We propose to identify the excess of events with four charged leptons at
$E\sim 325\GeV$ seen by the CDF and CMS Collaborations with a new `sterile'
scalar particle characterized by a very narrow resonance of the same height and
branching ratios as the Standard Model Higgs boson, as predicted in the
framework of the so-called Conformal Standard ModelComment: 4 pages, 2 figures, text and references correcte

Buchmüller

Djouadi

Hermann Nicolai

Krzysztof A. Meissner

Latosinski

Maiani

Meissner

Volovik

Physics Letters B

English

arXiv

We propose to identify the excess of events with four charged leptons at $E\sim 325\GeV$ seen by the CDF and CMS Collaborations with a new `sterile' scalar particle characterized by a very narrow resonance of the same height and branching ratios as the Standard Model Higgs boson, as predicted in the framework of the so-called Conformal Standard Mode

Meissner, K.

Nicolai, H.

MPG.PuRe

arXiv:1208.5653v2  [hep-ph]  20 Sep 2012A narrow scalar resonance at 325 GeV?Krzysztof A. Meissner1,2 and Hermann Nicolai21 Faculty of Physics, University of Warsaw, Hoz˙a 69, Warsaw, Poland2 Max-Planck-Institut fu¨r Gravitationsphysik (Albert-Einstein-Institut)Mu¨hlenberg 1, D-14476 Potsdam, GermanyWe propose to identify the excess of events with four charged leptons at E ∼ 325GeVseen by the CDF [1] and CMS [2] Collaborations with a new ‘sterile’ scalar particlecharacterized by a very narrow resonance of the same height and branching ratiosas the Standard Model Higgs boson, as predicted in the framework of the so-calledConformal Standard Model [3].The long search for the Higgs particle culminated this summer with the announcementby both LHC groups [4] of the discovery of a particle with mass of approximately 125GeVthat most probably corresponds to the Standard Model (=SM) Higgs boson. Prior to thisdiscovery, the search had produced several candidate events possibly hinting at new physicsbeyond the SM. In our opinion, the most striking of these was the excess of Z0Z0 → l+l−l+l−events (four charged leptons) seen by the CDF Collaboration [1], with an invariant mass ofalmost precisely 325 GeV in all four cases, see Fig.1; a smaller excess in this region was alsoreported by the CMS collaboration [2]. The excess of CDF events was treated as a statisticalfluctuation [1], even though the probability of observing four such events in a narrow energyband is estimated at 10−4 – 10−5 in the SM. This negative conclusion was mainly based onthe fact that the two other decay channels that should accompany such events (two chargedleptons plus missing energy, and two charged leptons plus two jets) did not show any excessat this energy in comparison with the expected rates for a SM Higgs boson of this mass.In this letter we would like to point out a potential loophole in the argumentation leadingto the dismissal of these events. More specifically, we wish to call attention to the possibleexistence of a new scalar particle in this mass range that would show up as a narrow resonance(and in particular much narrower than a SM Higgs resonance of that mass), but of the sameheight and branching ratios as the SM Higgs boson (i.e. about 70% toW+W−, 30% to Z0Z0and below 0.1% to bb¯ and all remaining channels). The existence of such a scalar particlewith a mass close to the weak scale is a prediction the so-called ‘Conformal Standard Model’proposed in [3]. In addition to the usual Higgs doublet this model necessarily contains anelectroweak singlet (complex) scalar, which in the unbroken phase couples only to right-chiralneutrinos and induces a Majorana mass term for the right-chiral neutrinos via spontaneoussymmetry breaking1. Because of the mixing in the minimum of the potential the masseigenstates of the scalar particles not absorbed by the Brout-Englert-Higgs mechanism aremixtures of the SM Higgs particle and the new scalar with some mixing angle θ. As explainedbelow, this scenario would lead to two bumps in the cross section. Making the natural1Models with such an extra scalar field were considered long ago (see [5] and references therein), butthere the relevant scale was always of the order of the assumed