New low-energy leptoquark interactions

cm .__ _-

__ li!l!iB

ELSEVIER

2OJune1996

PHYSICS

LETTERS B

Physics Letters B 378 (1996) 17-22

New low-energy leptoquark interactions M. Hirsch a, H.V. Klapdor-Kleingrothaus a, S.G. Kovalenko a7b a Max-Plan&Institutf Kernphysik, P.O. IO 39 SO, D-69029 Heidelberg, Germany b Joint Institute for Nuclear Research, Dubna, Russia

Received 21 February 1996; revised manuscript received 1 April 1996 Editor: C. Mahaux

Abstract We discuss an extension of the standard model (SM) with vector and scalar leptoquarks. The renormalizable leptoquark Lagrangian consistent with the SM gauge symmetry is presented including the leptoquark-Higgs interactions previously not considered in the literature. We discuss the importance of these new interactions for leptoquark phenomenology. After the electro-weak symmetry breaking they generate non-trivial leptoquark mass matrices. These lead to mixing between different SU(Z)L-multiplets of the leptoquarks and induce at low energies new effective 4-fermion lepton-quark vertices. The latter affect the standard leptoquark phenomenology. We discuss constraints on these interactions from the helicity-suppressed TT+ v + e decay. PACS: 11.30; 12.30; 13.15; 14.80 Keywords: Leptoquarks; Higgs; Effective interaction;

Non-chiral;

Pion decay

The interest on leptoquarks (LQ) [ 11 has been renewed during the last few years since ongoing collider experiments have good prospects for searching these particles [ 21. LQs are vector or scalar particles carrying both lepton and baryon numbers and, therefore, have a well distinguished experimental signature. LQs can be quite naturally introduced in the low-energy theory as a relic of a more fundamental theory at some high-energy scale. In such a way LQs can emerge from grand unified theories (GUT) [ 3,4], including the superstring-inspired versions of GUT [ 41, models of extended technicoIour [ 51 and composite models [ 61. Possible LQ manifestations in various processes have been extensively investigated 12-71 (and references therein). Various constraints on LQ masses and couplings have been deduced from existing experimental data and prospects for the forthcoming experiments have been estimated. Direct searches of LQs as s-channel resonances in deep inelastic ep-scattering at HERA experiments [lo] placed lower limits on their mass h4~ > 140 - 235 GeV [ 111 depending on the LQ type and couplings. With larger accumulated luminosity HERA will be able to cover almost the whole kinematical region in the LQ masses up to 296 GeV, for couplings to quarks and leptons above lo-‘. There are also bounds from other collider experiments. The LEP experiments exclude any LQ lighter then 45 GeV [ 121, the DO collaboration rules out LQs lighter than 133 GeV if they couple to the first generation fermions [ 131, and the CDF collaboration sets a corresponding lower bound at 113 GeV [ 141. Dramatic improvements of these constraints are expected in future collider experiments (see for instance [ 71 and references therein). 0370-2693/96/$12.00 Copyright PIZ SO370-2693(96)00419-4

0 1996 Published

by Elsevier

Science B.V. All rights reserved.

18 Table I The Standard

M. Hirsch et al. /Physics

model assignments

LQ

Letters B 378 (1996) 17-22

of the scalar S and vector V, leptoquarks SV(3)C 3 3 3* 3* 3 3* 3* 3 3 3*

SUC2)L

1

1 2 2 3 1

1 2 2 3

(LQ).

(Y = 2(Qenl - Ts))

Y -213 -813 -713 -l/3 -213 -413 -1013 -513 l/3 -413

Qem -l/3 -4f3 (-213, -5/3) (l/3, -213) (213, -l/3,-4/3) -213 -5f3 (--l/3, -413) (213, -l/3) (l/3,

-2/3,-S/3)

