Higgs decay width in multiscalar doublet models

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1 PHYSICAL REVIEW D 77, (008) Higgs decay width in multiscalar doulet models Sonny Mantry, 1, * Michael Trott,, and Mark B. Wise 1, 1 California Institute of Technology, Pasadena, California 9115, USA Department of Physics, University of California at San Diego, La Jolla, California 9093, USA (Received 7 Septemer 007; pulished 17 January 008) We show that there are regions of parameter space in multiscalar doulet models where, in the first few hundred inverse femtoarns of data, the new charged and neutral scalars are not directly oservale at the LHC and yet the Higgs decay rate to is changed significantly from its standard model value. For a light Higgs with a mass less than 140 GeV, this can cause a large change in the numer of two photon and Higgs decay events expected at the LHC compared to the minimal standard model. In the models we consider, the principle of minimal flavor violation is used to suppress flavor changing neutral currents. This paper emphasizes the importance of measuring the properties of the Higgs oson at the LHC; for a range of parameters the model considered has new physics at the TeV scale that is invisile, in the first few hundred inverse femtoarns of integrated luminosity at the LHC, except indirectly through the measurement of Higgs oson properties. DOI: /PhysRevD PACS numers: Bn, Cp I. INTRODUCTION Experiments at the LHC will directly proe physics at the weak scale. Most physicists elieve that there is new physics at this energy scale, eyond what is in the minimal standard model (SM). This elief is motivated to a large extent y the hierarchy puzzle and y the fact that the scalar sector of the standard model has yet to e directly proed y experiment. The single doulet in the SM is the simplest example of a scalar sector ut many extensions have een studied. Amongst the most widely considered are two Higgs doulet models. 1 A prolem that immediately arises in such models is the possiility of flavor changing neutral current (FCNC) effects that are unacceptaly large. In particular, when the SM fermion fields couple to oth doulets, and the couplings are aritrary, FCNC effects are possile at tree level. Glashow and Weinerg gave a simple prescription for how to avoid such effects through imposing a discrete symmetry []. One can also suppress FCNC effects y adopting an ansatz suppressing the coupling of the new doulet [3 6]. In this paper, we use the principle of minimal flavor violation (MFV) [7 1] which causes tree level FCNC to vanish (or at least e suppressed y small mixing angles) in multidoulet models in a natural way. We are interested in the possile effects of new physics on the properties of the Higgs oson and we characterize the impact of new physics on the Higgs through an operator analysis [13 19]. We assume that the new physics mass scale M is much larger than the Higgs oson mass and add higher dimension operators that are invariant under the SU3SUU1 symmetry of the standard model. *mantry@theory.caltech.edu mrtrott@physics.ucsd.edu wise@theory.caltech.edu 1 See [1] for a review. Since the operators give small corrections to the SM, one does not expect them to influence standard model processes that are unsuppressed. For example, the Higgs coupling to W osons is an unsuppressed tree level coupling and new physics contriutions to it should e negligile. However the dominant Higgs production mechanism through gluon fusion, gg! h occurs at leading order in perturation theory through a top quark loop. Hence, in the SM it is suppressed and new physics can easily compete with the standard model contriution [13]. Similar remarks hold for the h! decay amplitude. Some of the tree level couplings of the standard model Higgs are also very small. For example, the Higgs to Yukawa coupling is of order m =v 0:75 10 and the Higgs to -quark Yukawa coupling is of order m =v 10. New physics characterized y higher dimension operators can also compete with the standard model in the h! [17] and h! decay amplitudes. A light Higgs with a mass less than 140 GeV is likely to e