Two Higgs doublet model with vectorlike leptons and contributions to pp → W W and H → W W

Journal of High Energy Physics, Feb 2016

Abstract We study a two Higgs doublet model extended by vectorlike leptons mixing with one family of standard model leptons. Generated flavor violating couplings between heavy and light leptons can dramatically alter the decay patterns of heavier Higgs bosons. We focus on pp → H → ν 4 ν μ → W μν μ , where ν 4 is a new neutral lepton, and study possible effects of this process on the measurements of pp → W W and H → W W since it leads to the same final states. We discuss predictions for contributions to pp → W W and H →WW and their correlations from the region of the parameter space that satisfies all available constraints including precision electroweak observables and from pair production of vectorlike leptons. Large contributions, close to current limits, favor small tan β region of the parameter space. We find that, as a result of adopted cuts in experimental analyses, the contribution to pp → W W can be an order of magnitude larger than the contribution to H → W W . Thus, future precise measurements of pp → W W will further constrain the parameters of the model. In addition, we also consider possible contributions to pp → W W from the heavy Higgs decays into a new charged lepton e 4 (H → e 4 μ → W μν μ ), exotic SM Higgs decays, and pair production of vectorlike leptons.

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Two Higgs doublet model with vectorlike leptons and contributions to pp → W W and H → W W

HJE Two Higgs doublet model with vectorlike leptons and contributions to pp Radovan Derm sek 0 1 2 3 Enrico Lunghi 0 1 3 Seodong Shin 0 1 3 0 Seoul National University , Seoul 151-747 , Korea 1 Bloomington , IN 47405 , U.S.A 2 Department of Physics and Astronomy and Center for Theoretical Physics 3 Physics Department, Indiana University We study a two Higgs doublet model extended by vectorlike leptons mixing with one family of standard model leptons. Generated heavy and light leptons can dramatically alter the decay patterns of heavier Higgs bosons. Higgs Physics; Beyond Standard Model - We focus on pp ! H ! 4 ! W , where 4 is a new neutral lepton, and study possible e ects of this process on the measurements of pp ! W W and H ! W W since it leads to the same nal states. We discuss predictions for contributions to pp ! W W and H ! W W and their correlations from the region of the parameter space that satis es all available constraints including precision electroweak observables and from pair production of vectorlike leptons. Large contributions, close to current limits, favor small tan region of the parameter space. We nd that, as a result of adopted cuts in experimental analyses, the contribution to pp ! W W can be an order of magnitude larger than the contribution to H ! W W . Thus, future precise measurements of pp ! W W will further constrain the parameters of the model. In addition, we also consider possible contributions to pp ! W W from the heavy Higgs decays into a new charged lepton e4 (H ! e4 ! W Higgs decays, and pair production of vectorlike leptons. ), exotic SM 1 Introduction 2 Model 3 Branching ratios 2.1 Couplings of the Z and W bosons 2.2 Couplings of the Higgs bosons 4.1 4.2 4.3 and direct production The muon lifetime Invisible width of Z Direct production of vectorlike leptons 4 Parameter space scan and constraints from precision electroweak data 5 Main results: contributions of H ! W 6 Contributions from H ! e4 7 Contributions from SM-like Higgs boson 8 Contributions from Drell-Yan production of vectorlike leptons 9 Conclusions 1 Introduction Among simple extensions of the standard model (SM) are those with extended Higgs sector and extra vectorlike leptons near the electroweak (EW) scale. Since masses of vectorlike leptons are not related to their Yukawa couplings, in the absence of mixing with SM leptons, they are not strongly constrained by experiments. However, even small Yukawa couplings between SM leptons and vectorlike leptons can signi cantly a ect a variety of processes and can dramatically alter the decay patterns of heavier Higgs bosons. We consider an extension of the two Higgs doublet model type-II by vectorlike pairs of new leptons: SU(2) doublets LL;R, SU(2) singlets EL;R and SM singlets NL;R, where LL and ER have the same hypercharges as SM leptons. We further assume that the new leptons mix only with one family of SM leptons and we consider the mixing with the second family as an example. The mixing of new vectorlike leptons with leptons in the SM generate avor violating couplings of W , Z and Higgs bosons between heavy and light leptons. These couplings can result in new decay modes for heavy CP even (or CP odd) Higgs { 1 { and H ! e4 , where e4 and 4 are the lightest new charged and neutral leptons. These decay modes, when kinematically open, can be very important, especially when the mass of the heavy Higgs boson is below the tt threshold, about 350 GeV, and the this case, avor violating decays H ! 4 or H ! e4 compete only with H ! bb (for su ciently heavy H also with H ! hh) and can be large or even dominant. Subsequent , e4 ! Z , e4 ! h and 4 ! W , 4 ! Z , 4 ! h lead to In this paper, we focus on pp ! H ! 