some phenomenological predictions of charged higgs bosons in electroweak interactions

Z, Phys, C - Particles and Fields 23, 175-180 (1984) Ze,sch,. P a r t i e s Eir Physik C

and Fields @ Springer-Verlag 1984

Some Phenomenological Predictions of Charged Higgs Bosons in Electroweak Interactions i

C.A. Garcia Canal and E.M. Santangelo

Laboratorio de Fisica Tedrica, Departamento de Fisica, 15niversidad Nacional de La Plata, C,C 67-La Plata, Argentina

Received 6 January 1984

Abstract. Some phenomenological consequences of an extended Salam-Weinberg model are studied. In particular, the existence, or absence, of e - # asymmetry in beam-dump experiments is analyzed and an increase in same sign dilepton cross sections is shown to exist due to the contribution of charged Higgs-mediated diagrams. The model is shown to be compatible with experimental results for other processes.

I. Introduction

The achievements of the minimal standard model for the electroweak interactions are widely known [1]. However, there exist various reasons, both phenomenological and theoretical, for believing that physics could go beyond iL From the theoretical side, we know that the building of grand unified theories [2] always implies the enlargement of the Higgs sector. The proposal of composite models and right handed currents are other currently explored possibilities. From a phenomenological point of view, beam- dump results and neutrino-produced same sign dileptons might find a sensible explanation in the framework of some extended model. Certainly, the simplest enlargement of the Higgs sector of the standard model is through the introduction of a second scalar doublet [3].

In this paper we analyze some phenomenological consequences of this extended standard model. In particular, we address ourselves to the study of neutrino production of same sign dileptons, an experimental evidence that has, for a long time, defied

1 Partially supported by CONICET, CIC Prov. de Buenos Aires and SUBCYT, Argentina

sensible explanations, We relate this study to the electron-muon asymmetry eventually present in beam- dump experiments [4] that we have revisited from this viewpoint_

We found that the inclusion of a second scalar doublet gives rise to an appreciable enhancement of the production rate of same sign dileptons in the mentioned neutrino-initiated reactions. This enhancement comes from the predicted new coupling of a charged Higgs particle to the fermion fields. This coupling, which is proportional to the fermion masses, introduces only one new parameter. It is precisely here, in connection with the fixing of this new parameter, that we find a possible phenomenological connection with the beam-dump experimental results. It was suggested [5] that a charged Higgs- mediated contribution to weak interactions could, under particular conditions, account for the e - /~ asymmetry shown by the Cern experiments [4]. We argue that the free parameter of the extended standard model can be adjusted by fitting these experimental results. It can also be determined in terms of the new Fermilab [6] data, where the asymmetry is almost absent. In this way we find a range of values for the unknown parameter of the model that are used in the calculation of the corresponding cross section for equal sign dileptons.

Needless to say, we have analyzed the compati- bility of the model with other well established and understood experimental results, as for example different sign neutrino produced dimuons.

In the present analysis, the enhancement of the cross section under consideration comes from the excitation, and further semileptonic decay, of bot- tomed mesons. For that reason we take profit of this study in order to evaluate the effects of different rescaling variables [7, 8] designed to cope with the

176 C.A. Garcla Canal and E.M. Santangelo: Phenomenological Predictions

threshold effects implied in the weak production of heavy flavours from heavy flavours.

The paper is organized as follows: In Sect. II, the extended version of the standard model is described. The determination of the free parameter from beam- dump experiments is done in Sect. III. In Sect. IV, the cross section of equal sign dilepton production is shown to increase when the contribution due to the production and decay of bot tomed measons is prop- erly taken into account. Finally, the conclusions of our analysis are detailed in Sect. V.

II. An Extension of the Salam-Weinberg Model

The number of Higgs isodoublets in the Salam- Weinberg model is not limited by any theoretical reason. The minimal version of this model makes use of only one scalar doublet for giving masses to the relevant fields. If one gives one step further and introduces two such doublets as

it can be shown [9] that the minimum condition on the Higgs potential determines the absolute values of both vacuum expectation values as well as their relative phase, allowing us to write

( q ~ ) = ( : ) ( ~ 2 ) =exp(i~)(20) (2)

with t/, 2 and e being real numbers. In order to identify the Goldstone bosons, com-

ing from the spontaneous breaking of the symmetry of the model, it is convenient to define the rotated fields

gives rise to a new contribution to the charged weak currents.

