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Electron EDM in the complex two-Higgs doublet model

Wolfgang Altmannshofer, Stefania Gori, Nick Hamer, and Hiren H. Patel
Phys. Rev. D 102, 115042 – Published 31 December 2020
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  • INTRODUCTION
  • FORMULATION OF THE C2HDM
  • BACKGROUND FIELD EVALUATION
  • REEVALUATION IN THE FEYNMAN-’t HOOFT…
  • LIGHT QUARK EDMs
  • COMPARISON WITH LITERATURE
  • DECOUPLING LIMIT AND EFT ANALYSIS
  • SUMMARY
  • ACKNOWLEDGMENTS
  • APPENDICES
    • Supplemental Material
    References

    Abstract

    We present the first complete two loop calculation of the electron EDM in the complex two-Higgs doublet model. We confirm gauge independence by demonstrating analytic cancellation of the gauge parameter ξ in the background field gauge and the ’t Hooft Rξ gauge. We also investigate the behavior of the electron EDM near the decoupling limit and determine the short- and long-distance contributions by matching onto an effective field theory. Compared with earlier studies of the electron EDM in the complex two-Higgs doublet model, we note disagreements in several places and provide diagnoses where possible. We also provide expressions for EDMs of light quarks.

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    • Received 30 September 2020
    • Accepted 19 November 2020

    DOI:https://doi.org/10.1103/PhysRevD.102.115042

    Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Electric momentElectroweak radiative corrections
    1. Physical Systems
    ElectronsQuarks
    1. Properties
    CP violationForm factors
    Nuclear PhysicsParticles & Fields

    Authors & Affiliations

    Wolfgang Altmannshofer*, Stefania Gori†, Nick Hamer‡, and Hiren H. Patel§

    • Department of Physics and Santa Cruz Institute for Particle, Physics University of California, Santa Cruz, California 95064, USA

    • *waltmann@ucsc.edu
    • †sgori@ucsc.edu
    • ‡nhamer@ucsc.edu
    • §hpatel6@ucsc.edu

    Article Text

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    Issue

    Vol. 102, Iss. 11 — 1 December 2020

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    Images

    • Figure 1
      Figure 1

      Representative fermion loop contribution to electromagnetic δfEM (photon exchange) and neutral current δfNC (Z exchange) Barr-Zee diagrams. The symbol “⊗” denotes the background electromagnetic field A¯μ. Additional diagrams are obtained by reflections along the vertical axis or by exchanging the γ/Z and hk lines attached to the external electron.

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    • Figure 2
      Figure 2

      Representative charged Higgs contributions to left: electromagnetic δH+EM and neutral current δH+NC Barr-Zee diagrams, and right: charged current δH+CC Barr-Zee diagrams.

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    • Figure 3
      Figure 3

      Representative W boson contributions to left: electromagnetic δWEM(ξ) and neutral current δWNC(ξ) Barr-Zee diagrams, and right: charged current δWCC(ξ) Barr-Zee diagrams. Diagrams involving the three-point coupling of the background field A¯μ to one W gauge boson and one charged Goldstone boson are absent in the background field gauge. The third diagram with a ghost loop involving the four-point coupling in Eq. (21) is specific to the background field gauge.

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    • Figure 4
      Figure 4

      Representative contributions to left: neutral current kite δkiteNC and right: charged current δkiteCC(ξ) kite diagrams.

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    • Figure 5
      Figure 5

      Class of diagrams additionally contributing to W loop neutral current Barr-Zee, δWNC, in the ’t Hooft Rξ gauge.

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    • Figure 6
      Figure 6

      Additional charged current Barr-Zee diagrams in the ’t Hooft Rξ gauge. The R-subtracted finite parts of diagrams (a) and (b) contribute to δH+CC and δWCC, respectively. The UV-singular R subtractions cancel against the tadpole diagrams in Figs. 7 and 8.

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    • Figure 7
      Figure 7

      Diagrams involving the Goldstone-Higgs transition function that contribute to the electron EDM in the ’t Hooft Rξ gauge.

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    • Figure 8
      Figure 8

      Tadpole diagrams in the ’t Hooft Rξ gauge. Diagram (c) represents a contribution due to a CP-violating shift in the residue of the electron pole.

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    • Figure 9
      Figure 9

      Charged current kite diagram that contributes to quark EDMs in the background field gauge. Other diagrams do not contribute at O(GFmq).

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    • Figure 10
      Figure 10

      Predictions of the electron EDM in the left: type I, and right: type II C2HDM as a function of tanβ for the benchmark point in (67). The solid black line represents the full result in (43). The solid red, green, and blue curves are obtained by summing all contributions within each column of Table 1 labeled “Fermion loop,” “Charged Higgs loop,” and “Gauge boson loop,” respectively. The dashed lines are the corresponding contributions without the charged and neutral current kite diagrams in the background field Feynman gauge, ξ=1. The shaded region corresponds to the 90% C.L. exclusion limit from the ACME collaboration. In the future, ACME is expected to improve the bound by at least an order of magnitude. This is indicated by the horizontal dashed line.

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    • Figure 11
      Figure 11

      Gauge-dependence of individual contributions to the electron EDM listed in the last column of Table 1 in the background field gauge for the type II model at the benchmark point in (67) with tanβ=5. The horizontal black line is the total gauge-independent EDM in (43), and the dashed black curve is the total excluding the charged current δkiteCC(ξ) and neutral current δkiteNC kite contributions.

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    • Figure 12
      Figure 12

      Generation of the CP-violating effective operator in (81) by integrating out H2 at tree level.

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    • Figure 13
      Figure 13

      Diagrams involving the four-point interactions in (83) that contain the leading logarithmic contribution to the electron EDM.

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    • Figure 14
      Figure 14

      Approximations to predictions of the electron EDM in the type II C2HDM as a function of mH+, at the benchmark point (67) with tanβ=2. The black line is the full two loop result in the C2HDM (43). The dashed red line is its asymptotic approximation near the decoupling limit through O(v2/M2) given in (86). The solid red curve is the leading logarithmic approximation in (73) and the dashed blue curve is the EFT result in the MS¯ scheme given by the IR part of (74) with μ=M. The shaded blue region is obtained varying the scale between μ=M/2 and μ=2M.

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