×

zbMATH — the first resource for mathematics

Effective operators in SUSY, superfield constraints and searches for a UV completion. (English) Zbl 1388.81146
Summary: We discuss the role of a class of higher dimensional operators in 4D \(N=1\) super-symmetric effective theories. The Lagrangian in such theories is an expansion in momenta below the scale of “new physics” (\(\lambda'\)) and contains the effective operators generated by integrating out the “heavy states” above \(\lambda'\) present in the UV complete theory. We go beyond the “traditional” leading order in this momentum expansion (\(in/\lambda'\)). Keeping manifest supersymmetry and using superfield constraints we show that the corresponding higher dimensional (derivative) operators in the sectors of chiral, linear and vector superfields of a Lagrangian can be “unfolded” into second-order operators. The “unfolded” formulation has only polynomial interactions and additional massive superfields, some of which are ghost-like if the effective operators were quadratic in fields. Using this formulation, the UV theory emerges naturally and fixes the (otherwise unknown) coefficient and sign of the initial (higher derivative) operators. Integrating the massive fields of the “unfolded” formulation generates an effective theory with only polynomial effective interactions relevant for phenomenology. We also provide several examples of “unfolding” of theories with higher derivative interactions in the gauge or matter sectors that are actually ghost-free. We then illustrate how our method can be applied even when including all orders in the momentum expansion, by using an infinite set of superfield constraints and an iterative procedure, with similar results.

