×

Feynman rules for the rational part of one-loop QCD corrections in the MSSM. (English) Zbl 1397.81012

Summary: The complete set of Feynman rules for the rational part R of QCD corrections in the MSSM are calculated at the one-loop level, which can be very useful in the nextto-leading order calculations in supersymmetric models. Our results are expressed in the ’t Hooft-Veltman regularization scheme and in the Four Dimensional Helicity scheme with non-anticommutating and anticommutating \(\gamma\)_{5} strategies.

MSC:

81-08 Computational methods for problems pertaining to quantum theory
PDF BibTeX XML Cite
Full Text: DOI arXiv

References:

[1] Fayet, P., Supergauge invariant extension of the Higgs mechanism and a model for the electron and its neutrino, Nucl. Phys., B 90, 104, (1975)
[2] Fayet, P., Supersymmetry and weak, electromagnetic and strong interactions, Phys. Lett., B 64, 159, (1976)
[3] Fayet, P., Spontaneously broken supersymmetric theories of weak, electromagnetic and strong interactions, Phys. Lett., B 69, 489, (1977)
[4] Dimopoulos, S.; Georgi, H., Softly broken supersymmetry and SU(5), Nucl. Phys., B 193, 150, (1981)
[5] Sakai, N., Naturalness in supersymmetric guts, Z. Phys., C 11, 153, (1981)
[6] Inoue, K.; Kakuto, A.; Komatsu, H.; Takeshita, S., Low-energy parameters and particle masses in a supersymmetric grand unified model, Prog. Theor. Phys., 67, 1889, (1982)
[7] Inoue, K.; Kakuto, A.; Komatsu, H.; Takeshita, S., Aspects of grand unified models with softly broken supersymmetry, Prog. Theor. Phys., 68, 927, (1982) · Zbl 0527.22022
[8] Inoue, K.; Kakuto, A.; Komatsu, H.; Takeshita, S., Renormalization of supersymmetry breaking parameters revisited, Prog. Theor. Phys., 71, 413, (1984)
[9] Berends, FA; Giele, W., Recursive calculations for processes with n gluons, Nucl. Phys., B 306, 759, (1988)
[10] Britto, R.; Cachazo, F.; Feng, B., New recursion relations for tree amplitudes of gluons, Nucl. Phys., B 715, 499, (2005) · Zbl 1207.81088
[11] Britto, R.; Cachazo, F.; Feng, B.; Witten, E., Direct proof of tree-level recursion relation in Yang-Mills theory, Phys. Rev. Lett., 94, 181602, (2005)
[12] Stelzer, T.; Long, W., Automatic generation of tree level helicity amplitudes, Comput. Phys. Commun., 81, 357, (1994)
[13] Alwall, J.; Herquet, M.; Maltoni, F.; Mattelaer, O.; Stelzer, T., Madgraph 5: going beyond, JHEP, 06, 128, (2011) · Zbl 1298.81362
[14] A. Pukhov et al., CompHEP: A Package for evaluation of Feynman diagrams and integration over multiparticle phase space, hep-ph/9908288 [INSPIRE].
