Volume 238, number 1 PHYSICS LETTERS B 29 March 1990

RARE Z 0 DECAYS F R O M R-PARITY VIOLATION ~

Riccardo BARBIERI Physics Department, University of Pisa, 1-56010 Pisa, Italy and INFN, 1-56010 Pisa, Italy

David E. BRAHM, Lawrence J. HALL and Stephen D.H. HSU Physics Department, University of California, Berkeley, CA 94720, USA and Theoretical Physics Group, Lawrence Berkeley Laboratory, 1 Cyclotron Road, Berkeley, CA 94720, USA

Received 4 January 1990

Supersymmetric theories violating R-parity allow a sneutrino VEV, which mixes neutrinos with neutralinos (~o), and charged leptons with charginos ()U). This gives neutrinos a mass, and causes such distinctive Z ° decays as Z°~v~z ° and Z°--* z+~ -, where ~o and ~- subsequently decay. We place limits on these branching ratios from current neutrino mass limits.

I. Introduction

The supersymmetric s tandard model imposes a discrete symmetry called R-parity (Rp) to eliminate lepton- and baryon-number violation. As several authors have emphasized [ 1,2 ], there is no fundamental reason to believe nature conserves Rp, though one needs some symmetry (such as L or B separately) to avoid fast proton decay. Rp may be broken spontaneously or explicitly; in either case a sneutr ino VEV results.

As neutr ino VEV causes mixing of the neutr ino and zino, which gives neutr inos a mass. Thus, the v, mass l imit of 35 MeV restricts v~ < 5 GeV. The sneutr ino VEV also mixes charged leptons with winos. Since the gauge eigenstates being mixed have different couplings to the Z °, the Z ° couplings to the mass eigenstates are not diagonal, and decays such as Z ° ~ 9 ~ ° and Z ° ~ z + ~ - occur. Here Z °, Z- are the lightest neutral ino and chargino, respectively.

Most models violating Rp explicitly start with the term Lh 2 (h a is the Higgs responsible for up masses), and eliminate it by rotating the superfields L and h~. The resulting superpotential term QDCL allows Z ° and E- to decay to b-jets and a lepton. Models with spontaneous Rp-breaking also allow Eo and )~- to decay, though with

less distinctive signatures. We calculate the branching ratios for these Z ° decays to be as large as 3 × 10-s if my is at its experimental

limit, and supersymmetry parameters are favorable. I f z ° and ~ - are heavier than 45 GeV, this may be the best way to detect them at LEP I.

2. Fermion mass mixing

In the presence o f a sneutr ino VEV, the neutral fermion mass matrix is

This work was supported in part by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the US Department of Energy under Contract DE-AC03-76SF00098 and in part by the National Science Foundation under grant PHY85-15857.

86 0370-2693/90/$ 03.50 © Elsevier Science Publishers B.V. (North-Holland)

Volume 238, number 1 PHYSICS LETTERS B 29 March 1990

b 0 -½g'v, ½g 'v2 - ½ g ' v ~ \ / [ 3 \

([3 w -o-o , , o lifO/ hi h2 v ) [ - ~ g Vl ½gvl 0 --lZ ½g' V2 -- ½gY2 -- ].Z 0 0 / ~ ~0 ]

\ - ½g'u, ½gv~ 0 0 0 / \ v /

(1)

Here < h ° > = v, /x/2, < h2 ° > = Vz/x/2, and < v~ > = v~/~/2. We will assume gaugino masses scale as gauge couplings, b = 5oq/3ot2 = 0.49.

For given (/t, M) and v~/v2 we can diagonalize ( 1 ) to find the masses m~ and eigenvectors q~ for the five neutralinos Z ° (with g ° = v~). We fix v~ by setting m s = 35 MeV (see the Appendix); in the regions o f interest to us we find v~ < 5 GeV from

2 cos 0w v¢- ~ x/I (M2 /p)sv - f lMI , (2) g

where we define

b f l - l + ( b - 1 ) cos20w =0.81 ,

tan0v-~V~/v2, Cv-COS 0v, S v - s i n 0v, c x - c o s 20v, ST=--sin 20v. (3)

Let A be a diagonal matrix with entries (g /cos 0w) ( T 3 c - Q sin 2 0w) for each of the gauge eigenstates,

A - g diag (0, 0, ~, - ½, ½ ) . cos 0w

The the effective coupling o f Z ° to 9@ o is

Aerf=q~Aqi ,

and the branching ratio is

BR i=0.71(A~ff)ea2(1 1 a - 3 i ) , a i = - l - - ( m i / M z ) 2

In terms of Feynman diagrams, Z°-+%Z ° occurs through the diagrams of fig. 1. The charged fermion mass matrix is