Let us first consider the interaction of the Higgs scalar with the quark fields, defined by the weak interaction eigenstates

U'= c' D '= s' .

\ t ' / \ b ' /

(6)

In order to suppress strangeness-changing neutral currents mediated by neutral Higgs, it is necessary to impose an extra discrete symmetry to the La- grangian [10]. We choose the one related to the changes:

/ U~ ~ U L D L ~ D r

~ l ~ ~2 4~2 ~ 452

U; ~ U~ D' R ~ D R

(7)

where as usual

TL= 1/2(1 --Ts) T TR= 1/2(1 +75) T.

Then, the most general SU(2) | U(1) interaction that preserves (7) is

~e= U~gl ~0 v i+6~gl ~7 v~

+/.TLg 2 @~- D~ --6L g2(~~ * D~ + H.C. (8)

where g~ and g2 are 3 x 3 matrices. From this last expression one can easily read the non-diagonal quark masses

M'v= - g i r l M'D=g22exp( - - i e ) . (9)

(P l = cos c ~ 1 + exp ( - it) sin ~ 2 (P2 = - sin eg' l + exp ( - it) cos c ~ 2

(3)

where

sin ~=,~(22 + r/2) -t/2 cos ~ = ~ (,~2 -~- ~2) -l/2 . (4)

Notice that only one of the rotated fields (3), q01, has a non-vanishing vacuum expectation value, given by

<(p 1) = ((~12 ~-0~2) 1/2 ) (5)

and for that reason it is called effective Higgs field: its charged components join the charged gauge fields in order to build the massive W -+ intermediate bosons, while one of its neutral components gives mass to the neutral carrier Z ~ On the other hand, the charged component of q)2, which does not combine,

After diagonalizing them and rotating the fields as in (3), we obtain for the quark-charged Higgs boson interaction

2'q, of = (g~~ 1/2 row) ~ {tan c~MvK(1-75 )

+ c ~ +75)} D +H.C. (10)

where M U and M v are the diagonal mass matrices, K the standard Kobayashi-Maskawa matrix, m w the intermediate boson mass and

tan ~=2/t/. (11)

Now the lepton-Higgs interaction is immediately obtained through the formal replacement

U - ~ L D -~ X (12)

C.A. Garcia Canal and E.M. Santangelo: Phenomenological Predictions 177

with

L = N = v,

\ v ~ /

(13)

and using the left-handedness of N, to get

Y'L, et = (g q) ~-/2 l f2 row) L tan eML(1 -- 75) N + H.C.

(14) where M L is the lepton mass matrix.

In what follows we shall consider the phenomenological implications of the condition tan ~ >> 1 and, for the sake of simplicity, we take m , = m a = m ~ = O , without loosing any generality.

Let us now go to the analysis of the model just introduced.

I lL Beam-dump e - / z Asymmetry

Beam-dump experiments are designed to detect neutrinos coming from the decay of short-lived particles produced at the target. They have, for a long time, shown a marked asymmetry in the number of v~ versus v e. This asymmetry is measured by

e = (y e -t- Ve)/(Y, -[- %) (15)

and the experimental value is

R -~ 2/3. (16)

In [5] it was already suggested the possible explanation of the asymmetry in terms of a new charged Higgs coupling. In order to obtain a quantitative prediction for the semileptonic bandwidth of the charmed hadrons-origin of R 4:1 - we need to com- pute the contribution of both diagrams in Fig. 1. Due to the fact that the coupling of the charged Higgs to leptons is proportional to their masses as shown by (14) we find that the contribution of diagram 1.b) can be ignored when calculating the decay into electrons as compared to the decay into muons. Moreover, in our analysis we neglect the contribution of the current (dc) due to the smallness of the corresponding mixing angle. Under the as- sumption IKscl 2= 1, we obtain

w + e w 4- 2 2 FSL = FSL + (1/4) r m u m ~ (17)

where we have introduced

r = tan , / m , (18)

which is the already mentioned free parameter of the model, and we remind that

S C . S C I, I ) . . . . . . . w ";

I i W§ I I (#+

el a) b)

Fig. 1 a and b. The two diagrams contributing to charm decay

Fs w = G 2 m~/(192n3). (19)

Notice that we have made the approximation m e ~>m C in obtaining (17), where m, and m c stand for the muon and charm masses respectively. On the other hand, the ( p - W interference term, being at least one order of magnitude smaller, can be safely neglected.

