Research Express@NCKU - Articles Digest (Volume 4 Issue 6)

Quarks and leptons are the elementary particles that consist of our universe. The interactions of these particles are dictated by the gauge bosons in which the theories are based on gauge symmetries. In the standard model (SM) of particle physics, the gauge symmetries are G=SU(3)C×SU(2)L×U(1)Y, where SU(3)C, SU(2)L and U(1)Y could bring us the strong, weak and electromagnetic interactions, the subscripts C, L and Y denote the color, left-handed chirality and hypercharge quantum numbers, respectively and the corresponding gauge bosons are gluons, W^±, Z⁰ and photon. Unlike leptons, which can propagate freely in the space and be observed directly by detectors, quarks are always confined to be colorless and bound states at low energy scale due to the strong interaction. Therefore, ordinary detectable matter, such as proton and neutron etc, must be made of quarks.

Figure 1 Illustration of how three quarks consist of baryon octet.

Although there are six species of quarks in the world, the most observed matter of the universe is made of u, d and s quarks. If one set the masses of these particles be equal, the system of light quarks owns SU(3) flavor symmetry. Based on the flavor symmetry, the observed matter could be classified as mesonic and baryonic states, where the former is composed of one quark and one anti-quark while the latter is composite of three quarks. The proton and neutron are the well known baryons and they are made of uud and udd quarks, respectively. For illustration, we display the lowest baryonic states in figure 1. From the figure, we see clearly that we have eight ground states in the (qqq) system. According to the mathematical language of symmetry, the number 8 could be decomposed in terms of

, where the 3 denotes u, d and s flavors, the 10, 8 and 1 stand for the decuplet, octet and singlet states, respectively. Clearly, since proton and neutron belong to the same multiplet, this could explain why their masses are so close to each other. In addition, besides proton and neutron, we also know that there are other baryons such as Σ and

etc in the same octet.

One of main goals in high energy experiments is to discovery the new particles and new interactions in the universe. As known that although SM can explain most observed experimental data, however, it is just an effective theory at the electroweak scale. And also, some phenomena such as matter-antimatter asymmetry can not be understood well in the SM framework. Inevitably, these lead people to think the effects of new physics. Needless to say, it will be exciting if high energy experiments could indicate the existence of new physics.

In 2005, the HyperCP collaboration at Fermilab has presented the branching ratio of Σ⁺→pμ⁺μ^- to be

, which is hardly explained within the SM, and suggested a new boson X with a mass of 214.3±0.5 MeV to induce the flavor changing transition of s→dμ⁺μ^-. It has been demonstrated that to explain the data the new particle cannot be a scalar (vector) but pseudoscalar (axial-vector) boson XP(A) based on the direct constraints from K⁺→π⁺μ⁺μ^- and KL→μ⁺μ^-. A possible candidate with a light sgoldstino in spontaneously local supersymmetry breaking theories has been extensively discussed in the literature. Recently, He, Tandean and Valencia have also shown that the light pseudoscalar Higgs boson in the next-to-minimal supersymmetric SM can be identified as XP.

In this Letter, we will explore the implications of the HyperCP Data on flavor changing B and τ decays. In particular, we will examine constraints on the effective interactions induced by XP,A from the experimental data in B processes and study the possibility of having large effects in semileptonic Bd,s decays. For the tau decays, we will concentrate on the decays of τ→lμ⁺μ^-.

We start by writing the effective interactions for the new pseudoscalar XP or axial-vector XA particle couplings to quarks and leptons to be

(1)

where

(F=Q, L) denote the couplings of XP (XA) to quarks and leptons, respectively, and the indices i,j stand for the quark or lepton flavors. Although the exotic events observed in the HyperCP are associated with the flavor changing neutral current (FCNC) in the first two generations of quark flavors and lepton flavor (LF) conservation, to study the effects of the new particle on B and τ decays, we will include all FCNCs in both quark and lepton sectors. It has been studied and known that the constraint on the s-d-X coupling from the decay branching ratio (BR) of KL→μ⁺μ^- is more strict than that from the

mixing. In order to search for the most strict bounds on X-mediated B-meson decay processes, we will examine those measured well in experiments, such as the

mixings and the decays of Bd,s→μ⁺μ^- and B→K^*μ⁺μ^-.

