Composite Higgs: searches for new physics at future e + e − colliders
Daniele Barducci, Stefania De Curtis, Stefano Moretti, Giovanni Marco Pruna
aa r X i v : . [ h e p - ph ] D ec PSI-PR-13-19
Composite Higgs: searches for new physics at future e + e − colliders D. Barducci, ∗ S. De Curtis, † S. Moretti,
1, 3, ‡ and G. M. Pruna § School of Physics and Astronomy, University of Southampton, Southampton SO17 1BJ, U.K. INFN, Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino, Italy Particle Physics Department, Rutherford Appleton Laboratory,Chilton, Didcot, Oxon OX11 0QX, UK Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland (Dated: August 16, 2018)
Abstract
In this proceeding, we extend a previous analysis concerning the prospects of a future electron-positroncollider in testing the 4-Dimensional Composite Higgs Model. In particular, we introduce two motivatedbenchmarks and study them in Higgs-Strahlung, for three possible energy stages and different luminosityoptions of such a machine and confront our results to the expected experimental accuracies in the variousaccessible Higgs decay channels. ∗ E-mail: [email protected] † E-mail: decurtis@fi.infn.it ‡ E-mail: [email protected] § E-mail: [email protected] . INTRODUCTION The discovery at the Large Hadron Collider (LHC) of a Higgs boson [1, 2] represents a triumphfor the Standard Model (SM). Nowadays, the primary question that requires an answer is whethersuch a particle belongs to the minimal SM Higgs sector or to some Beyond the SM (BSM) scenario.Indeed, it is well-known that the SM suffers from the so-called “hierarchy” problem (see, e.g. ,[3]), pointing out that it could be a low energy effective theory valid only up to some cut-off energyΛ. Such energy scale is unknown and phenomenological indications about it are missing. Surelythough, there is the possibility that Λ is lying around the TeV/multi-TeV scale (so that BSMphysics could be discovered at the CERN machine in the coming years).For this reason, many BSM scenarios with new physics at the TeV/multi-TeV scale were pro-posed in the last decades. In this spirit, we embrace the possibility that the Higgs particle maybe a composite state arising from some strongly interacting dynamics at a high scale instead ofbeing a fundamental state. In this description, the Higgs state arise as a Pseudo Nambu-GoldstoneBoson (PNGB) from a particular coset of a global symmetry breaking [4–7] and it offers an elegantsolution for the long-standing hierarchy problem.Even in the situation where new physics is outside the discovery range of the present colliders,a composite Higgs state arising as a PNGB has modified couplings with respect to the SM [8],hence the measurement of these quantities represents a powerful way to test the possible non-fundamental nature of the newly discovered state. In this case, a TeV/multi-TeV electron-positroncollider would represent the cleanest environment for studying possible deviations from the SMsignals. For this reason, in this proceeding, we will resume a previous analysis [9] concerningthe potential of the proposed e + e − colliders in testing a specific realisation of a composite Higgsmodel, the so-called 4-Dimensional Composite Higgs Model (4DCHM) of ref. [10], by extendingour approach to encompass two new benchmarks and focusing on one of the most interestingHiggs production channel: Higgs-Strahlung (HS) from Z bosons. As in our earlier paper, weborrow energy and luminosity configurations from machines prototypes such as the InternationalLinear Collider (ILC) [11], the Compact Linear Collider (CLIC) [12] and the Triple Large Electron-Positron (TLEP) collider [13]. 2 I. RESULTS
We have implemented the 4DCHM into numerical tools in order to perform dedicated analyses upto event generation. Our simulations have been mainly performed with the CalcHEP package [14]in which the model had been previously implemented via the LanHEP tool [15], see [16, 17]. SinceCalcHEP allows by default the analysis of tree-level processes only, we have also added by hand theone-loop
Hgg , Hγγ and
HγZ vertices (computed at the leading order without approximations).For beamstrahlung, CalcHEP implements the Jadach, Skrzypek and Ward expressions ofrefs. [18, 19]. Regarding the Initial State Radiation (ISR), we adopted the parametrisation specifiedfor the ILC project in [11], that is: beam size ( x + y ) = 645 . µ m, bunchpopulation = 2 · .We will be considering throughout three values for the Centre-of-Mass (CM) energy, which arestandard benchmark energies for future e + e − proto-types: 250 GeV, 500 GeV and 1 TeV. Then,we focus on the phenomenology of a Higgs boson obtained via the HS process. When combiningproduction cross sections and decay Branching Ratios (BRs), our simulated data will always berelated to the experimental accuracies presented in refs. [20–22]. Following their notation, weindicate the production cross section with σ ( ZH ) for HS. In keeping with the aforementionedreferences, we have will assume a luminosity of 250/500/1000 fb − in correspondence to an energyof 250/500/1000 GeV.In the following subsections we will present