Searching for Doubly-Charged Higgs Bosons at Future Colliders J.F. Gunion (U.C. Davis), C. Loomis (Rutgers), and K.T. Pitts (Fermilab) ABSTRACT limitson the latter'svacuum expectation value (vev) required for 2 2 2 m =[cos m ]= 1 W ++ at tree-level are generally severe. W Z = Doubly-charged Higgs bosons ( ) appear in several =1=2 =1 (The ®rst singlerepresentation beyond T for which extensions to the Standard Model and can be relatively light. We T =3;Y = 4 T =0 regardless of the vev is , whose 3 member review the theoretical motivation for these states and present a =1 T =2 is doubly-charged.) Models with T and can have study of the discovery reach in future runs of the Fermilab Teva- =1 at tree-level by combining representations. However, tron for pair-produced doubly-charged Higgs bosons decaying such models generally require ®ne-tuning in order to preserve to like-sign lepton pairs. We also comment on the discovery po- =1 at one-loop. The simplest way to avoid all problems is to tential at other future colliders. either consider representations that simply do not have a neutral = 3 Y = 4 member (for example, a Y doublet or a triplet I. INTRODUCTION representation), or else models in which the vev of the neutral member is precisely zero. We will only consider models of this Doubly-charged Higgs bosons ( ) appear in exotic Higgs representations such as found in left-right symmetric models. type in what follows. Further constraints on Higgs representations arise if we re- m > 45 GeV The current experimental bound is [1] from a ++ 0 quire uni®cation of the coupling constants without intermediate ! search for Z at LEP. At the Tevatron, the two production mechanisms with poten- scale physics. In the Standard Model, uni®cation is possible for jY j =2 0 a relatively simple Higgs sector that includes a single p ! =Z X ! tially large cross section are pair production, p jY j =1 ++ triplet in combination with either one or two dou- X WW pp ! or single production via fusion, blets (the preferred number of doublets depends upon the pre- W X ! X W . However, existing phenomenolog- (m ) Z ical and theoretical constraints are only easily satis®ed if the cise value of s ). In the case of the minimal supersymmet- ric extension of the Standard Model, precise uni®cation requires W ! W coupling is vanishing (or very small). There- fore, in this analysis we will consider the discovery reach for de- exactly two doublet Higgs representations (plus possible sin- ++ glet representations); any extra doublet representations (includ- tecting pair production at the Tevatron. ing ones with a doubly-charged boson) or any number of triplet In many models, it is possible for the to couple to like- or higher representations would destroy uni®cation. However, ` W W ! sign lepton pairs, ` .Ifthe coupling is vanishing, it is then very likely that the doubly-charged Higgs by going beyond the minimal model and including appropriate intermediate-scale physics, supersymmetric models (in particu- ` will decay to ` via the lepton-number-violating coupling. lar, supersymmetric left-rightsymmetric models [5]) with triplet ! e e ! We will therefore concentrate upon , and higher representations can be made consistent with uni®ca- ! and . tion. ! ` ` ! W W Alternatively, if the and In short, the popular two-doublet MSSM need not be nature's couplings are both vanishing or very small, then the can have a suf®ciently long lifetime that it will decay outside the choice. We should be on the look-out for signatures of exotic ++ Higgs representations, the clearest of which would be the exis- detector. Identi®cation of the pair via the associated tence of a doubly-charged Higgs boson. Thus, it is important to dE =dx distributionsin the tracking chamber would then be pos- sible. consider how to search for and study such a particle. The phenomenology of the derives from its couplings. W ! Tri-linear couplings of the type W are not II. THEORETICAL MOTIVATION present in the absence of an enabling non-zero vev for the neu- 0 q Doubly-charged scalar particles abound in exotic Higgs rep- tral member (if present) of the representation, and q cou- resentations and appear in many models [2, 3, 4]. For example, plings are obviously absent. There are always couplings of the ++ Z; ! = 3 a Higgs doublet representation with Y contains a doubly- form . In addition, and of particular inter- ` ` ! charged and a singly-charged . If part of a multiplet est, there is the possibility of lepton-number-violating Y Q = T + = 2 3 couplings in some models. For