Mono-Higgs: a new collider probe of dark matter
We explore the LHC phenomenology of dark matter (DM) pair production in association with a 125 GeV Higgs boson. This signature, dubbed ‘mono-Higgs,’ appears as a single Higgs boson plus missing energy from DM particles escaping the detector. We perform an LHC background study for mono-Higgs signals at and TeV for four Higgs boson decay channels: , , and , . We estimate the LHC sensitivities to a variety of new physics scenarios within the frameworks of both effective operators and simplified models. For all these scenarios, the channel provides the best sensitivity, whereas the channel suffers from a large background. Mono-Higgs is unlike other mono- searches (=jet, photon, etc.), since the Higgs boson is unlikely to be radiated as initial state radiation, and therefore probes the underlying DM vertex directly.
Although most of the matter in the Universe is dark matter (DM), its underlying particle nature remains unknown and cannot be explained within the Standard Model (SM). Many DM candidates have been proposed, largely motivated in connection with new physics at the electroweak symmetry breaking scale Jungman et al. (1996); Bertone et al. (2005). Weak-scale DM also naturally accounts for the observed relic density via thermal freeze-out Scherrer and Turner (1986). With the discovery of the Higgs boson Aad et al. (2012a); Chatrchyan et al. (2012a), a new window to DM has opened. If DM is indeed associated with the scale of electroweak symmetry breaking, Higgs-boson-related signatures in colliders are a natural place to search for it.
Invisible Higgs boson decays provide one well-known avenue for exploring possible DM-Higgs-boson couplings, provided such decays are kinematically allowed. Null results from searches at the Large Hadron Collider (LHC) for an invisibly decaying Higgs boson produced in association with a boson, combined with current Higgs boson data, already provide a model-independent constraint on the Higgs invisible branching ratio of at CL Belanger et al. (2013a); see Ref. Aad et al. (2013a) for results in . On the other hand, invisible Higgs boson decays are not sensitive to DM with mass above GeV. Therefore, it is clearly worthwhile to investigate other Higgs-boson-related collider observables.
DM production at colliders is characterized by missing transverse energy () from DM particles escaping the detector and recoiling against a visible final state . Recent mono- studies at the LHC have searched for a variety of different signals, such as where is a hadronic jet () Chatrchyan et al. (2012b); Aad et al. (2011), photon () Aad et al. (2013b); Chatrchyan et al. (2012c), or boson Carpenter et al. (2012); Aad et al. (2013a). The discovery of the Higgs boson opens a new collider probe of dark matter. This paper explores the theoretical and experimental aspects of this new LHC signature of dark matter: DM pair production in association with a Higgs boson, , dubbed ‘mono-Higgs’, giving a detector signature of . We consider mono-Higgs signals in four final state channels for : , , and and .
There is an important difference between mono-Higgs and other mono- searches. In proton-proton collisions, a /// can be emitted directly from a light quark as initial state radiation (ISR) through the usual SM gauge interactions, or it may be emitted as part of the new effective vertex coupling DM to the SM. In contrast, since Higgs boson ISR is highly suppressed due to the small coupling of the Higgs boson to quarks, a mono-Higgs is preferentially emitted as part of the effective vertex itself. In a sense, a positive mono-Higgs signal would probe directly the structure of the effective DM-SM coupling.
Mono- studies have largely followed two general paths. In the effective field theory (EFT) approach, one introduces different non-renormalizable operators that generate without specifying the underlying ultraviolet (UV) physics. Since the operators are non-renormalizable, they are suppressed by powers of , where is the effective mass scale of UV particles that are integrated out. Alternatively, in the simplified models approach, one considers an explicit model where the UV particles are kept as degrees of freedom in the theory. Although the EFT approach is more model-independent, it cannot be used reliably when the typical parton energies in the events are comparable to Cirelli et al. (2013), and additionally it is blind to possible constraints on the UV physics generating its operators (e.g., dijet resonance searches). Simplified models avoid these short-comings, but at the expense of being more model-dependent. The two approaches are therefore quite complementary and in the present work, we consider both.