several results concerning the studies of the afore-mentioned Higgs production process, organised as follows. Firstly, we investigate the behaviour ofour benchmarks with respect to the mere rescaling of the couplings due to the decoupling of newphysics (the so-called “decoupling limit”). By considering points that respect exclusion limits fromdirect and indirect observation of new physics (see [9] for details on the selection criteria), againwe will show that genuine 4DCHM effects cannot be relegated to a simple rescaling of the relevantHiggs couplings, as, for example, the presence of Z ′ propagator effects in the HS production cannotgenerally be neglected.In essence, to generalise our findings, quantitative studies of Higgs boson phenomenology in com-posite Higgs models at future electron-positron colliders should take into account possible effectsfrom realistic mass spectra, whereby extra particles are retained in the calculation of observables,rather than integrated out. 3 . Decoupling limit In order to disentangle rescaling effects (due to both the non-linear realisation of the Goldstonesymmetry and the mixing between SM and extra particles) from the ones due to the additionalpropagators, we have introduced the R and ∆ parameters for inclusive HS production cross sectionas follows: R = σ ( ZH ) σ ( ZH ) SM , ∆ = R − κ HZZ , κ
HZZ = g HZZ g SM HZZ . (1)Then, by numerical computation, we have proven that, if the new class of neutral gauge bosonsare completely stripped off the calculations, ∆ tends to 0 with a negligible deviation ∼ . C V and C A couplings of the SM-like Z to the initial leptons, dueto the aforementioned mixing. Since HS is one of the most useful process to extract informationabout deviations of the Higgs couplings from the SM values, we are essentially making the genericstatement that, even when the CM energy of the collider is below the scale of BSM physics, f inthis case (the compositeness scale), where the additional boson and fermion masses of the 4DCHMnaturally tend to cluster, the HS cross section is basically always affected by propagator effects.This is well illustrated by fig. 1, where we quantify the R and ∆ parameters for two newbenchmarks ( f = 1000 GeV, f = 1200 GeV) as a function of the total width of the dominantextra-vectorial contribution, i.e., Γ Z , for the three customary values of CM energy. The rescalingfactors are κ HZZ ≈ .
94 for f = 1000 GeV and κ HZZ ≈ .
96 for f = 1200 GeV. The slopes presentin the plots, the more noticeable the larger the CM energy, show that propagator effects are atwork. In fact, the trend of R (or equivalently ∆) is almost constant but, from some threshold( ∼
600 GeV) on, it decreases with Γ Z , reflecting the nature of the interference contribution thatis proportional to 1 / Γ Z when the CM energy is smaller than the Z mass involved . Beside this,the non-zero positive ∆ value definitely points to a constructive interference taking place especiallyfor small values of Γ Z .As in the previously analysed benchmarks in [9], the deviations from the SM limit span from ∼
2% when √ s = 250 GeV up to ∼
20% when √ s = 1 TeV. Again, we have verified that theeffect is completely due to the constructive interference term arising from the SM-like Z resonanceand the Z + Z contributions, with Z being dominant among the two extra vectors. R valuesare always above the expected “reduction” from the decoupling limit: at √ s = 1 TeV and even at We remark that M Z ∼ .
5) TeV for f = 1 . g ρ = 1 . . .850.90.9511.051.11.151.21.251.3 0 500 1000 1500 2000f=1000 GeV, g r =2.5250 GeV500 GeV1000 GeV G Z3 (GeV) R r =1.6 G Z3 (GeV) R r =2.5 G Z3 (GeV) D / R % r =1.6 G Z3 (GeV) D / R % FIG. 1: The R and ∆ quantities defined in eq. (1) plotted against the width of the Z resonance for thebenchmark points with f = 1000 GeV and g ρ = 2 . f = 1200 GeV and g ρ = 1 . R , according to refs. [20, 22]. √ s = 500 GeV for f = 1200 GeV the R value is above 1, which is not compatible with a decoupledscenario.In fig. 1, we show that the benchmark with higher values of M Z , ≡ f × g ρ is related to smallerdeviations from the decoupling limit, as expected. These results point at the fact that a completestudy of composite Higgs models via the HS process should also take into account the possibilityof non-decoupled extra resonances. 5 . Higgs coupling analysis at e + e − colliders in HS The presence of extra-vectors in the TeV/multi-TeV range can thus affect the HS cross section dueto interference effects. As a consequence, modifications to the various observables can also ariseand manifest in the analysis of the Higgs couplings. Therefore, such an alteration would affect theextraction of both the Higgs-vector-vector and vector-fermion-fermion tree-level couplings, as wellas the loop-induced couplings
HγZ , Hγγ and/or
Hgg . In other words, these effects can modifythe signal strengths in a way that may be detectable with the experimental accuracies expected atfuture electron-positron colliders.In this respect, we present our results in terms of scatter plots for our proposed benchmarks: f = 1000 GeV, g ρ = 2 . f = 1200 GeV, g ρ = 1 .
