Doubly-charged Higgs bosons in the diboson decay scenario at the ILC
aa r X i v : . [ h e p - ph ] M a y Doubly-charged Higgs bosons in the diboson decay scenario at the ILC ∗ Kei Yagyu Department of Physics, National Central University, Chungli 32001, Taiwan
Abstract
The Higgs Triplet Model (HTM) is one of important examples for extended Higgs sectors, because tinyneutrino masses can be simply explained. Unlike the canonical type-I seesaw model, a scale of new particles canbe taken as O (100) GeV keeping an enough amount of production cross section for direct searches at colliderexperiments. In the HTM, there appear doubly-charged Higgs bosons H ±± , and detection of them is a key toprobe the model. The decay property of H ±± depends on the magnitude of the vacuum expectation value ofthe triplet field v ∆ . When v ∆ is smaller than about 1 MeV, H ±± can mainly decay into the same-sign dilepton,and the lower mass limit for H ±± had been taken to be about 400 GeV at the LHC. On the other hand, if v ∆ is larger than about 1 MeV, H ±± can mainly decay into the same-sign diboson. In this case, the massbound cannot be applied, so that the scenario based on light H ±± is still possible. In this talk, we discuss thephenomenology of the same-sign diboson decay scenario of H ±± . First, we review the mass bound from thecurrent collider experiments given in Ref. [1]. We then discuss the strategy for detection of H ±± at the ILC. ∗ This talk is based on the paper [1], and the collaboration with Shinya Kanemura, Mariko Kikuchi, and Hiroshi Yokoya. nternational Workshp on Future Linear Colliders (LCWS13), 11-15 November 2013 I. INTRODUCTION
The Higgs boson has been discovered at the LHC, and its properties are consistent with those ofthe Higgs boson in the Standard Model (SM) [2]. Although the minimal Higgs sector assumed inthe SM can explain this situation by the most economical way, we still do not know what is the truestructure of the Higgs sector . In fact, in the Higgs sector with additional isospin scalar multipletssuch as singlets, doublets and triplets, the discovered Higgs boson can be well explained as in the SM.Such a non-minimal Higgs sector often appears in a new physics model which can explain phenomenabeyond the framework of the SM; e.g., neutrino oscillations, the existence of dark matter and baryonasymmetry of the Universe. Therefore, by the determination of the structure of Higgs sector fromcollider experiments, we can get a clue for new physics models.The type-II seesaw scenario [3] is one of important examples for new physics which deduces anon-minimal Higgs sector, where tiny neutrino masses can be simply explained. The Higgs sector inthis scenario corresponds to the Higgs Triplet Model (HTM) which is composed of the isospin doubletscalar field Φ with the hypercharge Y = 1 / Y = 1. Fromnew Yukawa interactions h ij L icL ( iτ )∆ L jL for the left-handed lepton doublet field L L , Majorana massesare generated at the tree level as ( M ν ) ij = √ h ij v ∆ , (1)where v ∆ = √ h ∆ i is the vacuum expectation value (VEV) of ∆. The important point in Eq. (1) isthat the mass of triplet scalar field does not enter in this expression. Therefore, we can consider tripletscalar boson masses to be O (100) GeV. In such a case the HTM can be tested at collider experiments.In this talk, we focus on the direct detection of H ±± at the LHC and at the ILC. There are threedecay modes for H ±± , i.e., the same-sign dilepton decay ( H ±± → ℓ ± ℓ ± ), the same-sign diboson decay( H ±± → W ± ( ∗ ) W ± ( ∗ ) ), and the cascade decay ( H ±± → H ± W ±∗ ), where H ± are the singly-chargedHiggs bosons mainly originated from the triplet field. Collider phenomenology of H ±± with the same-sign dilepton, the same-sign diboson and the cascade decay has been studied in Refs. [11, 12], [12]and [13], respectively. Among these three decay channels, when H ±± mainly decay into the same-signdilepton, there had been a lower limit on the mass of H ±± ( m H ++ ) to be about 400 GeV from theLHC [14, 15]. However, this mass bound cannot be applied to the case where H ±± can mainly decayinto the same-sign diboson In this talk, we focus on the same-sign diboson decay scenario of H ±± . Wefirst discuss the current bound on m H ++ from the LEP and the LHC experiments. We then considerthe phenomenology of a light H ±± scenario at the ILC. nternational Workshp on Future Linear Colliders (LCWS13), 11-15 November 2013 -5 -4 -3 -2 v ∆ [GeV] BR ( H ++ )