4 ! W and study possible e ects of this process on the measurements of pp ! ! W W and H W W since it leads to the presented in terms of the Higgs mass, the mass of 4 and the product of branching ratios predictions for contributions to pp ! W W and H ! W W and their correlations from the region of the parameter space that satis es all available constraints including precision electroweak observables [3] and constraints from pair production of vectorlike leptons [4]. Large contributions, close to current limits, favor small tan region of the parameter space. We nd that, as a result of adopted cuts in experimental analyses, the contribution to pp ! W W can be an order of magnitude larger than the contribution to H ! W W . In addition, we also consider possible contributions to pp ! W W from H ! e4 ! W from similar processes involving SM-like Higgs boson and from pair production of vectorlike leptons. Vectorlike leptons near the electroweak scale provide a very rich phenomenology and were studied in a variety of contexts. Most of the previous studies would apply also to the two Higgs doublet model we consider here since we assume type-II couplings of Higgs doublets to fermions relevant for supersymmetric extensions and we also consider the limit when the light Higgs is SM-like which is relevant for SM extensions by vectorlike fermions. For example, analogous processes involving SM-like Higgs boson decaying into 2`2 or 4` through a new lepton were previously studied in ref. [5] and the 4` case also in ref. [6]. Possible explanation of the muon g 2 anomaly with vectorlike leptons was studied in [7, 8]. Further extensions with vectorlike quarks and possibly Z0 are straightforward and o er possibilities to explain anomalies in Z-pole observables [9{12]. In addition, extensions with complete vectorlike families were considered that provide an understanding of values of gauge couplings from IR xed point behavior and threshold e ects of vectorlike fermions, as in insensitive uni cation [13, 14]. Many studies were also done in supersymmetric framework, see for example refs. [15{20], and in various frameworks the constraints from precision electroweak data have been analyzed [21{27]. Further discussion and more references can be found in a recent review [28]. This paper is organized as follows. In section 2 we present two Higgs doublet model type-II with vectorlike leptons mixing with one family of the SM leptons and derive formulas for couplings of Z, W and Higgs bosons to leptons. In section 3 we discuss branching { 2 { SU(2)L U(1)Y Z2 2 1 2 + doublets. The electric charge is given by Q = T3 + Y , where T3 is the weak isospin, which is +1=2 for the rst component of a doublet and 1=2 for the second component. H ! e4 ! W remarks in section 9. 2 Model ratios of the heavy Higgs boson H and neutral lepton 4 and nd approximate expressions in section 6, from the SM-like Higgs boson in section 7 and from pair production of vectorlike leptons in section 8. We summarize and present concluding We consider an extension of a two Higgs doublet model by vectorlike pairs of new leptons: SU(2) doublets LL;R, SU(2) singlets EL;R and SM singlets NL;R. The quantum numbers of new particles are summarized in table 1. The LL and ER have the same quantum numbers as the muon doublet L (we use the same label for the charged component as for the whole doublet) and the right-handed muon R respectively. We further assume that the new leptons mix only with one family of SM leptons and we consider the mixing with the second family as an example. This can be achieved by requiring that the individual lepton number is an approximate symmetry (violated only by light neutrino masses). The results for mixing with the rst or the third family could be obtained in the same way. The mixing of new leptons with more than one SM family simultaneously is strongly constrained by various lepton avor violating processes and we will not pursue this direction here. Finally, we assume that leptons couple to the two Higgs doublets as in the type-II model, namely the down sector couples to Hd and the up sector couples to Hu. This can be achieved by the Z2 symmetry speci ed in table 1. The generalization to the whole vectorlike family of new leptons, including the quark sector, would be straightforward. With these assumptions, the most general renormalizable Lagrangian containing Yukawa and mass terms for the second generation of SM leptons and new vectorlike leptons and couplings of the neutral leptons, and nally mass terms for vectorlike leptons. The components of doublets are labeled as follows: L = LL;R = Hd = Hu = (2.2) L0L;R LL;R ! ; H+ ! d H0 d ; Hu0 ! Hu ; L ! ; Higgs doublet model with qvu2 + vd2 = v = 174 GeV and we de ne tan where the neutral Higgs components develop the vacuum expectation values hHu0i = vu and hHd0i = vd. We assume that both are real and positive as in the CP conserving two vu=vd. After spontaneous symmetry breaking the resulting mass matrices in the charged and neutral sectors can be diagonalized and we label the two new charged and neutral mass eigenstates by e4 and e5 and 4 and 5 respectively. Couplings o all involved particles to the Z, W and Higgs bosons are in general modi ed because SU(2) singlets mix with SU(2) doublets. The avor conserving couplings receive corrections and avor violating couplings between the muon (or muon neutrino) and heavy leptons are generated. The couplings resulting from the mixing in the charged sector were discussed in detail in ref. [8] in the connection with the muon g 2 anomaly. Here we will focus on couplings resulting from the mixing in the neutral sector. These are also more relevant for the discussion of the contribution of the Higgs boson decays to pp ! W W . The mass matrix in the neutral lepton sector is given by: L0R NR C = A L0L NL N vu L0R NR C ; A where we inserted R = 0 for the right-handed neutrino which is absent in our framework in order to keep the mass matrix 3 3 in complete analogy with the charged sector. For the discussion of couplings it is convenient to de ne vectors Ra ( R = 0; L0R; NR)T . The mass matrix M transformation La ( ; L0L; NL)T and can be diagonalized by a biunitary 0 0 0 0 0 0 0 C ; 1 A m 5 resulting in masses for 4 and 5 leaving the muon neutrino massless. The light neutrino masses can be generated by a variety of ways. Once they are generated, the mixing of light neutrinos with vectorlike leptons results in corrections to both the masses and mixing angles controlled by Yukawa couplings in eq. (2.1). For better understanding of corrections to gauge and Yukawa couplings discussed later, approximate analytic formulas for diagonalization matrices are useful. These can be obtained in analogy with those in the charged lepton sector given in ref. [8]. In the limit N