The remainder of our work is outlined as follows. In Sec. II, we construct both EFT operators and simplified models for generating mono-Higgs signatures at the LHC. Our simplified models consist of DM particles coupled to the SM through an -channel mediator that is either a vector boson or a scalar singlet . In Sec. III, we assess the sensitivity of LHC experiments to mono-Higgs signals at the 8 TeV and 14 TeV LHC, with 20 fb and 300 fb respectively, in four Higgs boson decay channels (, , , ), including both new physics and SM backgrounds. In Sec. V, we conclude.
Ii New physics operators and models
We describe new physics interactions between DM and the Higgs boson that may lead to mono-Higgs signals at the LHC. In all cases, the DM particle is denoted by and may be a fermion or scalar. We also assume is a gauge singlet under .
First, we consider operators within an EFT framework where is the only new degree of freedom beyond the SM. Next, we consider simplified models with an -channel mediator coupling DM to the SM. For both cases, Fig. 1 illustrates schematically the basic Feynman diagram for producing (although not all models considered here fit within this topology). Quarks or gluons from collisions produce an intermediate state (e.g., an electroweak boson or a new mediator particle) that couples to .
At the end of this section, we identify several benchmark scenarios (both EFT operators and simplified models) that we consider in our mono-Higgs study, see Table 1.
ii.1 Effective operator models
The simplest operators involve direct couplings between DM particles and the Higgs boson through the Higgs portal McDonald (1994); Burgess et al. (2001); Patt and Wilczek (2006); Kim and Lee (2007); March-Russell et al. (2008); Low et al. (2012); Lopez-Honorez et al. (2012). For scalar DM, we have a renormalizable interaction at dimension-4:
where is a real scalar and is a coupling constant. For (Dirac) fermion DM, we have two operators at dimension-5:
suppressed by a mass scale . Mono-Higgs can arise via through these operators. However, it is important to note that these interactions lead to invisible Higgs boson decay for . Treating each operator independently, the partial widths in each case are
neglecting terms, where GeV is the Higgs vacuum expectation value. If invisible decays are kinetimatically open, it is required that ( TeV) for scalar (fermion) DM to satisfy obtained in Ref. Belanger et al. (2013a). In this case, since the couplings must be so suppressed, the leading mono-Higgs signals from DM are from di-Higgs production where one of the Higgs bosons decays invisibly, as we show below. On the other hand, if , invisible Higgs boson decay is kinematically blocked and the DM-Higgs couplings can be much larger.
At dimension-6, there arise several operators that give mono-Higgs signals through an effective --DM coupling. For scalar DM, we have
while for fermionic DM we have
When the Higgs acquires its vev, the Higgs bilinear becomes
where is the gauge coupling and is the cosine of the weak mixing angle. Thus, these operators generate mono-Higgs signals via . However, for , these operators are strongly constrained by the invisible width. The partial width for scalar DM is
neglecting terms. For fermionic DM, the partial width is larger by a factor of four for either of the operators in Eq. (5). Requiring MeV Beringer et al. (2012) imposes that GeV ( GeV) for scalar (fermion) DM if such decays are kinematically open.
At higher dimension, there are many different operators to consider for coupling to additional SM fields. Here we focus in particular on operators arising at dimension-8 that couple DM particles and the Higgs field with electroweak field strength tensors Chen et al. (2013). (Such operators have been considered recently in connection with indirect detection signals Chen et al. (2013); Fedderke et al. (2013).) For fermionic DM, there are many such operators, e.g.,
where and are the and field strength tensors, respectively. Additional operators arise where can be replaced by the axial current , or the field strength tensors are replaced with their duals. For illustrative purposes, we investigate the mono-Higgs signals from one operator
This operator leads to via . It is noteworthy that the Feynman rule for this process involves derivative couplings, i.e., . Consequently, compared to our other effective operators, this one leads to a harder spectrum and has by far the best kinematic acceptance efficiency, as we show below. We also note that the operators in (8) also induce mono- signals, as required by gauge invariance, when both Higgs fields are replaced by . For a single operator, the ratio between mono- is fixed, and therefore constraints on each channel are relevant. In the presence of a signal, on the other hand, all channels are complementary in disentangling the underlying operator(s).