However, at present the most stringent limits on LQs come from low-energy experiments [ 81, [ 91. Effective 4fermion interactions, induced by virtual LQ exchange at energies much smaller than their masses, can contribute to atomic parity violation, flavour-changing neutral current (FCNC) processes, meson decays, meson-antimeson mixing and some rare processes. For instance, a typical bound on non-chirally coupled LQs imposed by the helicity-suppressed r -+ ev decay is M&/lgLgR] > (lOOTeV)*, where gL,R are LQ couplings [ 81. To consider LQ phenomenology in a model-independent fashion one usually follows some general principles in constructing the Lagrangian of the LQ interactions with the standard model (SM) fields. Generic principles are renormalizability (pl)and invariance (~2) under the SM gauge group SU( 3) c 6%SU( 2) L @ U( 1) y. In order to obey the stringent constraints from (cl)helicity-suppressed r -+ ev decay, from (~2) FCNC processes and (Q) proton stability, the following three assumptions are also commonly adopted: (al) LQ couplings are “chiral”, i.e. each type of LQs couples either to left-handed or to right-handed quarks only (call them left- and right-type LQ) ; (a2) LQ couplings are generation “diagonal”, i.e. they couple only to a single generation of leptons and a single generation of quarks; (a3) LQ interactions conserve baryon (B) and lepton (L) numbers. Of course, if these empirical assumptions (al)-(a3) really determine the LQ interactions, they have to be explained in terms of an underlying theory predicting light LQs. We will show, however, that assumption (al) does not solve problem (cl) since the LQ couplings with the SM Higgs doublet reintroduce the non-chiral interaction terms. Therefore, to obey (cl) one should not only claim chirality of the LQ-quark couplings (al) but also absence of some LQ-Higgs couplings. It is unlikely that both requested properties can have the same origin in the underlying theory. In the following we consider changes in LQ phenomenology caused by the LQ-Higgs interactions. We base our consideration on the general principles (pl ) , (~2) as well as on the assumptions (al) -( a3). The SM symmetries allow 5 scalar S and 5 vector V* LQs with the following LQ( SU( 3), @ SU( 2)~ @I U( 1)~) assignments: &(3,, 1; -2/3), &(3,, 1; -8/3), S1,2(3c,2; -7/3), &,2(3,,2; -l/3), &(3,,3; -2/3), Vo(~,,1;-4/3),~0<~,,1;-10/3>,V,~~(3,,2;-5/3),~,2(3,,2;1/3),~(~,,3;-4/3),whereY=2(Q,,-T3). In the literature only LQ-lepton-quark interaction terms have been considered.

They have the following

form

[21

(1)

M. Hirsch et al. /Physics Letters B 378 (19961 17-22

. qCy@PRe ’ V$,

+A$:

+ A,CL). ~yl*P#--Z

Here PL,R = ( 1 F ys)/2; q and 1 are the quark with the weak isospin i = 0,1/2,1 coupled to (Our notations differ from those in Ref. [ 21) There are no fundamental reasons forbidding most general form of the LQ-Higgs interaction CLP-_H = h($HiT&p

(i) (HiQi,2) . &pp + YsI12

+Ys, (HiT&

H) . so + Yv, (HiT2p[pH)

(H+flcfj)

+ h.c.

and the lepton doublets; S: and @ are the scalar and vector LQs left-handed (j = L) or right-handed (j = R) quarks respectively. For LQ triplets @r = Sr, VI” we use the notation &r = 7 . @I. LQ interactions with the standard model Higgs doublet H. The Lagrangian, consistent with (pl ) and (~2) can be expressed as

,. _ . Sb + h,(9 Hir2v,T2 . V& + hs, H&S] 1&p

+hv, Hint,’

+,$

19

. %; _ (Q&$

1 ($,2H)

+ Y$

(HiTzV$y))

. v: + K:) (H+&H)

_ &‘“‘H+ff >

(2) . (qyzFH)

.$

c@l+& + h.c.

Here H is the SM SU(2)L-doublet Higgs field. @” is a cumulative notation for all leptoquark fields with i = L, R (the same for ir,~). We included diagonal mass terms ~&Vf$@t@ of the scalar (77s = 1) and the vector ( YZV= - 1) LQ fields. These terms can be generated by spontaneous breaking of the underlying symmetry down to the electro-weak gauge group at some high-energy scale. The subsequent electro-weak symmetry breaking at the Fermi scale produces additional non-diagonal LQ mass terms leading to non-trivial mixing between LQs from different SU( 2)~ multiplets as well as between left- and right-types of LQs, discussed above. The relevant LQ mass matrices can be read off from Eq. (2). There are 8 non-diagonal LQ mass matrices squared (I = S, V) :

(3)

M:(Q:?

=vI.

