hep-ph/0301203 KIAS-P02032 UCCHEP/22-03 January 2003 Searching for a light Fermiophobic Higgs Boson at the Tevatron 3 0 0 2 Andrew G. Akeroyda, Marco A. D´ıazb n a J 3 a: Korea Institute for Advanced Study, 207-43 Cheongryangri-dong, 2 Dongdaemun-gu, Seoul 130-772, Republic of Korea 1 b: Departamento de F´ısica, Universidad Cat´olica de Chile, v 3 Avenida Vicun˜a Mackenna 4860, Santiago, Chile 0 2 1 0 3 0 / h p Abstract - p e WeproposenewproductionmechanismsforlightfermiophobicHiggsbosons(h ) h f : with suppressed couplings to vector bosons (V) at the Fermilab Tevatron. These v mechanisms (e.g. qq′ H±h ) are complementary to the conventional process Xi qq′ Vh , which suffe→rs from af strong suppression of 1/tan2β in realistic models f → r with a h . The new mechanisms extend the coverage at the Tevatron Run II to the a f larger tanβ region, and offer the possibility of observing new event topologies with up to 4 photons. 1 1 Introduction The study of extensions of the Standard Model (SM) which include more than one Higgs doublet [1] has received much attention in last 20 years. The SM predicts one neutral Higgs scalar (φ0) with branching ratios (BRs) which are functions of m . It is predicted φ0 to decay dominantly via φ0 bb for m 130 GeV, and φ0 VV(∗) (where V = φ0 → ≤ → W±,Z) for m 130 GeV. The minimal extension of the SM contains an additional φ0 ≥ SU(2) U(1) Higgs doublet, the “Two Higgs Doublet Model” (2HDM), and the resulting × particle spectrum consists of 2 charged Higgs bosons H+, H− and 3 neutral members h0, H0 and A0. Assuming that each fermion type (up,down) couples to only one Higgs doublet [2], which eliminates tree-level Higgs mediated flavour changing neutral currents, leads to 4 distinct versions of the 2HDM [3]. Due to the increased parameter content of the 2HDM the BRs of the neutral Higgs bosons may be significantly different to those of φ0 [1],[4]. In recent years LEP2 has carried out searches [5] for such Higgs bosons with enhanced BRs to lighter fermions and bosons (e.g. cc,τ+τ−,gg). The phenomena known as “fermiophobia” [6] which signifies very suppressed or zero coupling to the fermions, may arise in a particular version of the 2HDM called type I [7]. Such a fermiophobic Higgs (h )[8, 9, 10, 11, 12, 13, 14] would decay dominantly to two bosons, either h γγ f f → (for m 90 GeV) or h VV(∗) for (m 90 GeV) [10, 11]. This would give a very hf ≤ f → hf ≥ clear experimental signature, and observation of such a particle would strongly constrain the possible choices of the underlying Higgs sector. Fermiophobic Higgs bosons have been searched for actively at LEP and the Tevatron. All four collaborations at LEP (OPAL[15], DELPHI[16], ALEPH[17], L3[18]) utilized the channel e+e− h Z, h γγ and obtained lower bounds of the order m 100 GeV. → f f → hf ≥ L3 [19] is the only collaboration yet to consider h WW∗ decays. OPAL [15] and f → DELPHI [16] also searched in the channel e+e− H A0, H γγ. In run I at the F F → → Tevatron the mechanism qq′ V∗ h V,h γγ was used, with the dominant contri- f f → → → bution coming from V = W±. The limits on m from the D0 and CDF collaborations hf are respectively 78.5 GeV[20] and 82 GeV [21] at 95% c.l. Run II will extend the coverage of m beyond that of LEP. hf However, all these mass limits assume that the h VV coupling is of the same strength f as the SM coupling φ0VV, which in general would not be the case for a h in a realistic f model e.g. the 2HDM (type I) or the Higgs triplet model of [22], [23]. Therefore one could imagine the scenario of a very light h (m << 100 GeV) which has eluded the current f hf searches at LEP and the Tevatron Run I due to suppression in the coupling h VV. Such f a h could also escape detection in the Tevatron Run II. In this paper we propose new f production mechanisms at the TevatronRun IIwhich areeffective even when thecoupling h VV is very suppressed. f Ourworkisorganizedasfollows. Section2givesanintroductiontothephenomenology of fermiophobic Higgs bosons while Section 3 presents the new production mechanisms. Section 4 contains our numerical results with conclusions in section 5. 