Volume 150B, number 1,2,3 PHYSICS LETTERS 3 January 1985
P H E N O M E N O L O G Y O F S U P E R S Y M M E T R Y W I T H B R O K E N R - P A R I T Y
John ELLIS, G. GELMINI, C. JARLSKOG 1, G.G. ROSS 2 and J.W.F. VALLE 3 CERN, Geneva, Switzerland
Received 28 September 1984
In some phenomenological supersymmetric models R-parity (+ 1 for particles, -1 for sparticles) is spontaneously broken along with tau-lepton number L r by a vacuum expectation value o r of the tau sneutrino v r. To avoid excess stellar energy loss through majorons, there should also be explicit L z violation through right-handed neutrinos. To have a sufficiently light vr, either o r is very small which is unnatural and boring, and/or the Higgs mixing parameter e is very small. We find that in the limit e ~ 0:
- both the forward-backward asymmetry in e÷e- ~ r÷r - and the r lifetime are unchanged, - Z ° ~ ' v ± decays are possible where u± is an extra neutrino, - squarks and gluinos may decayinto r or vr, - the photino ~ can decay into vj_ff with a detectable secondary vertex, - single production of (R-odd) spartieles may occur.
Most studies o f supersymmetric phenomenology have concentrated on models in which there is an exactly con- served multiplicative quantum number called R-pari ty, which is + 1 for all conventional particles and - 1 for all their supersymmetric partners. In such models sparticles can only be pair-produced, they always decay into a lighter sparticle, and the lighter sparticle (probably the photino ~ is absolutely stable. However, it is easy to con- struct models in which R-pari ty is broken, either explicit ly together with lepton number, e.g. by a I-Iiggs-lepton coupling H'L in the superpotential P [ 1 ] , or else spontaneously by a sneutrino vacuum expectat ion value (01Ve,u, r 10) --- Oe,tt,r ~ 0 [2] . Indeed, it has recently been pointed out that o r = O((0lnl0)--- o) is a generic feature o f many phenom- enological supergravity models [3] , while Oe, u ~ 0 is possible but less likely. In view of the stringent upper limits on L e and L u violation, we concentrate on models with only o r 4: 0, in which L~ is spontaneously broken together with R-pari ty.
In this paper we explore the phenomenological constraints on models with spontaneous violation of R-pari ty and Lr , and propose some experimental signatures.
We start by writing down the mass matrix for the charged fermions mixing with the r:
hrO r hrO T- L
where Mi, i = 1,2 are the U(1), SU(2) (supersymmetry violating) contributions to gaugino masses, gi, i = 1,2 the
1 Present address: Department of Physics, University of Stockholm, Stockholm, Sweden. On leave from: Department of Physics, University of Bergen, Bergen, Norway.
2 Present address: Department of Theoretical Physics, University of Oxford, 1 Keble Road, Oxford, England. 3 On leave from: Theory Group, Rutherford Appleton Laboratory, Chilton, Didcot, Oxon OX11 0XQ, UK, and also University
Volume 150B, number 1,2,3 PHYSICS LETTERS 3 January 1985
gauge couplings, and h r is the tau Yukawa coupling to the H Higgs. For reasons which will become apparent when we discuss the mixing of neutral fermions, we are interested in the limit e ~ O. Because eq. (1) has zero determi- nant as h r ~ 0 there exists a light state, the physical "7.". Expressed in terms of left-handed two-component spi- nors, we have
"7." = (7 .+ - (2hrvor/g 2 r2)W +, (uT.- - o r H - ) / r ) , (2a)
of mass
m r = hr(U2 - o2)/r, and r = (v 2 + 02) 1/2. (2b,c)
We will return later to the phenomenological implications of the decomposition (2a) of what we call the physical 7..
The heavier eigenstates can easily be found in two interesting limits: (a) M 2 "~g2 V and (b) M 2 >>g2 V, where V = (r 2 + v'2) 1/2 . In case (a) we find
~l = (~V + + [o'M2/g2(r2 - 0'2)] fi '+ + (2Ohror/g 2 r2)~ -*, (off - + o r 7.-)/r + [rM2/g2(r 2 - o'2)1W-),
g2(o 2 + O2) 1/2 , (3a) M~
" H " - ( ~ ' + - [v'M2/g2(r2 - v ' 2 ) ] ~ + , ~ - - [M2/g2(r 2 - v'2)](vH - + o r r - ) ) , m g t ~ g 2 v', (4a)
while case (b) yields
"W" -~ (W+ + (o /Mz)H , W - + ( o / M z ) H - + (or/M2)7.-) , (3b)
Notice that in case (b) there is a light charged state which would have already been observed at PETRA unless M does not exceed t TeV or so. In any event, if it is light enough, it could also be observed in W-decay at the CERN p~ coUider.