(4) ’

A&Q(~))

=vIs

Mf(~j~))

=T!.

l?rqo Jzy,,v* JzyI,v* ,m;* ’

)

WqL

(5)

4;:) b12

(-gj,~~~1i:121 7)d?$2

(6)

’

-1 where I@; = Mf + rZlgllvl* is the “shifted” diagonal mass, v* = (Z-Zc)*= (2fiG~) is the SM Higgs _ field ,I\ vacuum expectation value, GF is the Fermi constant and ~S,V = 1, -1. The cumulative notation M:(Q)” 1 encodes the mass matrices squared for the scalar (Z = S) and vector (I = V,) LQs with electric charges Q;” = Qb2) = -l/3, Q$‘) = Q$‘) = -Z/3, Q$“) = Qs4) = -4/3, Qh3) = Qi4) = -5/3 in the interaction

eigenstate

basises:

Z(Q1’3’) = (&,I,);

(k = 1) Z(Q,“‘)

= (Z,$,Z[,Jf/2,Zr);

(k = 4) I(Q1’4’) = U,L2J&).

(k = 2) Z(Qj*‘>

‘I%us, there is a non-trivial

= (fr,2,Z$2,Z$2,Z/); mixing

(k = 3)

of LQs from different

20

M. Hirsch et al. / Physics Letters B 378 (1996) 17-22

SU(2)t multiplets as well as the IL - ZR mixing. The latter spoils chirality of the LQ-quark-lepton couplings (al) and leads to reappearance of the problem with the constraint (cl). The mass matrices of all other LQ fields remain diagonal after electro-weak symmetry breaking. To obtain observable predictions from the LQ-lepton-quark interaction Lagrangian in Eq. ( 1) , fields with non-diagonal mass matrices have to be rotated to the mass eigenstate basis I’. This can be done in the standard way Z(Q) =N(‘)(Q) .1’(Q) where tit’) are orthogonal matrices such that n/(‘)r( Q) . My(Q) . NC’) (Q) = Ding{M~,,} with the A41 being the mass of the relevant mass eigenstate fieId I’. All phenomenological consequences of the LQ interactions in Eqs. (l)-(2) should be derived in terms of these fields I’. In this letter we concentrate on the LQ induced 4-fermion lepton-quark effective interactions. For vanishing LQ-Higgs couplings (Eq. (2) > these interaction terms are listed in Ref. [ 81. Mixing between different SU( 2) L multiplets of LQs leads to new terms, vanishing in the limiting case of decoupled LQ and Higgs sectors. Below we list only those new terms which can be most stringently restricted from low-energy processes. After Fierz rearrangement they take the form

1 (7) where

(8) Here we introduced

a mixing parameter

(9) where Q = - l/3, -213 and I = S, V. Common mass scales Ms of scalar and Mv of vector LQs were introduced for convenience. The interaction terms Eq. (7) contribute to various low-energy processes. Using existing experimental data one can obtain constraints on the relevant coupling constants. Here we are not going to discuss this subject in detail but rather present only the most stringent bounds from the helicity-suppressed decay rr --f ev. This process is especially sensitive to the first two scalar-pseudoscalar terms leading to a helicity-unsuppressed amplitude. Assuming no spurious cancellations between different contributions we derive on the basis of Ref. [ 81 the following severe constraints:

EJ,Wf

55

x 1o-7

(IOoMdeV)‘*

(10)

Other couplings in Eq. (7) are much weaker constrained by low-energy processes previously considered in connection with the LQ phenomenology [ 8,9]. We expect that new stringent constraints on these LQ couplings can be derived from neutrinoless double beta decay (Ovpp). Consider the conventional mechanism of Ov/3/3decay based on the Majorana neutrino exchange between decaying nucleons. Let the neutrino propagator connect