To see the effects of the new particle on low energy physics, we first consider its contributions to ΔF=2 processes. From the current experimental data, the mass differences in the K and Bq systems are given by ΔmK=(3.483±0.006)×10^-15,

and

GeV. By utilizing these values, the direct constraints on the couplings are found to be

(2)

Next, we discuss the decays of P→μ⁺μ^-. It is well known that the long-distance effect dominates the process of KL→μ⁺μ^-, while the short-distance contribution usually is taken to be BR(KL→μ⁺μ^-)SD<3.6×10^-10. As to the dileptonic decays in Bq decays, we also know the upper bounds of BR(Bd→μ⁺μ^-)<2.3×10^-8 and BR(Bs→μ⁺μ^-)<8.0×10^-8. With these constraints, we have

(3)

It has been shown that the current strict bounds on

and

are from muon g-2, given by

<2.6×10^-7 and

<6.7×10^-8, respectively. Thus, one gets the upper bounds on the rates as Γ(XP→μ⁺μ^-)<4.3×10^-10 GeV and Γ(XP→μ⁺μ^-)<2.7×10^-12 GeV. Hence, we obtain

(4)

respectively. It is clear that the constraints from Δmk are weaker than those from KL→μ⁺μ^-.

In the following, we study the BRs for semileptonic Bq decays. The decay of Bd→K^*0μ⁺μ^- has been measured at the B-factories with the world average on the decay BR being

. According to our calculations, we obtain

(5)

If we regard BR(Bd→K^*0μ⁺μ^-)=1.22×10^-6 as the upper bound, we have |

|²BR(XP→μ⁺μ^-)≤3.9×10^-17 and |

|²BR(XA→μ⁺μ^-)≤3.1×10^-20. For BR(XP,A→μ⁺μ^-)~1, we find that the decay Bd→K^*0μ⁺μ^- gives the strongest limits on the couplings of

and

. The first direct application is BS→

XP,A→

μ⁺μ^-. From previous constraints, we get BR(BS→

XP→

μ⁺μ^-)≤2.74×10^-6 and BR(BS→

XA→

μ⁺μ^-)≤2.81×10^-6. Interestingly, the bounds are just under the D0 upper limit of BR(BS→

μ⁺μ^-)≤3.2×10^-6. If the events observed by the HyperCp collaboration are indeed from the new particle, the decay of BS→

μ⁺μ^- should be observed soon as the SM prediction is around 1.6×10^-6.

As there is no any useful information on

, one can only investigate those decays associated with

. In order to apply

to decays related to

, we need some theoretical ansatz to connect them. One of the interesting ansatz is to relate the couplings with quark masses, such as

(6)

where λP(A)=v/vF denotes the ratio of electroweak scale (v) to the new scale (vF) associated with the new particle. Using the ansatz, the upper bound on BRs for some decays are given by

(7)

Similarly, we can use the same ansatz as that for quark sector, the upper bound on the flavor violating τ decays are estimates to be

(8)

Note that the current upper bounds for τ→lμ⁺μ^- are 2.0×10^-7.

In sum, we have studied the implications of the HyperCP Data on flavor changing B and τ decays. We have given constraints on the effective couplings due to the new pseudoscalar and axial-vector bosons of XP,A from experimental data in the K and B systems, respectively. We have pointed out that the strongest limits on

are from the decay of Bd→K^*0μ⁺μ^-. We have shown that the decay BR of BS→

l⁺l^- can be as large as 2.7(2.8)×10^-6 through XP,A , which are larger than the prediction of 1.6×10^-6 in the SM and close to the experimental upper limit of 3.2×10^-6. In addition, we have proposed an ansatz to relate the couplings with the fermion masses. Based on this ansatz, we have demonstrated that the decay BRs of Bu→ρ⁺μ⁺μ^-, BS→K^*0μ⁺μ^-,

can all be at the level of 10^-8. In particular, we have shown that BR(τ→μXP(A)→μμ⁺μ^-)=1.7(0.14)×10^-7.