vu; vu; vu ML; MN { 4 { (2.3) (2.4) (2.5) with ML and MN not close to each other, we nd and we nd: VL = BBB 0 2MN2 N v2 u MLMN MN2 ML2 (ML +MN )2vu2 2(MN2 ML2 )2 (ML +MN )vu MN2 ML2 0 (ML +MN )2vu2 2(MN2 ML2 )2 (ML +MN )vu MN2 ML2 1 1 0; ML + O( 2); MN + O( 2). However, in our numerical analysis we do not use any approx= ( N ; ; )vu=(ML; MN ). The mass eigenvalues are 2.1 Couplings of the Z and W bosons Couplings of the muon and new heavy leptons to the Z and W bosons are modi ed from their SM values because SU(2) singlets mix with SU(2) doublets. These couplings can be written in terms of VL and VR, de ned in eq. (2.4), and of the analogue matrices UL and UR that are related to the charged lepton sector and that were discussed in detail in ref. [8] (with the replacement v ! vd due to the two Higgs doublet model). The couplings of the Z boson to charged leptons can be found in ref. [8] and those to neutral leptons follow from the kinetic terms: Lkin LaiD= a La + RaiD= a Ra = ^La(VLy)aciD= c(VL)cb ^Lb + ^Ra(VRy)aciD= c(VR)cb ^Rb ; where the vectors of mass eigenstates are ^La (^ ; ^L4; ^L5) T and similarly for ^Ra (^R = 0; ^R4; ^R5)T . We label the components of vectors and diagonalization matrices by 2, 4 and 5 because they correspond to 2nd, 4th and 5th mass eigenstate. The covariant derivative is given by: i g cos W Ta3Z ; where the weak isospin Ta3 is +1=2 for neutral components of SU(2) doublets and 0 for singlets. De ning couplings of the Z boson to leptons fa and fb as L fLa gZfafb fLb + fRa L gZfafb fRb Z ; R L neutrinos ^a and charged leptons e^b as L ^La g LW aebe^Lb + ^Ra g RW aebe^Rb W + + h:c: ; We assume a CP conserving two Higgs doublet model in the limit with the light Higgs h being fully standard model like in its couplings to gauge bosons and the heavy CP even Higgs H having no couplings to gauge bosons. The mass eigenstates h and H in this limit are related to doublet components as follows (see for example ref. [29]): h H ! = cos sin sin cos ! p2(Re Hd0 p2(Re Hu0 vd) vu) ! : { 6 { we nd: where LY La Y ab Rb Hu0 + h:c: = ^La(VLy)ac Y cd (VR)db ^Rb Hu0 + h:c: ; 0 0 0 N 0 0 1 C : A g g 2 2 g g LW aeb = p (VLy)a2(UL)2b + (VLy)a4(UL)4b ; RW aeb = p (VRy)a4(UR)4b : 2.2 Couplings of the Higgs bosons As a consequence of explicit mass terms for vectorlike leptons, the usual relations between the mass of a particle and its coupling to Higgs bosons do not apply. The couplings of neutral Higgs bosons to neutral leptons can be obtained from the following Yukawa terms in the Lagrangian (2.1): (2.13) (2.14) (2.15) (2.16) (2.17) (2.18) (2.19) (2.20) (2.21) HJEP02(16)9 The Y matrix is not proportional to the mass matrix given in eq. (2.3) and thus the Higgs couplings are in general avor violating. De ning couplings of mass eigenstate leptons fa and fb to CP-even Higgs bosons by 1 2 L h p fLa fafb fRb h H p fLa fafb fRb H + h:c: ; 1 2 diag(0; ML; MN ), the Higgs boson couplings can be also written as: h a b v = B 0 m 4 0 0 0 0 0 0 C A where we used vu = v sin . The rst terms in above equations represent the expected relations between fermion masses and their couplings to Higgs bosons and the second term represents contributions from the ML;N terms. This form of couplings makes it obvious that in the absence of vectorlike masses the couplings of h to leptons are fully SM-like, while couplings of H are enhanced by tan as expected in the limit we assume. Couplings to charged leptons follow from Hd0 terms in eq. (2.1) and can be obtained from those in eqs. (2.23) with replacements: VL;R ! UL;R, Y ! Ye and ! + =2, see also ref. [8] in the case of SM. The corresponding formulas to eqs. (2.24) would show that couplings of h have the usual SM strength, up to contribution from ML;N , while couplings of H to charged leptons are suppressed by tan . Finally couplings of the CP-odd Higgs boson, A, copy those of H up to the usual 5 factor. We collect expressions for the relevant branching ratios for the process pp ! H ! 4 ! and provide several approximate formulas in the limit of small mixing between neutral leptons discussed in the previous section. These formulas will be useful for qualitative understanding of results. From now on, we drop the hat notation for mass eigenstates and also label the mass eigenstates ^L2 and e^2 as and . Sizable decay modes of the heavy CP even Higgs boson are 4 , bb and gg for mH < 250 GeV. As discussed in the previous section we assume that H does not have direct couplings to pairs of gauge bosons and that decay modes to other Higgs bosons are not kinematically possible. However, our results could be straightforwardly modi ed to account for additional sizable decay modes of H. { 7 { (2.22) (2.23) (2.24) where the second line is an appropriate approximate formula in the case of singlet-like lepton with mass originating from MN . The decay width of H ! bb is given by (H ! bb) = (where we include both 4 m24 m2H 2 ; ML (VLy)24(VR)44 + MN (VLy)25(VR)54 v M N2 + MN (ML + MN ) ML2 (ML + MN )2v2 sin2 2(M N2 ML2)2 where the second line is an approximate formula in the limit of small mixing discussed in section 2. Note, that this limit assume the 4 is mostly the doublet with mass originating from ML. For an approximate formula corresponding to a singlet-like neutral lepton, the 5 should be used instead. This coupling is given by ; ; nal (3.1) (3.2) (3.3) (3.4) (3.5) (3.6) (3.7) (3.8) (3.9) ( 4 ! h ) = 16 m 4 ( h 4 ) { 8 { where mb(mH ) is the running b-quark mass evaluated at the scale mH and the correction factors qq and 2H can be found in ref. [30]. The decay width of H ! gg is given by (H ! gg) = GF S2m3H cot2 = m2H =4mt2 and f ( ) = arcsin2 p The branching ratio of H ! 