MSC:
81Q60 Supersymmetry and quantum mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Buchmüller, W.; Wyler, D., Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys., B 268, 621, (1986)
[2] Georgi, H., Effective field theory, Ann. Rev. Nucl. Part. Sci., 43, 209, (1993)
[3] Hawking, SW; Hertog, T., Living with ghosts, Phys. Rev., D 65, 103515, (2002)
[4] S.W. Hawking, Whos afraid of (higher derivative) ghosts? (paper written in honor of the 60th birthday of E.S. Fradkin), in Quantum field theory and quantum statistics, volume 2, A. Batalin et al. eds., CRC Press (1985), Print-86-0124.
[5] Oliver, JF; Papavassiliou, J.; Santamaria, A., Can power corrections be reliably computed in models with extra dimensions?, Phys. Rev., D 67, 125004, (2003)
[6] Ghilencea, DM; Lee, HM; Schmidt-Hoberg, K., Higher derivatives and brane-localised kinetic terms in gauge theories on orbifolds, JHEP, 08, 009, (2006)
[7] Ghilencea, DM, Compact dimensions and their radiative mixing, Phys. Rev., D 70, 045018, (2004)
[8] D.M. Ghilencea, Threshold effects near the compactification scale for gauge couplings on orbifolds, hep-ph/0612185 [INSPIRE].
[9] Groot Nibbelink, S.; Hillenbach, M., Renormalization of supersymmetric gauge theories on orbifolds: brane gauge couplings and higher derivative operators, Phys. Lett., B 616, 125, (2005) · Zbl 1247.81303
[10] Groot Nibbelink, S.; Hillenbach, M., Renormalization of supersymmetric gauge theories on orbifolds: brane gauge couplings and higher derivative operators, AIP Conf. Proc., 805, 463, (2006) · Zbl 1114.81324
[11] Groot Nibbelink, S.; Hillenbach, M., Quantum corrections to non-abelian SUSY theories on orbifolds, Nucl. Phys., B 748, 60, (2006) · Zbl 1186.81093
[12] Ghilencea, DM, Higher derivative operators as loop counterterms in one-dimensional field theory orbifolds, JHEP, 03, 009, (2005)
[13] Ghilencea, DM; Lee, HM, Higher derivative operators from transmission of supersymmetry breaking on S(1)/Z(2), JHEP, 09, 024, (2005)
[14] Adams, A.; Arkani-Hamed, N.; Dubovsky, S.; Nicolis, A.; Rattazzi, R., Causality, analyticity and an IR obstruction to UV completion, JHEP, 10, 014, (2006)
[15] Antoniadis, I.; Dudas, E.; Ghilencea, DM, Supersymmetric models with higher dimensional operators, JHEP, 03, 045, (2008)
[16] Antoniadis, I.; Dudas, E.; Ghilencea, DM; Tziveloglou, P., Higher dimensional operators in the MSSM, AIP Conf. Proc., 1078, 175, (2009)
[17] Antoniadis, I.; Dudas, E.; Ghilencea, DM; Tziveloglou, P., MSSM with dimension-five operators (M SSM (5)), Nucl. Phys., B 808, 155, (2009) · Zbl 1192.81362
[18] Antoniadis, I.; Dudas, E.; Ghilencea, DM; Tziveloglou, P., MSSM Higgs with dimension-six operators, Nucl. Phys., B 831, 133, (2010) · Zbl 1204.81182
[19] Koehn, M.; Lehners, J-L; Ovrut, BA, Higher-derivative chiral superfield actions coupled to N = 1 supergravity, Phys. Rev., D 86, 085019, (2012)
[20] Khoury, J.; Lehners, J-L; Ovrut, B., Supersymmetric P(X, ϕ) and the ghost condensate, Phys. Rev., D 83, 125031, (2011)
[21] Koehn, M.; Lehners, J-L; Ovrut, B., Ghost condensate in N = 1 supergravity, Phys. Rev., D 87, 065022, (2013)
[22] Koehn, M.; Lehners, JL; Ovrut, BA, Scalars with higher derivatives in supergravity and cosmology, Springer Proc. Phys., 153, 115, (2014)
[23] Bufalo, R.; Pimentel, BM, Higher-derivative non-abelian gauge fields via the Faddeev-Jackiw formalism, Eur. Phys. J., C 74, 2993, (2014)
[24] Nitta, M.; Sasaki, S., BPS states in supersymmetric chiral models with higher derivative terms, Phys. Rev., D 90, 105001, (2014)
[25] Gama, FS; Gomes, M.; Nascimento, JR; Petrov, AY; Silva, AJ, On the one-loop effective potential in the higher-derivative four-dimensional chiral superfield theory with a nonconventional kinetic term, Phys. Lett., B 733, 247, (2014) · Zbl 1370.81161
[26] Gama, FS; Nascimento, JR; Petrov, AY, Effective superpotential in the generic higher-derivative superfield supersymmetric three-dimensional gauge theory, Phys. Rev., D 88, 045021, (2013)
[27] Gama, FS; Nascimento, JR; Petrov, AY, Effective superpotential in the generic higher-derivative three-dimensional scalar superfield theory, Phys. Rev., D 88, 065029, (2013)
[28] E.A. Gallegos, J. Senise, C.R. and A.J. da Silva, Higher-derivative Wess-Zumino model in three dimensions, Phys. Rev.D 87 (2013) 085032 [arXiv:1212.6613] [INSPIRE].
[29] Carena, M.; Kong, K.; Ponton, E.; Zurita, J., Supersymmetric Higgs bosons and beyond, Phys. Rev., D 81, 015001, (2010)
[30] R. Flauger, S. Hellerman, C. Schmidt-Colinet and M. Sudano, The one-loop effective Kähler potential. I: chiral multiplets, arXiv:1205.3492 [INSPIRE].
[31] Buchmüller, W.; Love, ST, Chiral symmetry and supersymmetry in the Nambu-Jona-Lasinio model, Nucl. Phys., B 204, 213, (1982)
[32] Buchmuller, W.; Ellwanger, U., On the structure of composite Goldstone supermultiplets, Nucl. Phys., B 245, 237, (1984)
[33] Ferrara, S.; Wess, J.; Zumino, B., Supergauge multiplets and superfields, Phys. Lett., B 51, 239, (1974)
[34] Cecotti, S.; Ferrara, S.; Villasante, M., Linear multiplets and super Chern-Simons forms in 4D supergravity, Int. J. Mod. Phys., A 2, 1839, (1987)
[35] Binetruy, P.; Girardi, G.; Grimm, R., Linear supermultiplets and nonholomorphic gauge coupling functions, Phys. Lett., B 265, 111, (1991)
[36] Ferrara, S.; Kallosh, R.; Linde, A.; Porrati, M., Minimal supergravity models of inflation, Phys. Rev., D 88, 085038, (2013)
[37] Fox, PJ; Nelson, AE; Weiner, N., Dirac gaugino masses and supersoft supersymmetry breaking, JHEP, 08, 035, (2002)
[38] A.E. Nelson, N. Rius, V. Sanz and M. Ünsal, The minimal supersymmetric model without a μ term, JHEP08 (2002) 039 [hep-ph/0206102] [INSPIRE]. · Zbl 1226.81307
[39] Cecotti, S.; Ferrara, S.; Girardello, L., Structure of the scalar potential in general N = 1 higher derivative supergravity in four-dimensions, Phys. Lett., B 187, 321, (1987)
[40] Farakos, F.; Ferrara, S.; Kehagias, A.; Porrati, M., Supersymmetry breaking by higher dimension operators, Nucl. Phys., B 879, 348, (2014) · Zbl 1284.81267
[41] Burgess, CP; Derendinger, J-P; Quevedo, F.; Quirós, M., Gaugino condensates and chiral linear duality: an effective Lagrangian analysis, Phys. Lett., B 348, 428, (1995)
[42] Burgess, CP; Derendinger, J-P; Quevedo, F.; Quirós, M., On gaugino condensation with field-dependent gauge couplings, Annals Phys., 250, 193, (1996) · Zbl 0897.58055
[43] Binetruy, P.; Gaillard, MK; Taylor, TR, Dynamical supersymmetric breaking and the linear multiplet, Nucl. Phys., B 455, 97, (1995) · Zbl 0925.81351
[44] Gates, SJ, Super p form gauge superfields, Nucl. Phys., B 184, 381, (1981)
[45] Kaloper, N.; Lawrence, A.; Sorbo, L., An ignoble approach to large field inflation, JCAP, 03, 023, (2011)
[46] Groh, K.; Louis, J.; Sommerfeld, J., Duality and couplings of 3-form-multiplets in N = 1 supersymmetry, JHEP, 05, 001, (2013)
[47] Dudas, E., Three-form multiplet and inflation, JHEP, 12, 014, (2014)
[48] J. Wess and J. Bagger, Supersymmetry and supergravity, 2\^{}{nd} edition, Princeton University Press, Princeton U.S.A. (1992).
[49] Roček, M., Linearizing the Volkov-akulov model, Phys. Rev. Lett., 41, 451, (1978)
[50] Lindström, U.; Roček, M., Constrained local superfields, Phys. Rev., D 19, 2300, (1979)
[51] Ivanov, EA; Kapustnikov, AA, General relationship between linear and nonlinear realizations of supersymmetry, J. Phys., A 11, 2375, (1978)
[52] Casalbuoni, R.; Curtis, S.; Dominici, D.; Feruglio, F.; Gatto, R., Nonlinear realization of supersymmetry algebra from supersymmetric constraint, Phys. Lett., B 220, 569, (1989)
[53] Brignole, A.; Feruglio, F.; Zwirner, F., On the effective interactions of a light gravitino with matter fermions, JHEP, 11, 001, (1997) · Zbl 0949.81511
[54] Komargodski, Z.; Seiberg, N., From linear SUSY to constrained superfields, JHEP, 09, 066, (2009)
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.