ii.2 Simplified models
Beyond the EFT framework, it is useful to consider simple, concrete models for how DM may couple to the visible sector. Simplified models provide a helpful bridge between bottom-up EFT studies and realistic DM models motivated by top-down physics Alves et al. (2012). Here, we explore a few representative scenarios where the dark and visible sectors are coupled through a new massive mediator particle. Mono-Higgs signals are a prediction of these scenarios since in general the mediator may couple to the Higgs boson.
ii.2.1 Vector mediator models ()
A vector boson is a well-motivated feature of many new physics scenarios, arising either as a remnant of embedding the SM gauge symmetry within a larger rank group or as part of a hidden sector that may be sequestered from the SM (see e.g. Langacker (2009) and references therein). The has an added appeal for DM since the corresponding gauge symmetry ensures DM stability, even if the symmetry is spontaneously broken.111It is required that the is broken by units, where the field carries unit of charge. This breaks the down to a discrete symmetry. Although how the couples to SM particles is highly model-dependent, we focus here on simple scenarios that are representative of both extended gauge models and hidden sector models. For practical purposes, this distinction affects whether the -quark vertex is a gauge-strength coupling or is suppressed by a small mixing angle, which in turn impacts DM production at the LHC.
One gauge extension of the SM is to suppose that baryon number () is gauged, with the being the gauge boson of Carone and Murayama (1995). The consistency of such theories often implies the existence of new stable baryonic states that are neutral under the SM gauge symmetry, providing excellent DM candidates Agashe and Servant (2004); Fileviez Perez and Wise (2010). Taking the DM particle to carry baryon number , the -quark-DM part of the Lagrangian is
depending on whether is a scalar or fermion. The couplings to quarks and DM are related to the gauge coupling by and , respectively. This scenario is an example of a leptophobic model, and many precision constraints are evaded since the does not couple to leptons del Aguila et al. (1986).
To investigate mono-Higgs signals, we ask whether the is coupled to the Higgs boson . To generate the mass, the minimal possibility is to introduce a “baryonic Higgs” scalar to spontaneously break . Analogous to the SM, there remains a physical baryonic Higgs particle, denoted , with a coupling . This coupling comes from the mass term
where is the baryonic Higgs vev. Generically will mix with the SM Higgs boson, giving rise to an interaction of the form
and similarly for scalar DM. The first term in Eq. (13) is relevant for mono- signals (through ISR), while the second term gives rise to mono-Higgs. It is clear that mono-Higgs, depending on a different combination of underlying parameters, offers a complementary handle for DM studies.
An alternate framework for the is that of a hidden sector (see e.g. Chang et al. (2006); Pospelov et al. (2008); Feldman et al. (2007); Feng et al. (2008); Gopalakrishna et al. (2008)). In this case, we suppose that DM remains charged under the , while all SM states are neutral. The Lagrangian we consider is
where is the usual SM neutral current coupled to the , and the is coupled to fermionic DM. Although the two sectors appear decoupled, small couplings can arise through mixing Holdom (1986); Babu et al. (1998); Gopalakrishna et al. (2008). One simple possibility is that the has a mass mixing term with the . In this case, one diagonalizes the system by a rotation
where is the - mixing angle, and and . Thus, the physical states are linear combinations of the gauge eigenstates, and each one inherits the couplings of the other from Eq. (14). We note that such mixing gives a contribution to the parameter of Babu et al. (1998). Current precision electroweak global fits exclude Beringer et al. (2012), although any tension is also affected by new physics entering other observables in the global fit.