The extended model under consideration pre- sents another interesting prediction: a large bandwidth for the leptonic decay of charmed-strange mesons, F • into muon and neutrino. It results

r~e- 2 2 m~f#6~ -- (m C mu/8 ~z) r ~ (20)

where m F is the mass of the meson F and fv its decay constant. This constant has been calculated for example in the framework of the M I T bag model [-112.

In summary, considering both the contributions of the semileptonic decay of all the charmed mesons and of the purely leptonic decay of F, R can be written as

R = 1/(1 + (r~/r~ w) + (nF/,)(fUrrY)) (21)

here n v stands for the number of F • and n for the total number of charmed hadrons produced at the target. Taking into account the reported [12] value of nF/n, we found

r = 2.6 G e V - 1 (22)

as an adequate value for reproducing R = 2/3. It is important to remark that a similar asym-

metry is not present in other decay processes; for example, the coupling of the charged Higgs to the current (su) is extremely small due to the vanishing masses of the light quarks involved. This fact en- sures universality in kaon decays.

Going now to the case of B meson decay, notice that the main contribution of the charged Higgs comes from the current (bc) in the semileptonic mode. On the other hand, there is no purely leptonic two body decay contribution because charmed B

178 C.A. Garcla Canal and E.M. Santangelo: Phenomenological Predictions

mesons have not been detected yet. Then we can write

RB= 1/[ 1 2 2 2 4 + IKbr m~ m u r /4] (23)

which equals 0.89 when r=2 .6 and the standard values of the remaining parameters are used. This result is certainly in good agreement with the experimental result [13].

Let us similarly consider z-lepton decay. In this case we obtain R~=0.8 which agrees with the experimental values given in [14]. It should be remem- bered that is this case, two body leptonic decays are forbidden.

We should finally mention that most of the latest experiments [6] seem to loose the e - # asymmetry. If this were the case, the highest value of the parameter r that allows to fit R within experimental errors reduces to r=2 . Then we use in our further phenomenological analysis the two fitted values of the free parameter of the model i.e., r=2 .6 and r=2 .4

IV. Same sign Dilepton Production

We found that the presence of charged Higgs-mediated diagrams contributing to deep inelastic scattering processes are able to predict an increase in the production rate of same sign dileptons in neutrino-initiated reactions. These events could be inter- preted as coming from a >produced /)quark, which hadronizes and decays via cascade or through B ~ _/~o mixing�9

In the extended model, the cross section for /7- excitation is given by

da/dx dy = ( G 2 m N E~/270

�9 {[1 - ( 1 - x / ~ ) y - x y 2 / ~ ]

�9 + =]

+ 2~ ( #) lK~bl2 E l /4 r 4 m~2 m;,2 y2 2 2 2 2 +(r /2ruNE,. { )m c re, I} (24)

where x and y are the usual scaling variables, { a standard rescaling variable [7] taking into account the quark-mass thresholds, M u the nucleon mass and E~ the incident neutrino energy.

The B-meson fragmentation function is taken to be a delta function. Finally, the corresponding decay was considered through the product of a simplified spectrum and a five percent /7--,e- semileptonic branching ratio: ninety percent proceeds via cascade decay and the remaining through B ~ ~ mixing [16]. The resulting expression for the differential cross section of same sign dilepton production, in- cluding (24), then reads

163

I

i

NRR H / ; ' "CFRR

/]',,'/ *CHARM

20 60 100 140 180 220-E~ (C~v)

Fig. 2. E~-dependence of p=a(# # )/a(# ). Usual rescaling variable [7]. - ...... Standard model; . . . . . Enlarged model with r =2; - - - Enlarged model with r=2.6. All of them were calculated with me = 1.5 GeV and na b = 4.5 GeV

da/[dx d y d z(d 3 k/k0) ]

=(da/dx d y) D(z) B(B -+ I~ t X)

�9 [1/F dF/(d 3 k/ko) ] (25)

with the standard notation. The E<dependence of p = a ( # - p - ) / a ( ~ - ) for

both fitted values r = 2 and r=2 .6 are compared to the prediction of the standard model and to the experimental data in Fig. 2. This result should be considered as an upper bound to p since we have allowed up to one percent extrinsic charm content in the nucleon and we have used the largest currently accepted values of the Kobayashi-Maskawa parameters [16]. The curve corresponding to r=2.6 includes an additional contribution due to the e - # asymmetry implied in those events proceeding via cascade decay. We have taken a ( # - # - ) to be a factor 3/2 higher than a ( # - e - ) for these events, which amounts to consider the rate of F -+ fragment- ed equal to the ratio of F -+ to total charmed particles produced in beam-dump experiments. The available experimental results for # e production [17] seem to disagree with this prediction, though the data are not yet conclusive. The curve corresponding to r = 2 does not receive this contribution. Nevertheless, for both considered r values, an appreciable increase in the rate of like sign dimuons appears over the standard model prediction.