detected first through its decay to two photons despite the fact that the ranching ratio for this process is quite small, i.e. of order Early detection through its decay to, which has a ranching ratio around 10 1, may also e possile. The dominant decay mode is to pairs. However this decay mode is much harder to oserve ecause of large theoretical uncertainties 3 on the cross section of the irreducile SM ackground tt. An integrated luminosity of order 500 f 1 may e required to oserve the standard model Higgs in the channel. If the rate for h! decay is changed y a factor f from its standard Here v 50 GeV is the vacuum expectation value that spontaneously reaks the weak gauge group down to the electromagnetic gauge group. 3 See [0] for a recent review on production and detection of the Higgs and [1] for a recent study on the tt SM ackground =008=77(1)=013006(7) The American Physical Society

2 SONNY MANTRY, MICHAEL TROTT, AND MARK B. WISE PHYSICAL REVIEW D 77, (008) model value (ut other properties of the Higgs are left unaltered) then the numer of h! or h! decay events oserved at the LHC is changed y a factor where 1 1 f 1 Brh! SM ; (1) and Brh! SM is the SM ranching fraction of h!. Even though h! decay will not e directly oservale until there are many years of LHC data, its rate is of crucial importance for all measurale properties of the low mass Higgs. In this paper, we consider multidoulet scalar models. 4 For simplicity we restrict our attention to two scalar doulets H and S. Here H denotes the usual SM Higgs doulet with a mass less than 140 GeV. S is a new scalar doulet with a mass M 1 TeV and has the same quantum numers as the SM Higgs doulet H. We demonstrate that there are regions in parameter space for which the new doulet S will e invisile at the LHC, at least in the first few hundred inverse femtoarns of data. The largest oservale effect of this new doulet S will e order one shifts in the h! rate which in turn will affect the ranching ratios for all light Higgs decay channels. It is straightforward to generalize our results to a scenario with more than two scalar doulets. In addition to the SM Yukawa couplings of the doulet H, the doulet S has the following Yukawa couplings to the quarks, L Y D d R ~g D S y Q L U u R ~g U SQ L H:c: (4) We make use of the principal of minimal flavor violation. This results in small loop level FCNC through the appearance of Yukawa coupling matrices ~g D and ~g U in the loops. We assume that possile multiple insertions of the Yukawa matrices in Eq. (4) are suppressed. In this model, the physical quark masses are the result of the sum of contriutions from the coupling of quarks to H and S. Thus in the mass eigenstate asis, the Yukawa matrices ~g U;D do not satisfy the usual relation to physical quark masses. In the SM, g i U;D p mi =v. In the down quark sector, in the mass eigenstate asis, the couplings of the heavy scalar doulet are p L Y D d ~m d p R v Vy u L S D d ~m d R v d LS 0 H:c: (5) p Here V is the CKM matrix, ~g D ~md =v and ~m d is related to the physical down quark mass m d y II. THE TWO DOUBLET MODEL The scalar potential for the model we consider is given y 5 VH; S 4 H y H v M S y S S 4 Sy S g 1 S y HH y HH:c:g S y SH y H g 0 Sy HS y HH:c:g 00 Sy HH y S g 3 S y SS y HH:c:: () We assume the phase of S is adjusted so that g 1 is real. S appears with a positive mass term and acquires a vacuum expectation value only through its coupling to H, which undergoes the usual electroweak symmetry reaking. Since M is much greater than the weak scale v, the neutral component S 0 gets a vacuum expectation value that is much smaller than v hs 0 i g 1v 3 p v: (3) M 4 New physics in the form of a second scalar doulet with an unroken Z symmetry can also provide a component of dark matter and the effect of such a second doulet on the SM Higgs was recently examined in []. 