Mono-Higgs signals arise through diagrams shown in Fig. 2(b). The vertex arises as a consequence of the fact - mixing violates and is given by
ii.2.2 Scalar mediator models
New scalar particles may provide a portal into the dark sector March-Russell et al. (2008). The simplest possibility is to introduce a real scalar singlet, denoted , with a Yukawa coupling to DM
By virtue of gauge invariance, may couple to the SM (at the renormalizable level) only through the Higgs field O’Connell et al. (2007). The relevant terms in the scalar potential are
where are new physics couplings and is the usual Higgs quartic. The second line in Eq. (18) follows once the Higgs field acquires a vev, thereby leading to a mixing term in the - mass matrix. (Without loss of generality, the vev of can be taken to be zero through a field shift O’Connell et al. (2007).) The two scalar system is diagonalized by a field rotation
where the mixing angle is defined by , with and . After the field rotation, the quark and DM Yukawa terms become
The mixing angle is constrained by current Higgs data, which is consistent with within uncertainties Belanger et al. (2013a); Falkowski et al. (2013); Djouadi and Moreau (2013); Giardino et al. (2013); Ellis and You (2013), thereby requiring .
where we have expressed and in terms of and , respectively. We note that the term is fixed (at leading order in ) once the mass eigenvalues and mixing angle are specified. However, the is not fixed and remains a free parameter depending on . Alternately, a Higgs can be radiated directly from the quark in the production loop, shown in Fig. 3(c). In our study, we include the box contribution through an effective Lagrangian
which we have evaluated in the large limit. Although this will likely overestimate our signal Haisch et al. (2013), we defer an evaluate of the true box form factor to future study.
ii.3 Benchmark Models
For the purposes of our collider study to follow, we consider several illustrative benchmark scenarios for both EFT operators and simplified models. These models are summarized in Table 1. For the models, we henceforth denote the coupled to baryon number as and the hidden sector mixed with the as . Otherwise, the parameters and interactions are as described above.
|Simplified models with -channel mediator|
|Scalar||GeV, , ,|
|GeV, , ,|
Iii Collider Sensitivity
In this section we estimate the sensitivity of the LHC to mono-Higgs production with collisions at TeV and 14 TeV with fb and fb, respectively.
Signal events are generated in madgraph5 Alwall et al. (2011), with showering and hadronization by pythia Sjostrand et al. (2006) and detector simulation with delphes Ovyn et al. (2009) assuming pileup conditions of and for TeV, respectively.
The critical experimental quantity is the missing transverse energy; a comparison of the for a few choices of dark matter or mediator masses for the models under study can be seen in Fig. 4. The production cross section for under the various models are shown in Fig. 5.
In the following sub-sections, we estimate the LHC sensitivity in four Higgs boson decay modes: .
iii.1 Two-photon decays
The decay mode has a small branching fraction, Heinemeyer et al. (2013), but smaller backgrounds than other final states and well-measured objects, which leads to well-measured .
Significant backgrounds to the final state include:
production with , an irreducible background;
production with where the lepton is not identified;
or non-resonant production, with from mismeasurement of photons or soft radiation;
Figure 6 shows distributions of the diphoton mass () and the missing transverse momentum for two example signal cases and the background processes.
The production cross section for is taken at NNLO+NNLL in QCD plus NLO EW corrections Heinemeyer et al. (2013) with 8% uncertainty due to renormalization and factorization scale dependence and 7% uncertainty due to parton distribution function (PDF) and uncertanties. For , we use the calculation of Ref. Heinemeyer et al. (2013) which employs a zero-width approximation with NNLO QCD + NLO EW in which the dominant uncertainties are 1-3% due to scales and 4% due to PDFs and . In each case, we use with a 5% relative uncertainty Heinemeyer et al. (2013).
The cross section for is calculated at LO by madgraph5, but normalized to NLO calculations using a -factor of Bozzi et al. (2011). The cross section for production is calculated at leading order by madgraph5, corrected using a -factor of extracted by comparing to the measured di-photon cross section Aad et al. (2012b).
Systematic uncertainties due to photon efficiency and resolution will be small compared to the uncertainty on the backgrounds, and are neglected. A potential significant source of systematic uncertainty is the modeling of the missing transverse momentum spectrum due to mismeasurement, as arises in the and backgrounds. For the purposes of this sensitivity study, the thresholds in are designed to suppress these backgrounds to essentially negligible levels. A future experimental analysis must consider these more rigorously.
