Advertisement

Renormalization group evolution of dimension-seven operators in standard model effective field theory and relevant phenomenology

  • Yi LiaoEmail author
  • Xiao-Dong Ma
Open Access
Regular Article - Theoretical Physics
  • 58 Downloads

Abstract

We showed in a previous publication that there are six independent dimension-seven operators violating both lepton and baryon numbers (L = −B = 1) and twelve ones violating lepton but preserving baryon number (L = 2, B = 0) in standard model effective field theory, and we calculated one-loop renormalization for the former six operators. In this work we continue our efforts on renormalization of the operators. It turns out this could become subtle because the operators are connected by nontrivial relations when fermion flavors are counted. This kind of relations does not appear in lower dimensional operators. We show how we can extract anomalous dimension matrix for a flavor-specified basis of operators from counterterms computed for the above flavor-blind operators without introducing singular inverse Yukawa coupling matrices. As a phenomenological application, we investigate renormalization group effects on nuclear neutrinoless double β decay. We also discuss very briefly its analog in the meson sector, K±πμ±μ±, and indicate potential difficulties to compute its decay width.

Keywords

Beyond Standard Model Effective Field Theories Renormalization Group Global Symmetries 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    S. Weinberg, Baryon and lepton nonconserving processes, Phys. Rev. Lett. 43 (1979) 1566 [INSPIRE].ADSCrossRefGoogle Scholar
  2. [2]
    W. Buchmüller and D. Wyler, Effective Lagrangian analysis of new interactions and flavor conservation, Nucl. Phys. B 268 (1986) 621 [INSPIRE].
  3. [3]
    B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek, Dimension-six terms in the Standard Model Lagrangian, JHEP 10 (2010) 085 [arXiv:1008.4884] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  4. [4]
    L. Lehman, Extending the Standard Model effective field theory with the complete set of dimension-7 operators, Phys. Rev. D 90 (2014) 125023 [arXiv:1410.4193] [INSPIRE].
  5. [5]
    Y. Liao and X.-D. Ma, Renormalization group evolution of dimension-seven baryon- and lepton-number-violating operators, JHEP 11 (2016) 043 [arXiv:1607.07309] [INSPIRE].MathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    L. Lehman and A. Martin, Hilbert series for constructing Lagrangians: expanding the phenomenologists toolbox, Phys. Rev. D 91 (2015) 105014 [arXiv:1503.07537] [INSPIRE].
  7. [7]
    B. Henning, X. Lu, T. Melia and H. Murayama, Hilbert series and operator bases with derivatives in effective field theories, Commun. Math. Phys. 347 (2016) 363 [arXiv:1507.07240] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    L. Lehman and A. Martin, Low-derivative operators of the Standard Model effective field theory via Hilbert series methods, JHEP 02 (2016) 081 [arXiv:1510.00372] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. [9]
    B. Henning, X. Lu, T. Melia and H. Murayama, 2, 84, 30, 993, 560, 15456, 11962, 261485,. . . : higher dimension operators in the SM EFT, JHEP 08 (2017) 016 [arXiv:1512.03433] [INSPIRE].
  10. [10]
    B. Henning, X. Lu, T. Melia and H. Murayama, Operator bases, S-matrices and their partition functions, JHEP 10 (2017) 199 [arXiv:1706.08520] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  11. [11]
    A. Aparici, K. Kim, A. Santamaria and J. Wudka, Right-handed neutrino magnetic moments, Phys. Rev. D 80 (2009) 013010 [arXiv:0904.3244] [INSPIRE].
  12. [12]
    F. del Aguila, S. Bar-Shalom, A. Soni and J. Wudka, Heavy Majorana neutrinos in the effective Lagrangian description: application to hadron colliders, Phys. Lett. B 670 (2009) 399 [arXiv:0806.0876] [INSPIRE].
  13. [13]
    S. Bhattacharya and J. Wudka, Dimension-seven operators in the Standard Model with right handed neutrinos, Phys. Rev. D 94 (2016) 055022 [Erratum ibid. D 95 (2017) 039904] [arXiv:1505.05264] [INSPIRE].
  14. [14]
    Y. Liao and X.-D. Ma, Operators up to dimension seven in Standard Model effective field theory extended with sterile neutrinos, Phys. Rev. D 96 (2017) 015012 [arXiv:1612.04527] [INSPIRE].
  15. [15]
    S. Antusch, M. Drees, J. Kersten, M. Lindner and M. Ratz, Neutrino mass operator renormalization revisited, Phys. Lett. B 519 (2001) 238 [hep-ph/0108005] [INSPIRE].
  16. [16]
    C. Grojean, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group scaling of Higgs operators and Γ(hγγ), JHEP 04 (2013) 016 [arXiv:1301.2588] [INSPIRE].
  17. [17]
    J. Elias-Miró, J.R. Espinosa, E. Masso and A. Pomarol, Renormalization of dimension-six operators relevant for the Higgs decays hγγ, γZ, JHEP 08 (2013) 033 [arXiv:1302.5661] [INSPIRE].