4 is then given by The neutral lepton 4 can decay into standard model leptons and the Higgs, W , and Z bosons. Neglecting the muon mass, the partial decay width of 4 ! h is given by: where where where Finally, the partial decay width of 4 ! Z Assuming only these decay modes of 4, the branching ratio of 4 ! W Parameter space scan and constraints from precision electroweak data and direct production We perform a scan over all the model parameters introduced in section 2 over the ranges ML;N 2 [0; 500] GeV; N ; ; tan We x the mass term of the SU(2) singlet charged vectorlike lepton ME = 1000 GeV. We simplify the decay patterns of the heavy Higgs by requiring m 5 > mH (to avoid 5X channels) and m 4 > mH =2 (to avoid decays into pairs of heavy vectorlike leptons). Moreover we include mixing exclusively in the neutral sector. We impose constraints from precision EW data related to the muon and muon neutrino that include the Z pole observables (Z partial width to + , the invisible width, forwardbackward asymmetry, left-right asymmetry), the W partial width, and the muon lifetime. We also impose constraints from oblique corrections, namely from S and T parameters. { 9 { Unless speci ed otherwise these are obtained from ref. [3]. Finally, we impose limits from direct searches: the LEP limits on masses of new charged leptons, 105 GeV, and the limits on pair production of vectorlike leptons at the LHC summarized in ref. [4]. Constraints on the production of heavy Higgs will be discussed in the following section together with results. Constraints on the muon couplings were already discussed in ref. [8]. Precision electroweak measurements constrain modi cation of couplings of the muon to the Z and W bosons at 0:1% level which, in the limit of small mixing, approximately translates into 95% C.L. bounds on E;L couplings: E vd ME . 0:03 ; Lvd ML assuming only mixing (Yukawa couplings) in the charged sector. In the neutral lepton sector the strongest limits are obtained from the muon lifetime. In what follows we discuss this limit together with the invisible widths of the Z boson and constraints from direct production of vectorlike leptons. 4.1 The muon lifetime The Fermi constant GF is determined with a high precision from the measurement of muon lifetime. In the standard model GF = (p2=8)g2=M W2 while in our model one of the g=p2 factors is replaced by gL (VLy)22(UL)22 + (VLy)24(UL)42 : The allowed range for g is obtained from the uncertainty in the W mass, MW = 80:385 0:015 GeV. The relative uncertainty in M W2 is 2 the 95% C.L. upper limit on the deviation of gL W from g=p 2 as: Assuming no mixing in the charged sector and using the small mixing approximation eq. (2.6), = p (VLy)22 ' p and we obtain an approximate 95% C.L. upper bound on the size of N coupling: Considering also mixing in the charged sector, the bound is shared between N and E : The partial decay width of W depends quadratically on the gL W coupling. However, it is measured with about 2% precision and thus the resulting constraint on the coupling is signi cantly weaker. corresponding gauge couplings. the left panel, we show the ( N vu=MN )2{gLZ =(gLZ EW precision constraints. The blue, cyan, magenta and red points have singlet fraction (de ned as j(VLy)45j2=2 + j(VRy)45j2=2) in the ranges [0; 5]%, [5; 50]%, [50; 95]%, and [95; 100]%, respectively. In )SM plane; on the right axis we show the exp = SZMinv ratio. In the right panel we show the o -diagonal jgLW 4 Zinv j and jgL Z 4 j 4.2 Invisible width of Z The partial width of Z ! where (Z ! Z L g g = where the second line is an appropriate approximate formula in the case of small mixing. In this limit, the upper bound on N obtained from muon lifetime, eq. (4.8), suggests that ) can be modi ed at most at 0.3% level (the sign of the correction is always negative). Since we assume that only one generation of SM leptons mix with vectorlike pairs, the invisible width of Z can be lowered at most by 0.1%. This is also visible in gure 1 where we consider randomly generated points in the N , , , ML and MN parameter space for xed mH = 155 GeV and m 4 = 135 GeV (di erent choices of masses do not sizably a ect the allowed ranges), assuming no mixing in the charged lepton sector, and impose all EW precision constraints (including direct productions bounds discussed in section 4.3 below). In the left and right panels of gure 1 we consider the ( N vu=MN )2{ g )SM, ( N vu=MN )2{ eZxinpv = SZMinv and jgL W 4 j{jgL j planes. Both the upper limit on N vu=MN , eq. (4.8), and the resulting largest possible e ect in Zinv follow closely those obtained from the approximate formulas. Points with 4 being mostly singlet (red points) or mostly doublet (blue points) cluster very near the line that assumes the approximate relation in eq. (4.7) is exact and even highly mixed scenarios (cyan and magenta) are not very far. [R 4 4 Since the ratio of the measured value of the Z-boson invisible decay width and its SM the invisible width does not provide additional constraint to that obtained from the muon lifetime. This however assumes that only the 2nd generation of SM leptons mixes with vectorlike leptons. The e ect on invisible width can be larger if more generations mix with vectorlike leptons or if one considers mixing with the 3rd generation instead of the 2nd since the constraints on 3rd generation couplings are weaker. In conclusion, couplings of SM gauge bosons to the second family of leptons, g W L , can deviate from their SM values by less than 0:1%. Moreover, within the explicit model we consider, these constraints imply upper limits of order 0:02 on the new gauge couplings as we can see in the right panel of gure 1. 