Skip to main content

Advertisement

SpringerLink
Scattering of Goldstone bosons and resonance production in a composite Higgs model on the lattice
Download PDF
Download PDF
  • Regular Article - Theoretical Physics
  • Open Access
  • Published: 13 April 2021

Scattering of Goldstone bosons and resonance production in a composite Higgs model on the lattice

  • Vincent Drach  ORCID: orcid.org/0000-0001-8948-02201,
  • Tadeusz Janowski2,
  • Claudio Pica3 &
  • …
  • Sasa Prelovsek4,5,6 

Journal of High Energy Physics volume 2021, Article number: 117 (2021) Cite this article

  • 139 Accesses

  • 4 Citations

  • 1 Altmetric

  • Metrics details

A preprint version of the article is available at arXiv.

Abstract

We calculate the coupling between a vector resonance and two Goldstone bosons in SU(2) gauge theory with Nf = 2 Dirac fermions in the fundamental representation. The considered theory can be used to construct a minimal Composite Higgs models. The coupling is related to the width of the vector resonance and we determine it by simulating the scattering of two Goldstone bosons where the resonance is produced. The resulting coupling is gVPP = 7.8 ± 0.6, not far from gρππ ≃ 6 in QCD. This is the first lattice calculation of the resonance properties for a minimal UV completion. This coupling controls the production cross section of the lightest expected resonance at the LHC and enters into other tests of the Standard Model, from Vector Boson Fusion to electroweak precision tests. Our prediction is crucial to constrain the model using lattice input and for understanding the behavior of the vector meson production cross section as a function of the underlying gauge theory. We also extract the coupling \( {g}_{\mathrm{VPP}}^{\mathrm{KSRF}} \) = 9.4 ± 0.6 assuming the vector-dominance and find that this phenomenological estimate slightly overestimates the value of the coupling.

Download to read the full article text

Working on a manuscript?

Avoid the most common mistakes and prepare your manuscript for journal editors.

Learn more

References

  1. D. B. Kaplan and H. Georgi, SU(2) × U(1) breaking by vacuum misalignment, Phys. Lett. B 136 (1984) 183 [INSPIRE].

    Article  Google Scholar 

  2. D. B. Kaplan, H. Georgi and S. Dimopoulos, Composite Higgs scalars, Phys. Lett. B 136 (1984) 187 [INSPIRE].

    Article  Google Scholar 

  3. M. J. Dugan, H. Georgi and D. B. Kaplan, Anatomy of a composite Higgs model, Nucl. Phys. B 254 (1985) 299 [INSPIRE].

    Article  Google Scholar 

  4. R. Contino and M. Salvarezza, One-loop effects from spin-1 resonances in composite Higgs models, JHEP 07 (2015) 065 [arXiv:1504.02750] [INSPIRE].

    Article  MathSciNet  MATH  Google Scholar 

  5. R. Contino, D. Marzocca, D. Pappadopulo and R. Rattazzi, On the effect of resonances in composite Higgs phenomenology, JHEP 10 (2011) 081 [arXiv:1109.1570] [INSPIRE].

    Article  MATH  Google Scholar 

  6. M. Gallinaro et al., Beyond the Standard Model in vector boson scattering signatures, in International workshop on BSM models in vector boson scattering processes, (2020) [arXiv:2005.09889] [INSPIRE].

    Google Scholar 

  7. D. Liu, L.-T. Wang and K.-P. Xie, Broad composite resonances and their signals at the LHC, Phys. Rev. D 100 (2019) 075021 [arXiv:1901.01674] [INSPIRE].

    Article  Google Scholar 

  8. C. Helsens, D. Jamin, M. L. Mangano, T. G. Rizzo and M. Selvaggi, Heavy resonances at energy-frontier hadron colliders, Eur. Phys. J. C 79 (2019) 569 [arXiv:1902.11217] [INSPIRE].

    Article  Google Scholar 

  9. D. Buarque Franzosi, G. Cacciapaglia and A. Deandrea, Sigma-assisted low scale composite Goldstone-Higgs, Eur. Phys. J. C 80 (2020) 28 [arXiv:1809.09146] [INSPIRE].

    Article  Google Scholar 

  10. D. Liu, L.-T. Wang and K.-P. Xie, Prospects of searching for composite resonances at the LHC and beyond, JHEP 01 (2019) 157 [arXiv:1810.08954] [INSPIRE].