2 2 Models with Fermiophobia A fermiophobic Higgs boson (h ) may arise in a 2HDM in which one SU(2) U(1) Higgs f × doublet (Φ ) couples to all fermion types, while the other doublet (Φ ) does not. Both 2 1 doublets couple to the gauge bosons via the kinetic term in the Lagrangian. One vacuum expectation value (v ) gives mass to all fermion types, while gauge bosons receive mass 2 from both v and v . This model (usually called “Type I”) was first proposed in [7]. Due 1 2 to the mixing in the CP–even neutral Higgs mass matrix (which is diagonalized by α) both CP–even eigenstates h0 and H0 can couple to the fermions. The fermionic couplings of the lightest CP–even Higgs h0 take the form h0ff cosα/sinβ (1) ∼ where f is any fermion, and β is defined by tanβ = v /v . 2 1 Small values of cosα would seriously suppress the fermionic couplings, and in the limit cosα 0 the coupling h0ff would vanish at tree–level, giving rise to fermiophobia → (sometimes called a “bosonic” or “bosophillic” Higgs): f h f 0 ∼ f However, at the 1–loop level there will be an effective vertex h ff mediated by loops f involving vector bosons and other Higgs particles. These loop contributions are infinite and a counterterm is necessary to renormalize it. The counterterm is fixed with an experimental input, leading to an arbitrariness in the definition of the tree level vertex, or equivalently, inthemixingangleα[11]. Itiscustomarytodefineanextremefermiophobia, where h remains fermiophobic to the 1-loop level/all orders with branching ratios given f by [10],[11]. In general, one would expect some (small) coupling to fermions, from both tree–level diagrams and one loop diagrams. f h f 0 ∼ f The Higgs Triplet model (HTM) discussed in [22],[23] is another possible origin for a h . In such models gauge invariance forbids the tree–level coupling of some triplet Higgs f bosons to fermions, and so suppressed BRs to fermions are expected without requiring specific mixing angles. The main decay modes of a fermiophobic Higgs are: 3 γ,W∗,Z∗ h f γ,W∗,Z∗ < h γγ is the dominant decay for m 95 GeV (sometimes called a “photonic Higgs”), f → < hf ∼ with a BR near 100% for m 80 GeV, decreasing to 50% at m 95 GeV and to 1% at m 145 GeV. In conthrfa∼st, BR(φ0 γγ) 0.22% is the lhafrg≈est value in the SM hf ≈ → ≈ for the two photon decay. In this paper we shall be focusing on the possibility of a light (m 100 GeV) for which the photonic decay mode always has a large BR. hf ≤ BR(h WW∗) supercedes BR(h γγ) when m >95 GeV, with a BR approach- f → f → hf ∼ ing 100% for 110 GeV < m < 170 GeV, and stabilizing at 70% for m 2M . The hf ∼ hf ≥ Z decay h ZZ∗ is always subdominant, but for m 2M approaches 30%. Recently, f → hf ≥ Z L3 [19] has included these VV∗ decays in their searches, and the discovery prospects of this decay mode at the Tevatron Run II have been presented in [24]. Apart from the 2HDM (Type I) and the HTM, there are other models beyond the SM which allow the possibility of a neutral Higgs boson with an enhanced BR to γγ, as explained in [25]. These include h0 of the MSSM, and h0 of top–condensate models. We will not consider these models, which have a smaller BR(h0 γγ) than the fermiophobic → models, and instead focus on the 2HDM (Type I)1. Our results can also be quite easily extrapolated to the case of the HTM. The conventional production mechanism for a h at e+e− colliders is e+e− Z∗ f → → h Z, and at Hadron colliders qq′ V∗ h V. Note that the gluon-gluon fusion mecha- f f → → nism (viaheavy quarkloops) isnot relevant forah . Inthe2HDM(Type I),thecondition f for tree–level fermiophobia (cosα 0) causes the coupling h VV to be suppressed by a f → factor h VV sin2(β α) cos2β 1/(1+tan2β) (2) f ∼ − → ≡ Taking tanβ 3(10) implies a strong suppression of 0.1( 0.01)for the coupling h VV f ≥ ≤ ≤ with respect to the coupling φ0VV. This suppression is always possible for the lightest CP–even neutral Higgs in any of the 4 types of the 2HDM [1] and also occurs for the h f in the HTM [23]. Therefore one can imagine the scenario of a very light h which has f eluded the