4.3 Direct production of vectorlike leptons Let us rst consider constraints from Drell-Yan production of 4 4 or 4e4 leading to at least 3 leptons in the nal state and Emiss. The cross section of pp ! T to (gLZ 4 4 )2 + (gRZ 4 4 )2 where the couplings are given in eqs. (2.11){(2.12). Thus the cross 4 4 is proportional section is modi ed from the one that corresponds to fully doublet 4 by factor At present, searches for anomalous production of multilepton events constrain only the case when both 4s decay to W and the limits on R 4 4 from table 2 of ref. [4]. They are summarized in our table 2 for reference values of m 4 . In our numerical analysis we interpolate these results for other values of m 4 . Similarly, the cross section of pp ! e4 4 is proportional to (gLW 4e4 )2 + (gRW 4e4 )2 where the couplings are given in eqs. (2.17){(2.18). Thus the cross section is modi ed from the BR2( 4 ! W ) can be read one that corresponds to fully doublet 4 and e4 by factor Re4 4 (VLy)42(UL)24 + (VLy)44(UL)44 2 + (VRy)44(UR)44 : 2 (4.15) The analysis in ref. [4], assuming me4 = m 4 , shows strong limits on this production cross section. Some decay modes of e4 and 4 are consistent with data only for masses higher than 500 GeV. In our analysis we are focusing on the case with no mixing in the charged 1 2 1 2 mixing in the neutral sector) and the limits on Re4 4 from table 2 of [4]. Other decay modes of 4 are not constrained in this case. The upper bounds are summarized in table 2. We again interpolate these results for other values ) = 1 (the required coupling originates from BR( 4 ! W ) can be obtained of m 4 . searches. Finally, let us comment on a single production of a new lepton. The W 4 T coupling results in a production of 4 through the process pp ! W ! can lead to at least 3 leptons with Emiss in the nal state. The bounds were discussed in 4 which also ref. [31] in the context of TeV scale seesaw models with very small lepton number violating terms, see for example ref. [32], which are not constrained from the same-sign dilepton The cross section of pp ! 4 is proportional to (gLW 4 )2 + (gRW 4 )2 where the couplings are given in eqs. (2.17){(2.18). Thus the cross section is modi ed from the one that corresponds to full strength coupling of the two leptons to W by factor R 4 (VLy)42(UL)22 + (VLy)44(UL)42 2 + (VRy)44(UR)42 2: We closely follow ref. [4] to set limits from the ATLAS searches for anomalous production of multilepton events [33] on three decay modes: pp ! W ! 4 ! W ; Z ; h ; where h is the SM Higgs with mass 125 GeV. The obtained upper bounds on R 4 BR( 4 ! W ; Z ; h ) are shown in gure 2 as functions of m 4 . We see that for any combination of branching ratios the constraint on R 4 is at most of O(10 2). This limit is much weaker than those obtained from precision EW data; in fact, for the surviving points in gure 1 the maximum value of R 4 is of O(10 3). (4.16) (4.17) In this section we explore the impact that this model has on pp ! (W W; H ! W W ) ! ` `0 0 measurements. We show detailed results for the two representative points (mH ; m 4 ) = (155 GeV; 135 GeV) and (250 GeV; 230 GeV) in gures 3 and 4. In gures 5{7 we show how these results vary for di erent values of mH and m 4 . In gure 3 we present the results of the scan described in section 4 for the reference point (mH ; m 4 ) = (155 GeV; 135 GeV) discussed in ref. [1]. The blue, cyan, magenta and red points have 4 with singlet fraction (j(VLy)45j2=2+j(VRy)45j2=2) in the ranges [0; 5]%, [5; 50]%, [50; 95]%, and [95; 100]%, respectively (note that in some of these plots blue/cyan/magenta colors are not easily distinguishable). In the two upper plots the black contours are the values of the e ective pp ! W W cross section as de ned in [1] for the e e and ([ NWPW ] ) nal states, respectively. In parenthesis we show the corresponding e ective pp ! H ! W W cross sections ([ NHP!W W ]e ; ). These e ective cross sections1 ([ NWPW ]e ) are explicitly de ned as: ) nal states and the NP and SM acceptances ANP and ASM are calculated using the experimental W W and H ! W W cuts (for the latter we follow ref. [34] and consider the six Higgs mass hypotheses discussed in refs. [35, 36] and show the most constraining e ective cross section). Note that points displayed in the two upper panels are identical and that the only di erence lies in the crucially on the very di erent acceptances for e and nal states as well as the factor NP W W contours that depend . Note that eq. (5.1) implies (5.1) (5.2) (5.3) NHP!W W = ANHP ASWMW ASHM ANWPW NWPW : The product of acceptances in this equation is the crucial parameter that controls the size of contributions to pp ! W W that are allowed by H ! W W searches. For most (but not all) masses that we consider, this ratio is of order 10% (typically ANHP=ASHM O(0:1) and ASWMW =ANWPW large di erence mH W W cross sections while simultaneously surviving H ! W W bounds. When the NP m 4 is large and m 4 is small, Emiss and mT increase while m`` decreases T O(1)). The smallness of ANHP=ASHM is the reason for which we can nd implying a larger ANHP=ASHM ratio. For instance, for mH = 250 GeV and m 4 = 135 GeV we nd that this ratio can be as large as 2. The yellow shaded area is excluded by H ! W W searches. The upper bound on the e ective NHP!W W cross section is independent of m 4 and is given by NHP!W W < min H H 95 ASHM 1 BR(W ! ` )2 ; where 9H5 is de ned in appendix A of ref. [1]. The measurement of the pp ! W W cross section is very sensitive to NNLO QCD corrections which have not been fully implemented 1An extended discussion of the e ective cross sections is presented in section 2 of ref. [1]. magenta and red points have singlet fraction in the ranges [0; 5]%, [5; 50]%, [50; 95]%, and [95; 100]%, respectively. In the two upper plots all constraints are imposed and we focus on the BR(H ! W ){tan plane for the e e and nal states, respectively. The black contours are the values of the e ective pp ! W W and pp ! H ! W W cross sections (in pb) de ned in eq. (5.1). The yellow shaded area is excluded by H ! W W searches. In the middle-left plot, we consider the R 4 4 BR( 4 ! W pp ! BR( 4 ! Z 4 4 ! W +W + ) BR( 4 ! W ). Here the light-shaded points do not satisfy the muon lifetime constraint and the impact of multilepton + ETmiss searches from Drell-Yan pair production process is indicated by the black curve. In the middle-right plot we show the ). Here the gray points are excluded by multilepton searches. In the two lower plots we consider the BR(H ! 