(co- hi- x - ) x/r2Mwsv Iz -m~v~/vl h~ . gv~/ v/2 0 ms /\ z c /

(4)

(5)

(6)

(7)

In addition to the usual mixing of winos and higgsinos, diagonalization of this matrix mixes z - with the negative charginos % Regions o f (p, M) space are ruled out by requiring the charginos (except the z) to be heavier than 40 GeV [ 3,4 ] ; these masses are

m2 = ½ ( M 2 + I t2 + 2 M 2 ) -+x/~ (M2 + /z2+ 2 M 2 ) 2 - (M2wST - -M/t) 2 (8)

"~ Rotation ofz c is suppressed by mJM, and the physical z mass differs from me by O(m,v~/M2).The effect on tau physics is negligible.

= B, W , h l , h2,

Fig. 1. Z°-*%Z °.

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with m~ > m2. A err for Z°- ,z+% - is calculated as for the neutralinos, though now we can write it explicitly:

g2 V,/Z (--COS ~_ "~ A ] , ~ - 2x /2cosO w MzST_M/2 \ sinO_ ] ' (9)

where [ 5 ]

tan 2 0 - = 2 x/~ Mw ( #Cv + M s v ) / ( M 2 - It 2 + 2M~v CT ) • ( 10 )

The branching ratio is again given by eq. (6) .

3. B r a n c h i n g r a t i o s

We fix tan 0v = ¼, and plot branching ratio contours in the (~t, M ) plane. The region ruled out by an excessively light chargino [see eq. (8) ] is shaded. The region allowing observable cascade decays not involving the neu- trino, e.g.

L ~ f ~ (11)

is not shown, but can be found in refs. [4,6]. Branching ratios for Z ° o ~ Z ° are shown in fig. 2, while those for Z°-~x+Z - are shown in fig. 3. Where several mass eigenstates are lighter than Mz, their branching ratios have been added.

We note that models with additional particle content could increase the size of the mass matrix ( 1 ), preserv- ing the neut r ino-neut ra l ino mixing but leaving a massless eigenstate. The v~ would not be so tightly restricted, and the branching ratios could be larger than we predict here.

BR

20O

150

100

50

Z~uX e) C o n t o u r s in t h e / z -M P l a n e , V z / V 1 = 4

-400 - 2 0 0 0 /~ (GeV)

200 400

Fig. 2. Branching ratio Z°--,9,X °.

BR(Z~T+X -) Contours in the ~ - M Plane, Vz/V I = 4

2ool ! ' ' ' ' ! ~ ~ ' ~ " . ' I . . . . I _

i:;/m,- ",'!

loo ........ 5~

0 -400 --200 0 200 400

u (c~v)

Fig. 3. Branching ratio Z°~z+% -.

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4. Signatures

Neutralinos and charginos may decay either through the QDCL term or through their mixing with leptons. We consider these two cases separately.

4.1.2b-jet decays

Models with explicit Rp violation and a fairly light squark predict the 7( 0 and 7(- will decay through the Q3D~L 3 term, which arose from an L*--'hl rotation on the b mass term. Assuming t's are not kinematically allowed in the final state, 7(0 and 7(- decay as in fig. 4, 7(°~b6v, and 7(- --,bt3z-.

Thus the primary signatures are

ZO----~ 9¢7( ° Z° - - -~ x+7( - L_~ bgv~ ~ bl3x- " ( 12 )

The first is characterized by two b-jets with a large amount of missing mass. The average jet energy is larger than for the cascade decays of eq. (11 ). Background for this signature comes from fig. 5, but this standard- model diagram produces jets of other flavors equally often. Thus, a predominance of b-jets signals neutralino production.

The second has two b-jets and two z's. This signature is more challenging than the previous one, since it has little missing energy and momentum, and has four secondary vertices.

4.2. Decays from z-L mixing

In models without a QDCL term, or in which squarks are very heavy, 7(0 and 7(- decay through their mixing with L, as in fig. 6.

Thus the primary signatures are

Z O ~ 9@ 0 ZO----~ z+Z- ZO----~ 90~ ° ZO---~ x+7( - I ~ udz- ~ dflv~ ~ uuv~ ~ u0z- ' (13)

where (u, d) can be replaced by other flavors or by leptons. The first two are characterized by two jets and a z, with a missing energy but low missing mass. The third and

~0 "% • ~ b

(a)

Z- " . . . ~ u,d,e,s,b

(b)

Fig. 4. (a) ?~°-*b6v~, (b) Z--- ,bbx-. Fig. 5. Background for two-jet decays with missing mass.

