New constraints on lepton nonconserving R-parity violating couplings

20June1996

PHYSICS

LETTERS B

Physics Letters B 378 (1996) 153-158

ELSEVIER

New constraints on lepton nonconserving R-parity violating couplings Debajyoti

Choudhury a*1,Probir Roy b-2

a Max-Planck-Institut fLir Physik, Werner-Heisenberg-Institut, Fiihringer Ring 6, 80805 Miinchen, Germany ’ Institute of Theoretical Physics, Santa Barbara, CA 93106, USA and Theoretical Physics Group, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India 3

Received 23 March 1996 Editor: PV. Landshoff

Abstract Strong upper bounds are derived on certain product combinations of lepton nonconserving couplings in the minimal supersymmetric standard model with explicit R-parity violation. The input is information from rare leptonic decays of the long-lived neutral kaon, the muon and the mu as well as from the mixings of neutral K- and B-mesons. One of these bounds is comparable and another superior to corresponding ones obtained recently from neutrinoless double beta decay.

The minimal supersymmetric standard model MSSM [ 1] is now a leading candidate for physics beyond the standard model. A natural question to ask is whether global conservation laws (such as those of baryon number B and lepton number L), valid in the standard model, hold as one goes to MSSM. This is related to the question of R-parity ( Rp = (-1) 3E+L+2s, with S the intrinsic spin [ 2] ) conservation for which no credible theoretical argument is in existence. It is therefore important to consider the phenomenology of possible R,,-violating terms [ 3,4] in the Lagrangian. We direct our attention to scenarios [3,4] of explicit R,,-violation instead of those with a spontaneous one since the former can be accommodated within the particle/sparticle spectrum of MSSM while the latter needs at least one additional singlet superfield.

’ E-mail: [email protected]. 2 E-mail: [email protected]. ’ Permanent address. 0370-2693/96/$12.00 Copyright PIZ SO370-2693(96>00444-3

0 1996 Published

It is difficult to accommodate both L-violating and B-violating J$ terms within the constraints of proton decay [ 51. Assuming that the baryon-number violating terms are identically zero [6] helps evade this constraint in a natural way, apart from rendering simpler the cosmological requirement of the survival of GUT baryogenesis through to the present day. This survival can then be assured if at least one of the lepton numbers Li is conserved over cosmological time scales [ 71. The R,-violating and lepton-nonconserving part of the superpotential, with the MSSM super-fields in usual notation, involves two kinds of couplings and Afik (i, j, k being family indices), and can be written as’ Aijk

W = k’&jkLiL.jz

+

A~jkLiQjDk,

where We have here omitted possible bilinear terms as they are not relevant to the discussion. Most phenomenological studies of these cou&jk

=

-A,jik.

by Elsevier Science B.V. All rights reserved.

D. Choudhury, P. Roy/Physics

154

plings have been aimed at deriving upper bounds [ 81 on the magnitudes of individual A- or A’-coupling in terms of observed or unobserved processes. However, recently there has been some interest in deriving bounds on the products [9,5,10,1 I] of two such couplings which are stronger than the products of known bounds on the respective individual couplings. This will be the approach taken here. Before such an analysis is attempted, one needs to consider the possible effects of fermion mixing on the $[, sector [ 5,111, if only because this can itself be a cause for the simultaneous presence of more than one such coupling. These effects are twofold. For one, it is, in some sense, more natural to consider Eq. (1) to be defined in the gauge basis rather than in the mass basis. In that case, even if there were only one particular nonzero A’-coupling, quark mixing would generate a plethora of such couplings, albeit related to one another. In this Letter, we do not confine ourselves to this particular theoretical motivation, but rather consider the most general lepton number violating 8, sector. The second effect is more subtle. Since the CabibboKobayashi-Maskawa matrix K is different from identity, the SU( 2) L symmetry of the A’ terms is no longer manifest when rexpressed in terms of the mass eigenstates. To wit,

\

/

P

where the A& have already been redefined to absorb some field rotation effects. In Eq. (2) we have chosen to suppress the effects of possible non-alignment of fermion and sfermion mass matrices. However, since any such non-alignment is already constrained severely [ 121, it is reasonable to neglect such interplay of different effects. In terms of the component fields, the interaction term in the Lagrangian density can then be expressed as cl

= hijk

+

h;ik

-

C

FiLGejL

fiiLGd,iL

!I,

+

ZjLGViL

+

_d,iL.dkRZ’iL+ GR(

(BiLdkRupL

+

+

t?;~ ( ViL)Ce,iL

ViL)