4 ){BR( 4 ! W ) and H 4 { h 4 planes. in the experimental analysis yet. Following, for instance, the discussion around eq. (1.7) of ref. [1], the deviation of the pp ! W W cross section with respect to the SM expectation found by ATLAS [2] and CMS [37] are: ( [ NWPW ]eATLAS = (12:7+65::28) pb [ NWPW ]ATLAS = (9:9+87::03) pb and ( [ NWPW ]CMS = ( 0:1 e [ NWPW ]CMS = (4:5 Since these two results adopt di erent theoretical setups, we refrain from combining them into a weighted average. For this reason do not use pp ! W W data to constrain our model and simply quote the allowed values. A prominent feature of gure 3 is that for a doublet-like 4 the product of branching ratio BR(H ! W ) = BR(H ! small. This is mainly due to bounds from the multilepton plus Emiss searches in the DrellT Yan pair production process pp ! looking at the middle-left panel of gure 3 where we consider the R 4 4 {BR( 4 ! W ) plane. The quantity R 4 4 is de ned in eq. (4.14). Here the light colored points are obtained without imposing any of the constraints discussed in section 4 and the darker colored points are those that survive after imposing the muon lifetime bound. Additional constraints from oblique corrections are very strong (especially from the S parameter) but W +W + . This can be understood by in the [BR(H ! W region. ); tan ] plane they do not modify signi cantly the overall allowed Bounds from multilepton searches exclude the region above the black contour separatand large R 4 4 1 with low BR( 4 ! W ).2 ing the surviving points in two disconnected regions at low R 4 4 with BR( 4 ! W ) 70% At small R 4 4 the 4 is mostly singlet, the second term in eq. (3.16) is suppressed by a factor (VLy)44 with respect to the rst and the 4 Z coupling is controlled by the single quantity (VLy)42 (we remind the reader that (VL)22 is very close to 1). Under the assumption of no mixing in the charged sector, the matrix U is the identity and the 4 W coupling in eq. (3.13) is also controlled by the parameter (VLy)42. As a consequence the ratio of these two couplings is the same as in the SM (i.e. independent of avor mixing parameters), implying an almost constant 4 ! W mostly doublet, both terms in the 4 Z branching ratio ( 70%). At large R 4 4 the 4 is coupling are of similar size, and the 4 ! W branching ratio can acquire any value depending on the choice of input parameters. On top of this one should note that the 4 ! h channel is phase space suppressed for the case m 4 = 135 GeV. These considerations are also illustrated in the middle-right plot of gure 3 where we show the points in the BR( 4 ! Z ){BR( 4 ! W ) plane. Here the gray points are excluded by multilepton searches and, to a lesser extent, oblique corrections. The surviving region at large R 4 4 is also characterized by a very small H 4 coupling as we can see in the lower-left panel of gure 3. In fact, an almost completely 2Note that these arguments rely strongly on the particular choice of masses ((mH ; m 4 ) = (155 GeV; 135 GeV) in this case); a completely di erent situation characterizes the con guration presented in gure 4 and discussed later on. gure 3 for further details. doublet 4 requires very small couplings and , implying a strong suppression of the H 4 Yukawa coupling given, for doublet 4, in eq. (3.3). This can be seen in the lower-right panel of gure 3 where we show the values of the Yukawa couplings H 4 and h 4 for the points that survive all constraints. Therefore BR(H ! 4 ), and hence BR(H ! W are very small for doublet-like 4. If 4 is singlet-like, the SM-like Higgs Yukawa coupling ), is given, in the limit of small mixing, by h 4 N sin , see eq. (3.5). In this case, at xed MN , the muon lifetime limit (4.8) translates into a direct constraint on the Yukawa coupling h 4 . ); tan ] plane of the parameter scan described in the main text for various values of mH and m 4 . The black contours are the values of the e ective pp ! W W and pp ! H ! W W cross sections (in pb) for the e e in gure 3 for further details. nal state. See the caption In gure 4 we present the (mH ; m 4 ) = (250 GeV; 230 GeV) case. Now, the large 4 mass implies that the decay mode 4 ! h is no more phase space suppressed and can be dominant in large part of the parameter space as we can seen directly in the middle-right plot in large as 60%. On top of this, the constraint from multilepton + Emiss searches is weaker gure 4 and indirectly in the middle-left plot where BR( 4 ! W ) can only be as (this happens generally for m 4 > 150 GeV as we can see in table 2), implying that there is a large region of allowed parameter space in which the 4 is mostly doublet as can be seen in the two top plots in gure 4. Even though there are many points for which the 4 T doublet fraction is large, the corresponding values for BR(H ! W than for typical singlet points. This is because the H 4 ) are much smaller coupling for a doublet-like 4 is suppressed compared to the singlet-like 4 by vu=MN , see eqs. (3.3) and (3.5). From the bottom-right plot in gure 4 we see that the actual bounds on h 4 and H 4 are 0.05 and 0.17, respectively. Given that the ratio of these couplings is equal to tan , the second bound is e ectively set by the perturbativity request tan & 0:3. In gures 5 (for the e nal state) and 6 (for the nal state) we present the result of similar scans for (mH ; m 4 ) = (140 GeV; 135 GeV), (250 GeV; 135 GeV), ); tan ] plane of the parameter scan described in the main text for various values of mH and m 4 . The black contours are the values of the e ective pp ! W W and pp ! H ! W W cross sections (in pb) for the in gure 3 for further details. nal state. See the caption (155 GeV; 125 GeV) and (155 GeV; 150 GeV). The interpretation of these plots is similar to that of gure 3. The main di erence between these plots is the maximum value ). In gure 7 we show the BR( 4 ! Z ){BR( 4 ! W ) plane allowed for BR(H ! W for each set of masses. In gure 8 we show the envelopes of the allowed parameter space for a wide range of masses; in the left plot we take m 4 = 135 GeV and mH 2 [140; 250] GeV and in the right plot we have mH = 155 GeV and m 4 2 [125; 150] GeV. This e ect is due to change in the phase space available for H ! 