500 GeV300 GeV150 GeV l + l + W + W + m H ++ FIG. 1: Decay branching ratio of H ++ as a function of v ∆ with m H + = m H ++ . The solid, dashed and dottedcurves respectively show the results in the case of m H ++ = 150, 300 and 500 GeV. II. IMPORTANT FEATURES AT THE TREE LEVEL
There are several characteristic features in the HTM. First of all, the electroweak rho parameterdeviates from unity at the tree level as ρ tree = v φ + 2 v v φ + 4 v ≃ − v v φ , (2)where v φ is the VEV of Φ, and it satisfies v = v φ + 2 v ≃ (246 GeV) . The experimental value is giveas ρ exp = 1 . +0 . − . [4], so that v ∆ is constrained to be smaller than about 3.5 GeV at the 95%confidence level (CL) from Eq. 2). Because of the smallness of v ∆ , the mixing between Φ and ∆ isvery weak. Therefore, the component scalar fields in ∆ are almost the mass eigenstates, where thereare the doubly-charged H ±± , the singly-charged H ± , a CP-odd A and a CP-even H scalar bosons.We can call them triplet-like Higgs bosons.Second, there appear relationships among the masses of triplet-like Higgs bosons under v ∆ ≪ v φ ;i.e., m H ++ − m H + ≃ m H + − m A and m H ≃ m A . From this relation, three patterns of the massspectrum can be considered; namely, m A > m H + > m H ++ , m H ++ > m H + > m A and all of them aredegenerate in mass [13, 16]. In the following discussion, we concentrate on the degenerate case, andwe discuss the phenomenology of H ±± .Finally, the gauge interactions and Yukawa interactions of H ±± are derived from the kinetic termand the neutrino Yukawa interactions as L int = − gm W √ v ∆ v g µν H ++ W − µ W − ν − ( M ν ) ij √ v ∆ ℓ ic P L ℓ j H ++ + h.c. , (3) nternational Workshp on Future Linear Colliders (LCWS13), 11-15 November 2013 H ++ [GeV]110100 Γ ( Z H ++ H -- ) [ M e V ] ↑ σ σ FIG. 2: Decay rate of Z → H ++ H −− as a function of m H ++ . The 1 σ and 2 σ error bars of the measured Zboson width are also shown by the dashed horizontal lines. where m W is the W boson mass. Assuming all the elements in ( M ν ) ij to be 0.1 eV, the decay branchingratio of H ±± is calculated as in Fig. 1. We can see that the dominant decay mode is changed fromthe same-sign dilepton mode to the same-sign diboson mode at v ∆ = 0 . III. CONSTRAINT ON m H ++ FROM COLLIDER EXPERIMENTS
At the LEP experiment, the width of the Z boson has been precisely measured as Γ Z (exp) =2 . ± . H ±± is smaller than the half of the Z boson mass, the Zboson width can be significantly modified due to the Z → H ++ H −− decay. In Fig. 2, we show thedecay rate of Z → H ++ H −− as a function of m H ++ . From this figure, we obtain the lower bound on m H ++ to be about 43 GeV at the 95% CL. Because the bound is obtained only from the width of theZ boson, this constraint does not depend on the decay channel of H ±± .At the LHC, H ±± are produced by the Drell-Yan process pp → Z ∗ /γ ∗ → H ++ H −− and theassociated process pp → W ∗ → H ±± H ∓ . The search for H ±± in the dilepton decay scenario has beenperformed at the LHC. The strongest lower limit on m H ++ has been given by 459 GeV [15] at the95% CL assuming the 100% decay of H ±± → µ ± µ ± from the 7 TeV and 4.9 fb − data. This boundbecomes weaker as 395 GeV [15] when we only use the pair production process. However, when H ±± mainly decay into the same-sign diboson, this bound can no longer be applied.In Ref. [1], the lower bound on m H ++ has been taken by using the same-sign dilepton event nternational Workshp on Future Linear Colliders (LCWS13), 11-15 November 2013
