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Volume 167B, number 2 PHYSICS LETTERS 6 February 1986

H I G G S - H Y P E R F E R M I O N INTERACTION AND LARGE MISSING TRANSVERSE ENERGY EVENTS

H. INAZAWA, T. MORII

College of Liberal Arts, Kobe University, Nada, Kobe 657, Japan

T. KITAZOE, S. TANAKA and T. WATANABE

Department of Physics, Kobe University, Nada, Kobe 657, Japan

Received 12 August 1985; revised manuscript received 13 November 1985

A strong Higgs-hyperfermion interaction in a two-Higgs-doublet model is introduced to explain the large missing transverse energy events. TT decaying from a high energy Higgs explain the monojet activity and b-b from another Higgs describe the two-jet activity. The A R G U S and the Crystal Ball experiments for the radiative decay constrain the monojet rate.

The discovery [1] of peculiar events associated with large missing transverse energy by the UA1 collaboration at the CERN ~p coUider may have shown the first rip of the minimal standard quark-lepton model. The salient features of the jet activity consist of: (A) the charge multiplicity (n c ~< 4) lower than that of a typical jet from quark and/or gluon at such high energies, E~ > 40 GeV, and (B) the rather small invariant jet mass termed narrow [ 1 ] . Also the 1984 run found similar events with jet multiplicity and effective mass slightly larger than those of the earlier events [2].

Most interest has been focused on the SUSY theory to explain these events [3]. The theory, however, tends to predict rather fat monojet events and also too many dijet events, though the prediction depends on a specific model. Recently the background has been estimated carefully. It is said that a sum of many kinds of QCD diagrams called Altarelli's "cocktail" amounts to I or 2 monojet events/100 nb -1 for 540 GeV energies [3,4]. However, the UA 1 collaboration describes that the monojet events have higher r likelihood than the QCD jets. Rubbia concluded at the Lepton-photon Conference (Kyoto, 1985) [5] that the missing energy story is not yet solved, stating: (1) A detailed Monte Carlo study of known physical processes predicts a number of missing energy events. (2) However, the data have a few more high E T narrow jets than expected; and: (3) Also two multi-jet events are found at high E T where backgrounds are estimated to be small.

The above features suggest the possibility that the origin of the jet is neither quark nor gluon. One of the sim- plest candidates is a jet originating from a single r. This possibility is, however, unlikely since UA1 has already ob- served those monojets which are not considered as a single r-jet. There are monojets whose size, multiplicity or invariant mass is larger than a z-jet. An idea is that a high-speed light Higgs particle H produced by ~p collision de- cays predominantly into r~ and that their subsequent decay pretends a monojet owing to almost parallel running of ~ [6]. Since the Higgs mass M H is 2m r < M H < 2m b in this scenario, the expected opening angle of r and ~ is restricted between 6 ° and 50 ° for various Higgs energies from 30 GeV to 50 GeV. The resulting hadronic cluster is consistent with a single jet which is def'med in pseudorapidity-azimuthal (r/-~b) space as d = (Ar~ 2 + A¢2)1/2 ~< 1.0 [7].

In the previous paper [8] we introduced bosonic states X 0 and X 8 (color singlet and octet states) which were bound states of heavy hyperfermions. When they were created through two-gluon fusion, the monojet process was considered as X 8 -+ g + Z 0 , Z 0 ~ v~. In this scheme, however, we had a fat monojet and had to introduce large

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g ~ monojet

X 0 //

g ~ V } missing V

Fig. 1. The diagram for the production of a composite Bose particle Xo through two-gluon fusion and its subsequent decay into a singly jet + ~T.

electromagnetic charges for U, D (Qu = 2, QD = 1) in order to get the actual production rate of the monojet. In the present paper we regard a Higgs as a source of a jet instead of a gluon. Consider a production process (see fig. l)

X 0 ~ H + Z 0 , zO~v~, H ~ r ~ - ~ j . (1)

Here we assume that X 0 is a 0 - bound state with mass around 140 GeV/c 2. The monojet production cross section is written for the two-gluon fusion process as

d'-yd° (pg ~ X0 -+ j + ~T ) = fan 0r2/am2)r(x0 ~ 2g) rr-1 {Mxo F(X0 .+ all)/[(m 2 _ M2 o)2 + M2 ° p2 (X 0 ~ all)] }