searches via the mechanisms e+e−/qq′ h V. The possibility of a light h f f → has been known for a long time [11] and has been emphasized in [12],[13]. LEP ruled out regions of the plane [m ,R BR(h γγ)], where R is defined by: hf × f → σ(e+e− Zh ) f R = → (3) σ(e+e− Zφ0) → 1AnotherinterestingpossibilityforalightHiggsbosonwithenhanceddecaystoγγhasbeenconsidered in [27],[28]. Here if A0 is extremely light ( 0.2 GeV) then BR(A0 γγ) may be large. ≤ → 4 In a benchmark scenario of R = 1, and assuming BR(h γγ) given by [10], [11], f → each collaboration derived a limit of around m 100 GeV [15],[16], [17],[18], with the hf ≥ combined LEP working group limit being m 109 GeV [19]. From the LEP plots it is hf ≥ trivial tosee thenecessary suppression inR which would permit a lighth ofa given mass, f e.g. m 80 GeV (50 GeV) requires R 0.1(0.01), which corresponds to tanβ 3(10) hf ≤ ≤ ≥ in the 2HDM (Type I). Therefore sizeable regions of the [m ,R BR(h γγ)] plane hf × f → remain unexcluded for small R and small m . OPAL [15] also performed a search which hf is sensitive to the production mechanism e+e− h A0. This process ( sin2β in the f → ∼ fermiophobic limit) is complementary to e+e− h Z ( cos2β). Therefore the condition f → ∼ m +m √s must also be satisfied in order for a light h to escape detection at LEP2. hf A ≥ f With the closure of LEP, the Tevatron Run II will continue the search for h . Run II f will usethesamemechanism asRunI(qq′ V∗ Vh )but hastheadvantageofamuch f → → increased luminosity. Ref.[25] has shown that (for R = 1) m can be discovered (at 5σ) hf up to 114 GeV (128 GeV) with 2 fb−1 (30 fb−1), which is an improvement over the LEP limits. Similar conclusions were reached in [26]. However, with the expected suppression in the h VV coupling (R < 1), m 80 GeV could still escape detection. The aim f hf ≤ of this paper is to show that other production mechanisms are available at the Tevatron Run II, and allow discovery of a h even in the region where the process qq′ Wh is f f → suppressed. We will be using the most general (CP conserving) 2HDM potential [1]. This potential is parametrized by 7 independent variables, which may be taken as the four Higgs masses, two mixing angles (α,β), and a real quartic coupling (λ ). 5 V(Φ ,Φ ) = V +V (4) 1 2 sym soft where V = µ2Φ†Φ µ2Φ†Φ +λ (Φ†Φ )2 +λ (Φ†Φ )2 + sym − 1 1 1 − 2 2 2 1 1 1 2 2 2 1 λ (Φ†Φ )(Φ†Φ )+λ Φ†Φ 2 + [λ (Φ†Φ )2 +h.c] (5) 3 1 1 2 2 4| 1 2| 2 5 1 2 and V = µ2 Φ†Φ +h.c (6) soft − 12 1 2 The condition for tree-level fermiophobia corresponds to cosα 0, with α being an → independent parameter. Ref. [13] considered the fermiophobic limit in the context of two 6 parameter 2HDM potentials (V and V ). In Ref. [13] the angle α is not a free A B parameter, and the condition cosα 0 requires certain relations among the Higgs masses → to be fulfilled. We shall take all the Higgs masses as free parameters and set cosα = 0, which guarantees tree-level fermiophobia. 3 Production Processes In this section we introduce the production processes which may offer sizeable rates for h f in the region where the coupling h VV is very suppressed. These production mechanisms f 5 make use of the cascade decays H± h W(∗) or A0 h Z(∗) which may have large BRs f f → → in the 2HDM (Type I) [29] and the HTM [23]. These large BRs arise since the coupling of H± and A0 to all the fermions scales as 1/tanβ, and thus for moderate to large tanβ even the 3–body decays (i.e. with V∗) can have sizeable or dominant BRs. We note that in the MSSM such decays (with h replaced by h0) never attain very large BRs since H± f and A0 couple to the down type fermions with strength tanβ. In addition, the decays H± h0W(∗) or A0 h0Z(∗) are proportional to cos2(β α) which is suppressed in a → → − large part of the MSSM parameter space, but (in contrast) is maximized in the parameter of h with suppressed coupling to vector bosons. f Refs.