[15] Krauss, F.; Kuhn, R.; Soff, G., AMEGIC++ 1.0: A matrix element generator in C++, JHEP, 02, 044, (2002)
[16] Caravaglios, F.; Moretti, M., An algorithm to compute Born scattering amplitudes without Feynman graphs, Phys. Lett., B 358, 332, (1995)
[17] Caravaglios, F.; Mangano, ML; Moretti, M.; Pittau, R., A new approach to multijet calculations in hadron collisions, Nucl. Phys., B 539, 215, (1999)
[18] Mangano, ML; Moretti, M.; Piccinini, F.; Pittau, R.; Polosa, AD, ALPGEN, a generator for hard multiparton processes in hadronic collisions, JHEP, 07, 001, (2003)
[19] Kanaki, A.; Papadopoulos, CG, HELAC: A package to compute electroweak helicity amplitudes, Comput. Phys. Commun., 132, 306, (2000) · Zbl 1031.81507
[20] Cafarella, A.; Papadopoulos, CG; Worek, M., Helac-phegas: A generator for all parton level processes, Comput. Phys. Commun., 180, 1941, (2009)
[21] Gleisberg, T.; Hoeche, S., Comix, a new matrix element generator, JHEP, 12, 039, (2008)
[22] Harris, B.; Owens, J., The two cutoff phase space slicing method, Phys. Rev., D 65, 094032, (2002)
[23] Catani, S.; Seymour, M., A general algorithm for calculating jet cross-sections in NLO QCD, Nucl. Phys., B 485, 291, (1997)
[24] Catani, S.; Dittmaier, S.; Seymour, MH; Trócsányi, Z., The dipole formalism for next-to-leading order QCD calculations with massive partons, Nucl. Phys., B 627, 189, (2002) · Zbl 0990.81140
[25] Dittmaier, S., A general approach to photon radiation off fermions, Nucl. Phys., B 565, 69, (2000)
[26] Phaf, L.; Weinzierl, S., Dipole formalism with heavy fermions, JHEP, 04, 006, (2001)
[27] Czakon, M.; Papadopoulos, CG; Worek, M., Polarizing the dipoles, JHEP, 08, 085, (2009)
[28] Frixione, S.; Kunszt, Z.; Signer, A., Three jet cross-sections to next-to-leading order, Nucl. Phys., B 467, 399, (1996)
[29] Frixione, S., A general approach to jet cross-sections in QCD, Nucl. Phys., B 507, 295, (1997)
[30] Kosower, DA, Antenna factorization in strongly ordered limits, Phys. Rev., D 71, 045016, (2005)
[31] Somogyi, G., Subtraction with hadronic initial states at NLO: an NNLO-compatible scheme, JHEP, 05, 016, (2009)
[32] Hasegawa, K.; Moch, S.; Uwer, P., Autodipole: automated generation of dipole subtraction terms, Comput. Phys. Commun., 181, 1802, (2010) · Zbl 1219.81244
[33] Frederix, R.; Gehrmann, T.; Greiner, N., Integrated dipoles with maddipole in the madgraph framework, JHEP, 06, 086, (2010) · Zbl 1288.81145
[34] Frederix, R.; Frixione, S.; Maltoni, F.; Stelzer, T., Automation of next-to-leading order computations in QCD: the FKS subtraction, JHEP, 10, 003, (2009)
[35] Passarino, G.; Veltman, M., One loop corrections for e\^{}{+}e\^{}{−} annihilation into μ\^{}{+}μ\^{}{−} in the Weinberg model, Nucl. Phys., B 160, 151, (1979)
[36] Denner, A.; Dittmaier, S., Reduction of one loop tensor five point integrals, Nucl. Phys., B 658, 175, (2003) · Zbl 1027.81517
[37] Denner, A.; Dittmaier, S., Reduction schemes for one-loop tensor integrals, Nucl. Phys., B 734, 62, (2006) · Zbl 1192.81158
[38] Bern, Z.; Dixon, LJ; Kosower, DA, One loop corrections to five gluon amplitudes, Phys. Rev. Lett., 70, 2677, (1993)
[39] Bern, Z.; Dixon, LJ; Dunbar, DC; Kosower, DA, One loop n point gauge theory amplitudes, unitarity and collinear limits, Nucl. Phys., B 425, 217, (1994) · Zbl 1049.81644
[40] Bern, Z.; Dixon, LJ; Dunbar, DC; Kosower, DA, Fusing gauge theory tree amplitudes into loop amplitudes, Nucl. Phys., B 435, 59, (1995)
[41] Bern, Z.; Dixon, LJ; Kosower, DA, One loop corrections to two quark three gluon amplitudes, Nucl. Phys., B 437, 259, (1995)
[42] Britto, R.; Cachazo, F.; Feng, B., Generalized unitarity and one-loop amplitudes in N = 4 super-Yang-Mills, Nucl. Phys., B 725, 275, (2005) · Zbl 1178.81202
[43] R.K. Ellis, Z. Kunszt, K. Melnikov and G. Zanderighi, One-loop calculations in quantum field theory: from Feynman diagrams to unitarity cuts, arXiv:1105.4319 [INSPIRE].