Letters B 378 (1996) 153-158

Here e (Z) stands for a charged lepton (slepton) and the fields for the other particles have been designated by the corresponding name letters. We first consider the constraints on products of A’couplings given by our knowledge of the neutral Band K-meson mass levels. The mass difference SmB between Bt and B2 (and similarly 6rnK between Kt and K2) arises out of the mixing between the Bz, @ (and Ku, 3) mesons. The A’-couplings of Eq. (3) make such mixing amplitudes possible at the tree-level through the exchange of a sneutrino & both in the sand t-channels. In fact, the effective Lagrangian terms for Bd - Bd and K - g mixings are C,,( B -+

B) = -

c -&l&3 -d&L -&h, n

L&K

--+i?) = -

m4,,

c -A’ n

A’*

m2,,

&&

&R.

(44

(4b)

We calculate the contributions of (4a) and (4b) to 6mB, SrnK respectively and require them not to exceed the corresponding experimental numbers (see Table 1). Though it is tempting to improve the bounds by first subtracting the SM contributions, we choose not do so as the latter involve considerable uncertainties, both experimental and theoretical. Before we present our numbers, it is useful (for notational purposes) to define the following “normalized” quantities :

d,L-

(“;y)‘.

Finally, our numbers tively are4 :

c

d,R= (10iT)2.

(5)

from SmB and SrnK respec-

AittAEtsni 5 3.3 X lOA

(64 (6b)

>

‘djL The upper bound in Eq. (6a) is only marginally weaker than that (3 x lo-*) obtained by Babu and

CpLdkReiL

I’ + &(eiL)CUpL

+

h.c.

(3)

4 Here, and in the rest of the discussion, quantity will apply to its magnitude.

bounds on any (complex)

D. Choudhury, P. Roy/Physics Table I Experimental

numbers

[ 131 used as upper bounds on the contribution

Letters B 378 (I 996) 153-158

155

of the & terms to the various observables

Quantity

Experimental value (bound)

6rnK

3.5 x lo-‘*

B~(KL + Ee)

< 4.1 x 10-l’ (7.4 i 0.4) x lo-” < 3.3 x IO-”

Br( KS -

Br(C -+ FP) Br( Kr. --f pe + ,uZ)

Br(& --t PLY) Br(K+ --f YWP)

< 1.0 x 10-S < 3.2 x 1O-7 < 5.2 x IO-”

Br(p -+ 3e) Br(T + pee) Br(T + j&e)

< IO--‘2 < 1.4 x 10-S < 1.9 x 10-5

Br(T --+ 3e) Br(7 -+ Pep) Br(T --f Z~,LL)

< 1.3 x 10-S < 1.4 x 10-5 < 1.6 x 1O-5

Br(7 --t 3~)

< 1.7 x 10-S

MeV

Mohapatra [ lo] very recently from the lack of observation of neutrinoless double-beta decay. In contrast, the bound of Eq. (6b) is three orders of magnitude stronger than the 10e6 obtained by those authors. Next, we focus on rare leptonic decay modes of the neutral K-mesons: KLJ --+ eZ or ,u,& e& ,G? as well as the semileptonic decay K+ -+ T+e$j. At the partonic level, the generic subprocess is one in which a downtype quark-antiquark pair (& and &, say) tranform into a charged lepton-antileptonpair (assumed to be ei and Z,i) : dk i-5 --+ ei +Z,i. Here i, j, k, .! are generation indices. The reaction can proceed via the exchange of a u-squat-k &L. in the t-channel as well as via an s-channel exchange of a sneutrino fin. The effective Lagrangian terms can be obtained in the same manner as above. We have then

The last term on the RHS comes from the t-channel exchange of a u-squark while the first two arise from the two s-channel diagrams (the first term with the sneutrino entering the hadronic vertex and the second with the sneutrino leaving it). On calculating the relevant matrix element of the effective Hamiltonian from (7)) we find that the new contributions to the decay

Quantity

Experimental value (bound)

6mB

3.4 x 1O-1o MeV Ze)

