Flavour-Changing Neutral Currents and Leptophobic Z' Gauge Bosons

Leptophobic Z' gauge bosons can appear in models with an E_6 gauge symmetry. We show that flavour-changing neutral currents can be generated in some of these models due to the mixing of the ordinary d_R, s_R and b_R quark fields with the exotic h_R. Because the Z' does not couple to charged leptons, the constraints on the flavour-changing couplings U^{Z'}_{db} and U^{Z'}_{sb} are relatively weak. Indeed, B_q--Bbar_q mixing (q=d,s) can be dominated by Z' exchange, which will affect CP-violating rate asymmetries in B decays. Rare hadronic B decays can also be affected, while decays involving charged leptons will be unchanged.

Many models of physics beyond the Standard Model (SM) predict the existence of exotic fermions with non-canonical SU(2) L × U(1) Y quantum numbers, i.e. lefthanded SU(2) L singlets and/or right-handed SU(2) L doublets. The ordinary SM fermions can mix with these exotic fermions. It is well known that such mixing may induce flavour-changing neutral currents (FCNC's) [1]: if two ordinary quarks mix with the same exotic quark, FCNC's are generated between the ordinary quarks.
This FCNC is second order in ordinary-exotic quark mixing. This fact has been used to construct models with Z-mediated FCNC's [2]. Here one introduces an additional vector-singlet charge −1/3 quark h, as is found in E 6 models, and allows it to mix with the ordinary down-type quarks d, s and b. Since the weak isospin of the exotic quark is different from that of the ordinary quarks, Z-mediated FCNC's among the ordinary down-type quarks are induced. Note that it is only the mixing between the left-handed components of the ordinary and exotic quarks which is responsible for the FCNC: since d R , s R , b R and h R all have the same SU(2) L × U(1) Y quantum numbers, their mixing cannot generate flavour-changing couplings of the Z.
The Z-mediated FCNC couplings U Z ds , U Z db and U Z sb , which are in general complex, are constrained by a variety of processes. U Z ds is bounded by the measurements of ∆M K (K 0 -K 0 mixing), |ǫ| (CP violation in the kaon system) and K L → µ + µ − [2], while the constraints on U Z db and U Z sb come principally from the experimental limit on B(B → ℓ + ℓ − X) [3,4]. To the extent that the constraints on U Z db and U Z sb allow significant contributions to B 0 q -B 0 q mixing (q = d, s), CP asymmetries in B decays may be affected by Z-mediated FCNC's [2,5].
In general, models of new physics which contain exotic fermions also predict the existence of additional neutral Z ′ gauge bosons. The same ideas which lead to Z-mediated FCNC's can be applied to the Z ′ . That is, mixing among particles which have different Z ′ quantum numbers will induce FCNC's due to Z ′ exchange [6]. Surprisingly, these effects can be just as large as Z-mediated FCNC's. Since the U Z pq are generated by mixings which break weak isospin, they are expected to be at most O(m/M), where m (M) is a typical light (heavy) fermion mass. On the other hand, the Z ′ -mediated couplings U Z ′ pq can be generated via mixings of particles with the same weak isospin, and so they suffer no such mass suppression. Therefore, even though processes with Z ′ exchange are suppressed relative to those with Z exchange by M 2 Z /M 2 Z ′ , this is compensated by the fact that U Z ′ pq /U Z pq ∼ M/m. Thus, the effects of Z ′ -mediated FCNC's can be comparable to those of Z-mediated FCNC's.
In this paper we apply these ideas to leptophobic Z ′ gauge bosons, whose couplings to charged leptons vanish. Leptophobic Z ′ bosons were introduced several years ago in the context of the R b -R c puzzle [7], and as a possible explanation of anomalous high-E T jet events at CDF [8]. Although these experimental effects ultimately disappeared, thereby removing the original motivation for such new physics, models with a leptophobic Z ′ still remain as viable candidates of physics beyond the SM, and it is therefore worthwhile exploring their phenomenology.
In Ref. [9] it was shown that a leptophobic Z ′ can appear in E 6 models due to the mixing of the gauge boson kinetic terms. In such models, if the d R , s R and b R have different U(1) ′ quantum numbers than the h R , then their mixing will induce Z ′ -mediated FCNC's among the ordinary down-type quarks. However, since the Z ′ is leptophobic, these FCNC couplings will not be constrained by limits on processes involving charged leptons, such as K L → µ + µ − and B → µ + µ − X. Thus, the constraints on such leptophobic Z ′ -mediated FCNC's may be considerably weaker than those for Z-mediated FCNC's and, as a consequence, there may be large effects in B decays. These are the issues which we examine in this paper.