Majorana mass scale, i.e. above 1010 GeV .1assumption that θ is small, the first bump would then coincide with the usual SM Higgsmaximum (now known to be atM1 ∼ 125 GeV) with the height as computed for a SM Higgsof that mass, but with a slightly smaller width Γ1 = ΓSM(M1) cos2 θ. The second bump,here assumed to lie at about M2 ∼ 325 GeV as suggested by the excess of CDF events [1],would have the same height as the SM Higgs boson of that mass but its decay width wouldbe reduced to Γ2 = ΓSM(M2) sin2 θ, and thus be very narrow in comparison with the widthof a SM Higgs boson of that mass. As can be seen from Fig.2 the SM Higgs decay widthincreases rapidly as a function of the Higgs mass, with ΓSM(325 GeV) ≈ 20 GeV. Takingθ = 0.1 as a plausible value, the mixing would reduce the decay width down to 200 MeV.This feature could explain the extremely small difference in the invariant masses measuredby CDF [1].In the scenario proposed in [3], the extra complex scalar field coupling only to right-chiral neutrinos is required by the assumed conformal invariance of the classical Lagrangian,which is a non-supersymmetric minimal extension of the SM Lagrangian without explicitmass terms of any type, and in particular no Majorana mass terms for the right-chiralneutrinos. The breaking of electroweak symmetry and conformal symmetry (jointly leadingto the generation of mass) is assumed to occur via a Coleman-Weinberg type mechanism,such that the conformal anomaly would be at the origin of mass generation. The verypreliminary analysis of [3] indicates that the mass of the second scalar is not much abovethe mass of the usual SM Higgs boson and possibly below 500 GeV. We note, however,that a reliable analysis of the symmetry breaking pattern for a Coleman-Weinberg typepotential with two independent scalar fields would require the consistent incorporation ofhigher order corrections, whence the mass values quoted in [3] should only be regarded asrough estimates. In the absence of a detailed analysis we shall therefore simply assume• Existence of a nontrivial stable minimum of the effective potential for the combinedscalar sector exhibiting mixing of the SM Higgs with the new scalar; and• Viability of the model up to the Planck scale under the RG evolution of all couplings(as evaluated at the minimum of the effective potential), and compatibility of thesevalues with the known Higgs mass.The phase of the extra complex field φ(x) has been identified with the axion in [6], andits modulus ϕ(x) ≡ |φ(x)| as the ‘heavy cousin’ of the Higgs boson. The special featureof the model that is important here is the mixing between the Higgs field H and the newscalar ϕ. The former couples to SM particles in the standard way, whereas the new scalaris almost completely decoupled2, since its coupling to the observable sector of the SM arisesonly through the left-right neutrino mixing [6]. More precisely, the mass eigenstates (withmass eigenvalues M1 and M2) are linear combinations of both fields:Φ1 = H cos θ + ϕ sin θ , Φ2 = −H sin θ + ϕ cos θ (1)With θ small, Φ1 would correspond to the recently discovered Higgs boson, while Φ2 isproposed here to cause the excess observed by CDF. Then the amplitude of Z0Z0 production2Which is why we refer to this scalar particle as ‘sterile’.2via the Higgs would be proportional to (ΓSM is the Higgs decay rate in the SM3A ∝i cos2 θp2 −M21 + iM1ΓSM(M1) cos2 θ+i sin2 θp2 −M22 + iM2ΓSM(M2) sin2 θ(2)Consequently, the decay widths are modified by factors cos2 θ and sin2 θ, respectively, whilethe amplitude |A| is equal to the value of the amplitude for a SM Higgs boson of thecorresponding mass for p2 = M21 or p2 = M22 , because the dependence on the mixing anglecancels at the poles. When θ is small, as we assume here, the second resonance is thusvery narrow in comparison with the expected width ΓSM(M2). The event rates are directlyobtained from the known ones for the SM Higgs by multiplication with sin2 θ. Since theincoming partons in proton-proton collisions range over a broad spectrum of energies andmomenta, with low initial probability of precisely ‘hitting’ the narrow resonance, the emissionof one jet or two jets