KL + eiZj can be parametrized binations

in terms of the com-

Two points need to be emphasised here : - On account of the particular Lorentz structure of the operators, the contributions of the Ai,i terms are chirality-suppressed. Hence, in the event of vanishing Bi,i, the constraints on -4i.i would be weaker than those operative in the reverse case. - In the limit of a trivial CKM matrix (K,,, = S,,), A$ = -A,ii, and thus -411 and A22 are purely imaginary. Though large imaginary parts in hiik cannot be ruled out per se, these are liable to generate unacceptably large CP violating effects. Nonetheless, we retain, for the time being, the possibility of complex &, couplings. Ignoring again the SM contributions, we demand that the & contribution by itself does not exceed the experimental upper bounds. Considering [ 131 KL --+ eZ, pup and ep +@ in turn, we have

1.3 x lo-t3 + 0.0024

2 []&,I* - 0.099 Re (J3i2)] \A221* + 0.10 Im(A22)

Im(&2),

D. Choudhury, P. Roy/Physics

156

Letters B 378 (1996) 153-158

Table 2 Upper bounds on the magnitudes of coupling products derived from rare K decays, under the assumption nonzero. In the entry marked with (*), we have assumed that K12 = -K21. For definitions, see Eq. (5) Decay Mode

Combinations

KL-'PP

huA;,,n~,

(*) KL + eZ K~+e,!i++p

K+ --f ma?

5.4x lo-t6

2 (1BJ

that only one such product

constrained h224,,n1.

&&,(u1

fU2)>

Upper bound 3.8 x 10-7 3.3 x 10-s

A232A;,2n39 A232Ai2,n3 &242,hfu2)

A121 &,nz,

A121 Ai2,n2,

A131 Ai,,n3,

A131 Ak2,n3

2.5 x 10-s 2.3 x 1O-8

&22&2n2,

h22Ai2ln2,

A132&2n3,

h132h;2ln3

h21&2nl,

~12142lW~

A231’&2n3.

A231A;21n3

GlA;,,ul,

4124llU2~

421h;22u2

A:22Ak2,U2~

‘;31’%32’3,

A:32A;31U3

A;,,,+,,d:,

A;,,,A;,,d,L

3.5 x 10-T

(For all i, j, n )

Lc,,( K+ +

+ 1B2,I”)

is

4.8 x lo@

1 T+.ViF,j) = - XypVj~

2

+ 0.0022(jd1212 + jd2,12)

+0.047 Re ({dT2- d21)Bn).

(9)

The 8, contribution to the rare KS decays, on the other hand, are parametrized by the combinations

Since the nine possible combinations (ij) cannot be distinguished experimentally, the bound [ 131 from the non-observation of such a mode leads to an upper bound on the incoherent sum (and hence also on the individual quantities) :

C lEOI5 2.3x

10-9,

(13)

i,j where Since all of the relevant Cijs are real even in the limit of a trivial CKM matrix, we cannot use the arguments proffered in the case of the KL to disentangle the contributions (the mass suppression continues nonetheless). The resulting expressions are quite analogous to those for KL decays and, in the case of [ 131 KS --+ p-,u”+, looks like

[l&l2

+ 0.099 Re (Y&J] + 0.1 Re (Ci2D22)

2N < 3.1 x 10-9. + 0.0025 IC221

(11)

The additional contribution to the decay K+ --+ r+viiji due to the 8P terms is in the form of two sets of t-channel diagrams (for each i, j),one each with 2~~ and do,, . The effective Lagrangian can be parametrized as

(14) n

Finally, we come to products of h-couplings which are probed by information on rare three-body leptonic decays of ,X and r. All these processes can be characterized by the generic transition e, -+ eb + e, + Zd where a, b, c, d are generation indices. The reaction proceeds by the exchange of a sneutrino 5, in the tchannel as well as in the u-channel. Analogous to the neutral K-decays, here too the sneutrino propagator may have both directions. The effective Lagrangian term now is ( 100 GeV)2 .C,n(e, 4 eb + e, + &) =

&bcd

+Facbd

ebR%L G%L

e,L%R ebLedR f

+ ficba

%hR

.;fhbca G%R

CedL %RedL

5

( 15 >

D. Choudhwy, P. Roy/ Physics Letters B 378 (1996) 153-158 Table 3 Upper bounds on the magnitudes of coupling products such product is nonzero. For definitions, see Eq. (5)

derived from flavour changing

Iepton decays,

under the assumption

that only one

Decay Mode

Combinations

p -

Al21 A122n2,

h31Al37J3.

b.31h31~3

6.6

A121 A123n2,

A131 A133n3r

A231 h21n2

5.6 x 10-s

3e

7-

-+

r-

+e

r-

+ p”- e+e-

3e --

e

pcL+

r-

-+

r-

+ e-l*+l*-

e+p-p-

A231A112n2r

A231A1331~3

A131 A121n1,

Al22Alun2,

A2szA121~r

A131&33n3

A131 A121n1,

A132 A233n3

A131 b.m,

A2321133n3,

AIZI Arunt 7 +

constrained

157

3p

*

~132b2~l~

=

c

%&nb&.d

h22h23W

(16)

.

