Even though the standard model of the strong and electroweak interactions has proven enormously successful, it need not be the case that a single Higgs-doublet field is responsible for giving masses to the weakly interacting vector bosons and the fermions. In this paper we explore the phenomenology of a Higgs sector for the standard model which contains both doublet and triplet fields [under SU(2)L]. The resulting Higgs bosons have many exotic features and surprising experimental signatures. Since a critical task of future accelerators will be to either discover or establish the nonexistence of Higgs bosons with mass below the TeV scale, it will be important to keep in mind the alternative possibilities characteristic of this and other nonminimal Higgs sectors. 1673It is useful to consider the transformation of the 4 and x fields under SU(2), XSU(2), , 4--. u,~u;, and tx-+ ULxUR, where UL,, = exp( -ieLXR^nL,, .TL,, 1, and the TL,, generators are represented as specified above. The SU(2)L and U(1) invariances of the standard model are to be associated with TL and T i , respectively. In particular, note that the U(1) hypercharge associated with the B field is represented by right multiplication by the appropriate T; matrix (so that Q = T; + T; ). The full SU(2), group will be associated with the custodial symmetry required to have p= 1. In particular, tree-level invariance for the gauge-boson-mass terms under the custodial SU(2), is arranged by giving the x0 and lo the same vacuum expectation value. [However, since the hypercharge interaction with the B field breaks the custodial SU(2), , there are potentially infinite contributions to p-1 at one loop. We shall return to this issue later.1 We define ( x O ) = ( $ ) = b , and also take (4°)=n/2/2. It will be convenient to use the notation where CH and sH are the cosine and sine of a doublettriplet mixing angle. We will also employ the subsidiary field for the complex neutral and charged fields, respectively. The W' and Z are given mass by absorbing the Goldstone bosons G : =cH4'+sH$*, ~! = i ( -c~~~~+ s~x~~). (2.6)The gauge-boson masses so obtained are A is a 2 X 2 representation of the Y = 2 complex triplet field,

Extensions of the Higgs sector of the standard model (SM) that employ only doublet and singlet Higgs-field representations are not the only ones that guarantee p= l at the tree level. Higgs sectors containing triplet (and higher) representations can be constructed in such a way that there is a treelevel custodial SU(2) symmetry yielding p = I. However, this custodial SU(2) is inevitably violated at the one-loop level. We explore the implications of this violation in the context of a Higgs sector containing triplet fields. In particular, we show that it leads to one-loop corrections t o p and to certain mixings among the Higgs bosons and gauge bosons of the model that are quadratically divergent, thereby creating a new naturalness problem for p and for certain Higgs-boson couplings. This new class of naturalness problems first arises for a Higgs sector with triplet representations. making such a sector an interesting case study. A priori, deviations from p= 1 induced at one loop are of arbitrary magnitude and sign. We demonstrate that the fine-tuning required to keep one-loop corrections to p and the Higgs-boson couplings small is similar in nature to that required in the SM to keep the SM Higgs-boson mass in the perturbative regime.

We discuss the relation between the CP symmetry and the custodial SU(2) symmetry in the Higgs sector. In particular, we show that CP violation in the Higgs-gauge sector is allowed only if the custodial SU(2) symmetry is broken. We exploit these facts to constrain CP violation using the experimental bounds on ρ−1. CP nonconservation in the Higgs-fermion interactions can also be constrained in a similar way although a possible exception is pointed out.