6. We show the results of these scans in fig. 2,where we notice that the deviations from the case in which the full particle spectrum is not takeninto account, represented by the stars, could modify the signal strengths for various channels.In the case of µ bb and µ W W , the signal strengths of the b ¯ b and W W channels, these deviationsare fully disentangleable while in the other cases this is not always true, depending on where thescan points fall relative to the SM expectations and according to the corresponding experimentalerror bars for a particular signature.Altogether, though, it is clear the potential that future leptonic machines can offer in pinningdown the possible composite nature of the Higgs boson discovered at CERN by measuring its“effective” couplings to essentially all SM matter and forces.
III. CONCLUSIONS
In this proceeding, we extended our previous analysis (see [9]) to two new benchmarks, albeitlimitedly to the HS channel. We found that, in such concrete realisations of the 4DCHM, theimpact of interference effects due to extra TeV/multi-TeV neutral vectors at future e + e − collidersis never negligible. We have shown that, as a consequence, also the Higgs signal strengths areaffected by such effects. In general, this requires a careful treatment of the methods adopted inthe extraction of the SM couplings from the main Higgs production channel, i.e. , HS, as the realcouplings are crucially altered with respect to those emerging in a fully decoupled scenario. Thisanalysis enforces our previous conclusions. 6 .70.80.911.11.21.30.6 0.8 1 1.2 1.4Higgs-strahlung (250 GeV) m WW m bb m ZZ m gg m WW m bb m ZZ m gg FIG. 2: Correlations among relevant µ i parameters, evaluated at a future e + e − collider for two energy andluminosity stages, as detailed in the text, in the HS process. Plots are for two 4DCHM benchmarks, with f = 1000 GeV and g ρ = 2 . f = 1200 GeV g ρ = 1 . Acknowledgements
The work of GMP has been supported by the European Community’s Seventh Framework Pro-gramme (FP7/2007-2013) under grant agreement n. 290605 (PSI-FELLOW/COFUND). DB andSM are financed in part through the NExT Institute. GMP would like to thank the ECT* in7rento for hospitality while part of this work was carried out. [1] G. Aad et al. [ATLAS Collaboration], Phys. Lett. B (2012) 1 [arXiv:1207.7214 [hep-ex]].[2] S. Chatrchyan et al. [CMS Collaboration], Phys. Lett. B (2012) 30 [arXiv:1207.7235 [hep-ex]].[3] M. J. G. Veltman, Acta Phys. Polon. B (1977) 475.[4] D. B. Kaplan and H. Georgi, Phys. Lett. B (1984) 183.[5] H. Georgi and D. B. Kaplan, Phys. Lett. B (1984) 216.[6] H. Georgi, D. B. Kaplan and P. Galison, Phys. Lett. B (1984) 152.[7] M. J. Dugan, H. Georgi and D. B. Kaplan, Nucl. Phys. B (1985) 299.[8] J. R. Espinosa, C. Grojean and M. Muhlleitner, JHEP (2010) 065 [arXiv:1003.3251 [hep-ph]].[9] D. Barducci, S. De Curtis, S. Moretti and G. M. Pruna, arXiv:1311.3305 [hep-ph].[10] S. De Curtis, M. Redi and A. Tesi, JHEP (2012) 042 [arXiv:1110.1613 [hep-ph]].[11] T. Behnke, J. E. Brau, B. Foster, J. Fuster, M. Harrison, J. M. Paterson, M. Peskin, M. Stanitzki etal. , arXiv:1306.6327 [physics.acc-ph].[12] M. Aicheler, M. Aicheler, P. Burrows, M. Draper, T. Garvey, P. Lebrun, K. Peach, N. Phinney et al. ,CERN-2012-007.[13] M. Bicer, H. Duran Yildiz, I. Yildiz, G. Coignet, M. Delmastro, T. Alexopoulos, C. Grojean, S. Antusch et al. , arXiv:1308.6176 [hep-ex].[14] A. Belyaev, N. D. Christensen and A. Pukhov, Comput. Phys. Commun. (2013) 1729[arXiv:1207.6082 [hep-ph]].[15] A. Semenov, arXiv:1005.1909 [hep-ph].[16] D. Barducci, A. Belyaev, S. De Curtis, S. Moretti and G. M. Pruna, JHEP (2013) 152[arXiv:1210.2927 [hep-ph]].[17] D. Barducci, A. Belyaev, M. S. Brown, S. De Curtis, S. Moretti and G. M. Pruna, JHEP (2013)047 [arXiv:1302.2371 [hep-ph]].[18] S. Jadach and B. F. L. Ward, Comput. Phys. Commun. (1990) 351.[19] M. Skrzypek and S. Jadach, Z. Phys. C (1991) 577.[20] M. E. Peskin, arXiv:1207.2516 [hep-ph].[21] D. M. Asner, T. Barklow, C. Calancha, K. Fujii, N. Graf, H. E. Haber, A. Ishikawa, S. Kanemura etal. , arXiv:1310.0763 [hep-ph].[22] H. Baer, T. Barklow, K. Fujii, Y. Gao, A. Hoang, S. Kanemura, J. List, H. E. Logan et al. ,arXiv:1306.6352 [hep-ph].,arXiv:1306.6352 [hep-ph].