21

M. Hirsch et al. /Physics Letters B 378 (1996) 17-22

the ordinary SM charged current vertex with the LQ-generated one related to the E or cr couplings in Eq. (7). The corresponding amplitude is proportional to PL [ qpcLy”+m,] PR(L) - q( m,), where m, and q are the neutrino mass and momentum. The case in the brackets ( > corresponds to both vertices being SM left-handed ones. It is seen that the LQ induced vertex in combination with the SM one produces an enormously large enhancement factor, (4)/m, N pF/m, N IO*, compared to the pure SM case. (Here, (q) is the averaged momentum transfer between two nucleons in a nucleus approximately equal to the Fermi motion momentum PF M 100MeV) This enhancement should be compensated by the smallness of E or (Ycouplings. To determine actual constraints on these parameters requests a calculation of the nuclear matrix elements within some nuclear structure model. This is beyond the scope of this letter and will be published in a separate paper. A similar effect in Ov,GP-decay was recently found within the minimal supersymmetric standard model with R-parity violation [ 151. In conclusion, we have derived the leptoquark interactions with the standard model Higgs field. We have shown that these interactions generate new 4-fermion lepton-quark couplings which contribute to various lowenergy processes. Considering the helicity-suppressed z- --t ev decay, we have found that special combinations of the leptoquark couplings to the quarks, leptons and the Higgs fields (see Eq. ( IO) ) are stringently constrained despite their chirality. This may indicate a dramatic impact of the LQ-Higgs interactions on the standard leptoquark phenomenology which should be reconsidered taking these new interactions into account. We stress that an underlying high-energy scale theory containing light leptoquarks must explain not only the chirality of leptoquark couplings to quarks and leptons (see (al ) at the beginning) but also the absence (or smallness) of at least those leptoquark-Higgs couplings which are suppressed by the constraints in Eq. ( 10).

Acknowledgments We thank V.A. Bednyakov for helpful discussions. meinschaft for financial support by grants kl 253/8-l

M.H. would like to thank the Deutsche and 446 JAP-113/101/O.

References 1 I 1 J.C. Pati and A. Salam, Phys. Rev. D 10 (1974) 275. [ 21 W. Buchmiiller, R. RiJckl and D. Wyler, Phys. Len. B 191 (1987) 442. 131 See for instance P Langacker, Phys. Rep. 72 (1981) 185; PH. Frampton, Mod. Phys. Lett. A 7 (1992) 559. [ 41 J. Hewett and T. Rizzo, Phys. Rep. 183 (1989) 193. IS ] S. Dimopoulos and .I. Ellis, Nucl. Phys. B 182 (1981) 505. [ 6 1 W. Buchmtiller, Phys. Lett. B 145 (1984) 151; B. Schrempp and E Schrempp, Phys. Lett. B 153 (1985) 101. 171 J. Wudka, Phys. Lett. B 167 (1986) 337; J.L. Hewett and T.G. Rizzo, Phys. Rev. D 36 (1987) 3367; J.E. Cieza Montalvo and 0.J.P Eboli, Phys. Rev. D 47 (1993) 837; G. B&anger, D. London and H. Nadeau, Phys. Rev. D 49 (1993) 3140; J. Bliimlein and R. Rtickl, Phys. Lett. B 304 (1993) 337; J. Bltimlein and E. Boos, Nucl. Phys. B (Proc. Suppl.) B 37 (1994) 181; J. Bltimlein, E. Boos and A. Pukhov, Mod. Phys. Lett. A 9 (1994) 3007; J. Ohnemus, S. Rudaz, T.F. Walsh and P Zerwas, Phys. Lett. B 334 (1994) 203; G. Bhattacharyya, J. Ellis and K. Sridhar, Phys. Lett. B 336 (1994) 100; D. Choudhury, Phys. Lett. B 346 (1995) 291; M.A. Doncheski and S. Godfrey, Phys. Rev. D 51 (1995) 1040. 18 I S. Davidson, D. Bailey and A. Campbell, Z. Phys. C 61 (1994) 613. [91 M. Leurer, Phys. Rev. I.&t. 71 (1993) 1324; Phys. Rev. D 49 (1994) 333; D 50 (1994) [ 101 HI Collaboration, I. Abt et al., Nucl. Phys. B 396 (1993) 3; ZEUS Collaboration, M. Derrick et al., Phys. Len. B 306 (1993) 173.

536.

Forschungsge-

22

M. Hirsch et al. /Physics Letters B 378 (19961 17-22

[ 1 I 1 T. Ahmed et al., Z. Phys. C 64 ( 1994) 545. I 12 I DELPHI Collaboration, P. Abreu et al., Phys. Lett. B 316 (1993) 620; L3 Collaboration, B. Adeva et al., Phys. Len. B 261 (1991) 169; OPAL Collaboration, G. Alexander et al., Phys. Lett. B 263 ( 1991) 123. 113 I DO Collaboration, S. Abachi et al., Phys. Rev. Lett. 72 (1994) 965. [ 141 CDF Collaboration, F. Abe et al., Phys. Rev. D 48 (1993) 3939. [ 15I KS. Babu and R.N. Mohapatra, Phys. Rev. Lett., 75 (199.5) 2276; M. Hirsch, H.V. Klapdor-Kleingrothaus and S.G. Kovalenko, Phys. Lett. B (1996),

hep-ph/9512

,237