    Article  Google Scholar 

  11. D. Buarque Franzosi, Implications of vector boson scattering unitarity in composite Higgs models, PoS(EPS-HEP2017)264 (2017).

  12. D. Greco and D. Liu, Hunting composite vector resonances at the LHC: naturalness facing data, JHEP 12 (2014) 126 [arXiv:1410.2883] [INSPIRE].

    Article  Google Scholar 

  13. G. Cacciapaglia and F. Sannino, Fundamental composite (Goldstone) Higgs dynamics, JHEP 04 (2014) 111 [arXiv:1402.0233] [INSPIRE].

    Article  MATH  Google Scholar 

  14. G. Cacciapaglia, C. Pica and F. Sannino, Fundamental composite dynamics: a review, Phys. Rept. 877 (2020) 1 [arXiv:2002.04914] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  15. A. Arbey, G. Cacciapaglia, H. Cai, A. Deandrea, S. Le Corre and F. Sannino, Fundamental composite electroweak dynamics: status at the LHC, Phys. Rev. D 95 (2017) 015028 [arXiv:1502.04718] [INSPIRE].

    Article  Google Scholar 

  16. D. Buarque Franzosi, G. Cacciapaglia, H. Cai, A. Deandrea and M. Frandsen, Vector and axial-vector resonances in composite models of the Higgs boson, JHEP 11 (2016) 076 [arXiv:1605.01363] [INSPIRE].

    Article  Google Scholar 

  17. M. Lüscher, Two particle states on a torus and their relation to the scattering matrix, Nucl. Phys. B 354 (1991) 531 [INSPIRE].

    Article  MathSciNet  Google Scholar 

  18. K. Rummukainen and S. A. Gottlieb, Resonance scattering phase shifts on a nonrest frame lattice, Nucl. Phys. B 450 (1995) 397 [hep-lat/9503028] [INSPIRE].

    Article  Google Scholar 

  19. CP-PACS collaboration, Lattice QCD calculation of the ρ meson decay width, Phys. Rev. D 76 (2007) 094506 [arXiv:0708.3705] [INSPIRE].

  20. CS collaboration, ρ meson decay in 2 + 1 flavor lattice QCD, Phys. Rev. D 84 (2011) 094505 [arXiv:1106.5365] [INSPIRE].

  21. X. Feng, K. Jansen and D. B. Renner, Resonance parameters of the ρ-meson from lattice QCD, Phys. Rev. D 83 (2011) 094505 [arXiv:1011.5288] [INSPIRE].

    Article  Google Scholar 

  22. C. B. Lang, D. Mohler, S. Prelovsek and M. Vidmar, Coupled channel analysis of the ρ meson decay in lattice QCD, Phys. Rev. D 84 (2011) 054503 [Erratum ibid. 89 (2014) 059903] [arXiv:1105.5636] [INSPIRE].

  23. Hadron Spectrum collaboration, Energy dependence of the ρ resonance in ππ elastic scattering from lattice QCD, Phys. Rev. D 87 (2013) 034505 [Erratum ibid. 90 (2014) 099902] [arXiv:1212.0830] [INSPIRE].

  24. F. Erben, J. R. Green, D. Mohler and H. Wittig, Rho resonance, timelike pion form factor, and implications for lattice studies of the hadronic vacuum polarization, Phys. Rev. D 101 (2020) 054504 [arXiv:1910.01083] [INSPIRE].

    Article  Google Scholar 

  25. C. Alexandrou et al., P -wave ππ scattering and the ρ resonance from lattice QCD, Phys. Rev. D 96 (2017) 034525 [arXiv:1704.05439] [INSPIRE].

    Article  Google Scholar 

  26. R. Arthur, V. Drach, M. Hansen, A. Hietanen, C. Pica and F. Sannino, SU(2) gauge theory with two fundamental flavors: a minimal template for model building, Phys. Rev. D 94 (2016) 094507 [arXiv:1602.06559] [INSPIRE].

    Article  Google Scholar 

  27. R. Arthur, V. Drach, A. Hietanen, C. Pica and F. Sannino, SU(2) gauge theory with two fundamental flavours: scalar and pseudoscalar spectrum, arXiv:1607.06654 [INSPIRE].