[44] Aguila, F.; Pittau, R., Recursive numerical calculus of one-loop tensor integrals, JHEP, 07, 017, (2004)
[45] R. Pittau, Formulae for a numerical computation of one-loop tensor integrals, hep-ph/0406105 [INSPIRE].
[46] Ossola, G.; Papadopoulos, CG; Pittau, R., Reducing full one-loop amplitudes to scalar integrals at the integrand level, Nucl. Phys., B 763, 147, (2007) · Zbl 1116.81067
[47] Ossola, G.; Papadopoulos, CG; Pittau, R., Numerical evaluation of six-photon amplitudes, JHEP, 07, 085, (2007)
[48] Ossola, G.; Papadopoulos, CG; Pittau, R., Cuttools: A program implementing the OPP reduction method to compute one-loop amplitudes, JHEP, 03, 042, (2008)
[49] Mastrolia, P.; Ossola, G.; Papadopoulos, CG; Pittau, R., Optimizing the reduction of one-loop amplitudes, JHEP, 06, 030, (2008)
[50] Ossola, G.; Papadopoulos, CG; Pittau, R., On the rational terms of the one-loop amplitudes, JHEP, 05, 004, (2008)
[51] Denner, A.; Dittmaier, S.; Roth, M.; Wieders, L., Electroweak corrections to charged-current e\^{}{+}e\^{}{−} → 4 fermion processes: technical details and further results, Nucl. Phys., B 724, 247, (2005)
[52] Bredenstein, A.; Denner, A.; Dittmaier, S.; Pozzorini, S., NLO QCD corrections to ttbb production at the LHC: 1. quark-antiquark annihilation, JHEP, 08, 108, (2008)
[53] Bredenstein, A.; Denner, A.; Dittmaier, S.; Pozzorini, S., NLO QCD corrections to top anti-top bottom anti-bottom production at the LHC: 2. full hadronic results, JHEP, 03, 021, (2010) · Zbl 1271.81172
[54] Binoth, T.; Guillet, JP; Heinrich, G., Algebraic evaluation of rational polynomials in one-loop amplitudes, JHEP, 02, 013, (2007)
[55] Garzelli, M.; Malamos, I.; Pittau, R., Feynman rules for the rational part of the electroweak 1-loop amplitudes in the R_{ξ} gauge and in the unitary gauge, JHEP, 01, 029, (2011) · Zbl 1214.81328
[56] Garzelli, M.; Malamos, I.; Pittau, R., Feynman rules for the rational part of the electroweak 1-loop amplitudes, JHEP, 01, 040, (2010) · Zbl 1269.81214
[57] Draggiotis, P.; Garzelli, M.; Papadopoulos, CG; Pittau, R., Feynman rules for the rational part of the QCD 1-loop amplitudes, JHEP, 04, 072, (2009)
[58] Garzelli, M.; Malamos, I., R2SM: A package for the analytic computation of the R_{2} rational terms in the standard model of the electroweak interactions, Eur. Phys. J., C 71, 1605, (2011)
[59] Shao, H-S; Zhang, Y-J; Chao, K-T, Feynman rules for the rational part of the standard model one-loop amplitudes in the ’t Hooft-veltman γ_{5} scheme, JHEP, 09, 048, (2011) · Zbl 1301.81360
[60] Campanario, F., Towards pp → V V jj at NLO QCD: bosonic contributions to triple vector boson production plus jet, JHEP, 10, 070, (2011) · Zbl 1303.81208
[61] Pittau, R., Primary Feynman rules to calculate the epsilon-dimensional integrand of any 1-loop amplitude, JHEP, 02, 029, (2012) · Zbl 1309.81283
[62] Boels, R.; Schwinn, C., CSW rules for a massive scalar, Phys. Lett., B 662, 80, (2008) · Zbl 1282.81136
[63] Nigel Glover, E.; Williams, C., One-loop gluonic amplitudes from single unitarity cuts, JHEP, 12, 067, (2008) · Zbl 1329.81283
[64] Elvang, H.; Freedman, DZ; Kiermaier, M., Integrands for QCD rational terms and N =4 SYM from massive CSW rules, JHEP, 06, 015, (2012)
[65] Hirschi, V.; etal., Automation of one-loop QCD corrections, JHEP, 05, 044, (2011) · Zbl 1296.81138
[66] R. Pittau, Status of MadLoop/aMC@NLO, arXiv:1202.5781 [INSPIRE].
