Hunting for possible Higgs-like boson beyond the Standard Model

A recent preliminary investigation based on Durgut's report at the American Physical Society site shows a structure at $18.4~ {\rm GeV}$ exists in the invariant mass distribution of $\Upsilon l^+l^- ~ (l = e,\, \mu)$ at the LHC center-of-mass energy of $7$ and $8~ {\rm TeV}$. Its appearance attracts attention of theorists and experimentalists of high energy physics, because it might be a Higgs-like boson of $18.4~ {\rm GeV}$ which would serve as a signal of the new physics beyond the Standard Model. We have carried out computations on the corresponding quantities (production and decay rates) based on quantum field theory and compared the results with experimental data. Our numerical results do not support the assertion that the $18.4~ {\rm GeV}$ peak corresponds to a neutral $0^{++}$ boson which decays into $\Upsilon l^+l^-$. Much further works (both experimental and theoretical) are badly needed.


I. Introduction
The Recently,a preliminary investigation based on the report by S. Durgut, which is available at the American Physical Society (APS) site [1], shows a structure around 18.4 GeV in four-lepton final state by using the four-lepton events collected during the LHC Run I stage. Below, we just refer the report as D-report. After carefully analysis, they conclude that a enhancement exists at around 18.4 GeV in the invariant mass distribution of Υl + l − (l = e, µ) [1][2][3].
Namely if Υl + l − comes from a unique enhancement, it would be a neutral boson φ, which is mainly produced via gluon-gluon fusion, and then sequently decays as ΥΥ * → µ + µ − l + l − , where Υ * might be off-mass-shell due to the energy constraint. The mass of the new enhancement, if it indeed exists, is a few hundreds of MeV lower than the total mass of a Υ pair. By analyzing the datasets collected by the CMS detector at a center-of-mass energy of 7 TeV and 8 TeV with an integrated luminosity of 25.6 fb −1 [3], and taking the kinematic requirements of p T,l > 2.0 GeV and |η l | < 2.4 on the final-state leptons [1,3], the experimenters observed a peaking structure.
Because this enhancement mass is close to the sum of the masses of four bottom quarks, thus some authors consider it to be a bbbb tetraquark state with a mass in the range of 18.4 GeV < m X bbbb < 20.3 GeV [4][5][6][7][8][9][10]. The authors of Ref. [11] show that σ(pp → X bbbb [0 ++ ] → 4l) 4 fb at √ s = 13 TeV and 2 fb at √ s = 8 TeV. In Ref. [12] the authors consider that the width of X bbbb → Υµ + µ − is too small to tolerate the data currently observed at the LHC. In Ref. [13] the authors calculate the decay width of X bbbb → Υl + l − and they prefer X bbbb to be a 2 ++ tetraquark state rather than a 0 ++ bound state. Furthermore, the authors of Ref. [14] believe that a bbbb tetraquark should lie above the lowest noninteracting bottomonium-pair threshold.
Because the mass is just a bit below the sum of two Υ bosons, being driven by the expec-  [15]. By the general method adopted for searching TeV-scale particles at LHC, alternatively, we, in this work, explore a new Higgs-like boson at low energy regions. As a common sense the strategy can be traced back from our experience gained at lepton colliders, such as BES, Belle, etc. For example, in the scattering process e + e − → J/ψ → final products, the resonance (J/ψ) overwhelmingly dominates the portal, while the direct production just provides a continuous background. For the same cause, a direct production of four leptons from the gluon-gluon fusion at the protonproton collider, i.e., gg → ΥΥ * → µ + µ − l + l − [16,17] where Υ * might be off-mass-shell, should just generate a background. If a medium Higgs-like boson φ(18.4) indeed exists, it induces the portal of ΥΥ * → Υl + l − , a peak would appear in the invariant mass spectrum of Υl + l − . With this assertion, we numerically calculate the contribution induced by the BSM Higgs-like boson φ(18.4) to pp → ΥΥ * → Υl + l − at the LHC. Comparing our numerical results with those in the D-report [1], we find that the assumption that the observed peak in the Υl + l − mass spectrum originates from a BSM Higgs-like boson decay should be ruled out.
This work is organized as follows. After this introduction, in section II, we present our analytical calculation for Υl + l − production at the LHC in the framework of a BSM model, in which we assume that the interaction of the BSM Higgs-like boson with SM particles is in analogue to that of the SM Higgs boson. In section III, we numerically evaluate all corresponding quantities and illustrate the invariant mass distribution of the final state. The last section is devoted to our conclusion and a brief discussion.
The contribution of the BSM Higgs-like boson comes from the Breit-Wigner propagator 1 , where s = (k 1 + k 2 ) 2 and k i (i = 1, 2) are the four-momenta of the two initial-state gluons. When s is close to m 2 φ , this factor turns into and a resonance would peak up from the background.
However, if s is far away from m 2 φ (below or above), the contribution of φ would be drowned into the background and no peak can be seen. In our case, 18.4 GeV is slightly below the threshold of 2m Υ . However, since its position is not too far from the threshold value and it possesses a relatively large width, the resonance effect still can manifest itself in the invariant mass spectrum of Υ pair at the threshold. In one aspect, the mass of φ cannot be larger than 2m Υ , otherwise a peak at the Υ pair invariant mass spectrum would be seen, but no such peak was experimentally observed.
To evaluate the contribution of the supposed BSM Higgs-like boson φ of 18.4 GeV to the Υl + l − production at the LHC, we write up the complete expression where the Breit-Wigner propagator of φ with a width observed in the concerned experiment would induce the peak in the Υl + l − invariant mass spectrum. Later our numerical results show that one only needs to account the contribution of the resonance above the threshold of 2m Υ . Indeed, because 18.4 GeV is smaller than 2m Υ , φ cannot be on its mass-shell for two on-shell Υs, while the production rate for pp → φ → ΥΥ * → Υl + l − is very tiny and can be neglected. Due to the extremely small decay width of Υ (Γ Υ ∼ 50 keV and Γ Υ ≪ Γ φ ), the parton-level cross section for the production of Υl + l − via gluon-gluon fusion can be written aŝ The cross sectionσ[gg → ΥΥ] is given bŷ to be real or virtual. The production of Υ pair via gluon-gluon fusion at hadron colliders has been much investigated in the framework of the SM [16,17]. The 31 Feynman diagrams for gg → ΥΥ in the SM can be created with the help of FeynArts [20] package. We also calculate this process with the same input parameters as given in Ref. [16] for comparison, and find that our numerical result for the production cross section at the 14 TeV LHC is in good agreement with the corresponding one of Ref. [16] within a tolerable calculation error. Then we step on to calculate the quantities concerning the new Higgs-like boson. As for the contribution from the new Higgs-like boson φ, the corresponding Feynman diagrams are shown in Fig.1.
Following Refs. [21,22], the effective coupling between the BSM Higgs-like boson and gluon can be written as where k 1 , k 2 and µ, ν are the four-momenta and Lorentz indices of the two gluons, respectively, g ggφ (µ R ) is a dimensionless effective running coupling constant, and µ R is the renormalization scale. It is reasonable to assume that the evolution of the effective coupling constant g ggφ is the same as that of QCD α s , i.e., g ggφ (µ R ) α s (µ R ) is independent of µ R . Thus, we obtain the quark-level amplitude for the Feynman diagrams in Fig.1 as where S, T and U are given by
The integrated cross sections and invariant mass spectra of Υµ + µ − for pp → Υµ + µ − at the 8 and 13 TeV LHC are provided in Tab.1 and Fig.2, respectively. The contributions from   are almost the same as those for pp → Υµ + µ − due to the lepton universality (Br(Υ → e + e − ) ≃