The event selection is:
at least two photons with and
invariant mass GeV
no electons or muons with and
or 250 GeV.
Figure 7 shows the distribution of expected events at and 14 TeV as a function of missing transverse momentum. We select a minimum threshold by optimizing the expected cross-section upper limit, finding GeV and GeV for the and 14 TeV cases, respectively. Note that the spectrum varies between the models, such that a single global optimal value of is not possible. We select a single threshold which gives the best aggregrate limits across choices of models and ; further optimization is not warranted given the approximate nature of our background model and systematic uncertainties. Table 2 shows the expected event yields for each of these cases.
iii.2 Four-lepton decays
The four-lepton decay mode, via , has the smallest branching ratio of the modes considered here, but also offers the smallest backgrounds.
Backgrounds to the final state include:
production with , an irreducible background;
production with and ;
production with where the lepton from the decay is not identified;
or the continuum production, with from mismeasurement of leptons or soft radiation.
As in the case for two-photon decays, the cross sections and uncertainties for , , and production, and the branching fractions are taken from Ref. Heinemeyer et al. (2013). We take branching fractions , and . The considerably larger branching fraction involving neutrinos results in a significant contribution from the non-resonant background.
Simulated samples of events, hereafter referred to simply as , are generated by madgraph5 at LO. The yield is compared against NLO values calculated with powheg and gg2ZZ in Aad et al. (2013c), and the difference is assigned as a systematic.
To improve the accuracy of the modeling of lepton reconstruction efficiency by delphes, we scale the per-lepton efficiencies to match those reported by ATLAS Aad et al. (2013c) in the final states and apply these efficiences to all simulated samples.
We define the leading lepton pair to be the same-flavor, opposite-sign pair with invariant mass closest to the -boson mass. The sub-leading pair’s invariant mass, , is the next closest to the -boson mass. Figure 9 shows distributions of the lepton pair masses, and , the four-lepton invariant mass, , and the missing transverse momentum. We also define as a function which is a constant for , then rises linearly to for and remains constant. Then each event must satisfy:
at least four leptons with each electron (muon) satisfying:
highest lepton is an electron (muon) with , and the second (third) lepton satisfies ()
or 150 GeV.
Figure 10 shows the distribution of expected events at and 14 TeV as a function of missing transverse momentum. We select a minimum threshold by optimizing the expected cross-section upper limit, finding GeV and GeV for the and 14 TeV cases, respectively. Table 3 shows the expected event yields for each of these cases.
Selection efficiency and upper limits on are shown in Fig. 11.
iii.3 Two--quark decays
The two--quark mode is the dominant Higgs boson decay mode, but suffers from a very large background due to strong production of dijets as well as the poorest resolution.
Backgrounds to the final state include:
production with , an irreducible background;
production with where the lepton from the decay is not identified;
or non-resonant production, with from mismeasurement of leptons or soft radiation;
top-quark pair production
The event selection is:
two -tagged jets with GeV and
invariant mass GeV
no electons or muons with and
no more than one additional jet with GeV and
and to suppress false
GeV ( TeV) or GeV ( TeV).
Figure 7 shows the distribution of expected events at and 14 TeV as a function of missing transverse momentum.
The production cross section and uncertaintaties for , and are calculated as above, with branching fraction with a 3% relative uncertainty Heinemeyer et al. (2013). The cross section for production is calculated at NNLO Czakon et al. (2013). The cross sections are calculated at LO with madgraph5 and scaled using the inclusive and boson production cross section -factors Febres Cordero et al. (2008, 2009). The cross section is calculated at leading order with madgraph5 scaled to NLO using a -factor Banfi et al. (2007).
We select a minimum threshold by optimizing the expected cross-section upper limit, finding GeV and GeV for the and 14 TeV cases, respectively. Table 2 shows the expected event yields for each of these cases.
Selection efficiency and upper limits on are shown in Fig. 14. Note that the small signal efficiency is largely due to the need for a high minimum threshold on to supress the backgrounds. Similar missing energy thresholds and efficiencies are seen in mono-jet analyses.
iii.4 Two-lepton and two-jet decays
The branching fraction of to four leptons is quite small due to the small charged-lepton decay fraction relative to hadronic decay modes. To balance that, we consider the mode.