[25],[26] considered two signatures from the qq′ WH mechanism, i) inclusive F → γγ and ii) exclusive γγV. The latter gives a better signal to background ratio and we will see that the cascade decay produces the necessary vector boson for the γγV signature. Below we list four production processes which are complementary to the standard qq′ WH mechanism. They all make use of the Higgs-Higgs-Vector boson coupling F → (g ) which is either proportional to sinβ (in the fermiophobic limit) or independent of HHV mixing angles (see Table 1). All mechanisms can offer non-negligible cross–sections in the large tanβ region. Moreover, double H production can occur, resulting in distinctive F γγγγ topologies. H±AW∓ H±h W± h AZ f f g 1 sinβ sinβ HHV Table 1: Mixing angle dependence of the couplings H H V i j (i) qq γ∗,Z∗ H+H−: Quark anti-quark pair annihilation produces a pair of → → charged Higgs bosons via an intermediate photon or Z boson in the s-channel: h q H+ f γ,Z H+ q H− W∗ The subsequent decay H± h W∗ may provide two W∗ and two h , resulting in f f → a distinctive γγγγ plus four fermion signal. (ii) qq′ W∗ H±h : Quark anti-quark annihilation into an intermediate W boson f → → producing a h in association with a charged Higgs: f q′ H± W± q 6 hf Thismechanism wascoveredinthecaseoftheMSSMin[30],butonlyfortheheavier CP–even H0. TherateforthelighterCP–evenh0 issuppressed bycos2(β α),which − issmallinalargeregionoftheMSSMparameterspace. Thecross–sectionsforH+h f and H−h are identical, and will be summed over in our numerical analysis. This f process is phase space favoured over (i) and provides direct production of h . A f vector boson (W∗) is provided by the decay H± W∗h . In this way, double h f f → production occurs with a signature of γγγγ plus V∗. (iii) qq′ W∗ H±A0: Quark anti-quark annihilation into an intermediate W pro- → → ducing a charged Higgs in association with a CP–odd neutral Higgs: h q′ H± f W A q A Z∗ This process is similar to (i) since no fermiophobic Higgs is produced directly. We sum over the rates for H+A0 and H−A0 as in (ii). The decay H± h W∗ or f → A0 Z∗h provides a gauge boson V and a h . Again, double h production may f f f → occur giving rise to a final state of γγγγ V∗V∗. This mechanism was considered in the context of the MSSM in [31]. (iv) qq Z∗ A0h : Quark anti-quark pair annihilation into an intermediate Z f → → producing a fermiophobic Higgs in association with a CP–odd neutral Higgs: q A Z q hf Thisprocessissimilarto(ii)andgivesdirectproductionofh withaZ bosonarising f from the decay A0 h Z∗. The γγγγ signal is also possible with this mechanism. f → Mechanisms i) and iv) are the hadron collider analogies of the LEP production pro- cesses e+e− H+H− and e+e− A0h , but have the advantage of the larger √s at the f → → Tevatron. Mechanisms ii) and iii) are exclusive to a hadron collider. The cross-section formulae for all the processes can be found in [32],[33]. One may write a generic formula for (ii),(iii) and (iv): G2M4 λ3/2 σ(qq H H ) = F Zg2 (v2 +a2) (7) → i j 96πsˆ HHV q q (1 M2/sˆ)2 − V 7 where H ,H (with mass M ,M ) refer to any of the Higgs bosons H±, A0, h , λ(M ,M ) i j i j f i j is the usual two body phase space function, and sˆ is the centre of mass energy for the partonic collision. In eq. (7), v and a represent the vector and axial vector couplings of q q the incoming quarks to the vector boson mediating the process, and are given in Table 2. In the same formula, g is the Higgs–Higgs–Vector Boson coupling which are listed in HHV Table 1. Z W± v 0.25 2 sin2θ √2cos2θ u − 3 w w a 0.25 √2/cos2θ u w v 0.25 1 sin2θ √2cos2θ d − − 3 w w a -0.25 √2/cos2θ d w Table 2: Values for v and a q q 4 Numerical Results We now outline the calculation of the cross–section for the processes (i) (iv) under → consideration. The partonic cross–sections are given by eq. (7). These must then be scaled up to a pp cross–section. In the partonic centre of mass system, the kinematic is defined as: sˆ= (pq +pq′)2 = (pHi +pHj)2 1 sˆ sˆ tˆ= (M2 +M2 ) + κcosθ 2 Hi Hj − 2 2 1 sˆ sˆ uˆ = (M2 +M2 ) κcosθ 2 Hi Hj − 2 − 2 sˆ+tˆ+uˆ = M2 +M2 Hi Hj Here κ2 = (sˆ (M +M )2)(sˆ (M M )2)/sˆ2. The hadronic cross–section for the − Hi Hj − Hi− Hj process pp qq′ H H can be expressed as follows: i j → → 1 d qq σ(pp qq′ H H ) = dτ L σˆ(sˆ= τs) . (8) → → i j