×

zbMATH — the first resource for mathematics

Threshold resummation in SCET vs. Perturbative QCD: An analytic comparison. (English) Zbl 1246.81423
Summary: We compare threshold resummation in QCD, as performed using soft-collinear effective theory (SCET) in the Becher-Neubert approach, to the standard perturbative QCD formalism based on factorization and resummation of Mellin moments of partonic cross-sections. We consider various forms of the SCET result, which correspond to different choices of the soft scale \(\mu_{s}\) that characterizes this approach. We derive a master formula that relates the SCET resummation to the QCD result for any choice of \(\mu _{s}\). We then use it first, to show that if SCET resummation is performed in \(N\)-Mellin moment space by suitable choice of \(\mu _{s}\) it is equivalent to the standard perturbative approach. Next, we show that if SCET resummation is performed by choosing for \(\mu_{s}\) a partonic momentum variable, the perturbative result for partonic resummed cross-sections is again reproduced, but, like its standard perturbative counterpart, it is beset by divergent behaviour at the endpoint. Finally, using the master formula we show that when \(\mu _{s}\) is chosen as a hadronic momentum variable the SCET and standard approach are related through a multiplicative (convolutive) factor, which contains the dependence on the Landau pole and associated divergence. This factor depends on the luminosity in a non-universal way; it lowers by one power of log the accuracy of the resummed result, but it is otherwise subleading if one assumes the luminosity not to contain logarithmically-enhanced terms. Therefore, the SCET approach can be turned into a prescription to remove the Landau pole from the perturbative result, but the price to pay for this is the reduction by one logarithmic power of the accuracy at each order and the need to make assumptions on the parton luminosity.

MSC:
81V05 Strong interaction, including quantum chromodynamics
81T15 Perturbative methods of renormalization applied to problems in quantum field theory
81U05 \(2\)-body potential quantum scattering theory
81V35 Nuclear physics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] de Florian, D.; Grazzini, M., Phys. lett. B, 674, 291, (2009)
[2] Cacciari, M.; Czakon, M.; Mangano, M.L.; Mitov, A.; Nason, P.
[3] Catani, S.; Trentadue, L., Nucl. phys. B, 327, 323, (1989)
[4] Sterman, G.F., Nucl. phys. B, 281, 310, (1987)
[5] Contopanagos, H.; Laenen, E.; Sterman, G.F., Nucl. phys. B, 484, 303, (1997)
[6] Forte, S.; Ridolfi, G., Nucl. phys. B, 650, 229, (2003)
[7] Laenen, E.; Stavenga, G.; White, C.D., Jhep, 0903, 054, (2009)
[8] Laenen, E.; Magnea, L.; Stavenga, G.; White, C.D., Jhep, 1101, 141, (2011)
[9] Moch, S.; Vogt, A., Phys. lett. B, 631, 48, (2005)
[10] Catani, S.; Mangano, M.L.; Nason, P.; Trentadue, L., Nucl. phys. B, 478, 273, (1996)
[11] Amati, D.; Bassetto, A.; Ciafaloni, M.; Marchesini, G.; Veneziano, G., Nucl. phys. B, 173, 429, (1980)
[12] Forte, S.; Ridolfi, G.; Rojo, J.; Ubiali, M., Phys. lett. B, 635, 313, (2006)
[13] Abbate, R.; Forte, S.; Ridolfi, G., Phys. lett. B, 657, 55, (2007)
[14] Bauer, C.W.; Fleming, S.; Luke, M.E., Phys. rev. D, 63, 014006, (2000)
[15] Bauer, C.W.; Fleming, S.; Pirjol, D.; Stewart, I.W., Phys. rev. D, 63, 114020, (2001)
[16] Bauer, C.W.; Stewart, I.W., Phys. lett. B, 516, 134, (2001)
[17] Bauer, C.W.; Pirjol, D.; Stewart, I.W., Phys. rev. D, 65, 054022, (2002)
[18] Bauer, C.W.; Fleming, S.; Pirjol, D.; Rothstein, I.Z.; Stewart, I.W., Phys. rev. D, 66, 014017, (2002)
[19] Manohar, A.V., Phys. rev. D, 68, 114019, (2003)
[20] Pecjak, B.D., Jhep, 0510, 040, (2005)
[21] Chay, J.; Kim, C., Phys. rev. D, 75, 016003, (2007)
[22] Idilbi, A.; Ji, X.-d., Phys. rev. D, 72, 054016, (2005)
[23] Becher, T.; Neubert, M., Phys. rev. lett., 97, 082001, (2006)
[24] Becher, T.; Neubert, M.; Pecjak, B.D., Jhep, 0701, 076, (2007)
[25] Becher, T.; Neubert, M.; Xu, G., Jhep, 0807, 030, (2008)
[26] Ahrens, V.; Becher, T.; Neubert, M.; Yang, L.L., Phys. rev. D, 79, 033013, (2009)
[27] Bonvini, M.; Forte, S.; Ridolfi, G., Nucl. phys. B, 847, 93, (2011)
[28] Ahrens, V.; Ferroglia, A.; Neubert, M.; Pecjak, B.D.; Yang, L.-L., Jhep, 1109, 070, (2011)
[29] Berger, C.F.; Marcantonini, C.; Stewart, I.W.; Tackmann, F.J.; Waalewijn, W.J., Jhep, 1104, 092, (2011)
[30] Catani, S.; de Florian, D.; Grazzini, M., Jhep, 0201, 015, (2002)
[31] Catani, S.; de Florian, D.; Grazzini, M.; Nason, P., Jhep, 0307, 028, (2003)
[32] Moch, S.; Vermaseren, J.A.M.; Vogt, A., Nucl. phys. B, 726, 317, (2005)
[33] Idilbi, A.; Ji, X.-d.; Ma, J.-P.; Yuan, F., Phys. rev. D, 73, 077501, (2006)
[34] Beneke, M.; Falgari, P.; Klein, S.; Schwinn, C., Nucl. phys. B, 855, 695, (2012)
[35] S. Catani, private communication.
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.