X B(X 0 -~ HZ0)B(Z 0 ~ v~)B(H ~ ~)B(~ ~j)R(y,M2),

R(y,M2x) = 2 M 2 M 2 (M~/S)fg/p(y, X)fg/~(y, X ),

(2)

where f l Xfglp(X,M2x) dx = 1/2. We can calculate the upper bound of the monojet production rate at X/~ -= 630 GeV by using F(X ~ 2g)

X B(X ~ HZ 0) <~ F(X 0 ~ all)/4 and B(H ~ r~)B(r~ -*j) ~< 1. When one chooses F(X 0 ~ all) = 20 GeV and B(Z 0 v~) = 0.18 for three generations, the upper bound of the cross section is 9(5) pb for Mxo = 140(150) GeV/c 2

with the help of the gluon distribution function of the GHR parametrization [9]. The gluon distribution function of EHLQ with set 1 parameters [10] gives a cross section smaller by 24% than the one in the GHR case. To take too large a F(X 0 ~ all) is unreasonable because of the E y distribution of a monojet.

The above result suggests that we have to have a model which predicts a cross section close to the upper bound. In what follows we study a model to realize such a large cross section. We assume a hyperfermion SU(2) doublet (Uai, D0i ) which has color degree of freedom ~ in SUc(3 ) and an extra internal space denoted by i = 1 ..... N. We set Qu = 2•3, QD = -1 /3 considering U, D as replica of ordinary quarks. Certainly X 8 -~ gZ 0 does not have a vis- ible contribution to the monojet rate with this charge assignment. The tight 0 - bound state of the lighter hyperfermion D is assumed to be X 0 having mass around 140 GeV/c 2

X0 = ( ~ i 3 , 5Di)[x/rf-~. (3)

Though the Higgs coupling to X 0 is fairly strong, it is difficult to reproduce the monojet event rates. When one assumes P(X 0 -~ all) to be several tens of GeV, the minimal one.Higgs-doublet model cannot reproduce the monojet event rate since it lacks adjustable free parameters. We take a two-Higgs-doublet model [11] in which we have two neutral Higgses H 1 and H2, one neutral pseudoscalar P and two charged Higgses H ± . They have interactions with U, D as

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Hin t = --(mD/Vl) sin ~ DDH 1 + (mu/O2) cos ~ UUH 1

+ (mD/Vl) cos ~ DDH 2 + (mu/V2) sin ~ UUH 2 + i(v2/vl)(mD/v ) D3,5 DP + i(vl/v2)(mu/V ) ~ 7 5 U P

+ v -1 [(v2/vl)mD~)(1 -- 75)U + (Vl/V2)muU(1 + 3,5)D ] n + + h.c. (4)

The Higgs bosons interact with ordinary quark/lepton with the same form as in eq. (4). It is actually possible to raise the monojet event rate in this model if one chooses a rather large ratio of the vacuum expectat ion values (VEVs), v2/v 1 [(02 + v2) 1/2 = o = 246 GeV] and an appropriate mixing angle ~. I t is also possible to have two-jet processes when the heavier Higgs plays a role. Note that the smaller Vl/V 2 promotes H ~ z~ but suppresses H -~ c~.

There is another problem to be considered. I f the decay modes X 0 -~ HI(2)P , H+H - are open in addit ion to X 0 --> gg, the branching ratio to X 0 -~ HZ 0 is suppressed and the rate becomes too small for the large missing transverse energy process (1). Therefore Mp > M x o and MH± > M X o / 2 is assumed in order to forbid X 0 ~ HI(2)P, H+H - . There is another suggestion against taking a small MH+. The allowable branching ratios for b ~ s + H 1 set the lower bound of MH÷ around 100 GeV/c 2 [12].

In this paper we study what roles H 1 and H 2 have in the large missing energy events and calculate each process numerically. H 1 is assumed to be the lighter one having mass between 2m~ and 2m b and is responsible for monojet product ion through (1). There are other decay modes o f ~ so that we have X 0 --> HIZ0 --> r~ ~ ej + ~T,/aj + ~T, e±/~± +~T . . . . . in which a lepton runs in a jet or e/a move in parallel. _When2m b <MH2 < 50 GeV/c 2, the process (1) will bring about two jets + missing energy events through H 2 --> bb or t t , giving a large opening angle between them. There are higher order diagrams like X 0 ~ HHZ 0 which contribute to a variety of product ion modes. Var- ious decay modes coming from the lowest order diagrams for large missing transverse energy events are shown in table 1 together with the typical product ion rates, which are calculated below.