[67] G. Bevilacqua et al., HELAC-NLO, arXiv:1110.1499 [INSPIRE].
[68] Christensen, ND; Duhr, C., Feynrules - Feynman rules made easy, Comput. Phys. Commun., 180, 1614, (2009)
[69] Cascioli, F.; Maierhofer, P.; Pozzorini, S., Scattering amplitudes with open loops, Phys. Rev. Lett., 108, 111601, (2012)
[70] Cullen, G.; etal., Automation of one-loop calculations with gosam: present status and future outlook, Acta Phys. Polon., B 42, 2351, (2011)
[71] Cullen, G.; etal., Automated one-loop calculations with gosam, Eur. Phys. J., C 72, 1889, (2012)
[72] Siegel, W., Supersymmetric dimensional regularization via dimensional reduction, Phys. Lett., B 84, 193, (1979)
[73] Jack, I.; Jones, D.; Roberts, K., Equivalence of dimensional reduction and dimensional regularization, Z. Phys., C 63, 151, (1994)
[74] Bern, Z.; Kosower, DA, The computation of loop amplitudes in gauge theories, Nucl. Phys., B 379, 451, (1992)
[75] Kunszt, Z.; Signer, A.; Trócsányi, Z., One loop helicity amplitudes for all 2 → 2 processes in QCD and N = 1 supersymmetric Yang-Mills theory, Nucl. Phys., B 411, 397, (1994)
[76] Catani, S.; Seymour, M.; Trócsányi, Z., Regularization scheme independence and unitarity in QCD cross-sections, Phys. Rev., D 55, 6819, (1997)
[77] Bern, Z.; Freitas, A.; Dixon, LJ; Wong, H., Supersymmetric regularization, two loop QCD amplitudes and coupling shifts, Phys. Rev., D 66, 085002, (2002)
[78] Hooft, G. ’t; Veltman, M., Regularization and renormalization of gauge fields, Nucl. Phys., B 44, 189, (1972)
[79] Bollini, C.; Giambiagi, J., Lowest order divergent graphs in nu-dimensional space, Phys. Lett., B 40, 566, (1972)
[80] Cicuta, G.; Montaldi, E., Analytic renormalization via continuous space dimension, Lett. Nuovo Cim., 4, 329, (1972)
[81] Ashmore, J., A method of gauge invariant regularization, Lett. Nuovo Cim., 4, 289, (1972)
[82] Breitenlohner, P.; Maison, D., Dimensional renormalization and the action principle, Commun. Math. Phys., 52, 11, (1977)
[83] Breitenlohner, P.; Maison, D., dimensionally renormalized Greens functions for theories with massless particles. 2, Commun. Math. Phys., 52, 55, (1977)
[84] Breitenlohner, P.; Maison, D., dimensionally renormalized Greens functions for theories with massless particles. 1, Commun. Math. Phys., 52, 39, (1977)
[85] Bonneau, G., Consistency in dimensional regularization with γ_{5}, Phys. Lett., B 96, 147, (1980)
[86] Bonneau, G., Preserving canonical Ward identities in dimensional regularization with a nonanticommuting γ_{5}, Nucl. Phys., B 177, 523, (1981)
[87] Korner, J.; Nasrallah, N.; Schilcher, K., Evaluation of the flavor changing vertex b → s + H using the breitenlohner-maison-’t Hooft-veltman γ_{5} scheme, Phys. Rev., D 41, 888, (1990)
[88] D. Kreimer, The Role of γ_{5}in dimensional regularization, hep-ph/9401354 [INSPIRE].