II

In Eq. ( 15) the first (last) two correspond to the t- (u-) channel Utilizing the known experimental on the relevant partial widths, we

terms on the RHS exchange diagrams. upper limits [ 131 have

/_I,-+ 3e:

4.3 X lo-13,

/3i112/* +

7 -+ 3e:

1Ftj1312

7 + 3&

(&sj*

r-

+

-+ +

2

IF31121

,U+e-e-:

7- + e-p+p-: +

/.F2[2312 5

f

IF322,1* +

e+e-f_i: lF31*11* 5

+ 1F3tt112

5

5

3.1 X 10w5,

+ ]5222]* j$ 4.1 x 10-5,

7- --+ efpu-pu-: r-

IF2111/*

1~21131* 5

3.3

X

3.3 x 10-s,

IYi2231* 5 3.8 x 1O-5,

1F1123j2 + IF321

1I* +

I&2131*

10m5,

/F3122/* + IF22131* +

4.5 x 10-5.

x

10-T

5.7 x 10-s Al32&33n3>

5.7 x 10-s 6.2 x 10-s

h232&22n2,

6.7 x 10-s

P A232A233n3

6.4 x IO-”

A231 A233n3

where &bcd

Upper bound

jF321212

(17)

It is thus clear that the rare decays considered here lead to myriad bounds on combinations of #p couplings. Since particular products do occur more than once (albeit with different scalar masses), it is instructive to ask what the bounds would be if only one product were non-zero. In Table 2, we give the constraints, under such assumptions, for the products relevant to K-decays. The corresponding Ah products (which are constrained from flavour violating lepton decays) are

listed in Table 3. We should mention here that weaker constraints on n2lA121h1221 and rqlA131A132j were earlier estimated from the non-observation of p + 3e decay [ 141. To conclude, we have derived quite strong upper bounds on certain product combinations of A and A’ couplings. The reason that the bounds are so restrictive is that they come from processes which are permitted by such couplings at the tree-level but are disallowed or have to proceed via loops both in the SM and in the MSSM. If we consider transitions such as ,u -+ ey or r --+ ey, which are loop-induced even with such couplings, the corresponding bounds would not be anything like as strong. Of course, our list is not fully exhaustive - all possible coupling product combinations have not been covered. It is interesting to note that, barring the constraints from ,u + 3e, the bounds on the AA products are, in general, weaker than those on the AA’ combinations5 . On the other hand, every single A-coupling appears in Tables 1 and 2. The same is not the case for the A’-couplings. For instance, Ai,, and Ai23 are unconstrained while couplings like A;,,, A’,,, (except A’,,,) are only weakly constrained [ 81. Thus one may still harbor good hope of detecting a nonzero signal, say at LEP2, from some of these couplings [ 1.51. A large top quark event sample, accumulated at Fermilab, will also provide [ 161 a

5 Since A and A’ couplings mimic a class of dilepton and leptoquark phenomenology respectively, it is likely that a similar conclusion may be reached in the generic case as well [ 171.

158

D. Choudhury,

P. Roy/Physics

good opportunity to probe certain &, couplings possible bounds on nonstandard top decays.

from

Note added in proof: It might be interesting to consider the effect of such the A-type couplings in low energy Moller scattering [ 181. Two cases need to be examined separately. (i) Only one At,ik is non-zero : since the interaction is a scalar one, it does not lead to an additional source of asymmetry. Induced changes in the asymmetry are negligibly small. (ii) More than one Aljk are non-zero : the striking signals here involve change in lepton flavour. While the experiment in Ref. [ 181 has just about enough energy for the process e-e-> e-p-, the luminosity is not high enough. For more meaningful bounds, one needs to consider high energy e-e- scattering. This research was initiated during a visit to CERN by P.R. who acknowledges the hospitality of the Theory Division. It has been supported in part by the National Science Foundation under Grant No. PHY9407194. We thank G. Bhattacharyya, H. Dreiner and H. Murayama for their helpful remarks. References [ 11 HP Nilles, Phys. Rep. 110 (1984)

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