from the top quark triangle or the initial gluons producing the resonancemay be needed in order to ‘adjust’ the energy to the required value s ≈ M22 . Therefore weexpect that the products of the decay at s ≈ M22 are generically accompanied by one ormore jets, and have very definite invariant mass in order to produce the enhancement in thecross section (in contradistinction to a Higgs resonance of the same mass whose invariantmass distribution would be rather broad). The assumption of the existence of such a narrowresonance at 325 GeV makes the events seen by CDF much more probable than if theywere just due to statistical fluctuations of the background. Nevertheless it is important toemphasize that the observation of four cases in one bin at 325 GeV (out of total of eightevents) still is a lucky coincidence since this number exceeds the expected number of eventseven in the presence of a resonance at this energy, as one can easily see by comparing theestimated number of cases from the background with and without an assumed Higgs bosonof mass 350 GeV [2]. Therefore it would require a dedicated search with much more statisticsthan presently available at the LHC, especially if the resonance is very narrow, to prove (ordisprove) the presence of such a resonance in this mass region.A different interpretation of the enhancement of the cross section around 320 GeV wasrecently suggested in [8], where the excess was linked to the second electroweak Higgs dou-blet required by low energy supersymmetry, and the CMS bump was tentatively identifiedwith the second neutral Higgs boson of the MSSM. 4 By contrast, the model of [3] avoidslow energy supersymmetry altogether, but invokes conformal symmetry to explain and sta-bilize the electroweak hierarchy, postulating the absence of any intermediate scales betweenthe electroweak scale and the Planck scale. Confirmation of the properties outlined above(sharpness of the resonance, and branching ratios identical to those of the SM Higgs parti-cle), together with the absence of any new fundamental fermions other than the right-chiralneutrinos would constitute strong evidence for such a conformal scenario. At any rate, itshould be relatively easy to discriminate between the present proposal and alternative onessuch as [8], once enough statistics is accumulated.Acknowledgment: We are grateful to M. Kazana and P. Chankowski for discussions. Wewould also like to thank P. Murat and A. Robson for their comments on a first version ofthis letter.3If the heavy neutrinos had mass < O(M2/2) the new scalar could also decay into a pair of heavyneutrinos. Then ΓSM and the branching ratio into missing energy should be appropriately enlarged.4No mention is made of the CDF events in [8].3References[1] CDF Collaboration, Phys. Rev. D85 (2012) 012008, arXiv:1111.3432[2] CMS Collaboration, Phys. Rev. Lett. 108, 111804 (2012), arXiv:1202.1997[hep-ex][3] K.A. Meissner and H. Nicolai, Conformal symmetry and the standard model, Phys. Lett.B648 (2007) 312; hep-th/0612165,[4] CMS Collaboration, Phys. Lett B716 (2012) 30; ATLAS Collaboration, Phys. LettB716 (2012) 1.[5] W. Buchmu¨ller, R.D. Peccei and T. Yanagida, Leptogenesis as the origin of matter,Nucl. Part. Sci. 55 (2005) 311, arXiv:hep-ph/0502169[6] K.A. Meissner and H. Nicolai, Neutrinos, axions and conformal symmetry, Eur.Phys.J. C 57 (2008) 493, arXiv:0803.2814[hep-th]; A. Latosinski, K.A. Meissner andH. Nicolai, Neutrino Mixing and the Axion-Gluon vertex, arXiv:1203.3886[hep-th][7] LHC Higgs Cross Section Working Group, arXiv:1101.0593[hep-ph]; A. Djouadi,J. Kalinowski, M. Spira, HDECAY, Comput.Phys.Commun. 108 (1998) 56-74,arXiv:hep-ph/9704448[8] L. Maiani, A.D. Polosa and V. Riquer, Probing Minimal Supersymmetry atthe LHC with the Higgs Boson Masses, New J.Phys. 14 (2012) 073029,arXiv:1202.5998[hep-ph]Figure 1: The four lepton events reported bythe CDF Collaboration [1]. [GeV]HM100 200 300 1000 [GeV]HΓ-210-110110210310LHC HIGGS XS WG 2010500Figure 2: ΓSM as a function of the SMHiggs mass [7].4

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A narrow scalar resonance at 325 GeV?

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