The range of parameters Ol/O 2 and ~ are constrained by the monojet product ion rate through X 0 ~ H 1 + Z 0. They are also restricted by the T ~ H 1 + 3' decay to which the ARGUS [13] and the Crystal Ball [14] collabora-

Table 1 Various decay modes for X o ~ HZ ° and the production cross sections at x/~ -= 630 GeV, 2000 GeV in the case (ii) with the GHR gluon distribution function. Input parameters are ~ = 50 ° , ol/o2 = 0.19,Mx o = 140 GeV/c 2 , rn D = 100 GeV/c 2 , r(Xo ~ all) = 20 GeV. j denotes either a single jet activity including associated neutrinos or a pure hadronic jet. ~ stands for # or e.

X Decay modes (do/dy)ly=o (pb)

xfs = 630 GeV x/~ = 2000 GeV

Xo H1 Z0 ~J +~T a) 4.01 ~J +iT 1.14 ~gJ + ~T 2.44 X 10 -2 ~" +~T 2.75 X 10 -1

H2 ZO ~JJ +~T 4.82 ~JJ +~T 3.12

+/~T 3.12 ~ J J +~T 2.09 ~JJ +~T 5.24 × 10 -1 ~'~J +~T 5.24 X 10 -1 ~£~JJ +~T 3.06 × 10 -1 £~-JJ + P T 3.06 X 10 -1 ~ J J +~T 5.69 X 10 -2

9.15 × 101 2.60 × 101 5.17 × 10 -1 6.26

1.21 X 102 7.98 × 101 7.98 X 101 5.24 × 101 1.31 × 101 1.31 × 101 8.65 8.65 1.43

a) 9% of the monojet rate is from H 1 ~ cE and the rest is from HI ~ 7~.

237

Volume 167B, number 2

Table 2 Table for C X in eq. (5). ab

PHYSICS LETTERS 6 February 1986

cXoz ° 3 i~[l + (v2/vl) 2 ] sin2~

CXOz ° a i-g- [1 + (v21ol)=] cos2~

tions have set upper bounds. We begin with the former constraint. The decay width for X -+ HZ 0 is given as

P(X0__>HZ0 ) Xo 2 2 0 2 ~/2M2 =Cnzoa~af4rrl~( )1 (4N/ x z °)

X [MxMzo(Mzo - MH) + mD(M 2 - M 2 o - M2)] ]MxMzo(M Z +M H) + mD(M2H - M2o - MX2)]

X [MxM2 - m D ( M 2 - M 2 + M2)] -2 [(M2 - M2o + M2) 2 - 4M2M 2] 1/2, (5)

where a~ = ~2/4¢r = g2/4rr cos20w, t~f = f2/4rr = m2/arrv 2 and the "color" factor C x are shown in table 2. Other decay modes of X 0 are expressed similarly [8]. B(H -~ r~) is given as B ~ 1/[1 + (Ol-/O2) 2 cot2~]. B(r~ ~ j ) = B(r~ -~ q~w + ~t@) --- 0.42 and B(Z 0 --> vP) ---- 0.18 are obtained by assuming three generations for quark-lepton.

To evaluate the production rates for various modes, we take the following two typical cases for the Higgs masses:

(i)Mnl = 5 GeV/c 2, MH2 = 20 GeV/c 2, (ii)MH1 = 8 GeV/c 2, MH2 = 20 GeV/c 2,

together with m D = 100 GeV/c 2 and F(X 0 ~ all) = 20 GeV. The production rate does not depend on the mass MH2 largely, while the opening angle of two jets does. To study allowed ranges of parameters Vl/V 2 and ~.

We consider the latter constraints. The parameters Vl/O 2 and ~ cannot be moved freely in fig. 2, since the product branching ratio PB [= B(T ~ ?H1)B(H 1 ~ r~)] is bounded experimentally by the radiative decay o f t as [13, 14]

