The 30 GeV Dimuon Excess at ALEPH
Abstract
A simple variation of a twoHiggsdoublet model is proposed to describe the dimuon excess reported by Heister in his reanalysis of events in ALEPH data taken in 199295. The heavier CPeven Higgs is the Higgs boson discovered at the LHC. The model admits two options for describing the dimuon excess: (1) The lighter CPeven Higgs and the CPodd state are approximately degenerate and contribute to the excess. (2) Only the is at while the and are approximately degenerate at . The ALEPH data favor option 1. Testable predictions are presented for LHC as well as LEP experiments. A potential nogo theorem for models of this type is also discussed.
1 Introduction
In a recent paper, Heister analyzed archived data of the ALEPH experiment at LEP and found apparent evidence for a narrow dimuon () resonance at [1]. The data, taken in 199295, involve 1.9 million hadronic decays of bosons produced at rest in annihilation. This excess appears in decays. The oppositesign dimuon spectrum data is shown in Fig. 1a along with the expected background. The samesign dimuon spectrum in Fig. 1b has no significant excesses. The data have the following characteristics:

Two benchmark methods were used to estimate the significance of the excess. One gave a local significance of about , the other . The second method requires using the lookelsewhere effect; it reduces its significance by 1.4–. See Ref. [1] for details.

There is an excess of events in the resonant peak of Fig. 2 corresponding to a mass of with a BreitWigner width of (Gaussian width of ), consistent with the expected ALEPH dimuon mass reconstruction performance at . Using the tag and muonID efficiencies quoted in Ref. [1], this yields the branching ratio
(1) It should be understood that, if the dimuon excess is due to the decay of a new particle , it is not known whether it is emitted from the , as in with and , or from one of the quarks, as in , or from two new particles, , with and .

The decay angle () distribution for muons in the dimuon rest frame, where is the angle between the dimuon boost axis and the , is shown in Fig. 3a for the signal region, a mass range of around the fitted mean mass value, . There is a clear preference for forwardbackward production, i.e., with each muon close to a jet. Presumably, most of these events are semileptonic decays. There is also a smaller, approximately isotropic component for . This may be indicative of a different – scalar – production mechanism in the signal region. However, Fig. 3b shows the angular distribution of events in sidebands, with – but excluding the signalregion events of Fig. 3a. It does not appear substantially different from Fig. 3a (though the ratio of events at to those in between is greater than it is in Fig. 3a).
Figure 3: The decay angle () distribution for muons (left) in the signal region, and (right) in the sidebands , excluding the signal region; from Ref. [1]. 
As noted above, there is no significant excess near excess in the samesign data, . Nor is there an excess in the oppositesign electronmuon data, .

There is a small excess of events near in the data.

There is no evidence for the 30 GeV dimuon excess in events for which the tag has been inverted; see Fig. 4 from Ref. [1]. Comparison of Fig. 4 with Fig. 1a shows that most of the events near are still , so it is not clear how dispositive this is of the excess being produced only in association with .