[89] Korner, J.; Kreimer, D.; Schilcher, K., A practicable γ_{5} scheme in dimensional regularization, Z. Phys., C 54, 503, (1992)
[90] Kreimer, D., The γ_{5} problem and anomalies: a Clifford algebra approach, Phys. Lett., B 237, 59, (1990)
[91] Grinstein, B.; Springer, RP; Wise, MB, Effective Hamiltonian for weak radiative B meson decay, Phys. Lett., B 202, 138, (1988)
[92] Grigjanis, R.; O’Donnell, PJ; Sutherland, M.; Navelet, H., QCD corrected effective Lagrangian for B → s processes, Phys. Lett., B 213, 355, (1988)
[93] Martin, C.; Sánchez-Ruiz, D., Action principles, restoration of BRS symmetry and the renormalization group equation for chiral nonabelian gauge theories in dimensional renormalization with a nonanticommuting γ_{5}, Nucl. Phys., B 572, 387, (2000) · Zbl 0947.81046
[94] Schubert, C., The Yukawa model as an example for dimensional renormalization with γ_{5}, Nucl. Phys., B 323, 478, (1989)
[95] Pernici, M.; Raciti, M.; Riva, F., Dimensional renormalization of Yukawa theories via Wilsonian methods, Nucl. Phys., B 577, 293, (2000)
[96] Pernici, M., Seminaive dimensional renormalization, Nucl. Phys., B 582, 733, (2000) · Zbl 0984.81087
[97] Pernici, M.; Raciti, M., Axial current in QED and seminaive dimensional renormalization, Phys. Lett., B 513, 421, (2001) · Zbl 0969.81654
[98] Ferrari, R.; Yaouanc, A.; Oliver, L.; Raynal, J., Gauge invariance and dimensional regularization with γ_{5} in flavor changing neutral processes, Phys. Rev., D 52, 3036, (1995)
[99] Hahn, T., Generating Feynman diagrams and amplitudes with feynarts 3, Comput. Phys. Commun., 140, 418, (2001) · Zbl 0994.81082
[100] Hahn, T.; Schappacher, C., The implementation of the minimal supersymmetric standard model in feynarts and formcalc, Comput. Phys. Commun., 143, 54, (2002) · Zbl 1009.81589
[101] Haber, HE; Kane, GL, The search for supersymmetry: probing physics beyond the standard model, Phys. Rept., 117, 75, (1985)
[102] Gunion, J.; Haber, HE, Higgs bosons in supersymmetric models. 1, Nucl. Phys., B 272, 1, (1986)
[103] J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson, The Higgs Hunters Guide, SCIPP-89-13.
[104] Denner, A.; Eck, H.; Hahn, O.; Kublbeck, J., Feynman rules for fermion number violating interactions, Nucl. Phys., B 387, 467, (1992)
[105] Chamseddine, AH; Arnowitt, RL; Nath, P., Locally supersymmetric grand unification, Phys. Rev. Lett., 49, 970, (1982)
[106] Barbieri, R.; Ferrara, S.; Savoy, CA, Gauge models with spontaneously broken local supersymmetry, Phys. Lett., B 119, 343, (1982)
[107] Ibáñez, LE, Locally supersymmetric SU(5) grand unification, Phys. Lett., B 118, 73, (1982)
[108] Hall, LJ; Lykken, JD; Weinberg, S., Supergravity as the messenger of supersymmetry breaking, Phys. Rev., D 27, 2359, (1983)
[109] Kane, GL; Kolda, CF; Roszkowski, L.; Wells, JD, Study of constrained minimal supersymmetry, Phys. Rev., D 49, 6173, (1994)
[110] Ohta, N., Grand unified theories based on local supersymmetry, Prog. Theor. Phys., 70, 542, (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.