40 50 60 70 80 90 100 m H++ [GeV] C r o ss s ec ti on [f b ] -1
20 fb -1 FIG. 3: The signal cross section expressed in Eq. (4) as a function of m H ++ with the collision energy to be7 TeV from Ref. [1]. The light (dark) shaded band shows the 95% CL (expected) upper bound for the crosssection from the data with the integrate luminosity to be 4.7 fb − (20 fb − ). measured at the LHC with 7 TeV and 4.7 fb − data [17]. In Fig. 3, the sum of the cross sections of pp → H ++ H −− → W +( ∗ ) W +( ∗ ) H −− → µ + µ + E miss H −− ,pp → H ++ H − → W +( ∗ ) W +( ∗ ) H − → µ + µ + E miss H − , (4)processes are shown as a function of m H ++ in the case of m H + = m H ++ . It is seen that m H ++ smallerthan about 60 GeV is excluded at the 95% CL. By the extrapolation of the data to 20 fb − with thesame collision energy, the lower limit is given to be 85 GeV. Therefore, a light H ±± such as around100 GeV is still allowed by the current data at the LHC. IV. DETECTION OF H ±± AT THE ILC
In this section, we discuss the detection of H ±± in the diboson decay scenarios at the ILC. Wefirst classify possible three scenarios which are expected after the 300 fb − data will be accumulatedat the LHC with the 14 TeV energy as follows1. H ±± will be discovered at the LHC,2. H ±± will not be discovered at the LHC, and its mass bound is smaller than √ s/ H ±± will not be discovered at the LHC, and its mass bound is larger than √ s/ √ s is the center of mass energy at the ILC. Case 1 is the most attractive scenario for testingthe HTM, where m H ++ would be measured at the LHC. Therefore, by focusing on the collision energy nternational Workshp on Future Linear Colliders (LCWS13), 11-15 November 2013
100 200 300 400 500 m H ++ [GeV] σ ( e + e - H ++ H -- ) [f b ] ↑ Root(s) = 250 GeV500 GeV 1000 GeV
FIG. 4: Production cross section of the e + e − → H ++ H −− process as a function of m H ++ . The black, blueand red curves are respectively the results with the collision energy √ s =250, 500 and 1000 GeV. to be the half of m H ++ , precise measurements of the properties of H ±± such as the mass, width anddecay branching ratios are possible. In addition, loop effects of H ±± to the Higgs boson couplings canbe calculated by fixing m H ++ , and then we can compare the predictions with the precisely observedvalues. This can be the consistency check for measured H ±± . When Case 2 is realized, we can use the e + e − → H ++ H −− production as the discovery mode of H ±± . As the indirect search, we can calculatedeviation in Higgs boson couplings by fixing m H ++ to be larger than the lower bound given from theLHC data. If Case 3 is realized, only the indirect search can be used to test the HTM.Let us suppose that Case 1 or Case 2 is realized. The production cross section of the e + e − → γ ∗ /Z ∗ → H ++ H −− process is given at the leading order by σ ( e + e − → H ++ H −− ) = πα s β ( x H ++ ) (cid:20) Q e + 4 v e Q e − x Z − s W s W c W + v e + a e (1 − x Z ) (1 − s W ) s W c W (cid:21) , (5)where β ( x ) = √ − x , x i = m i /s , v e = I e / − s W Q e , a e = I e / c W = cos θ W and s W = sin θ W with I e , Q e and θ W being the isospin of electron, the electric charge of electron and weak mixingangle, respectively. In Fig. 4, the pair production cross section is shown as a function of m H ++ in thecases with √ s = 250, 500 and 1000 GeV.We consider the signal and background events for the e + e − → H ++ H −− process. In the dibosondecay scenario, we expect the final state with the same-sign dilepton, missing energy and multi-jets;i.e., e + e − → H ++ H −− → ℓ + ℓ + E miss jjjj , where ℓ = e, µ . The background comes from the four Wbosons production; e + e − → W + W + W − W − → ℓ ± ℓ ± E miss jjjj . When we take √ s = 500 GeV and the m H ++ = 230 GeV as an example, we get the signal (background) cross section of ℓ ± ℓ ± E miss j finalstate to be 1.07 fb (2.37 × − fb) by using MadGraph5 [18]. The above numbers are obtained after nternational Workshp on Future Linear Colliders (LCWS13), 11-15 November 2013 M l + l + [GeV] -2 -1 N u m b e r o f E v e n t / b i n HTM with m H ++ = 230 GeVSM M T [GeV] -2 -1 N u m b e r o f E v e n t / b i n HTM with m H ++ = 230 GeV SM FIG. 5: The invariant mass distribution (left panel) and the transverse mass distribution (right panel) for the ℓ + ℓ + and ℓ + ℓ + E miss systems, respectively, in the case of m H ++ = 230 GeV and √ s = 500 GeV. The integratedluminosity is assumed to be 500 fb − . taking the following basic kinematic cuts p ℓT ≥
15 GeV , | η ℓ | ≤ . , (6)where p ℓT and η ℓ are the transverse momentum and pseudo rapidity for ℓ , respectively. Therefore, thisprocess is almost background free.Fig. 5 shows the invariant mass M ℓ + ℓ + for the ℓ + ℓ + system (left panel) and the transverse mass M T (right panel) distributions for ℓ + ℓ + E miss system. The red and black curves denote the distributionfrom the signal and background, respectively. There is an end point in the M T distribution at around230 GeV which corresponds to m H ++ . Therefore, the M T distribution is useful to measure m H ++ .Finally, we would like to comment on the indirect search for the HTM from the precision measure-ments of the Higgs boson coupling constants. At the ILC, the Higgs boson couplings are expected tobe precisely measured. For example, the Higgs boson couplings with the weak gauge bosons ( hZZ and hW W ) and the Yukawa couplings ( hb ¯ b , hτ ¯ τ and ht ¯ t ) are expected to be measured with O (1)%accuracy [9, 10]. In the HTM, the loop induced hγγ coupling has been calculated in Refs. [5–7]. Theone-loop corrections to the hW W , hZZ and hhh vertices have also been calculated in Refs. [6, 8].According to Ref. [6], it has been found that there is a correlation among the deviation in the Higgsboson couplings. For example, when the decay rate of h → γγ deviates by 30% (40%) from the SMprediction, deviations in the one-loop corrected hV V and hhh vertices are predicted to be about − . − −
10% (150%), respectively. By comparing these deviations with the precisely measuredvalue at the ILC, we can discriminate the HTM from the other models. nternational Workshp on Future Linear Colliders (LCWS13), 11-15 November 2013 V. CONCLUSION
We have discussed how we can test the HTM at collider experiments. The detection of H ±± canbe a direct evidence for the HTM, so that we have focused on the direct search for H ±± . The colliderphenomenology of H ±± can be drastically different depending on the main decay mode of H ±± . When v ∆ is smaller (larger) than about 1 MeV, H ±± can mainly decay into the same-sign dilepton (diboson).If the same-sign dilepton mode is dominate, the lower mass bound of H ±± has been taken to be about400 GeV. However, this bound cannot be applied when the same-sign diboson decay is dominate.We then have studied the bound of m H ++ in the same-sign diboson decay scenario. It has beenfound in Ref. [1] that the lower limit on the mass to be about 60 GeV can be obtained by usingthe same-sign dilepton data collected at the LHC with 7 TeV and 4.7 fb − . Therefore, a light H ±± scenario is still possible in the same-sign diboson decay scenario.We have simulated the process e + e − → H ++ H −− → W + W + W − W − → ℓ + ℓ + E miss j at the ILC.When we take m H ++ = 230 GeV and 500 GeV for the collision energy, the signal cross section isabout 1.1 fb. On the other hand, the corresponding background cross section from the four W bosonsproduction is about 2.4 × − fb, so that this process can be regarded almost background free. Wehave found that by looking at the end point in the transverse mass distribution of the same-signdilepton plus missing system, we may be able to reconstruct the mass of H ±± . Acknowledgments
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