Skip to main content

A new theory framework for the electroweak radiative corrections in Kl3 decays

A preprint version of the article is available at arXiv.

Abstract

We propose a new theory framework to study the electroweak radiative corrections in Kl3 decays by combining the classic current algebra approach with the modern effective field theory. Under this framework, the most important \( \mathcal{O} \)(GFα) radiative corrections are described by a single tensor Tμν involving the time-ordered product between the charged weak current and the electromagnetic current, and all remaining pieces are calculable order-by-order in Chiral Perturbation Theory. We further point out a special advantage in the \( {K}_{l3}^0 \) channel that it suffers the least impact from the poorly-constrained low-energy constants. This finding may serve as a basis for a more precise extraction of the matrix element Vus in the future.

References

  1. [1]

    N. Cabibbo, Unitary symmetry and leptonic decays, Phys. Rev. Lett. 10 (1963) 531 [INSPIRE].

    ADS  Article  Google Scholar 

  2. [2]

    M. Kobayashi and T. Maskawa, CP violation in the renormalizable theory of weak interaction, Prog. Theor. Phys. 49 (1973) 652 [INSPIRE].

    ADS  Article  Google Scholar 

  3. [3]

    Particle Data Group collaboration, Review of particle physics, Phys. Rev. D 98 (2018) 030001 [INSPIRE].

  4. [4]

    S. Bauman, J. Erler and M. Ramsey-Musolf, Charged current universality and the MSSM, Phys. Rev. D 87 (2013) 035012 [arXiv:1204.0035] [INSPIRE].

  5. [5]

    M. Gonzalez-Alonso, O. Naviliat-Cuncic and N. Severijns, New physics searches in nuclear and neutron β decay, Prog. Part. Nucl. Phys. 104 (2019) 165 [arXiv:1803.08732] [INSPIRE].

    ADS  Article  Google Scholar 

  6. [6]

    V. Cirigliano, A. Garcia, D. Gazit, O. Naviliat-Cuncic, G. Savard and A. Young, Precision beta decay as a probe of new physics, arXiv:1907.02164 [INSPIRE].

  7. [7]

    C.-Y. Seng, M. Gorchtein, H.H. Patel and M.J. Ramsey-Musolf, Reduced hadronic uncertainty in the determination of Vud , Phys. Rev. Lett. 121 (2018) 241804 [arXiv:1807.10197] [INSPIRE].

    ADS  Article  Google Scholar 

  8. [8]

    W.J. Marciano and A. Sirlin, Improved calculation of electroweak radiative corrections and the value of Vud, Phys. Rev. Lett. 96 (2006) 032002 [hep-ph/0510099] [INSPIRE].

  9. [9]

    C.Y. Seng, M. Gorchtein and M.J. Ramsey-Musolf, Dispersive evaluation of the inner radiative correction in neutron and nuclear β decay, Phys. Rev. D 100 (2019) 013001 [arXiv:1812.03352] [INSPIRE].

  10. [10]

    M. Gorchtein, γW box inside out: nuclear polarizabilities distort the beta decay spectrum, Phys. Rev. Lett. 123 (2019) 042503 [arXiv:1812.04229] [INSPIRE].

  11. [11]

    R. Petti, Neutrinos/LBNF connection, in the 9th International Conference on Physics Opportunities at an ElecTron-Ion-Collider, Lawrence Berkeley National Laboratory, Berkeley, CA, U.S.A. (2019).

  12. [12]

    C.-Y. Seng and U.-G. Meißner, Toward a first-principles calculation of electroweak box diagrams, Phys. Rev. Lett. 122 (2019) 211802 [arXiv:1903.07969] [INSPIRE].

    ADS  Article  Google Scholar 

  13. [13]

    A. Czarnecki, W.J. Marciano and A. Sirlin, Radiative corrections to neutron and nuclear beta decays revisited, Phys. Rev. D 100 (2019) 073008 [arXiv:1907.06737] [INSPIRE].

  14. [14]

    Fermilab Lattice and MILC collaborations, |Vus| from Kl3 decay and four-flavor lattice QCD, Phys. Rev. D 99 (2019) 114509 [arXiv:1809.02827] [INSPIRE].

  15. [15]

    V. Cirigliano, G. Ecker, H. Neufeld, A. Pich and J. Portoles, Kaon decays in the Standard Model, Rev. Mod. Phys. 84 (2012) 399 [arXiv:1107.6001] [INSPIRE].

    ADS  Article  Google Scholar 

  16. [16]

    V. Cirigliano, M. Knecht, H. Neufeld, H. Rupertsberger and P. Talavera, Radiative corrections to Kl3 decays, Eur. Phys. J. C 23 (2002) 121 [hep-ph/0110153] [INSPIRE].

  17. [17]

    V. Cirigliano, M. Giannotti and H. Neufeld, Electromagnetic effects in Kl3 decays, JHEP 11 (2008) 006 [arXiv:0807.4507] [INSPIRE].

    ADS  Article  Google Scholar 

  18. [18]

    A. Sirlin, Current algebra formulation of radiative corrections in gauge theories and the universality of the weak interactions, Rev. Mod. Phys. 50 (1978) 573 [Erratum ibid. 50 (1978) 905] [INSPIRE].

  19. [19]

    T. Kinoshita and A. Sirlin, Radiative corrections to Fermi interactions, Phys. Rev. 113 (1959) 1652 [INSPIRE].

    ADS  Article  Google Scholar 

  20. [20]

    W. Pauli and F. Villars, On the invariant regularization in relativistic quantum theory, Rev. Mod. Phys. 21 (1949) 434 [INSPIRE].