  28. R. Arthur, V. Drach, M. Hansen, A. Hietanen, C. Pica and F. Sannino, Scattering lengths in SU(2) gauge theory with two fundamental fermions, PoS(LATTICE2014)271 (2014) [arXiv:1412.4771] [INSPIRE].

  29. V. Drach, A. Hietanen, C. Pica, J. Rantaharju and F. Sannino, Template composite dark matter: SU(2) gauge theory with 2 fundamental flavours, PoS(LATTICE2015)234 (2016) [arXiv:1511.04370] [INSPIRE].

  30. A. Hietanen, R. Lewis, C. Pica and F. Sannino, Fundamental composite Higgs dynamics on the lattice: SU(2) with two flavors, JHEP 07 (2014) 116 [arXiv:1404.2794] [INSPIRE].

    Article  Google Scholar 

  31. A. Hietanen, R. Lewis, C. Pica and F. Sannino, Composite Goldstone dark matter: experimental predictions from the lattice, JHEP 12 (2014) 130 [arXiv:1308.4130] [INSPIRE].

    Article  Google Scholar 

  32. K. Kawarabayashi and M. Suzuki, Partially conserved axial vector current and the decays of vector mesons, Phys. Rev. Lett. 16 (1966) 255 [INSPIRE].

    Article  MathSciNet  Google Scholar 

  33. Riazuddin and Fayyazuddin, Algebra of current components and decay widths of ρ and K∗ mesons, Phys. Rev. 147 (1966) 1071 [INSPIRE].

  34. D. Nogradi and L. Szikszai, The model dependence of mϱ/fπ, PoS(LATTICE2019)237 (2019) [arXiv:1912.04114] [INSPIRE].

  35. D. Nogradi and L. Szikszai, The flavor dependence of mϱ/fπ, JHEP 05 (2019) 197 [arXiv:1905.01909] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  36. E. Bennett et al., Sp(4) gauge theories on the lattice: quenched fundamental and antisymmetric fermions, Phys. Rev. D 101 (2020) 074516 [arXiv:1912.06505] [INSPIRE].

    Article  MathSciNet  Google Scholar 

  37. E. Bennett et al., Sp(4) gauge theories on the lattice: Nf = 2 dynamical fundamental fermions, JHEP 12 (2019) 053 [arXiv:1909.12662] [INSPIRE].

    Article  Google Scholar 

  38. V. Ayyar et al., Spectroscopy of SU(4) composite Higgs theory with two distinct fermion representations, Phys. Rev. D 97 (2018) 074505 [arXiv:1710.00806] [INSPIRE].

    Article  Google Scholar 

  39. Lattice Strong Dynamics collaboration, Nonperturbative investigations of SU(3) gauge theory with eight dynamical flavors, Phys. Rev. D 99 (2019) 014509 [arXiv:1807.08411] [INSPIRE].

  40. K. G. Wilson, Confinement of quarks, Phys. Rev. D 10 (1974) 2445 [INSPIRE].

    Article  Google Scholar 

  41. B. Sheikholeslami and R. Wohlert, Improved continuum limit lattice action for QCD with Wilson fermions, Nucl. Phys. B 259 (1985) 572 [INSPIRE].

    Article  Google Scholar 

  42. M. Lüscher and P. Weisz, On-shell improved lattice gauge theories, Commun. Math. Phys. 97 (1985) 59 [Erratum ibid. 98 (1985) 433] [INSPIRE].

  43. S. Borsányi et al., High-precision scale setting in lattice QCD, JHEP 09 (2012) 010 [arXiv:1203.4469] [INSPIRE].

    Google Scholar 

  44. O. Bär and M. Golterman, Chiral perturbation theory for gradient flow observables, Phys. Rev. D 89 (2014) 034505 [Erratum ibid. 89 (2014) 099905] [arXiv:1312.4999] [INSPIRE].

  45. G. Martinelli, C. Pittori, C. T. Sachrajda, M. Testa and A. Vladikas, A general method for nonperturbative renormalization of lattice operators, Nucl. Phys. B 445 (1995) 81 [hep-lat/9411010] [INSPIRE].

    Article  Google Scholar 

  46. M. Gockeler et al., Nonperturbative renormalization of composite operators in lattice QCD, Nucl. Phys. B 544 (1999) 699 [hep-lat/9807044] [INSPIRE].