Ref. [1] states that, for in the vicinity of , the minimum angle between one of the two muons and the leading jet was always found to be less than .^{1}^{1}1Ref. [1] also observed a tendency for at least one of the leading jets to be broadened when the dimuon mass is high. This may make it difficult for to define the jet axis precisely in such events.
The obvious and simplest explanation of these features of the ALEPH data is that the 30 GeV excess is just a statistical fluctuation in semileptonic decays. On the other hand, it is possible to construct a rather minimal model that accounts for the ALEPH data and makes several testable predictions. It is a twoHiggs doublet model (2HDM) in which the heavier CPeven Higgs boson is the Higgs boson discovered in 2012 at the LHC [2, 3]. The two other neutral Higgs bosons are a CPeven one and a CPodd one . The additional neutral and charged Higgs bosons couple mainly to the muon doublet and secondarily, but more weakly, to quarks. We shall choose parameters so that . There are then two “natural” options for the ; either (1) or (2) . In option 1, with and viceversa. There are also two “Higgsstrahlung” processes: with and ; and with or radiating or which then decays to . In option 2, there are only the Higgsstrahlung processes involving radiation. The branching ratio (1) is easily fit by the first option, but not the second. If the charged Higgs bosons in this model, , are heavier than , they may have evaded previous searches because they decay mainly to and rarely to , , and ; see, e.g., Refs. [4, 5, 6] for and other searches at LEP and the LHC.
The rest of this paper is organized as follows: In Sec. 2 we describe our 2HDM model: its assumptions and their rationale; its potential, extremal conditions and mass matrices; the Higgs couplings to leptons, quarks, electroweak gauge bosons and to each other. In Sec. 3 we present the two options for describing the 30 GeV dimuon excess. There we see that only option 1 can explain Eq. (1) and we present numerical values for the model’s parameters and the corresponding signal branching ratio of the . Sec. 4 catalogs predictions of our model. Some of these may be useful for looking for the dimuon in LHC experiments. Finally, in Sec. 5, we present what appears to be a fatal flaw of the model, and a potential nogo theorem for any Higgsbased (and other scalarbased) model of the 30 GeV dimuon. However, if the excess seen in ALEPH is confirmed in other LEP and LHC experiments, it will be difficult to dismiss the dimuon as a background fluctuation and this fly in the ointment will stand as a significant challenge to modelbuilders.
2 The 2HDM model
The model uses the two Higgs doublets (see Ref. [7] for a review),
(2) 
where for . Both doublets have weak hypercharge . To account for the appearance of a dimuon excess only in association with the decays of bosons, we assume a symmetry with hypercharge assignments for the Higgs doublets, left handed fermion doublets and righthanded fermion singlets as follows:^{2}^{2}2This is a simple version of the BrancoGrimusLavoura models of Ref. [8] which has no Higgsinduced flavorchanging neutral current interactions; also see Refs. [9, 10].
(3) 
This symmetry is softly broken by the dimensiontwo term in the potential^{3}^{3}3The quartic couplings in Eq. (4) are half the corresponding ones in Ref. [7]. The term in that reference is forbidden here by the (softlybroken) symmetry.
(4)  
Here, , all ’s are real, for vacuum stability, and we will want to assume that . For a range of these parameters, then, these fields have the real vacuum expectation values (vevs)
(5) 
and they satisfy the extremal conditions
(6)  
(7) 
The square of the electroweak vev is . The mass matrices, mass eigenstate fields and eigenvalues of the CPeven Higgs bosons are (after shifting them by their respective vevs):
(9)  
For the CPodd Higgs bosons, they are:
(12)  
(13) 
The is a pseudoGoldstone boson of the spontaneously broken symmetry which is also softly broken by the term in the Higgs potential. For the charged Higgs bosons:
(15)  
(16) 
To be consistent with the ALEPH data, we assume that the scalar doublet couples to all fermions except the muon and electron, while couples only to the and doublets.^{4}^{4}4Alternatively, we could just as well couple the electron to . As noted above, this is implemented by the (softlybroken) symmetry on Higgs and fermion fields. Without loss of generality, the Yukawa terms for the leptons may then be written in terms of masseigenstate lepton fields as
These interactions induce no detectable chargedlepton flavor violation.^{5}^{5}5The contribution to the rate for is suppressed by . The Yukawa interactions of the quarks are