    ADS  MathSciNet  Article  Google Scholar 

  21. [21]

    S. Descotes-Genon and B. Moussallam, Radiative corrections in weak semi-leptonic processes at low energy: a two-step matching determination, Eur. Phys. J. C 42 (2005) 403 [hep-ph/0505077] [INSPIRE].

  22. [22]

    B. Ananthanarayan and B. Moussallam, Four-point correlator constraints on electromagnetic chiral parameters and resonance effective Lagrangians, JHEP 06 (2004) 047 [hep-ph/0405206] [INSPIRE].

  23. [23]

    G. Ecker, J. Gasser, A. Pich and E. de Rafael, The role of resonances in chiral perturbation theory, Nucl. Phys. B 321 (1989) 311 [INSPIRE].

    ADS  Article  Google Scholar 

  24. [24]

    J. Gasser and H. Leutwyler, Chiral perturbation theory: expansions in the mass of the strange quark, Nucl. Phys. B 250 (1985) 465 [INSPIRE].

    ADS  Article  Google Scholar 

  25. [25]

    R. Urech, Virtual photons in chiral perturbation theory, Nucl. Phys. B 433 (1995) 234 [hep-ph/9405341] [INSPIRE].

  26. [26]

    M. Knecht, H. Neufeld, H. Rupertsberger and P. Talavera, Chiral perturbation theory with virtual photons and leptons, Eur. Phys. J. C 12 (2000) 469 [hep-ph/9909284] [INSPIRE].

  27. [27]

    V. Bernard, M. Oertel, E. Passemar and J. Stern, \( {K}_{\mu 3}^L \) decay: a stringent test of right-handed quark currents, Phys. Lett. B 638 (2006) 480 [hep-ph/0603202] [INSPIRE].

  28. [28]

    V. Bernard and E. Passemar, Matching chiral perturbation theory and the dispersive representation of the scalar Kπ form-factor, Phys. Lett. B 661 (2008) 95 [arXiv:0711.3450] [INSPIRE].

    ADS  Article  Google Scholar 

  29. [29]

    V. Bernard, M. Oertel, E. Passemar and J. Stern, Dispersive representation and shape of the Kl3 form factors: robustness, Phys. Rev. D 80 (2009) 034034 [arXiv:0903.1654] [INSPIRE].

  30. [30]

    V. Bernard, D.R. Boito and E. Passemar, Dispersive representation of the scalar and vector Kπ form factors for τ → Kπντ and Kl3 decays, Nucl. Phys. Proc. Suppl. 218 (2011) 140 [arXiv:1103.4855] [INSPIRE].

  31. [31]

    V. Bernard, First determination of f+(0)|Vus| from a combined analysis of τ → Kπντ decay and πK scattering with constraints from Kl3 decays, JHEP 06 (2014) 082 [arXiv:1311.2569] [INSPIRE].

    ADS  Article  Google Scholar 

  32. [32]

    D. Giusti et al., First lattice calculation of the QED corrections to leptonic decay rates, Phys. Rev. Lett. 120 (2018) 072001 [arXiv:1711.06537] [INSPIRE].

  33. [33]

    USQCD collaboration, The role of lattice QCD in searches for violations of fundamental symmetries and signals for new physics, Eur. Phys. J. A 55 (2019) 197 [arXiv:1904.09704] [INSPIRE].

  34. [34]

    M. Di Carlo et al., Light-meson leptonic decay rates in lattice QCD+QED, Phys. Rev. D 100 (2019) 034514 [arXiv:1904.08731] [INSPIRE].

  35. [35]

    R. Baur and R. Urech, Resonance contributions to the electromagnetic low-energy constants of chiral perturbation theory, Nucl. Phys. B 499 (1997) 319 [hep-ph/9612328] [INSPIRE].

  36. [36]

    J. Bijnens and J. Prades, Electromagnetic corrections for pions and kaons: masses and polarizabilities, Nucl. Phys. B 490 (1997) 239 [hep-ph/9610360] [INSPIRE].

  37. [37]

    L.S. Brown, Perturbation theory and selfmass insertions, Phys. Rev. 187 (1969) 2260 [INSPIRE].

    ADS  Article  Google Scholar 

  38. [38]

    A. Sirlin, Large mW, mZ behavior of the O(α) corrections to semileptonic processes mediated by W, Nucl. Phys. B 196 (1982) 83 [INSPIRE].

  39. [39]

    J.D. Bjorken, Applications of the chiral U(6) × U(6) algebra of current densities, Phys. Rev. 148 (1966) 1467 [INSPIRE].

    ADS  Article  Google Scholar 

  40. [40]

    K. Johnson and F.E. Low, Current algebras in a simple model, Prog. Theor. Phys. Suppl. 37 (1966) 74 [INSPIRE].

    ADS  Article  Google Scholar 

Download references

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

Author information

Affiliations

Authors

Corresponding author

Correspondence to Chien-Yeah Seng.

Additional information

ArXiv ePrint: 1910.13208

Rights and permissions

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.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Seng, CY., Galviz, D. & Meißner, UG. A new theory framework for the electroweak radiative corrections in Kl3 decays. J. High Energ. Phys. 2020, 69 (2020). https://doi.org/10.1007/JHEP02(2020)069

Download citation

Keywords

  • Chiral Lagrangians
  • Kaon Physics
  • Precision QED