We begin with a brief review of models with a leptophobic Z ′ gauge boson [10].
We assume that the low-energy gauge symmetry is SU(2) L ×U(1) Y ×U(1) ′ , in which the U(1) ′ arises from the breaking chain where θ is the usual E 6 mixing angle. The fundamental representation of E 6 is a 27, which decomposes under SO(10) as a 16 + 10 + 1. The conventional embedding is to put all the ordinary SM particles, along with a right-handed neutrino, into the 16. Within this embedding, the quantum numbers of all particles are shown in Table 1.
It is straightforward to show that if the Z ′ coupling to fermions is proportional to Q ′ , there is no value of θ which leads to leptophobia (i.e. Q ′ (L) = Q ′ (e c ) = 0). kinetic mixing term between the U(1) Y and U(1) ′ gauge bosons: where the W a ,B andZ ′ represent the SU(2) L , U(1) Y and U(1) ′ fields. Due to the presence of kinetic mixing, the physical Z ′ can exhibit leptophobia. This can be seen as follows [10].
The off-diagonal coupling of theB andZ ′ can be removed by making the nonunitarity transformationB With this transformation, the couplings of the physical gauge bosons to fermions can be written as where Q em = T 3L + Y SM and δ ≡ −g Y sin χ/g Q ′ (g Y andg Q ′ are, respectively, the U(1) Y and U(1) ′ coupling constants). Assuming the couplings to be "GUT" normalized, the Z ′ -fermion interaction term can be written where x W ≡ sin 2 θ W = e 2 /g 2 and λ = g Q ′ /g Y . The key point here is that, due to kinetic mixing, the Z ′ coupling to fermions is no longer proportional to Q ′ . It is this feature which leads to the possibility of leptophobia.
The Z ′ -fermion coupling involves two unknown parameters: θ and δ. Since leptophobia requires two couplings to vanish (the Z ′ coupling to e − and e + ), obviously this can be satisfied for some choice of the two parameters. For example, for the conventional embedding of Table 1, one obtains a leptophobic Z ′ for tan θ = 3/5 In order to answer this question, for each of the six models of Table 2, we calculate  Table 3. Of the six models, two of themmodels 4 and 5 -have Q ′ (d c ) = Q ′ (h c ). Thus, in these models, the mixing of d R , s R and b R with the h R will lead to FCNC's mediated by the exchange of a leptophobic Z ′ gauge boson. Table 3: U(1) ′ quantum numbers of d c and h c for each of the six models given in Table 2, calculated using Q ′ = Q ψ cos θ − Q χ sin θ.
In order to examine the constraints on such Z ′ -mediated FCNC couplings, we parametrize them as As is the case for Z-mediated FCNC's, the coupling U Z ′ ds is strongly constrained by measurements of ∆M K and |ǫ| in the kaon system [2]: Note that, unlike the flavour-changing coupings of the Z, there are no constraints on U Z ′ ds from K L → µ + µ − since the leptophobic Z ′ does not couple to charged leptons. Similarly, the couplings U Z ′ db and U Z ′ sb are unconstrained by the experimental limit on B(B → µ + µ − X), which is the main constraint on the flavour-changing couplings of the Z to the b quark. On the other hand, Z ′ -mediated FCNC's do contribute to the process b → sνν [11], for which ALEPH has an experimental limit [12]: In order to compute the contribution of the U Z ′ sb coupling to this process, we need the coupling of the Z ′ to νν. Since the Z ′ is leptophobic, it does not couple to L L , which includes both e − L and ν eL . However, it does couple to the right-handed neutrino, and this must be taken into account.
In E 6 , there are two candidates for the right-handed neutrino: the fields labelled ν c and S c in Table 1. In Table 4 we present the U(1) ′ charges of these two fields.
(Note that, as before for L/H and d c /h c , one can always exchange the fields ν c ↔ S c , so that the labels are arbitrary.) From this table we see that the leptophobic Z ′ does indeed couple to the right-handed neutrino, and so it can contribute to b → sνν 3 . Table 4: U(1) ′ quantum numbers of ν c and S c for models 4 and 5 of Table 2, calculated using Q ′ = Q ψ cos θ − Q χ sin θ.
