c IC/82/108

INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS

NECESSITY OF INTERMEDIATE MASS SCALES IN GRAND UNIFIED THEORIES WITH SPONTANEOUSLY BROKEN CP IHVARIAHCE

Goran Senjanovic INTERNATIONAL ATOMIC ENERGY AGENCY

UNITED NATIONS EDUCATIONAL, SCIENTIFIC AND CULTURAL ORGANIZATION 1982MIRAMARE-TRIESTE

IC/82/108

International Atomic Energy Agency and United Nations Educational Scientific and Cultural Organization

INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS

NECESSITY OF INTERMEDIATE MASS SCALES IN GRAND UNIFIED THEORIES f«TH SPONTANEOUSLY BROKEN CP INVARIANCE*

Goran Senjanovic" Physics Department, Brookhaven National Laboratory, Upton, N.Y.11973, USA** and International Centre for Theoretical Physics, Trieste, Italy

ABSTRACT

It Is demonstrated that the spontaneous breakdown of CP invariance in grand unified theories requires the presence of intermediate mass scales. The simplest realization is provided by weakly broken left-right symmetry in the context of SU(2). x SU{2)TJ x U(l)o nodel embedded in grand unified theories.

MIRAMARE - TRIESTE July 1982

* To be submitted for publication. ** Permanent address.

Almost two decades after its discovery, the origin of CP violation la symmetry breaking above K.rf in grand unified theories Since this provides the still not known. Although It can be broken explicitly in the original essence of our argument in favour of intermediate mass scales, and left-right Lsgrangian, in the context of unified gauge theories it is in many ways symmetry in particular, we repeat briefly tbenein features of our point. aesthetically pleasing to assume that symmetries like CP (or P) are exact symmetries of the original theory, broken only spontaneously through the Higgs 1.. SPONTANEOUS BREAKING OF CP INVARIANCE IN SU(5) mechanism ' . Actually, there are some physical arguments in favour of spontaneous CP violation The Higgs sector of the minimal SU(5> model, everybody knows, contains Ik multlplet T. and vector 1 representation ^ . He imagine the original theory (i) the resolution of the strong CP problem to be CP conserving in the absence of symmetry breaking, i.e. we take all (ii) the connection between CP and P violation. couplings to be real. Since by a gauge rotation < H^ can be made real, we need In the case (1), one can naturally construct, especially In the context the additional J>-plot H™ . of left-right symmetric theories, models with strong CP violation calculable and One searches for the CP violating minimum in the symbolic form small , with the parameter that measures its strength ©• ~ 10 . One thus 4) 5) = v H = el (1) eliminates the presence of the axion , which is either ruled out or °S invisible , in the case of Peccei-Quinn solution of strong CP problem. A where V V V2 and Ji are real numbers. The vacuum expectation values further interesting feature of left-right symmetric models of CP violation, is determine the scales of the theory: Mx = g Vx = 10 - 10 GeV and (ii) the possible connection between CP and P violation , through the natural M= g ( 2 + vZ ) "*=. 80 GeV. Now, in ref. 9, we have carefully analysed the 2 R v relation between the strength of CP breaking and (M / M ) ratio (K and !t Higgs potential and shown that the condition for nonvanishing takes the form WL WR WL W] are the masses of left-handed and right-handed gauge bosons, respectively). I (A + S cos rf. )MJ + C 0 (2) should add, though, that the connection between (i) and (ii) is still lacking at the moment. where A, B and C are functions of Higgs self couplings. But \\^ ° In what follows we shall, without further ado, concentrate on the question so the above condition, in order to hold true would require miraculous cancellation of the nature of spontaneous breaking of CP Invariance in the context of grand of parameters - another fine tuning. It is therefore in conflict with the unification. We will demonstrate the necessary existence of intermediate mass requirement of naturalness we have decided to follow. scales in grand unified models with CP broken spontaneously. The only requirement The source of the problem can be easily identified: the dominant term will be that no further ad hoc fine tuning of the parameters of the theory is "12 in the potential which knows about the CP phase oC is allowed, beyond the one needed to fix the original gauge hierarchy In practice that means that Higgs particle masses will be required to take on natural values determined by the basic mass scales of the theory. V(cO = ... (3) This in turn leads to the validity of the survival principle 9) for these particles, which can be most simply phrased as follows: only those particles which have to be light by whatever physical reason, do remain light: the others so that the minimum occurs for either ot = 0 or W , both CP conserving solution. become superheavy unless protected by some'symmetry. The learned reader can 9) already see the potential problem; since to have CP spontaneously broken we have We can offer a more physical argument 'to explain what is going on . To to increase the light sector of the theory beyond the minimal SU(2) x U(l) doublet. generate CP violation, two light SU(2)L x U(l) doublets are needed. However, Actually, recently Mohapatra and T?' have been able to d.««isrrate the in SU(5) one becomes superheavy. Let us show that. Denote the SU<2) doublets incompatibility of spontaneous breakdown of CP invariance with the single step from H (a - 1 , 2 ) by (t* and construct the following states (5) (4) ,

so that <") j« 0 , <<£'> = 0 . But then <|) contains the usual light physical it is seen that it automatically contains two SU{2)L x U(l.) doublets Higgs field, whereas

decouples from the effective low energy theory r direction, which makes theory a more natural candidate for spontaneous CP and so

This is clearly a general phenomenon, valid in theories with a single mass scale above My . We have discussed SU(5) case only for the sake of a simple o illustration. What are the ways out of this impasse? The simplest possibility is the existence of some symmetry, related to an intermediate mass scale which as In (1) . The phase c< naturally emerges in the minimal left-right symmetric

would keep the second SU(2)L x U(l) doublet relatively light, as to insure theory.