80

60

~v~ 40

20

0 0

.,+," Z--

.'\.. 21 ~ cs :~

t I 1 I l I I I I I I I

0.10 0.20 V! ~V 2

80

6O

40

20

' ' ' . o 1 ' 1 t ' ' I ~ ' ] I ' I ~

\ / / L.g/, / / / ,

. ..," o • / . ' / . . /I

7 '~" . ~ CS :I p b ~

t I I I I I i I i J i t

0.10 0.20 Vl/V2

Fig. 2. The monojet cross section at y = 0: CS = (da/dy)ly=0(PP ~ J + ~T) and the product branching ratio: PB = B( ' r ~ -rH 1 )B(H1 r~) for various values of ol/o2 and f. (a) is for the case (i) and (b) is for the case (ii). Solid lines show the cross section CS with

specific numerical values in pb, where the GHR gluon distribution function is used. The input parameters are x~ "= 630 GeV, MXo = 140 GeV/c 2, m D = 100 GeV/c 2, MzO = 93 GeV/c 2, M r 1.784 GeV/c2,Mc = 1.5 GeV[c 2 and sin20w = 0.223. Dot-dashed lines show PB for the typical numerical values corresponding to ARGUS and Crystal Ball bounds [13,14].

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PB < 1 X 10 -3

< I X 10 -2

P B < 2 X 10 -3

(2 - 3) X 10 -3

for MH1 < 8.4 GeV/c 2,

for 3.6 GeV/c 2 <MH1 < 9.46 GeV[c 2

for 6 GeV/c 2 <MHI < 8 GeV/c 2 ,

for 8 GeV/c 2 <MHa < 9 GeV/c 2

(ARGUS),

(Crystal Ball).

PB depends on two physical parameters, 01/02 and ~, and is calculated in the lowest order perturbation. The re- suits are shown in fig. 2 with the help of the experimental value B(T ~ £~) = 0.03. The typical production rates for each channel are exhibited in table 1 in the case (ii) by setting the parameters as 01/02 = 0.19 [12], ~ = 50 °, which are inside the ARGUS and the Crystal Ball bounds in fig. 2.

The calculated monojet production rate is at most several pb, which seems rather small. The model, however, has ambiguity in deciding the rate. When F(X 0 -~ all) is moved from 20 GeV to 30 GeV, the cross section is raised by 43% more than the one in table 1. B(Z 0 ~ vP) depends on the generation number and is bounded by 0.40 experimentally, corresponding to N v < 7 * 1 [16]. The resulting upper bound of the monojet production rate is twice larger than the one in table 1.

To raise the production rate we have to approach the border line in fig. 2, which is given by the ARGUS or the Crystal Ball collaboration. In fig. 3 we show PB versus MHI for some typical values of v 1/v 2 and ~ = 50 ° and com- pare it with the experimental bounds. From fig. 3 it seems possible to observe the lightest Higgs H 1 in the radiative decay T ~ ~,H 1 . However Ellis et al. [17] discussed that there are large reductions in calculating the branching ratio B(T -~ 7H1) due to perturbative QCD radiative corrections and mixing with P-wave bottomonium states. The

* l This value is consistent with other works. See, for example, ref. [ 15 ].

iI,,a

E : f

II rn

lo-2

10 -s

I I I

(I) i~

.I / I

A.J

I f I 4 6 8

MH! (GeV /c 2 )

10

Fig. 3. The MHI dependence of the product branching ratio PB in the lowest order perturbation. Solid lines represent the calculated PB for the case of (1) v l / 0 2 = 0.14, (2) v l / v 2 =

0.19 and (3) v l / v 2 = 0.24 with ~ = 50 °. Dotted and dot-dashed lines denote the ARGUS [13 ] and the Crystal Ball [14 ] bounds, respectively.

239


effects reduce the ratio by a factor 0 (2 ) so that the present model may require a far more sensitive search for T

?H 1 . The small magnitude of Ol/O 2 suppresses H 1 ~ c~ seriously. Thus a single jet originates mainly from the r~

channel and results in a slim one. The relative product ion ratio of X 0 ~ H1Z0 and X 0 + H2Z0 is decided by the mixing angle ~ according to eq. (4). 1 + j + ~T events in table 1 amount to about a quarter o f j + PT events and are a characteristic mode of the present model. Various product ion rates are calculated at Tevatron energy, where the copious product ion of large missing energy events will be seen.

Some comments are in order. (i) The two-jet cross section coming from the processes ~p ~ X0(Xs) + gg -~ j + j is below the unitari ty bound

of the cross section. The monoje t events originating from X 8 + gZ'°-~ j + ~T is about 1/19 of the ones from the process ( I ) . The product ion rate for X 8 ~ g? -~j + ? is about two times larger than the monojet rate.