IV. Discussions and conclusion
Based on the data of the Run I of LHC at 7 and 8 TeV, we investigate the origin of the peak at 18.4 GeV in the invariant mass spectrum of Υl + l − newly reported in Refs. [1,3]. We postulate it to be a 0 ++ BSM Higgs-like boson, and by the anzatz calculate the production rate of Υl + l − via gluon-gluon fusion at the LHC and discuss the effect of this BSM Higgs-like boson. In our calculations, we assume the effective coupling of the 0 ++ BSM Higgs-like boson to SM gluon pair, g ggφ , has the same evolution behaviour as that of the SM Higgs boson.
For the peak observed in the invariant mass spectrum of Υl + l − at 18.4 GeV whose width was not accurately fixed yet, the situation might imply that the peak corresponds to a BSM Higgs-like boson which decays into ΥΥ * and later turns into Υl + l − and eventually goes to the four-lepton final state. The peak position is located at 18.4 GeV which is lower than the threshold value of 2m Υ , so that it impossibly directly decays into a real Υ pair if we do not consider its width. If it possesses a relatively large width whose edge covers the region of 2m Υ , it may result in an asymmetric peak at M Υl + l − ≃ 2m Υ in the invariant mass spectrum of Υl + l − via the threshold effect. We carefully analyze the possibility and our numerical results ( Fig.2) assure that there cannot exist an even-not-very apparent asymmetric peak above 2m Υ . All of our estimates are based on the experimental results reported in Refs. [1,3]. Our numerical results decide that the peak may not corresponds to a 0 ++ BSM Higgs-like boson (18.4 GeV). Definitely much more accurate measurements which will be carried out at future high energy facilities (including the updated LHC) will give more information about this peak.
By our assumption, the observed peak is a BSM Higgs-like boson, if it is true, it would set a scale for the BSM and the significance is obvious. Indeed, for the peak appearing at the invariant mass spectrum of Υl + l − , Refs. [11][12][13] consider it to be a composite of bbbb, but all their study show that the decay width are too small to be currently observed at the LHC. The observation is important and following the data, the theoretical interpretation can be made. Since it implies new understanding on new physics beyond the SM and sets a new scale, obviously, the study along this line cannot be neglected. We hope the experimentalists of high energy physics to continue the investigation on the peak by more accurate measurement and analysis. The conclusion would greatly help theorists making a definite judgement to verify the validity of our ansatz or negate it. Now let us make a brief summary and draw our conclusion (so far, but by no means for the future). In this work we are trying to investigate whether the enhancement observed at LHC is a structureless BSM boson. If it indeed is, it can contribute to the process of pp → Υl + l − , but how it behaves, can it result in a peak at the invariant mass spectrum of Υl + l − , in other words, does it induce the peak at 18.4 GeV reported in Refs. [1,3]? It demands a clear answer. Even though a BSM boson φ exists and possesses a certain width, an inequality m φ +Γ φ < 2m Υ holds.
Our explicit computation indicates that φ as an on-shell real particle may not directly contribute to pp → φ → ΥΥ * → Υl + l − . Thus even though a BSM Higgs-like boson φ of 18.4 GeV exists and may contribute to pp → Υl + l − , the sizable rate only occurs above the threshold of 2m Υ .
But then φ must be off-shell (or contributes via t-and u-channels), therefore our conclusion is that the experimentally observed peak located at 18.4 GeV with a narrow width does not correspond to a BSM structureless Higgs-like boson. The peak of 18.4 GeV must originate from other mechanism and its appearance cannot be a signature of existence of BSM as expected.