•=< + 0. Here I will discuss a simple and realistic model of weak interactions What is the difference between this case and the SU(5) example? Namely, which does that through the realization of left-right symmetry at fairly low since SU(2) x SU(2)n x U(l) is embedded in G , we could Imagine the L R D—ti energies. repetition of the situation we have encountered before, which would require wt = 0 . The answer is: left-right symmetry. Namely, since

My , and the other gets the We can imagine the following general pattern for a gauge group G that mass at most ~J fL . 10) contains left-right symmetric model based on SU(2) x SU{2)D x U(l)_ . groups' Alternatively, this means that Independently of unifying group G, the dominant term in the potential which knows about the phase will have the form ^l M^M2. COSOC . If Mj, is close to Mj, , one has the same problem as before; and so the condition of naturalness, therefore, leads to an approximate bound

SU(2) x SU(3)c jT^ O(l)e (7) where M^ < K^ S M^. and G 2 S0(l) . We shall see how the requirement of where, we should add, the most natural case is H.-' tL .

spontaneous CP breaking makes tL fairly low, i.e. 3M, £ M_ :£• (10-100)M,, . As repeatedly emphasised before, in order to produce spontaneous CP

To see that, recall that the minimal Higgs sector contains a. multiplet breaking naturally, without fine tuning of the parameters, we must have an intermediate symmetry. In this simplest example, parity must be restored at (2, 2, 0) (representation content under SU(2), SU(2),, and U(l)n T) which 1 . fairly low energies, independently of the phenomenological details of the theory. gives the mass to charged fermions and W? If we write this field in the matrix Li form 12)

Is this compatible with grand unification? The answer is yes , even in the REFERENCES AHD FOOTNOTES simplest S0(10) theory12^, and also SU(16).;13^ especially if the right-handed neutrino Is a heavy Majorana neutral lepton which does not participate In 1. For an original work, see T.D. Lee, Phys. Rev. D8, 1226 (1973). Also low energy charged or neutral current processes. R.N. Mohapatra and J.C. Fati, Phys. Rev. Dll, 560 (1975). The right-handed charged boson W could be as light as ~ 200 GeV, if 2 K 2. For a review and references on strong and weak CP violation, especially sin 9 H is simultaneously increased beyond the value in the standard model. The essential point is that the equivalent of the f parameter of the standard In the context of spontaneous syraietry breaking, see G. Senjanovic", model is allowed to be substantially larger than one, due to the presence of the Proceedings of the XX International Conference on High Energy Physics, additional neutral gauge boson. Wisconsin (1980), ed. H. Wolf. This paper contains many further references. Finally, we should comment on the usual cosmological objections to the models with discrete symmetries, such as L - R symmetry. If symmetry is restored 3. M.A.B. Beg and H.S. Tsao, Phys. Rev. Lett. 4^, 278 (1978); at high temperature, then there will domains ' of different vacuua, and too much R.N. Mohapatra and G. Senjanovic, Fhys. Lett. 79B, 283 (1978); energy would be stored in the domain walls. The answer to this, as we repeatedly H. Georgi, Hadr. J. I, 155 (1978). For further references, see ref. 2. emphasized, Is that symmetries may remain broken at high T, consistent with all 4. 3, Weinberg, Phys. Rev. Lett. «), 223 (1978); the requirements of quantum field theory. F. Wilczek, ibid 40, 279 (1978).

In summary, we have demonstrated the necessity of an intermediate low mass 5. See e.g. R. Feccei, Max-Planck preprint (1982). scale in GUTS In order to generate spontaneous CP violation. Our result was 6. J.E. Kim, Phys. Rev. Lett. 43_, 103 (1979); based on the recently demonstrated consequeaces of the survival principle for M. Dine, H. Fischler and M. Srednick, Phys. Lett. 104B, 199 (1981); Higgs boson masses: If only H^C <—• 10 T^) exists above IV. > CP phase has M. Wise, H. Georgi and S.L. Glashow, Phys, Rev. Lett. ^J_, 402 (1981). to vanish in the case of minimal fine tuning. In the simplest, realistic

SU(2)L x SU(2)R x U(1)BL left-right symmetric model of CP violation, we find 7. R. Peccel and H. Quinn, Phys. Rev. D16, 1791 (1977). that the scale of parity breaking should be no more than one or two orders of 8. Mohapatra and Pati, ref. 1. magnitude above M^ . This provides further strong motivation for the idea of 9. This has been discussed in detail by R.N. Mohapatra and G. Senjanovic1 low energy parity restoration, "Higgs effects in grand unified theories", BNL preprint (1982) and references therein. ACKNOWLEDGMEHTS 10. J.C. Pati and A. Salam, Phys. Rev. D10, 275 (1974); R.N. Mohapatra and J.C. Pati, Phys. Rev. Dll, 566; 2588 (1975); I wish to acknowledge the discussions with Jogesh Pati which have provided G. Senjanovic, and R.N. Mohapatra, Phys. Rev. D12_, 1502 (1975). an impetus to this work, and to thank him for suggestions on the manuscript. Thanks are due to Abdus Salad and Neil Craigie for the warta hospitality at the 11. G. Senjanovic", Nucl. Phys. B153, 334 (1979).

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