the with a neutral member, a would immediately signal the 2 =1 presence of a Higgs representation with total isospin T or allowed cases are: Y = 2 higher. Most popular are the complex triplet Higgs rep- ` ` ! (T =0;T =0;Y = 4) ; 3 R R 1 resentations, such as those required in left-rightsymmetric mod- 1 ` ` ! (T = ;T = ;Y = 3) ; 3 (1) 0 L R 2 2 els, that contain a ,a and a . ` ` ! (T =1;T = 1;Y = 2) : 3 L In assessing the attractiveness of a Higgs sector model con- L taining a many constraints need to be considered. For =3;Y = 4 Note that the above cases do not include the T triplet and higher representations containing a neutral member, =1 T =1;Y = 4 representation that yields , nor the triplet =1=2;Y = 3 Work supported by U.S. Department of Energy and the National Science with no neutral member, but do include the T Foundation. doublet representation with no neutral member, and the popular 603 =1;Y = 2 T triplet representation. In left-right symmet- ric models there is a `right-handed' and a `left-handed' Higgs Y j =2 triplet, both with j . Our analysis applies to the left- handed triplet (whose neutral member must have a very small =1 vev to preserve ); the phenomenology of the right-handed triplet is completely different. Y j =2 In the case of a j triplet representation (to which we now specialize) the lepton-number-violating coupling to (left- handed) leptons is speci®ed by the Lagrangian form: T L = ih C +h:c:; ij 2 jL Y (2) iL = e; ; where i; j are generation indices, the 's are the two- =( ;` ) ` component left-handed lepton ®elds ( `L ), and L 2 is the 2 matrix of Higgs ®elds: p = 2 p : = (3) 0 = 2 h Limits on the ij coupling strengths come from many sources. h ! Experiments that place limits on the ij by virtue of the (g 2) ` ` couplings include Bhabha scattering, , muonium- ++ = + Figure 1: pair production cross section as a function ! e e e antimuonium conversion, and . These limits [3, 6] suggest small off-diagonal couplings (as assumed in our of mass for both the Tevatron and the LHC. analysis). Writing + ++ 2 2 e e ! jh j c m ( GeV ) ; In , kinematic reach is limited to `` `` (4) p < m s=2 230 240 GeV , i.e. no more than about at p 5 5 < < c 10 c 6 10 ee = 500 GeV the limits imply and . s a future NLC. We will ®nd that the discov- Regarding production mechanisms, the fusion process [3, 4, ery reach at the Tevatron can cover much, if not all, of this W W ! 7], , is absent since the required tri-linear cou- range, depending upon the dominant decay mode. The pling is zero if the vev of the neutral member (if there is one) of mass reach for pair production at a pp collider increases rapidly ++ =1 the Higgs representation is zero (as we assume so that with machine energy. Figure 1 shows the pair pro- p ++ ; =2TeV naturally). Single production of ( ) is possible duction cross section for both the Tevatron (at s )and + pair e e ep 0:9(0:24) fb m = in ( ) collisions at LEP2 (HERA) via diagrams involv- the LHC. At the Tevatron, at ++ + + 1 ! e e ! e e c ee 30 fb ing the or couplings. If 250(300) GeV. With total accumulated luminosity of saturates its upper limit, then LEP2 and HERA will probe up to (as planned for the TeV33 upgrade) there would be about 27(7) ++ m 150 GeV c ee [8, 9]. However, it is likely that is much events. The marginality of the latter number makes < 300 GeV smaller than its current bound and that these sources of single m it clear that will be the ultimate mass reach production will be negligible. possible at the Tevatron. ? ? ++ ;Z ! 0 Thus, we focus on pair production, the Decays of a are generally quite exotic [3, 4]. For ! W W cross section for which is determined entirely by the quantum coupling, the only two-body decays that B ! W ! numbers of the . For a general spin-0 boson , with weak might be important are , T Q f t q 3 3 ! ` ` isospin and charge , and a fermion , with and ,the and, if the lepton coupling is present, . Typ- f f ! B B pair-production cross section is: ically, the and have similar masses, in which case ( ! is likely to be disallowed. Thus, we will fo- 2 3 2Qq A(a + a ) L R s pair 2 2 W ` ` T =1;Y = 2 cus on the and ®nal states. For a (s) = 2Q q P + P Z 6 x y W W triplet we ®nd [3, 4] ) 2 2 2 3 3 2 A (a + a ) m 3 m g L R 3 W ; (1:3 GeV) ; +P = 2 ZZ (5) 2 2 16 100 GeV m W x y W W 2 3 m jh j c `` ` ` `` : = m (0:4 GeV) 5 10 100 GeV 8 (6) f f = where s is the center of mass energy squared, p 2 2 where is the usual phase space suppression factor, and we 1 4m =s x = sin y =1x A=T x Q W W W 3 W , W , ,, B 2 m = 360 GeV m = used Eq.