Implications of perturbative unitarity for scalar di-boson resonance searches at LHC

The European Physical Journal C, Jan 2017

We study the constraints implied by partial wave unitarity on new physics in the form of spin-zero di-boson resonances at LHC. We derive the scale where the effective description in terms of the SM supplemented by a single resonance is expected to break down depending on the resonance mass and signal cross section. Likewise, we use unitarity arguments in order to set perturbativity bounds on renormalizable UV completions of the effective description. We finally discuss under which conditions scalar di-boson resonance signals can be accommodated within weakly coupled models.

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Implications of perturbative unitarity for scalar di-boson resonance searches at LHC

Eur. Phys. J. C Implications of perturbative unitarity for scalar di-boson resonance searches at LHC Luca Di Luzio 1 2 Jernej F. Kamenik 0 5 Marco Nardecchia 3 4 0 Jožef Stefan Institute , Jamova 39, 1000 Ljubljana , Slovenia 1 Institute for Particle Physics Phenomenology, Department of Physics, Durham University , Durham DH1 3LE , UK 2 Dipartimento di Fisica, Università di Genova and INFN, Sezione di Genova , via Dodecaneso 33, 16159 Genova , Italy 3 Theoretical Physics Department, CERN , Geneva , Switzerland 4 DAMTP, University of Cambridge , Wilberforce Road, Cambridge CB3 0WA , UK 5 Faculty of Mathematics and Physics, University of Ljubljana , Jadranska 19, 1000 Ljubljana , Slovenia We study the constraints implied by partial wave unitarity on new physics in the form of spin-zero di-boson resonances at LHC. We derive the scale where the effective description in terms of the SM supplemented by a single resonance is expected to break down depending on the resonance mass and signal cross section. Likewise, we use unitarity arguments in order to set perturbativity bounds on renormalizable UV completions of the effective description. We finally discuss under which conditions scalar di-boson resonance signals can be accommodated within weakly coupled models. 1 Introduction . . . . . . . . . . . . . . . . . . . . . 1 2 Brief review on partial wave unitarity . . . . . . . . 2 3 Effective field theory of a scalar resonance . . . . . 3 3.1 Scalar mediated boson scattering . . . . . . . . 4 3.2 Fermion-scalar contact interactions . . . . . . 5 3.3 Unitarity bounds . . . . . . . . . . . . . . . . 5 4 Weakly coupled models . . . . . . . . . . . . . . . 7 4.1 Single fermion case . . . . . . . . . . . . . . . 9 4.2 Single scalar case . . . . . . . . . . . . . . . . 11 4.3 Generalization in flavor space . . . . . . . . . . 12 4.4 Application to mediator models . . . . . . . . . 14 5 Conclusions . . . . . . . . . . . . . . . . . . . . . 15 Appendix A: Amplitudes . . . . . . . . . . . . . . . . 16 A. 1 γ γ → γ γ scattering . . . . . . . . . . . . . . 16 A.2 ψ ψ → ψ ψ scattering . . . . . . . . . . . . . . 17 References . . . . . . . . . . . . . . . . . . . . . . . . 18 - Contents 1 Introduction Unitarity of the time evolution of an isolated quantum system and in particular of the associated S-matrix is one of the cornerstones of quantum field theory. In practical perturbative calculations however, S-matrix unitarity is always approximate and asymptotic. Nonetheless, significant violations of unitarity at low orders in perturbation theory are heralds of a strongly coupled system and can be used to constrain the range of validity of a given (effective) quantum field theory description. Perhaps most famously, constraints imposed by perturbative unitarity in W W scattering have been used in the past to infer an upper bound on the Higgs boson mass or, alternatively, on the scale where the standard model (SM) description of weak interactions would need to be completed in the ultraviolet (UV) in terms of some new strongly coupled dynamics [1, 2]. Correspondingly it allowed one to narrow down the relevant mass search window and motivate the construction of the LHC with capabilities that ensured the eventual Higgs boson discovery (cf. [3] for a review). More generally, perturbative unitarity constraints on the validity of a certain theoretical description are applicable both in non-renormalizable as well as renormalizable models. In both cases they allow one to assess the limitations of a perturbative expansion. In the non-renormalizable effective field theory (EFT) approach this amounts to a truncated power expansion in (E / ), where E is a typical energy in a process and is the EFT cut-off scale. Violations of perturbative unitarity signal the breakdown of such an expansion, when the leading powers do not represent a good approximation to the physical result. A notable standard example is the pion scattering in chiral perturbation theory, where the loop and power expansion are adequate at low enough scattering energies but violate perturbative unitarity at higher energies and eventually need to be UV completed with the inclusion of dynamical vector resonances. On the other hand within renormalizable models, the expansion proceeds in terms of positive powers of the renormalizable couplings. Sizable violations of unitarity at leading (tree) order signal the breakdown of such an expansion and the onset of strongly coupled dynamics. Here the most renown case is that of the aforementioned W W boson scattering in the presence of a heavy SM Higgs boson. The recently rekindled interest in new physics (NP) in the form of (possibly broad) di-photon resonances [4–8] at the LHC prompt us to reconsider the implications of perturbative unitarity for EFT interpretations of resonances decaying to di-boson final states. In particular, focusing on promptly produced scalar SM singlets decaying to two SM gauge bosons we aim to addres (...truncated)


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Luca Di Luzio, Jernej F. Kamenik, Marco Nardecchia. Implications of perturbative unitarity for scalar di-boson resonance searches at LHC, The European Physical Journal C, 2017, pp. 30, Volume 77, Issue 1, DOI: 10.1140/epjc/s10052-017-4594-2