The mass matrix for the neutral supersymmetry fermions mixing with the v r is
0 -g20/X/~ g20'/X/~ -g2or/x/'2
-Ov/x/~g2 M1 glv /X/~ - g l v ' / x / ~ glVr/X/r2
g l V/V~ 0 --e 0
g2v' /x/~ - g l v ' / x / ~ --e 0 0
[ -g2or/~ gxo/,/~ o o o
(~3 , g, riO, fi,O, v ) ( M 2 ~3
B
rio
/) r
(5)
For a viable theory there must be a light tau-neutrino v r. It has been recently argued that m v must be < 0(1 MeV) to avoid e+e-v decay [4]. In this case it is expected that the decay v r ~ 3v will typically prorceed only with life- time greater than the age of the universe [5]. Thus conventional limits on stable neutral relics should apply, un- less there are new fast decay modes.
The determinant of this mass matrix is e2v21"2Mrv'2 2 + g~M1)" There are various limits in which there will be a light neutral state (needed for the v_); namely, o r ~ O, or e -+ O, or M, , M, ~ oo. In the latter limit there are two
~ " 2 2 2 2 states with mass M 2 and M1 so the determinant of the remaining masses is e v r (g2M2 + g 1M1)/M1 M2" The case o r ~ 0 restores the usual supersymmetric phenomenology, with the exception that the lightest super-
symmetric state may be unstable. We will not consider this (boring) limit, but turn to the possibilities if Or/O' = 0(1).
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Volume 150B, number 1,2,3 PHYSICS LETTERS 3January 1985
Since M 1 a n d M 2 cannot be > > > O ( m w ) in order to keep the r neutrino mass < O ( 1 0 0 eV), e must be small ,1 .
e < I00 eV. (6)
In the limit e ~ 0, there are two massless states given by
"v r " = ( l / r ) (or r - or~IO), v± = ( l /V)[ (v ' [ r ) (orv r + oH 0) + rff'°], (7,8)
where V 2 = o 2 + o '2 + 02 and r 2 = o 2 + o 2. r r
Here we have used the freedom to choose a basis amongst the massless states so that u r is the SU(2) current eigenstate partner of the r - given in eq. (2a). This shows that the ~- lifetime is unchanged in this limit. For e small, but non-zero, the mass eigenstates will be mixtures of v r and v±, but the r decay rate will be only changed at most at O(e[mr)2, a negligibly small correction.
The remaining neutral eigenstates are orthogonal to v r and v±. They are given by
~b .z = N - l ( , " ~13 + b l ''~ + °'~ O - v 'H' O + vr vr ) ' (9)
where the N i are normalisation factors and a i and b i are given by
ai = - g 2 V2/X/~(X - M2), bi = g l V2/x/~(X - M1), (10)
and h i is the mass given by the solutions of
X(;k - MI) (X - M2) = 1 V 2 [g2(X _ M1 ) +g2(X _ M2)]" (1 l )
Let us consider the solution of eq. (10) in various limits. As discussed above the most interesting new possibility is (or/o') = O(1) and, indeed, in many models this is its natural value. What is the expectation for the other param- eters Mi, o? The -ino masses M i are supersymmetry breaking masses. In supergravity models with non-minimal ki- netic energy terms these masses appear at tree level and should be O(mw). Radiative corrections will split these masses at low scales, so we expect M~, > M 2 > M1, where M~~ is the gluino mass. Even if absent at tree level, in theories with a broken continuous R symmetry M i will be 0 ( ~ i m 3 / 2 ) through radiative corrections. In standard supersymmetric models the VEV of H 0 is expected to be of O(v'). In R parity breaking models this no longer is true and (o[o) can be arbitrarily small. However in order to preserve this pat tern o f electroweak symmetry break- down we should have h t > h b and so rio' > m b / m t. In table 1 we give the mass eigenstates ~k i for two interesting limits (a) Mi/g 2 V ,~ 1,2 and (b) Mi/g 2 V >> 1. Before we discuss their phenomenology we must first consider the scalar sector.