(ii) H 1 and H 2 have large couplings to hyperfermions, whose typical magnitude is mD/o 1 ~-- 2.2. I t is interesting to study the higher order diagrams, ~-p ~ X -~ ZOHH. Various kinds of je t activities are expected in this connec-

tion. (iii) The minimal Weinberg-Salam model with one Higgs-doublet gives the monojet cross section two orders of

magnitude smaller than the experimental data. (iv) The hyper-glueball [6] , which is composed o f hyper-gauge bosons G mediating the force between hyper-

fermions, can be ejected from X 0 as a missing particle if it is lighter than X 0. (In QCD this is not the case.) We have not calculated this process because we are short of knowledge about the hyper-interactions.

In conclusion, it is said that the strong Higgs couplings to hyper-fermions in the two-Higgs-doublet model are able to reproduce the large missing transverse energy events. The situation is, however, in a critical stage to at- tain the monoje t event rate. The ARGUS-Crys t a l Ball experiments set another constraint on the model. To test the present model, however, it is hoped that the ongoing searches for T ~ ?H 1 will become more sensitive.

[1] UA1 CoUab., G. Arnison et al., Phys. Lett. 139B (1984) 115; UA1 Collab., C. Rubbia, Physics results of the UA1 Collaboration at the CERN proton-antiproton collider, presented at the Intern. Conf. on Neutrino physics and astrophysics (Nordkirchen, 1984), preprint CERN-EP/84-135 (1984); UA1 Collab., J. Rohlf, New physics from UA1, presented at the XXII Intern. Conf. on High energy physics (Leipzig, 1984), preprint CERN-EP/84-126 (1984).

[2] UA1 Collab., M. Mohammadi, Experimental observation of events with large missing transverse energy, presented at the Conf. on Collider physics at ultra-high energies (Aspen, (1985), preprint CERN-EP/85-52 (1985); J.L. Rosner, Searching for new neutral particles, preprint EFI 85/13 (1985).

[3] J. Ellis, talk presented at the 1985 Intern. Symp. on Lepton and photon interactions at high energies (Kyoto, 1985). [4] S.D. Ellis, R. Kleiss and W.J. Stkling, CERN preprint CERN-TH.4185/85; Phys. Lett. 154B (1985) 435. [5] C. Rubbia, talk presented at the 1985 Intern. Symp. on Lepton and photon interactions at high energies (Kyoto, 1985). [6] S.L. Glashow, Phys. Lett. 143B (1984) 130. [7] UA1 Collab., G. Arnison et al., Phys. Lett. 123B (1983) 115; Phys. Lett. 132B (1983) 214. [8] H. Inazawa, T. Morii, T. Kitazoe and T. Watanabe, Z. Phys. C28 (1985) 81. [9] M. Glilck, E. Hoffmann and E. Reya, Z. Phys. C13 (1982) 119.

[10] E. Eichten, I. Hinchlfffe, K. Lane and C. Quigg, Rev. Mod. Phys. 56 (1984) 579. [11] See, e.g.S.L. Glashow and S. Weinberg, Phys. Rev. D15 (1977) 1958;

R.D. Peccei and H.R. Quinn, Phys. Rev. Lett. 38 (1977) 1140; Phys. Rev. D16 (1977) 1791; D. Toussaint, Phys. Rev. DIS (1978) 1626; H.E. Haber, G.L. Kane and T. Sterling, Nucl. Phys. B161 (1979) 493; L.F. Abbott, P. Sikivie and M. Wise, Phys. Rev. D21 (1980) 1393.

[12] R.M. Barnett, G. Senjanovic, L. Wolfenstein and D. Wyler, Phys. Lett. 136B (1984) 191. [13] ARGUS Collab., H. Albrecht et al., Phys. Lett. 154B (1985) 452. [14] Crystall Ball Collab., C.W. Peck et al., SLAC-PUB-3380 and DESY-report 84-064 (1984);

H. Trost, contributed paper XXII Intern. Conf. on High energy physics (Leipzig, July, 1984); B. Niczyporuk, SLAC Summer Institute on Particle Physics (July-August, 1984).

[15] G.G. Athanasin and F.J. Gilman, Phys. Lett. 153B (1985) 274. [16] L. Mapelli, CERN preprint CERN-EP/85-84 (March, 1985);

UA2 CoUab., CERN preprint CENR-EP/85-166 (October 1985). [17] J. Ellis, K. Enqvist, D.V. Nanopoulos and S. Ritz, Phys. Lett. 158B (1985) 417.

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