phys. Lett. B 379 (1996) 283 [arXiv:hep-ph/9602417].
S. Laporta, “High-precision calculation of multi-loop Feynman integrals by difference equations,” Int. J. Mod. Phys. A 15, 5087 (2000) [arXiv:hep-ph/0102033].
R. H. Lewis, Fermat’s User Guide, http://www.bway.net/∼lewis.
P. A. Baikov, K. G. Chetyrkin and J. H. Kuhn, “Five-loop vacuum polarization in pQCD: O(alpha(s)**4 N(f)**2) results,” Nucl. Phys. Proc. Suppl. 116 (2003) 78.
P. A. Baikov, K. G. Chetyrkin and J. H. Kuhn, “Vacuum polarization in pQCD: First complete O(alpha(s)**4) result,” Nucl. Phys. Proc. Suppl. 135 (2004) 243.
P. A. Baikov, K. G. Chetyrkin and J. H. Kuhn, “Strange quark mass from tau lepton decays with O(alpha(s**3)) accuracy,” Phys. Rev. Lett. 95 (2005) 012003 [arXiv:hep-ph/0412350].
P. A. Baikov, K. G. Chetyrkin and J. H. Kuhn, “Scalar correlator at O(alpha(s)**4), Higgs decay into b-quarks and bounds on the light quark masses,” Phys. Rev. Lett. 96 (2006) 012003 [arXiv:hep-ph/0511063].
K. G. Chetyrkin and F. V. Tkachov, “Integration By Parts: The Algorithm To Calculate Beta Functions In 4 Loops,” Nucl. Phys. B 192 (1981) 159.
P. A. Baikov, “Explicit solutions of the multi-loop integral recurrence relations and its application,” Nucl. Instrum. Meth. A 389 (1997) 347 [arXiv:hep-ph/9611449].
P.A. Baikov, “Explicit solutions of the three loop vacuum integral recurrence relations,” Phys. Lett. B 385 (1996) 404 [arXiv:hep-ph/9603267].
P. A. Baikov, “The criterion of irreducibility of multi-loop Feynman integrals,” Phys. Lett. B 474 (2000) 385 [arXiv:hep-ph/9912421].
P. A. Baikov, K. G. Chetyrkin and J. H. Kuhn, “The cross section of e+ e- annihilation into hadrons of order alpha(s)**4 n(f)**2 in perturbative QCD,” Phys. Rev. Lett. 88 (2002) 012001 [arXiv:hep-ph/0108197].
P. A. Baikov and K. G. Chetyrkin, “Higgs decay into hadrons to order alpha(s)**5,” Phys. Rev. Lett. 97 (2006) 061803 [arXiv:hep-ph/0604194].
G. Martinelli, C. Pittori, C. T. Sachrajda, M. Testa and A. Vladikas, “A General Method For Nonperturbative Renormalization Of Lattice Operators,” Nucl. Phys. B 445 (1995) 81 [arXiv:hep-lat/9411010].
M. Gockeler et al., “Nonperturbative renormalisation of composite operators in lattice QCD,” Nucl. Phys. B 544 (1999) 699 [arXiv:hep-lat/9807044].
D. J. Broadhurst and A. G. Grozin, “Matching QCD And Hqet Heavy - Light Currents At Two Loops And Beyond,” Phys. Rev. D 52 (1995) 4082 [arXiv:hep-ph/9410240].
V. M. Braun, T. Burch, C. Gattringer, M. Gockeler, G. Lacagnina, S. Schaefer and A. Schafer, “A lattice calculation of vector meson couplings to the vector and tensor currents using chirally improved fermions,” Phys. Rev. D 68 (2003) 054501 [arXiv:hep-lat/0306006].
D. Becirevic, V. Lubicz, F. Mescia and C. Tarantino, “Coupling of the light vector meson to the vector and to the tensor current,” JHEP 0305 (2003) 007 [arXiv:hep-lat/0301020].
P. A. Baikov and K. G. Chetyrkin, “New four loop results in QCD,” Nucl. Phys. Proc. Suppl. 160 (2006) 76.
D. J. Broadhurst, “Four-loop Dyson-Schwinger-Johnson anatomy,” Phys. Lett. B 466 (1999) 319 [arXiv:hep-ph/9909336].
A. Connes and D. Kreimer, “Renormalization in quantum field theory and the Riemann-Hilbert problem,” JHEP 9909 (1999) 024 [arXiv:hep-th/9909126].
J. H. Kuhn, M. Steinhauser and C. Sturm, “Heavy quark masses from sum rules in four-loop approximation,” arXiv:hep-ph/0702103.
R. Boughezal, M. Czakon and T. Schutzmeier, “Four-loop tadpoles: Applications in QCD,” Nucl. Phys. Proc. Suppl. 160 (2006) 160 [arXiv:hep-ph/0607141].
K. G. Chetyrkin, J. H. Kuhn and M. Steinhauser, “Heavy quark current correlators to O(alpha(s)**2),” Nucl. Phys. B 505 (1997) 40 [arXiv:hep-ph/9705254].
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kühn, J., Steinhauser, M., Tentyukov, M. (2008). Massless Four-Loop Integrals and the Total Cross Section in e+ e− Annihilation. In: Nagel, W., Kröner, D., Resch, M. (eds) High Performance Computing in Science and Engineering `07. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-74739-0_3
Download citation
DOI: https://doi.org/10.1007/978-3-540-74739-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-74738-3
Online ISBN: 978-3-540-74739-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)