    Article  Google Scholar 

  47. P. F. Bedaque, Aharonov-Bohm effect and nucleon nucleon phase shifts on the lattice, Phys. Lett. B 593 (2004) 82 [nucl-th/0402051] [INSPIRE].

    Article  Google Scholar 

  48. C. T. Sachrajda and G. Villadoro, Twisted boundary conditions in lattice simulations, Phys. Lett. B 609 (2005) 73 [hep-lat/0411033] [INSPIRE].

    Article  Google Scholar 

  49. L. Del Debbio, M. T. Frandsen, H. Panagopoulos and F. Sannino, Higher representations on the lattice: perturbative studies, JHEP 06 (2008) 007 [arXiv:0802.0891] [INSPIRE].

    Article  Google Scholar 

  50. M. Lüscher, Signatures of unstable particles in finite volume, Nucl. Phys. B 364 (1991) 237 [INSPIRE].

    Article  Google Scholar 

  51. T. A. Ryttov and F. Sannino, Ultra minimal technicolor and its dark matter TIMP, Phys. Rev. D 78 (2008) 115010 [arXiv:0809.0713] [INSPIRE].

    Article  Google Scholar 

  52. C. Michael, Adjoint sources in lattice gauge theory, Nucl. Phys. B 259 (1985) 58 [INSPIRE].

    Article  MathSciNet  Google Scholar 

  53. M. Lüscher and U. Wolff, How to calculate the elastic scattering matrix in two-dimensional quantum field theories by numerical simulation, Nucl. Phys. B 339 (1990) 222 [INSPIRE].

    Article  MathSciNet  Google Scholar 

  54. B. Blossier, M. Della Morte, G. von Hippel, T. Mendes and R. Sommer, On the generalized eigenvalue method for energies and matrix elements in lattice field theory, JHEP 04 (2009) 094 [arXiv:0902.1265] [INSPIRE].

    Google Scholar 

  55. V. Drach, T. Janowski and C. Pica, Update on SU(2) gauge theory with NF = 2 fundamental flavours, EPJ Web Conf. 175 (2018) 08020 [arXiv:1710.07218] [INSPIRE].

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre for Mathematical Sciences, Plymouth University, Drake Circus, Plymouth, PL4 8AA, U.K.

    Vincent Drach

  2. The Higgs Centre for Theoretical Physics, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh, EH9 3FD, U.K.

    Tadeusz Janowski

  3. CP3-Origins and eScience Center, University of Southern Denmark, Campusvej 55, DK-5230, Odense M, Denmark

    Claudio Pica

  4. Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000, Ljubljana, Slovenia

    Sasa Prelovsek

  5. Jozef Stefan Institute, Jamova 39, 1000, Ljubljana, Slovenia

    Sasa Prelovsek

  6. Institute for Theoretical Physics, University of Regensburg, 93040, Regensburg, Germany

    Sasa Prelovsek

Authors
  1. Vincent Drach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tadeusz Janowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Claudio Pica
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Sasa Prelovsek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vincent Drach.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

ArXiv ePrint: 2012.09761

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

Drach, V., Janowski, T., Pica, C. et al. Scattering of Goldstone bosons and resonance production in a composite Higgs model on the lattice. J. High Energ. Phys. 2021, 117 (2021). https://doi.org/10.1007/JHEP04(2021)117

Download citation

  • Received: 22 December 2020

  • Accepted: 09 March 2021

  • Published: 13 April 2021

  • DOI: https://doi.org/10.1007/JHEP04(2021)117

Share this article

Anyone you share the following link with will be able to read this content:

Sorry, a shareable link is not currently available for this article.

Provided by the Springer Nature SharedIt content-sharing initiative

Keywords

  • Lattice field theory simulation
  • Phenomenological Models
Download PDF

Working on a manuscript?

Avoid the most common mistakes and prepare your manuscript for journal editors.

Learn more

Advertisement

Over 10 million scientific documents at your fingertips

Switch Edition
  • Academic Edition
  • Corporate Edition
  • Home
  • Impressum
  • Legal information
  • Privacy statement
  • California Privacy Statement
  • How we use cookies
  • Manage cookies/Do not sell my data
  • Accessibility
  • FAQ
  • Contact us
  • Affiliate program

Not affiliated

Springer Nature

© 2023 Springer Nature Switzerland AG. Part of Springer Nature.