5 We thank Lisa Randall for pointing out the sign error of g 1 in Eq. () in the previous version. m d ~m d p 1 D hs 0 i=v : (6) We assume that the constant U in Eq. (4) is very small so that the S coupling to the up-type quarks can e neglected. When U 1 the production of S via its coupling to the top quarks is suppressed. On the other hand, we take D to e large, D 10 and for simplicity we choose it to e real. Since the down type quark Yukawa couplings in the matrix ~g D are very small, the effective coupling D ~g D is still perturative. The choice of D 1 makes the coupling of quarks stronger to S compared to H resulting in a large shift in h! once S is integrated out. Thus, with U 1, D 1, and M v an almost invisile S can e produced at the LHC and will leave its footprint through large shifts in the h! rate. III. FCNC CONSTRAINTS Even though we imposed MFV eliminating the possiility of tree level FCNC, in our two doulet model, there are at one loop corrections to standard model FCNC processes. In particular, we want to check that the choice of j D j 10 1 is consistent with constraints from FCNC. Consider the weak radiative decay! s with two doulets [3]. Calculating the Feynman diagrams in Fig. 1 we find that charged S exchange induces at one loop the effective Hamiltonian,

3 HIGGS DECAY WIDTH IN MULTISCALAR DOUBLET MODELS PHYSICAL REVIEW D 77, (008) s s s s FIG. 1. The one loop contriution to! s due to the doulet S. H eff e m 96 t G F D M p VtsV ~m t ~m m s s R F L ; (7) where e<0 is the electron charge. For inclusive decay, this does not interfere with the standard model contriution from O 7 [4] since the strange quarks have opposite chirality. Hence, we find! s 1 D ~m s ~m m t : (8)! s SM 4C 7 m m M Taking D 10, g 1 1, M 1 TeV, and jc 7 m j 0:3 in Eq. (8)gives! s=! s SM 10 5, which is much too small to e oserved. 6 For exclusive decays there can e interference etween the standard model contriution and the contriution of the effective Hamiltonian in Eq. (7) ut there hadronic uncertainties cloud our aility to constrain the new physics [31,3]. There are contriutions from the interactions of the new doulet S to the Wilson coefficient C 7 that are proportional to D U and are not suppressed y ~m s =m. However, ecause we have focused on the region of parameter space where U is very small these have een omitted. Our assumption of very small U greatly diminishes the constraint that! s places on the model. IV. EFFECTS ON LIGHT HIGGS DECAYS So far we have descried the general features of the two doulet model we are considering and demonstrated the compatiility of a large j D j10 with! s constraints. Next we investigate how this simple extension of the SM affects light Higgs decay to quarks y integrating the heavy doulet S out of the theory to induce the effective operator L eff D H y H g 1 M d R ~g D H y Q L H:c: (9) 6 See [5,6] for the latest calculation of BR B! X s at NNLO in QCD and its comparison to the results from Baar [7,8] and Belle [9] as averaged y the Heavy Flavor Averaging Group [30]. The remaining uncertainties in theory and experiment preclude a exclusion of our model ased on! s constraints for the parameter space of interest. Including the effects of this operator and using Eqs. (3) and (6) we find that the h! rate is modified relative to the SM as h! 1 3v g 1 D =M 1: (10) h! SM 1 v g 1 D =M Note we have included terms suppressed y more powers of v =M in Eq. (10) which are accompanied y the large factor D. However, we can still consistently ignore the effects of dimension 8 operators contriuting to h! since their contriutions start at order D v 4 =M 4 1. At M 1 TeV, the parameter choices of g 1 0:5, D 10 or g 1 1, D 5 give the rate for h! which is 1.6 times its SM value. An even more dramatic effect is seen for the parameter choices of g 1, D 0 and g 1 1, D 10 which give a rate that is 11 and times the SM value, respectively. Thus, the presence of an additional TeV scale scalar doulet with a coupling to quarks aout 10 times the SM value can have dramatic changes in the decay width and ranching fractions of a light Higgs. For example, with g 1, D 0 the ranching ratio for the experimentally promising modes of h! and h! will e down y a factor of 1=80. Such a scenario would make detection of the light Higgs very difficult. On the other hand for g 1 1, D 10 in which case the h! rate is its SM value. In this case, the ranching fractions for h! and h! will increase y the factor 3 for m h 10 GeV. This would apply for Higgs searches at the Tevatron as well [33]. 7 One can also generalize the aove analysis to the lepton sector and induce a corresponding effective operator L eff H y H g 1 M e R~g H y L L H:c:; (11) which contriutes to the decay of the Higgs to charged leptons h!. By choosing a large value for one 7 New physics in the form of a massive fourth generation neutrino [34] or additional scalar singlets [35] have also een shown to affect the possiility of the detection of the Higgs at LHC