~o

(n)

;'. ~ "¢ )(

V~ W ~ U zO Vx

d Z• v~ )(

Z" u

(b) u

Fig. 6. (a))~o decays, (b))~- decays.

u

u

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fourth are similar to the signatures of the previous subsection (and subject to the same background, fig. 5), but without the characteristic b-jet dominance.

5. Conclusions

If R-parity is violated and ,~, takes a VEV, Z ° decays involving a single neutralino or chargino can occur with branching ratios large enough to be seen at LEP I. )~o and )¢- subsequently decay to either b-jets and leptons, or jets and leptons, depending on the model. The decay Z ° ~ 2 b-jets+missing mass, is particularly distinctive. If ½Mz< mx<Mz, these rare Z ° decays may be the best way to observe neutralinos and charginos.

Acknowledgement

We wish to thank M. Barnett, G. Goldhaber, and E. Carlson for helpful conversations. L. Hall acknowledges a Sloan Foundat ion Fellowship and a Presidential Young Investigator's Award. D. Brahm acknowledges a National Science Foundat ion Graduate Fellowship. S. Hsu acknowledges a US DOE Fellowship.

Appendix. v mass limits

Standard cosmology rules out a stable 35 MeV v, which annihilates predominantly through the Z °. However, unstable 35 MeV v~'s produced in supernovae would decay and flood the galaxy with characteristic photons (511 keV from v ~ e + e - v , , or 17.5 MeV from v~-,veT). Below we give a few ways to circumvent these argu- ments and allow a 35 MeV neutrino:

(1) Make the decay v~--,e+e-v, occur very rapidly, with lifetime less than 1000 s. Then the decays occur within the supernova, and the photons are not detected from Earth. This increases the predicted supernova luminosity; however, since few 35 MeV v~'s are produced in the 3.5 MeV neutrinosphere, a small window may exist here. This idea also requires large violation of both x- and g-number: the coefficients of G°kLiLjECk would need to satisfy C~31× C121~ 4X 10 -5.

(2). Make v~ stable, and alter the standard cosmological picture. For example, let the universe reheat after inflation to only a few MeV. The v~'s do not overclose the universe; they could even be the cold dark matter. This idea requires low-temperature baryogenesis [ 7 ].

(3) Make v~ stable, and enhance the v~-9~ annihilation rate by introducing a singlet majoron M, the Goldstone bosons of broken lepton number [8 ]. Then v~9~--.MM prevents overclosure, as noticed by Carlson and Hall [ 9 ], and makes v, a dark matter candidate. We will present a supersymmetric singlet majoron model which links Rp and L-breaking in a future paper [ 2 ].

References

[ 1 ] C. Aulakh and R. Mohapatra, Phys. Lett. B 119 ( 1983 ) 136; F. Zwirner, Phys. Lett. B 132 (1983) 103. L.J. Hall and M. Suzuki, Nucl. Phys. B 231 (1984) 419; I.H. Lee, Nucl. Phys. B 246 (1984) 120; J. Ellis, G. Gelmini, C. Jarlskog, G.G. Ross and J.W.F. Valle, Phys. LeU. B 150 ( 1985 ) 142; G.G. Ross and J.W.F. Valle, Phys. Lett. B 151 ( 1985 ) 375; S. Dawson, Nucl. Phys. B 261 ( 1985 ) 297; R. Barbieri and A. Masiero, Nucl. Phys. B 267 (1986) 679;

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S. Dimopoulos and L.J. Hall, Phys. Lett. B 207 (1987) 210; S. Dimopoulos, R. Esmailzadeh, L.J. Hall and G.D. Starkman, SLAC report SLAC-PUB-4797 (September 1988), Phys. Rev. D, to be published; D. Brahm and L.J. Hall, Phys. Rev. D 40 (1989) 2449; H. K6nig, Z. Phys. C 44 (1989) 401.

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R. Barbieri, M. Frigeni and G.F. Giudice, Nucl. Phys. B 313 (1989) 725. [ 5 ] H.E. Haber and G.L. Kane, Phys. Rep. 117 ( 1985 ) 75. [6] J. Ellis, J.S. Hagelin, D.V. Nanopoulos and M. Srednicki, Phys. Lett. B 127 (1983) 233;

R. Barbieri, G. Gamberini, G.F. Giudice and G. Ridolfi, Phys. Lett. B 195 ( 1987 ) 500; Nucl. Phys. B 296 ( 1988 ) 75, and references therein.

[7] S. Dimopoulos and L.J. Hall, Phys. Lett. B 196 (1987) 135. [8] T. Chikashige, R. Mohapatra and R. Peccei, Phys. Lett. B 98 ( 1981 ) 265. [ 9 ] E.D. Carlson and L.J. Hall, Phys. Rev. D 40 (1989) 3187.

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