Taking Q ′ (ν c ) = 1/4, the coupling of the Z ′ to the right-handed neutrino can be written as with [see Eq. (5)] where we have taken λ = 1 (its precise value depends on the details of unification).
The contribution of Z ′ -mediated FCNC's to b → sνν is then given by where F ps ≃ 0.5 is a phase-space factor. This yields the constraint This can be turned into a bound on U Z ′ sb if one assumes a value for M Z ′ . The only experimental constraint on leptophobic Z ′ gauge bosons comes from the D0 experiment [13], which excludes the mass range 365 GeV ≤ M Z ′ ≤ 615 GeV for a Z ′ with quark couplings equal to those of the Z. (Interestingly, light leptophobic Z ′ bosons are not ruled out.) There are two points to be stressed here. First, the constraints on Z ′ -mediated b → s transitions are quite a bit weaker than those on the corresponding Z-mediated FCNC's. The most recent result from BELLE gives [3] B(B → X s e + e − ) ≤ 1.01 × 10 −5 , which leads to the constraint This is about an order of magnitude more stringent than the corresponding Z ′ FCNC constraint of Eq. (12). Thus, effects due to leptophobic Z ′ -mediated FCNC's in b → s processes may be larger than those due to Z-mediated FCNC's.
Second, unlike Z-mediated FCNC's, there are no constraints on b → d transitions from B decays. Thus, here too the effects of Z ′ -mediated FCNC's can be considerably larger than those due to Z exchange.
Of course, Z ′ -mediated FCNC's will contribute to B 0 q -B 0 q mixing (q = d, s): These contributions can be compared with those of the SM: where we have taken |V tb | = 1 and m t = 170 GeV.
Consider first B 0 s -B 0 s mixing. As a figure of merit, we assume that U Z ′ sb = 0.1 and M Z ′ = 750 GeV, which satisfy the bound of Eq. (12). Taking |V ts | = |V cb | = 0.04, Thus, B 0 s -B 0 s mixing can be completely dominated by the exchange of a leptophobic Z ′ . This is in stark contrast to Z-mediated FCNC's. With the constraint of Eq. (14), The contribution of Z-mediated FCNC's to B 0 s -B 0 s mixing is therefore negligible compared to that of the SM. q -B 0 q mixing is significantly affected by this type of new physics, one expects that rare B decays will also be affected [5]. What distinguishes leptophobic Z ′ -mediated FCNC's from other models of new physics is that its effects will only show up in rare hadronic B decays; leptonic decays such as b → qℓ + ℓ − and B 0 q → ℓ + ℓ − will be unaffected. This provides a rather unique "smoking-gun" signal for this type of new physics.
To sum up: leptophobic Z ′ gauge bosons can appear in models with an E 6 gauge symmetry due to mixing of the gauge-boson kinetic terms. There are a total of six fermion embeddings in the 27 of E 6 which can produce leptophobia. Of these, we have shown that flavour-changing neutral currents (FCNC's) can be generated in two of these models. This is due to the mixing of the right-handed components of the ordinary d, s and b quarks with the exotic h quark. Since all of these particles have the same weak isospin, this mixing can be quite large.
The flavour-changing coupling U Z ′ ds is strongly constrained by measurements of ∆M K and |ǫ| in the kaon system. However, because the Z ′ does not couple to charged leptons, the constraints on U Z ′ db and U Z ′ sb are relatively weak -they are bounded only by the experimental limit on B(b → sνν). (This is in contrast to Z-mediated FCNC's. For these, the constraints on the U Z qb (q = d, s) from B(B → Xℓ + ℓ − ) are quite stringent.) The result is that both B 0 d -B 0 d and B 0 s -B 0 s mixing can be dominated by Z ′ -mediated FCNC's. If there are significant new-physics effects due to Z ′ exchange in B 0 q -B 0 q mixing, this will affect CP-violating rate asymmetries in B decays. In addition, one expects that rare hadronic B decays will also be affected.
The fact that only hadronic decays are affected, and not leptonic decays such as b → qℓ + ℓ − and B 0 q → ℓ + ℓ − , provides a unique signal for leptophobic Z ′ -mediated FCNC's.