4 SONNY MANTRY, MICHAEL TROTT, AND MARK B. WISE PHYSICAL REVIEW D 77, (008) can similarly induce order one shifts in the decay rate to h!. Such order one shifts can e seen at the LHC in the experimentally promising channel of h!. The effect of the operator in Eq. (11) was recently studied in [17] where naturalness criteria were used to constrain the size of the Wilson coefficient. It was shown that order one shifts are indeed possile and compatile with experimental constraints. The ranching ratio for h! can e influenced oth y the effect of the operator in Eq. (11) on the rate for h! and y the effect of the operator in Eq. (9) on the total Higgs width. Order one shifts in the rate for h! can also affect the total width of the light Higgs since its ranching ratio is not negligile. For example, if m h 10 GeV then the ranching ratio for h! is aout 7%. As order one corrections are possile to partial decay widths for oth h! and h!, the relative impact of the two decays on the total width can e changed dramatically. This can make the total decay width even more sensitive to the effects of S. However, for the sake of simplicity we will assume in this paper that is small so that effects on the width of the Higgs from the coupling of S to leptons are negligile. The numer of oserved h! events can also e affected y higher dimension operators that induce a direct coupling etween h and and etween h and gg as discussed in [13]. The latter affects the Higgs production rate y gluon fusion. New physics effects of this form are distinguishale from a change in the total width as the new physics effects on the total width will cancel in the ratios of the numer of expected events for different Higgs production mechanisms and decay channels. V. PRODUCTION AND DECAY OF THE NEW SCALAR DOUBLET We now study the production and decay of the new scalar doulet S and discuss the possiility for its oservation at the LHC. The doulet contains new neutral and charged scalars with masses approximately equal to M. If M 1 TeV the LHC has enough energy to produce these states. However, we will show that for a range of parameters their production rates are quite small and that the dominant decay channels have poor experimental signatures making them invisile at the LHC, at least for the first few hundred inverse femtoarns of data. The production of the charged S is suppressed compared with the neutrals and the pseudoscalar S 0 I does not have a significant ranching ratio to the most promising detection channels WW and ZZ. Hence we present in detail a discussion of the neutral scalar. 8 Expanding H and S aout their vacuum expectation values we write 8 Similar conclusions hold for the charged scalar and neutral pseudoscalar. H 0 hh 0 ip h0 ; S 0 hs 0 i S0 R is0 I p : (1) The fields h 0 and S 0 R mix and the resulting mass eigenstate fields h and S R are approximately given y 9 h h 0 3g 1v M S0 R ; S R S 0 R 3g 1v M h0 : (13) The production rate for S R is very small. The dominant production mode is through! S R. In this process the initial and each come mostly from collinear gluon splitting and the remaining spectator quarks have very low transverse momentum to e oserved in the final state. The large logarithms associated with collinear gluon splitting into light quark pairs leads to an enhancement of the rate y one or orders of magnitude [36 38] over gg! S 10 R where the scalar is radiated off one of the final state -quarks. This is ecause the final state -quark which radiates the scalar is far offshell efore emission and thus the rate does not receive the enhancement of large logarithms