The backgrounds to the final state include:
production with and , an irreducible background;
Additional decay modes of and production, all with final state ;
Higgs boson production with ;
Diboson production: and ;
Production of plus additional jets, with ;
boson plus jets production, with ;
boson plus jets production, with and one jet misreconstructed as an isolated lepton;
production with and .
The event selection is
Two opposite-sign leptons of the same flavor with leading lepton GeV, second leading lepton , and .
No additional leptons with GeV.
Two or more jets with and .
Dilepton invariant mass between and GeV.
between the dilepton system and the dijet system (formed by the two highest- jets) less than 2.25 radians.
Invariant mass of both leptons plus the jet in the direction with smallest from the dilepton system less than 124 GeV.
Figure 15 shows distributions of kinematic variables used in the event selection, and missing transverse momentum. Figure 16 shows distributions of missing transverse momentum, after event selection, for both and TeV.
To increase the number of simulated events used to model the -boson+jets background, where one jet is misreconstructed as a lepton, the +jet events were weighted by a fake rate for a randomly choosen jet, to match the event yield determined from delphes. As this represents a small contribution to the final selection, a large uncertainty here has only a small effect on the calculated limits.
We select a minimum threshold by optimizing the expected cross-section upper limit, finding GeV for both the and 14 TeV cases. Table 5 shows the expected event yields for each of these cases.
Selection efficiency and upper limits on are shown in Fig. 17.
A comparison of sensitivities between final states is shown in Figs. 18 and 19. The di-photon final state has the strongest sensitivity across all models and masses. The two--quark final state also has significant power, which may be improved by more aggressive rejection of the background and use of jet-substructure techniques to capture events with large Higgs boson .
Note that these comparisons assume the SM Higgs boson branching fractions, which may be diluted in cases where is large, but the relative BFs will be unaltered, allowing a comparison of the relative power of each channel.
The systematic uncertainty on the background estimate typically controls the sensitivity of each channel. In this study, we have used simulated samples to describe the background contributions. In future experimental analyses, many of these backgrounds can be estimated by extrapolating from signal-depleted control regions, which significantly reduces the systematic error due to modeling of the tail. For example, in the final state, one can measure the rate of and in final states with one or two leptons, respectively.
Iv Discussion and results
For a range of different models and DM mass , the LHC sensitivity to mono-Higgs production is approximately . (More precise values are given in Figs. 18 and 19.) In this section, we compare these projected sensitivities to the predicted cross sections for our benchmark theories (Fig. 5) in order to constrain the parameter space of these scenarios. We also consider other important constraints, such as invisible or decays, as well as the recent bound on the spin-independent (SI) direct detection cross section from the LUX experiment Akerib et al. (2013). The SI cross section for DM scattering on a nucleus with atomic and mass numbers is
where is the - reduced mass and are the DM couplings to protons/neutrons. We emphasize, however, that direct detection constraints can be avoided if DM is inelastic Tucker-Smith and Weiner (2001), i.e., if the complex state is split into real states with an or larger mass splitting, with no change to the collider phenomenology provided it is much smaller than the typical parton energy.
Our results are shown in Figs. 20-22. The “” contours show the LHC reach on our models at and TeV, based on 20 and 300 fb respectively, from mono-Higgs searches with final states, which provides the stronger bound compared to and . The limit contours shown exclude larger values of couplings and mixing angles, or smaller values of the effective operator mass scale .
iv.1 Higgs portal effective operators
The simplest models for coupling DM and the Higgs boson are the Higgs portal effective operators (1) and (2). For real scalar DM there is one operator with a dimensionless coupling , while for fermion DM there are two operators and suppressed by a mass scale . All three operators, which we consider separately, are qualitatively similar, and all three contribute to the invisible branching ratio for . The LHC reach depends on whether is above or below .
For , mono-Higgs signals cannot be observed for these operators unless LHC sensitivities can be improved by a factor of over our estimates. Actually, this is true for any value of