4 ! W as the masses vary. Assuming that the acceptances ratios ANWPW =ASWMW and ANHP=ASHM remain constant when increasing the center of mass energy from 8 to 13 TeV, the NP W W contours in gures 3{6 will simply scale with pp ! mH = 250 GeV the rescaling factor is about 2.776 [38]. H production cross section. For instance, for Finally let us comment on the reach of the next LHC run at 13 TeV with a luminosity L = 100 fb 1 . Taking into account that (pp ! W W )t1h3 TeV= (pp ! W W )t8hTeV ' 2 [39] and that the uncertainty on NWPW is e8xTpeV Moreover, our new physics contributions to ' 5 pb (see eq. (5.4)), we estimate e1x3pTeV 3 pb. W W scale with the pp ! H cross section and NP Figure 7. Projection onto the [BR( 4 ! Z ); BR( 4 ! W )] plane of the parameter scan described in the main text for (mH ; m 4 ) = (140 GeV; 135 GeV), (250 GeV; 135 GeV), (155 GeV; 125 GeV) and (155 GeV; 150 GeV). See the caption in gure 3 for further details. and mH 2 [140; 250] GeV. In the right plot we take mH = 155 GeV and m 4 2 [125; 150] GeV. increase by a factor 2:5 [38] at 13 TeV. Taking these considerations into account, direct inspection of gures 3{6 shows that most of the presently allowed parameter space will be tested. For instance, with respect to the top-left panel of gure 3, LHC8 with 20 fb 1 is BR(H ! e4 ) BR(e4 ! W and nal state (right). ) = 1 (this de nition applies only here) for the e nal state (left) sensitive to points below the 5 pb contour while LHC13 with 100 fb 1 will be sensitive to points roughly below the 1.2 pb one (that will correspond to [ NWPW ]13 TeV ' 3 pb). 6 Contributions from H ! e4 In this section we discuss contributions to pp ! ``0 ` `0 stemming from heavy Higgs production and decay into a charged vectorlike lepton and a muon: pp ! H ! e4 ! W ! ` ` : (6.1) We begin our analysis with a model independent study of this channel along the lines of the analysis presented in ref. [1]. Our main results are summarized for the e and modes in the two panels of gure 9. These gures are very similar to blue contours are the values of the e ective W W cross section )). The yellow contours are the upper bounds on gure 1 of ref. [1]. The NP W W that we obtain for NP W W (in pb) implied ) BR(H ! are labelled with the value of BR(H ! W ) cot2 that leads to NP W W = 1 pb. by the H ! W W limits and are controlled by the dependence of our signal acceptances (for the W W and H ! W W analyses) on the H and e4 masses. The red dashed contours Focusing on the e case (for which there is a larger statistics), we see that in the bulk of the parameter space we consider the maximum allowed W W e ective cross sections are smaller than 10 pb and well within the allowed 2 experimental ranges (see eq. (5.4)). This is in contrast to what happens for H ! 4 as one can see from gure 1 of ref. [1] where H ! W W constraints allow for very large e ective W W cross sections in most of the parameter space. This feature is due to the di erent behavior of the ratio of acceptances ANWPW =ANHP for the H ! 4 and H ! e4 channels. This ratio controls the upper limit on the e ective W W cross section (as we explain in appendix A of ref. [1], the larger the ratio, the larger the allowed cross section). Both channels have similar ANWPW =ANHP ratio at moderately large mH and small m 4;e4 ; this implies that the 10 pb yellow contours for the 4 and e4 cases are close to each other. As we explain below, when moving to smaller mH and larger m 4;e4 the 4 ratio increases while the e4 one decreases. Because of this behavior, in the bulk of the parameter space in which we are interested (smaller mH and larger m 4;e4 ), we nd large allowed W W values for the H ! 4 NP channel but not for the H ! e4 one. The behavior of the acceptances ratio is essentially controlled by the di erence mH m 4;e4 . This di erence determines the transverse mass mT in the 4 case and the dilepton invariant mass m`` in the e4 one. The H ! W W acceptance decreases for channels with lower mT and increases for channels with lower m`` (because the CMS Higgs cuts include a range for mT and an upper bound on m``). The W W acceptance, on the other hand, is controlled by a m`` > 10(15) GeV cut (for e and nal states): for the e4 case it decreases at low mH me4 , while, for the 4 one, the dilepton invariant mass is controlled by m 4 and tends to always pass the cut implying a mild dependence of the W W acceptance on the choice of masses. In conclusion, small mH m 4;e4 implies a small acceptances ratio for e4 and a large one for 4 . The discussion of the mode is similar. The main di erences are that the experimental H ! W W cuts are much tighter in order to suppress Drell-Yan backgrounds and that the e ective cross section is enhanced by a combinatorial factor of 2 with respect to the e case (see eq. (5.1)). Note that in order to obtain similar e ective cross sections for the e and modes one needs to include a second vectorlike lepton family as discussed in section 4 of ref. [1]. charged lepton sector. Since the W W e ective cross sections that we nd in the H ! e4 channel are typically smaller than 10 pb, we refrain from performing a detailed scan that includes mixing in the 7 Contributions from SM-like Higgs boson In this section we consider exotic decays of the SM-like Higgs into vectorlike leptons. We begin by considering the h ! 