associated with collinear gluon splitting. The cross section for! S R at leading log takes the form! S R LHC D ~m Z 1 dx M 3s v M =s x x; xs ; ; (14) where x; and x; are the quark and antiquark parton distriution functions, respectively, and s is the center of mass energy squared. The large logs from collinear gluon splitting are summed into the parton distriution functions y choosing M. As seen from Eq. (14), the! S R cross section receives an additional enhancement y a factor of D 100 compared to the production of a SM Higgs with the same mass. This production cross section as a function of the mass M is shown in Fig. as the solid lack curve. This curve was generated for the choice of D 10 and g 1 0:5. We see that at M 1 TeV the! S R cross section is aout 10 f. Thus, for 100 f 1 of data one can expect the production of aout 1000 neutral scalars S R from fusion. Note that this dominant production mechanism does not exist for the heavy charged scalars. The next largest production mode of S R is through gluon fusion and is given y a direct modification of the SM cross section [43] gg! S R LHC s M 64s v ~m M D I m 4m 3g 1v M M I F; M; s; (15) 4m t 9 We assume that the parameters in the scalar potential are real so there is no S 0 R S0 I mixing. 10 This result is ased on the NLO QCD calculation for tt h production in [39 4]

5 HIGGS DECAY WIDTH IN MULTISCALAR DOUBLET MODELS PHYSICAL REVIEW D 77, (008) S R Production qq! qqs R 3g1 v 1: (18) 10 qq! qqh SM M 5 The pattern of possile decays of the new scalars in the model depends on the mass splittings etween the various states. To simplify our discussion of the spectrum we neglect the S 0 R h0 mixing and assume that the coupling 1 constants in the scalar potential are real. Then there is no S 0 I S0 R mixing and the mass spectrum is 0.5 m S M g v ; σ f M GeV FIG.. The production cross section of! S R for the parameter choices of D 10 and g 1 0:5. The production cross section (for the same parameter choices) for gg! S R is approximately 0: f for M 800 GeV and falls quickly with increasing M and thus is not shown. The curve was generated using CTEQ5 parton distriution functions [47]. The and t masses were evaluated at 1 TeV using leading log running. We chose QCD 0:1 GeV and used the initial values m 4:6 GeV determined from converting the result of the 1S fit to the quark mass [48] and the value m t 170 GeV from the PDG [49] where we have used the functions F; M; s Z 1 M =s dx x gx; g M xs ; ; (16) m S 0 R m S 0 I M g g 0 M g g 0 g00 =v ; g00 =v : (19) We focus on the region of parameter space where the lightest scalar is S 0 R. For its decays it is important to include the effects of S 0 R h0 mixing. The most important decay modes of S R have the partial rates S R! tt 7g 1 v4 mt ; (0) 3M 3 v S R! 3j Dj M 8 ~m ; (1) v S R! W W g 1 v 16M ; () and Iy for y>1 which is given y [44] y 1 p y i log y Iy 1 y log p p y y 1 p y 1 4 : (17) Here gx; denotes the gluon parton distriution function. As seen in Eq. (15) this production channel receives significant contriutions from ottom and top loops. The ottom loop has a significant contriution due to the direct coupling of S R which involves D Although the direct coupling of S 0 R to the top quark is negligile for U 1, the top loop still gives a significant contriution due to the mixing of S 0 R with the Higgs h0. The gg! S R cross section as a function of the heavy scalar mass M is shown in Fig. as the dashed red curve. At M 1 TeV one can expect the production via gluon fusion of aout 8 neutral scalars S R for 100 f 1 of data. Other production mechanisms are similarly small. For example Higgs production (via vector-oson fusion) in association with massless jets, qq! qqh, where q fu; d; sg, is dominated y the Higgs eing radiated off a virtual W or Z oson. So S R! ZZ g 1 v 3M ; (3) S R! hh 9g 1 v 3M ; (4) S R! hhh 3g 1 M : (5) A plot of the ranching fractions of S R as a function of the mass M is shown in Fig. 3 for g 1 0:5, M 1 TeV, and D 10. The dominant decay channels are S R! hh and S R!. The S R! channel is known to have a large SM ackground. As we will discuss later, even the S! hh channel can e difficult to oserve. The final states where the S R decays to gauge osons and at least one of the gauge osons decays to electrons and/or muons have a cleaner experimental signature. Note that for the parameters used in Fig. 3 the total width of an S R scalar of mass 1 TeV is only 3 GeV. For comparison, note that the width of a standard model Higgs with a mass of 1 TeV is aout 700 GeV [45]. This is ecause of the small vacuum expectation value of the heavy doulet which suppresses the coupling of S R to two gauge osons