C.A�9 Garcia Canal and E.M. Santangelo: Phenomenological Predictions 179

~(F W) a~#c)

10-3

10 -z

i0-. c

J

1

r

�9 --4 7, /

/

/ /

t �9 , I

20 60

~- . . . . 2"-

/ ~ / /" /

I i i i i i I

100 140 180 220 E~ (Gev)

Fig. 3. E~-dependence of p. Modified rescaling variable [8]. Sym- bols are the same as in Fig. 1

~.-'(%)

1.2

1.

.8

.6

.4

i2

I l l I 1 I

!

- - f ! , ~ , ~

/

/

*CDHS ~BFHSM IF/ ~ L-'C~ bia [ �9 BCS Fe*

L L I l

20 60 100 140 180 220 Eo

(Gev) Fig. 4. E-dependence of p ' - a ( l l+)/a(l ). Both continuous curves correspond to r=2.6. The upper one is for dimuon and the lower one is for/~ e + production

We have taken profit of our scheme for recal- culating the Ev-dependence of p, but this time using the recently proposed rescaling variable [8]

4' = (Q2 +(mr + mb)2)/(2Mu V) (26)

which is supposed to be adequate for heavy-to-heavy quark transitions. The result is presented in Fig. 3, where all the curves are seen to be slightly higher than the corresponding ones in Fig. 2.

Before concluding, we want to analyze whether the predictions of the present version of the enlarged model agree with other well established neutrino- initiated experimental processes.

It has already been shown [18] that no con- tradiction arises for charged-current inclusive processes whenever r<40. However the situation was not so clear for the rate p'=a(l l+)/~(l -) of different sign dilepton production. We have considered, as usual, that they are coming from charm excitation and decay. If one includes the contribution of charged Higgs-mediated diagrams, the cross section for charm production reads

dcr/dx dy = (G 2 m u Evl2 ~)

�9 {[1 + (x) ~ - 1)y + x y2/~.]

�9 [(u(d) + d(~.))IKdcl 2 + 2s(~)IKscI 2]

+ 2s( ~) iKsci2(1/4 rr me2 m.Z y2 2 2 _ (r2/2 {2 mN E~) m c m.)} (27)

The resulting answer for p' shown in Fig. 4 includes a semileptonic c--*e + branching ratio of ten percent. Once again, the e - # asymmetry predicts an increase in p' for dimuon with respect to (e,#) for r=4 .3 which seems to be absent in the experimental data. For r = 2, which is compatible with no e - # asymmetry, the agreement with experimental results [19] is man- ifestedly maintained. Notice finally that had we used the variable 4', given in (26), no effect would have appeared because the charmed quark proceeds from light quarks in the nucleon.

V. Conc lus ions

We have analyzed some predictions of the enlarged Salam-Weinberg model with two Higgs doublets. The free parameter of the theory was fitted so as to reproduce the presence, or lack, of e - # asymmetric behaviour in beam-dump experiments�9 Both r values so obtained predict a considerable increase in the cross section for same sign dilepton production, but only the smallest r value, compatible with no asymmetry (which seems to be the trend of the latest beam-dump results), maintains an optimum accord with other well established experimental result, such as the cross section of different sign dilepton production.

We would like to stress that our numbers were given to illustrate the order of magnitude of charged Higgs effects and their inherent theoretical viability

180 C.A. Garcia Canal and E.M. Santangelo: Phenomenological Predictions

even if some variations around them could be ex- pected from changes of fragmentation functions, branching ratios, etc.

Acknowledgements. We wish to thank all members of the Labora- torio de Fisica Tedrica and, specially, Dr. Huner Fanchiotti for many useful remarks about the manuscript. We also thank Fun- daci6n Sauberan for financial support to our library.

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some phenomenological predictions of charged higgs bosons in electroweak interactions

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