Z(MHi+MHj)2/s dτ In the case of the Tevatron Run II √s = 2 TeV. d qq′ 1 dx Ldτ = Z x fq(x;Q2)fq′(τ/x;Q2) (9) τ where τ = x x , with x and x being the momentum fraction carried by each incoming 1 2 1 2 parton. The parton distributions fq and fq′ shall be taken at the typical scale Q ≈ MHi. We shall be using the MRST2002 set from [34]. Note that QCD corrections increase the 8 tree–level cross–section by a factor of around 1.3 [33]. In our analysis we shall present results using the tree–level formulae only. For the BRs of the fermiophobic Higgs we also work at tree–level and set cosα = 0 to ensure exact fermiophobia. The four new production mechanisms under consideration are generally expected to be ineffective for searches where the Higgs boson decays to quarks, since backgrounds will be sizeable. However, in the case of h we will show that they offer promising detection f prospects despite the moderate cross–sections. This is because the efficiency for the γγV channel is high ( 25%) [25], and the decays H± h W∗ or A0 Z∗h may have f f ≈ → → very large BRs in the 2HDM (Model I) discussed here. In much of the parameter space of interest (tanβ 1 and m < 100 GeV), BR(H± h W(∗)) and BR(A0 Z(∗)h ) ≥ hf → f → f are close to 100%. Hence a light h can be produced in a cascade with almost negligible f BR suppression (see [29] for a quantitative analysis of these BRs). The cascade decays provide distinctive γγγγ signatures from all four mechanisms. In our numerical analysis we will vary mhf with particular emphasis on mhf < 100 GeV. We will take mH± ≥ 90 GeV (roughly the lower bound from LEP2) and M is constrained by m + m 200 A A hf ≥ GeV from negative searches in the channel e+e− h A0. For the expected 2 fb−1 of f → data from Run IIa, which might be available by 2005/2006, we assume a threshold of observability of 10 fb for the cross–sections. Larger data samples of up to 15 fb−1 would require even smaller values. In Fig. 1 we plot all five mechanisms as a function of tanβ for fixed values of the CP– odd Higgs mass m = 150 GeV, charged Higgs mass m = 90 GeV, and fermiophobic A H+ Higgs mass m = 50 GeV. For a fermiophobic Higgs of this mass to escape detection hf at LEP2 one requires tanβ > 10. The traditional mechanism pp W±h dominates at f → low tanβ as expected, but falls fast with increasing tanβ due to the cos2β suppression mentioned earlier. For tanβ > 10 all the new mechanisms offer larger cross–sections than the traditional one. The process pp H±h is dominant for tanβ > 3 with a cross– f → ∼ section growing from 30 fb for tanβ = 0.5 up to 155 fb for tanβ = 50. In the parameter space of interest (tanβ 10) one finds BR(H± h W∗) 100% and so this mechanism f ≥ → ≈ essentially leads to a signature of γγγγ plus W∗. The pp H+H− mechanism has a production cross–section of 29 fb and is inde- → pendent of tanβ. This cross–section becomes larger than σ(pp W±h ) at tanβ 7, f → ≈ and leads to a signature of γγγγ plus W∗W∗. Similarly, pp H±A0 has a cross– → section σ = 14 fb (independent of tanβ) and supercedes the traditional mechanism at tanβ 10. As above, h is produced via a cascade decay, which also provides the vector f ≈ boson. Both H± h W∗ and A0 h Z∗ are effectively 100% which leads again to the f f → → γγγγ plus V∗V∗ signature. The behaviour of σ(pp A0h ) with tanβ is similar to that f → of pp H±h . It grows with tanβ and is essentially constant for large values of that f → parameter. This mechanism produces a fermiophobic Higgs directly, but has a lower rate due to the constraint m +m 200 GeV. Since BR(A0 h Z) 100% the γγγγ plus hf A ≥ → f ≈ V∗ signature also arises from this mechanism. In Fig. 2 we plot the five mechanisms as a function of the charged Higgs mass m , for H+ a constant value of the fermiophobic Higgs mass m = 50 GeV. We also fix tanβ = 20 hf which ensures that a h of this mass would have had too low a rate to be dectected at f 9 Figure 1: Production cross–section of five different modes leading to a fermiophobic Higgs boson as a function of tanβ, for fixed values of the charged, the CP–odd, and the fermio- phobic Higgs masses. 10