6 SONNY MANTRY, MICHAEL TROTT, AND MARK B. WISE PHYSICAL REVIEW D 77, (008) Branching Fractions for S R Decays BR M [GeV] FIG. 3 (color online). Branching fractions for S R decays as a function of its mass M. The solid lack curve denotes the ranching ratio for S R!, the gray very-long-dashed curve denotes S R! hh, the red short-dashed curve is for S R! tt, the lue medium-dashed curve is for S R! W W, and the green long-dashed curve is for S R! Z 0 Z 0. We have not shown the curve for S R! hhh in order to avoid too much clutter. These curves were generated with the parameter choices of D 10 and g 1 0:5. In Tale I we show the numer of expected events for 100 f 1 of data at the LHC when S R decays to gauge osons and M 1 TeV. For example with g 1 0:5, M 1 TeV, and D 10 we find that pp! S R X BrS R! W W BrW W! 0:05 f, where we have summed over l e, leading to aout five events with 100 f 1 of data. For these parameters, the heavy scalar S R will not e detected at the LHC in the first few hundred femtoarns of integrated luminosity. In fact, within much of the region of parameter space where the coupling of the new S-doulet to charge =3-quarks is suppressed (i.e., U very small) the heavy scalar degrees of freedom associated with the doulet S are difficult to detect at the LHC as shown in the first two columns of Tale I. However, as seen in the third column of Tale I, even with U small, there are regions of parameter space that are more promising for detection at LHC. For example, for g 1, M 1 TeV, and D 0 we find that pp! S R X BrS R! W W BrW W! 1:6 fand detection of the new heavy scalar S R at the LHC with a few hundred inverse femtoarns of integrated luminosity is more likely. In Tale II we show the numer of expected events when S R decays to a pair of light Higgses and one of them decays to the experimentally favored or channels. As seen in the tale, for the parameters chosen detection is unlikely. The numer of events in the last column are suppressed ecause for these parameters the Higgs decay rate to is enhanced y a factor of aout 100 which reduces the Higgs ranching ratio to and y a similar factor. VI. CONCLUDING REMARKS We have demonstrated that for regions of parameter space in multidoulet models the states of the new doulets are impossile to directly detect at LHC, using the first few hundred inverse femtoarns of data, and yet the effect of the new doulet on the total width of the light Higgs is very significant. In the simple two doulet model we considered in detail, the promising h! and h! signals at the LHC for detecting a light Higgs could e significantly enhanced or suppressed. This demonstration emphasizes TABLE I. Expected numer of events for 100 f 1 of data at the LHC in the experimentally favored decay modes of S R for different choices of the parameters g 1, D. The production cross section is the sum of the gg! S R LHC and! S R LHC cross sections. We use to denote either an electron or muon (i.e., we have summed over l e, ) and j denotes a single jet. We have chosen the mass of S R at M 1 TeV and a center of mass energy of 14 TeV. After realistic selection cuts, the final numer of accepted events will e lower. Decay channel g 1 0:5, D 10 g 1 1, D 5 g 1, D 0 S R! Z 0 Z 0! S R! Z 0 Z 0! S R! W W! S R! W W! jj; jj 3: : TABLE II. Expected numer of events for 100 f 1 of data at the LHC in the experimentally favored channels when S R first decays to a pair of light Higgses [46]. We have chosen the mass of S R at M 1 TeV and the Higgs mass at m h 10 GeV. Decay channel g 1 0:5, D 10 g 1 1, D 5 g 1, D 0 S R! hh! S R! hh!

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