Here, are the diagonal up and downquark matrices and is the CabibboKobayashiMaskawa (CKM) matrix. For small and , and decay mainly to and, at most at the percent level, to . The decay almost entirely to . Because of this, the limits on charged Higgses from and decay appear to be inapplicable because they assume [4], modes with very small branching ratios in our model. In Sec. 3, we shall find it prudent to assume , hence .
The most important couplings of the Higgses to electroweak bosons are (in unitary gauge):
For small and , the couplings of are close to the Standard Model (SM) in all cases. Note the strong coupling.
Finally, for light , and , there is the possibility of decay to pairs of them. The relevant Lagrangian for this is:
(20)  
where , etc.
3 Options for the 30 GeV Dimuon Excess
We identify as the 125 GeV Higgs boson and and possibly as the 30 GeV excess in Ref. [1]. In order that this be consistent with LHC data on , particularly the Higgs signal strengths [4], we require rather weak coupling between and . This means small for – mixing and small for mixing of the CPodd scalars and of the charged scalars, i.e.,
(21) 
Then we can make the further reasonable assumption that , and we obtain
(22) 
Thus, there are two options for the extra Higgs bosons’ masses:^{6}^{6}6Option 1 is the same as considered in Ref. [11], except that we forbid the quartic couplings of the 2HDM.
(24) 
The solution is the SM formula for the Higgs boson’s mass. If this option is preferred by the ALEPH data, then and are nearly degenerate. In either case, the charged Higgs boson mass, , depends on the sign and magnitude of .
For small there is not much leeway in the masses of these two options. In option 1, making quickly leads to an order of magnitude larger than and potentially to trouble with decays to the light scalars (see below). Anyway, there is little motivation for . Making even more quickly leads to and an unstable Higgs potential.
Another feature of option 1 is that can decay to , and . A glance at Eq. (20) shows that these decays are strongly dominated by the terms in the and interactions; for moderate values of and , their interactions contribute negligibly to the Higgs width. For few , these processes contribute several 10’s of MeV to the Higgs width, an order of magnitude more than its SM width of . We choose so that the and contributions to the Higgs width are each
(25) 
In addition, we shall take so that .^{9}^{9}9It is possible that the main decay mode, , has evaded searches for lighter charged Higgses; see Ref. [4, 5, 6]. It is also possible that limits on supersymmetric scalar muons decaying as require [4]. A mass this large does not affect our results in Tables 1 and 2.
The range of in Eq. (25) may seem unnaturally small. But it is not our model’s purpose to be devoid of all finetuning. Certainly not with the enormous renormalizations of the Higgs boson masses in this or any such model. The point here is that we can choose the model’s parameters to be consistent with ALEPH’s and Higgsdecay data, and so we will.
In option 2, we will see that it would be desirable to have there. But this is also excluded by the simultaneous requirements of a stable Higgs potential, perturbative , — a generous lower bound given the signal strength, and achieving the branching ratio (1) for the ALEPH signal.
In option 1, with , the plausible origins of the dimuon signal at ALEPH are with and , and viceversa. There are also the “Higgsstrahlung” processes (1) with and and (2) with or and .
In option 2, with and nearly degenerate at , the only kinematically plausible candidates for ALEPH are the Higgsstrahlung processes with radiation. Their contribution to the branching ratio is tiny, for any , mainly because of suppression by the offshell propagator, the smallness of , and the weak coupling of to . So, option 2 cannot explain the 30 GeV dimuon excess.
The only source of the excess in option 1 is because the Higgsstrahlung processes are still negligible. In the narrowwidth approximation, the decay rate is
(26) 
with the momentum of in the rest frame. For , this gives .^{10}^{10}10The question of what to do about an additional in the width is discussed briefly in Sec. 5. Tables 1 and 2 list quantities of interest for a range of and other inputs, including the choice .^{11}^{11}11We used , and at . There is no difficulty choosing parameters that produce a branching ratio in the neighborhood of the value deduced from the ALEPH data [1]. Note that, because of the relative smallness of , most of the dimuon signal comes from .
10  0.04066  36.6  0.1293  
12.5  0.05084  45.7  0.1294  
15  0.06101  54.8  0.1295  
20  0.08139  72.9  0.1299 
10  0.9999  0.9923  
12.5  0.9998  0.9814  
15  0.9997  0.9622  
20  0.9991  0.8889 
4 Predictions
This model makes a number of predictions, some obvious, some not so, that we enumerate here.