I f the only violation o f r lepton number is spontaneous ((v r) 4: 0), there exists a corresponding Goldstone bo- son, the majoron J [7]. The process 7 + e -+ J + e inside red giant stars would lead to excessive energy loss unless o r < 100 KeV [8] . Such a small though nonzero value of v r is unnatural from the point o f view of existing models and boring phenomenologically. Therefore we assume that lepton number is also violated explicitly. One way of doing this is via L-violating superpotential terms such as H'L or QQeL, or via analogous soft SUSY breaking terms. These possibilities have been considered in the literature [1,2,9], and we prefer an alternative with a long phenom- enological pedigree, namely L violation by right-handed neutrino mass terms
P 9 m N N N + (m f / v ' )NLH' , (12)
,1 The weaker bound • < 160 MeV (corresponding to the laboratory bound on the mass of the r-neutrino) holds if neutrinos can decay within the lifetime of the universe. Models exist [6] in which the vr decays into a Goldstone boson, the majoron, and another light neutrino. In this case additional singlet Higgs fields, whose VEV give large Majorana masses to the right-handed neutrinos should be included. Lepton number would then be only spontaneously broken and the majoron would be a true Goldstone boson but invisible.
,2 Notice that in this approximation the zino becomes a Dirac fermion. This is, however, not a general feature of these models, as can be seen, e.g., in table 1 (limit Co)).
144
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Volume 150B, number 1,2,3 PHYSICS LETTERS 3 January 1985
rt~312 m N
m312 rnN N # "" " ~ N
L H" L H' Fig. 1. Graphs giving rise to the soft LH' supersymmetry breaking term.
where m N and rnf are general matrices in flavor space. In these models it is necessary that the majoron be heavier than 10 MeV or so, so as not to have been produced in red giant stars whose characteristic temperature is T < O(1) MeV. The contribution from eq. (12) to the majoron mass is O((m 3/2 mu)l/2) where the neutrino mass has the usual form m~, = m~/m N. (Thus neutrinos would not decay through majoron emission.) For m u < 100 eV, (i.e. m n > 10 9 GeV fo~ mf ~ 10 GeV) consistent with the cosmological bounds, and m3/2 = 1 TeV, th~ majoron mass would be O(10 MeV) as required. We have found that in many models there are additional contributions to the majoron mass coming from induced soft terms of the form [LH'] A. For example the superpotential of eq. (12) plus an interaction term XN 3 leads, via the graphs of fig. 1, to a term ~ (~2/47r2)m219 LH', even in the limit m~
oo. This would generate a majoron mass m 2 = O((X2/azr2)m23/2) which is easily of'several GeV in magnitudeS" In this way one can live with VEVs for'Yr of order of o'. In this case J has significant components along the
Higgs directions and can be seen in axion searches in beam dump experiments. These exclude J with mass < 10 MeV, the same limit as we found from red giant stability.
A second Goldstone boson will arise in models with a Peccei-Quinn U(1) symmetry, under which H and H' transform differently. This axion-like field a will acquire a mass through an eH'H superpotential term,
m a = 0((em3/2)1/2). (13)
With the bound on e derived above, for m3/2 = 1 TeV, this gives m a = 10 MeV,just consistent with beam dump bounds. Thus there is an interesting narrow window for models with an approximate Peccei-Quinn symmetry, in which the pseudo-axion would soon be found while the vr (or v±) could play an important role in galaxy forma- tion.
Alternatively, one can construct models which do not possess a Peccei-Quinn U(1) symmetry when e ~ 0, for example by introducing a heavy gauge singlet chiral super field Y with superpotential couplings
P 3 H'HY, y3. (14)
In this case the pseudo-axion acquires a mass,
m a = O((k/Zn)m3/2), (15)
which can easily be large enough to avoid the bounds discussed previously. We turn now to the phenomenology of these R-parity breaking models. The main difference (cf. eq. (2a)) is
that the physical T- is a mixture mostly of the original r - , a current eigenstate, and H - , the higgsino carrying the same weak hypercharge. There are (in addition to v e and uu) two light "neutrino" states u r (the SU(2) dou- blet partner of the z - ) and the orthogonal combination, u± (of. eq. (8)). As discussed above, the r lifetime is es- sentiaUy unchanged.
e+e- ~ r+r - . The r + has very small mixing O(mr/mw) with the W+ while the ~-- only has substantial mixing ~vith the H - (2a), which has the same weak isospin 13 = -~ as the r - . Therefore the Z 0 couplings to the ~- are in- distinguishable from those of the standard model, and the total cross section and the forward-backward asymme- try in e+e - ~ T+T - are completely canonical.
Cosmological bounds. From eqs. (5)-(8) we see there are two light states which would be in kinetic equilibri- um during Big Bang Nucleosynthesis (BBN) [10]. This is just consistent with the bound that there should be at
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Volume 150B, number 1,2,3 PHYSICS LETTERS 3 January 1985
most one additional neutrino-like species. The (pseudo) majoron and (pseudo) axion do not contribute to the ef- fective neutrino number since their masses are >O(10) MeV.