4 ! W cross sections W W as a function of m 4 2 [95; 125] GeV for the e NP process. In gure 10 we show the e ective and modes. Here h we set BR( 4 ! W ) = 1 and consider two representative values of the avor violating Yukawa couplings j 4 j = 0:02 and 0:03. These values are close to the largest possible as one can see from the parameter scan presented in gure 11 where we show the j h 4 j { BR( 4 ! W ) plane for m 4 = 120 GeV. The thick solid red line in gure 10 is the 95% C.L. upper bound from the SM h ! W W ATLAS search [40]. We see that, for the e mode, Higgs searches are not constraining while in the mode they require m 4 & 105 GeV. In both cases, the e ective W W cross section cannot exceed 2{3 pb. These cross sections are far from the ranges allowed by ATLAS (blue shaded region) and the CMS upper bound (purple line) for the e nal state but are close to the allowed ATLAS region for the case (see eq. (5.4) and the related discussion). The thick solid red line in search [40]. as a function of m 4 2 [95; 125] GeV for the e and to the e ective cross section NWPW modes. We set BR( 4 ! W ) = 1 and h consider two representative values of the avor violating Yukawa couplings j gure 10 is the 95% C.L. upper bound from the SM h ! W W ATLAS 4 {BR( 4 ! W ) plane for m 4 = 120 GeV. Similar results are obtained for other choices of m 4 < 125 GeV. See the caption in gure 3 for further details on the scan. We do not discuss in detail the h ! e4 ! W process because we found that it does not lead to appreciably large e ective cross sections (typically smaller than 1 pb) and it is severely constrained by h ! W W searches. 8 Contributions from Drell-Yan production of vectorlike leptons In this section we discuss contributions to the e ective cross section the following vectorlike lepton Drell-Yan production processes (` = e; ): NP W W that stem from pp ! ( ; Z) ! e4 e4 ! W W pp ! Z ! 4 ! W ! ` 2 : ! 2`4 ; (8.1) (8.2) Z 4 j . 0:02. Similar bounds are found for di erent 4 masses. and gLZ 4 for m 4 = 110 GeV. We see that R 4 . 1:5 10 3 Note that there are many more processes (involving up to four light leptons in the nal state) that one can consider and the two modes we consider in eqs. (8.1) and (8.2) are the two most promising ones.3 The e4e4 pair production channel is avor diagonal and the Z e4 e4 coupling can be as large as the corresponding Z ` ` SM one. On the other hand, in the channel (8.2) the production of a single 4 is constrained by the values of the o -diagonal coupling g allowed by EW precision data. To quantify this e ect we de ne R 4 (gLZ 4 ) 2 g2=(4 cos2 W ) ; (8.3) SM process pp ! Z ! m 4 = 110 GeV. which shows how the production of 4 through Z boson is suppressed compared to the . In gure 12 we see that R 4 can be at most 1:5 10 3 for gure 13 we show the most optimistic values of e ective cross sections for the processes in eqs. (8.1) and (8.2). For the latter case we set R 4 Consequently one can see that allowed values of W W for the pp ! ( ; Z) ! e4e4 and NP BR( 4 ! W ) = 10 3. channels are at most of order 1 pb and 0:1 pb respectively. We studied decay modes of a heavy CP even Higgs boson, H ! 4 and H ! e4 followed by 4 ! W and e4 ! W , where e4 and 4 are the lightest charged and neutral mass eigenstates originating from vectorlike pairs of SU(2) doublet and singlet new leptons. We showed that, with Yukawa couplings as in two Higgs doublet model type-II, these decay modes, when kinematically open, can be large or even dominant. After imposing all the 3If more than two light charged leptons are present, the third hardest lepton must have pT < 7 GeV in order to avoid detection and this requirement suppresses the acceptance. NWPW [pb] for Drell-Yan processes. In the left panel we consider the channel pp ! ( ; Z) ! e4 e4 ! W W ! 2`4 assuming SM-like strength of the Z e4 vertex, BR(e4 ! W ! W ! ` 2 for R 4 ) = 1 and me4 = 105{250 GeV. In the right panel we show BR( 4 ! W ) = 10 3 and m 4 = 95{250 GeV. experimental constraints, the H ! 4 about 35%. decay channel can have branching ratio of up to As we discussed in sections 4 and 5, electroweak precision data impose very strong bounds on various gauge and Yukawa couplings: the new avor violating gauge couplings W 4 and gL Z 4 have to be smaller than O(10 2), the couplings of SM gauge bosons to , can deviate from their SM values by less 4 and H 4 are constrained to the second family of leptons, gL W and gL Z than 0:1%, and the avor violating Yukawa couplings h be smaller than 0:05 and 0:17, respectively. Focusing on pp ! H we studied possible e ects of this process on the measurements of pp ! W W and H ! W W . Contributions from this process to 2`2 nal states can be very large since only one W has to decay to leptons unlike in the case of pp ! W W and H ! W W . We present predictions of the model in terms of e ective cross sections for pp ! W W and H ! W W in e2 2 2 nal states from the region of the parameter space that satis es all available constraints including precision electroweak observables and constraints from pair production of vectorlike leptons. Parts of the parameter space are already excluded by these measurements and thus possible contributions to these processes can be as large as current experimental limits. Large contributions, close to current limits, favor small tan region of the parameter space. In addition, we studied correlation of the contributions to pp ! W W and H ! W W . We showed that, as a result of adopted cuts in experimental analyses, the contribution to pp ! W W can be more than an order of magnitude larger than the contribution to H ! W W . Thus more precise measurement of pp ! W W in future will signi cantly constrain the parameter space of the model. W Furthermore, we also considered possible contributions to pp ! W W from H ! e4 , from similar processes involving SM-like Higgs boson and from pair production of vectorlike leptons. These however lead to much smaller contribution to the e ective cross section for pp ! W W while satisfying limits from H ! W W and h ! W W in rst two cases. In the case of pair production of vectorlike leptons, the cross sections are very small, and the contribution to the e ective pp ! W W is at most of order 1 pb. Finally, as we discussed at the end of section 5, the next LHC run at 13 TeV with 100 fb 1 of integrated luminosity will be able to explore most of the parameter space currently allowed by electroweak precision data and H ! W W constraints. Acknowledgments RD thanks Hyung Do Kim and Seoul National University for kind hospitality during nal stages of this project. 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Radovan Dermíšek, Enrico Lunghi, Seodong Shin. Two Higgs doublet model with vectorlike leptons and contributions to pp → W W and H → W W, Journal of High Energy Physics, 2016, 119, DOI: 10.1007/JHEP02(2016)119