The dimuon signal in ALEPH and in other detectors, at LEP or at the LHC, will be observed only in decay and almost exclusively in association with .

Dimuons from the signal will have a common production vertex. Those outside the signal region are due to semileptonic decays and will not.

Signal dimuons have an isotropic distribution. Its flat shape is modified to a hump when there is a cut of – on both muons. In that case, all of the signal lies in , where is an increasing function of the cut. The effect is illustrated in Fig. 5 for LEP, where the is produced at rest, and for the LHC, where the tends to be produced with low and a large boost. Note that the histograms are normalized to unit area so that, for a large cut, little signal data remains.
Figure 5: The distribution of the in as a function of the cut on each muon for LEP (left), where the is produced at rest, and the LHC for collisions at (right), assuming negligible . From A. Heister, private communication. 
In our model, signal dimuons will not have a strong tendency to be close to the jets in the boson’s rest frame. We have checked that this obvious kinematical fact is true in any model in which with and , for with spinzero or one. This is in contradiction with the ALEPH data for which, when , the minimum angle between a muon and a leading jet is always less than degrees [1]. We have no explanation for this difference. On the other hand, at the LHC, the rather large boost makes the signal as well as semileptonic background muons less isolated. This tendency is stronger at than at . If muon isolation is an important signal criterion at , it may be possible to enhance it by selecting production. According to Ref. [14], approximately 15% of production at is accompanied by one jet with .

In the dimuon signal region, the invariant mass should have a significant excess near , nominally in our model.

Charged Higgses, , decay mainly to . Light charged Higgses may not have been excluded in this mode by previous searches [4, 5, 6]. If they were, they need to be heavier than . If they are excluded by LEP searches for supersymmetric scalar muons, they must be heavier than [4]. They are most readily sought in at the LHC. in LEP2 data and at the LHC and in

If , as in Table 1, couples only weakly to , so this decay mode may be unobservably small.

There will be no observable excess in in events.
An interesting question is how to tell from . The answer is not obvious if they are nearly degenerate at . Another question for which we have no ready answer is how to determine the mixing angles and other than by naive fitting.
5 A NoGo Theorem?
To account for the apparently exclusive appearance of the 30 GeV dimuon excess in association with , we used a 2HDM in which the Yukawa couplings of the second Higgs doublet involve only the muon and electron doublets. The Yukawa couplings of the and quark doublets are to .^{12}^{12}12We remind the reader that this setup induces no observable chargedlepton flavor violation. Only option 1 with can explain the rate of the ALEPH dimuon. In our model, for parameters that give in the vicinity of Eq. (1), we have for and for . This makes , 3300 times larger than its measured value of [4].
We have considered several modifications of our model that decrease the branching ratios of and to while increasing the yield. We already mentioned that, for small and , cannot be much different from . In our model, and , with . So, the next simplest thing we considered was to decrease . But since several production decayrate signal strengths of the Higgs boson are also proportional to , their measured values would no longer agree with the SM expectation of unity. If we counter this by increasing , with still small and still in the range, we find again that the decay rates for , are many 10’s of MeV. Further, when increasing , other conflicts may arise, e.g., with mediated by exchange.
In the context of a 2HDM, we also tried to ameliorate the 4muon problem with the BrancoGrimusLavoura (BGL) mechanism [8, 9, 10] to dilute . The BGL scheme admits Higgsinduced flavorchanging neutral current interactions (FCNC) through a softlybroken symmetry that allows a set of quarks with the same electric charge and color to couple to and get mass from both Higgs doublets [15]. The resulting FCNC involve only the quark masses and elements of the CKM matrix . If the third generation is treated differently than the first two, the FCNC are suppressed by factors of or and they can be sufficiently small even for Higgs masses much less than the 1001000 TeV scale ordinarily required by and constraints.
We considered plausible alternatives in which the Yukawa couplings to and of one type of quark, up or down, have the form (here denotes a nonzero entry):
(27) 
while those of the other type are
(28) 
The Yukawa textures of the leptons are the same as those displayed in Eq. (28). The “viceversa” textures in these two equations are excluded for the and the sectors. If used for the sector, they imply couplings to of and to of . This ruins the agreement of the signal strengths with the SM and implies that by far the dominant decay modes of are to two gluons! Using them for the sector implies, among other things, that , so that it is impossible to have .
For the displayed textures, the interactions induced by light and exchange are all very small because of a near cancellation between the two terms as well as the suppression by or .^{13}^{13}13This cancellation  was noted in Ref [9] but there was no reason for in that paper. However, the textures in Eq. (27) for the sector give which are times larger than their experimental upper limits. Furthermore, for and as displayed in either of these two sets of textures, is almost as large as for . Such a large rate would have been captured in the ALEPH data for which the tag was inverted (see Fig. 4).
For sector FCNC with Eq. (27),