W, Z decays• The new light neutrino states will also be produced in Z decays potentially in conflict with the UA2 experimental result [ I 1 ]
£xN~JA2~<0 (90%CL), ~<2 (95%CL). (16)
However this bound is obtained assuming a conventional W width and full strength Z coupling to v±. In the pres- ent model (limit (a)) ,3 this coupling may be substantially smaller than the usual coupling by a factor
g(Zv ± v ± )/g(Zv r vr) = (0 '2 - r2)/(o '2 + r2). (17)
Moreover, from eq. (4) we see that W ~ Hv± may be kinematically possible. Because of this the limit of eq. (16) does not directly apply.
Off-diagonal Z decays. Since we are mixing states with different 13 and Y it is possible in principle to have off- diagonal Z 0 couplings. It is easy to check using eqs. (2 ) - (4 ) that the Z 0 has no large off-diagonal couplings to charged fermions. However, eqs. (7 ) - (10) tell us that it can have sizeable off-diagonal couplings to neutral fer- talons. For example, in limit (a),
g(ZO'~v ± )/g( ZO~eve) = 2~¢~ g lg2 (M1 - M2 )ro'/g 3 V 3 = O ( m ~ / m z ). (18)
The above result means that the Z 0 could have a substantial decay rate into ~" + v±.
-~ qr, ~" -~ qv r, etc. We see from eq. (2) that decays into r + are suppressed by O(mr /mw) 2 coming from the W - admixture and into r - by O(mq/mw)2 coming from the ~'q H - coupling. We see from eqs. (7), (8) that decays • ' 2 D 0 into v r or v± are suppressed by O(mq /mw)2 or O((mq / m w ) v / v ) coming from the and ~ '0 admixture, or
~3 u d by (e /mw)2 coming from the W and ~'admixtures. We expect ~" ~ q + ~" (and ~"~ q + ?t + ~ to dominate as usual, if kinematically allowed. I f not, as is the case in
limit (b), the new decay modes may be significant.
decays. It is easy to see from (2) and table 1 (limit (a)) that there is no charged current coupling of the ~" to the z. Therefore ~" ~ r (ff ') decays do not occur• However, we saw that, for example in limit (a), there is a ~ - v± neutral current coupling (see eq. (18))• Therefore the ~ can decay into v±(e+e - or/~+/~- or r+r - or q?t or V v or ff v or ~ v ) with a rate P(~ ~ v-x) = O(G2m 5/192n 3) (rn~/rnz)2. Ifm~. ~< O(10) GeV the corre- e e u u r r . x ~ ~', sponding lifetime could easily be /> O(10 -~ ~)s, providing the useful signature of a separated decay vertex. The ~'-+ vx(Vv) decays would give a pure missing energy signature analogous to conventional stable photinos. For photinos lighter than O(1 GeV) (this value depends on the charged stau mass) we expect the radiative decay into neutrino plus a photon to be dominant. In this case there are strong cosmological limits on the lifetime. Typical- ly one requires r < O(10 s), which implies rn~- > O(1 MeV) so as to avoid photo disassociation of primordially synthesized light elements. (Alternatively, one could have extremely long lifetimes, r > O(1024 s) but this would require a ultralight photino, which is unlikely.)
Unstable photinos may be the clearest experimental signature of models with R-parity broken in the manner discussed in this paper ,4.
,3 In case (b),gV ~ Mi, there are additional couplings of the Z to neutral fermions. ,4 It may also be possible to choose parameters in the R-parity broken model in such a way that the photino decays invisibly in-
to a Goldstone boson and a neutrino. In such a case the usual experimental signature for the photino as missing energy would be recovered.
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Volume 150B, number 1,2,3 PHYSICS LETTERS 3 January 1985
g ~ , y ~ , - ~ _ _ _q_" _ _ _ . ~ q \ 0
el
g r~ -¢ ,~ ,~ . . . . . .
el'" el t q
(a)
~,V~
q
. . . . . . . . el
q 0
(b)
,el J
q
Fig. 2. Typical g~aphs leading to single production of supersymmetric (R-odd) states. (a) Gluino production. (b) Squark production.
Single production of squarks, gluinos, etc. If R-parity is broken, the new supersymmetric (R-odd) states may be singly produced. Typical graphs are shown in fig. 2. These modes are suppressed by O(mqu[Mw)2 or O((mqd/ MW)O'/o)2 as the r, v r, u± couple only through their ~0 and N 0' admixture.
For a top quark o f 0(40 GeV) mass the suppression factor is not large and the production of (Vv± would be sizeable. If (o'/o) is large the production of bb'vr or ±, b~ ' r - could also be appreciable. It is straightforward to ex- tend this analysis to the production of other supersymmetric states.
The work of J. Valle was partially supported by CNPq, Brazil.
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