  18. [18]
    J. Elias-Miro, J.R. Espinosa, E. Masso and A. Pomarol, Higgs windows to new physics through d = 6 operators: constraints and one-loop anomalous dimensions, JHEP 11 (2013) 066 [arXiv:1308.1879] [INSPIRE].
  19. [19]
    E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the Standard Model dimension six operators I: formalism and λ dependence, JHEP 10 (2013) 087 [arXiv:1308.2627] [INSPIRE].
  20. [20]
    E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the Standard Model dimension six operators II: Yukawa dependence, JHEP 01 (2014) 035 [arXiv:1310.4838] [INSPIRE].ADSCrossRefGoogle Scholar
  21. [21]
    R. Alonso, E.E. Jenkins, A.V. Manohar and M. Trott, Renormalization group evolution of the Standard Model dimension six operators III: gauge coupling dependence and phenomenology, JHEP 04 (2014) 159 [arXiv:1312.2014] [INSPIRE].ADSCrossRefGoogle Scholar
  22. [22]
    R. Alonso, H.-M. Chang, E.E. Jenkins, A.V. Manohar and B. Shotwell, Renormalization group evolution of dimension-six baryon number violating operators, Phys. Lett. B 734 (2014) 302 [arXiv:1405.0486] [INSPIRE].
  23. [23]
    R. Alonso, E.E. Jenkins and A.V. Manohar, Holomorphy without supersymmetry in the Standard Model effective field theory, Phys. Lett. B 739 (2014) 95 [arXiv:1409.0868] [INSPIRE].
  24. [24]
    C. Cheung and C.-H. Shen, Nonrenormalization theorems without supersymmetry, Phys. Rev. Lett. 115 (2015) 071601 [arXiv:1505.01844] [INSPIRE].
  25. [25]
    E.E. Jenkins, A.V. Manohar and M. Trott, Naive dimensional analysis counting of gauge theory amplitudes and anomalous dimensions, Phys. Lett. B 726 (2013) 697 [arXiv:1309.0819] [INSPIRE].
  26. [26]
    Y. Liao and X.-D. Ma, Perturbative power counting, lowest-index operators and their renormalization in Standard Model effective field theory, Commun. Theor. Phys. 69 (2018) 285 [arXiv:1701.08019] [INSPIRE].
  27. [27]
    C. Arzt, Reduced effective Lagrangians, Phys. Lett. B 342 (1995) 189 [hep-ph/9304230] [INSPIRE].
  28. [28]
    V. Cirigliano, W. Dekens, J. de Vries, M.L. Graesser and E. Mereghetti, Neutrinoless double beta decay in chiral effective field theory: lepton number violation at dimension seven, JHEP 12 (2017) 082 [arXiv:1708.09390] [INSPIRE].ADSCrossRefGoogle Scholar
  29. [29]
    V. Cirigliano, W. Dekens, J. de Vries, M.L. Graesser and E. Mereghetti, A neutrinoless double beta decay master formula from effective field theory, JHEP 12 (2018) 097 [arXiv:1806.02780] [INSPIRE].ADSCrossRefGoogle Scholar
  30. [30]
    NA48/2 collaboration, Searches for lepton number violation and resonances in K ±πμμ decays, Phys. Lett. B 769 (2017) 67 [arXiv:1612.04723] [INSPIRE].
  31. [31]
    W. Rodejohann, Neutrino-less double beta decay and particle physics, Int. J. Mod. Phys. E 20 (2011) 1833 [arXiv:1106.1334] [INSPIRE].
  32. [32]
    KamLAND-Zen collaboration, Search for Majorana neutrinos near the inverted mass hierarchy region with KamLAND-Zen, Phys. Rev. Lett. 117 (2016) 082503 [Addendum ibid. 117 (2016) 109903] [arXiv:1605.02889] [INSPIRE].
  33. [33]
    GERDA collaboration, Improved limit on neutrinoless double-β decay of 76 Ge from GERDA phase II, Phys. Rev. Lett. 120 (2018) 132503 [arXiv:1803.11100] [INSPIRE].
  34. [34]
    nEXO collaboration, nEXO pre-conceptual design report, arXiv:1805.11142 [INSPIRE].
  35. [35]
    H. Pas, M. Hirsch, H.V. Klapdor-Kleingrothaus and S.G. Kovalenko, A superformula for neutrinoless double beta decay. 2. The short range part, Phys. Lett. B 498 (2001) 35 [hep-ph/0008182] [INSPIRE].
  36. [36]
    F.F. Deppisch, M. Hirsch and H. Pas, Neutrinoless double beta decay and physics beyond the Standard Model, J. Phys. G 39 (2012) 124007 [arXiv:1208.0727] [INSPIRE].
  37. [37]
    M. Horoi and A. Neacsu, Towards an effective field theory approach to the neutrinoless double-beta decay, arXiv:1706.05391 [INSPIRE].
  38. [38]
    Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].
  39. [39]
    L.N. Mihaila, J. Salomon and M. Steinhauser, Renormalization constants and β-functions for the gauge couplings of the Standard Model to three-loop order, Phys. Rev. D 86 (2012) 096008 [arXiv:1208.3357] [INSPIRE].
  40. [40]
    A. Nicholson et al., Heavy physics contributions to neutrinoless double beta decay from QCD, Phys. Rev. Lett. 121 (2018) 172501 [arXiv:1805.02634] [INSPIRE].ADSCrossRefGoogle Scholar
  41. [41]
    X. Feng, L.-C. Jin, X.-Y. Tuo and S.-C. Xia, Light-neutrino exchange and long-distance contributions to 0ν2β decays: an exploratory study on ππee, Phys. Rev. Lett. 122 (2019) 022001 [arXiv:1809.10511] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.School of PhysicsNankai UniversityTianjinChina
  2. 2.Center for High Energy PhysicsPeking UniversityBeijingChina

Personalised recommendations