List of examples of charged particles from new physics discussed in this review showing

## Abstract

We have new charged particles in many scenarios of physics beyond the Standard Model where these particles are sometimes motivated to explain experimental anomalies. Furthermore, such new charged particles are important target at the collider experiments such as the Large Hadron Collider in searching for a signature of new physics. If these new particles interact with known particles in the Standard Model, they would induce interesting phenomenology of flavor physics in both lepton and quark sectors. Then, we review some candidate of new charged particles and its applications to flavor physics. In particular, vector-like lepton and leptoquarks are discussed for lepton flavor physics and B-meson physics.

### Keywords

- flavor physics
- charged particle from beyond the standard model
- B-meson decay
- vector-like lepton/quark
- leptoquarks
- charged scalar boson

## 1. Introduction

Charged particles are often considered in the physics beyond the Standard Model (BSM) of particle physics as new heavy particles which are not observed at the experiments. Such charged particles can have rich phenomenology since it would interact with particles in the Standard Model (SM). Furthermore they are motivated to explain some experimental anomalies indicating deviation from predictions in the SM. For example, some charged particle interaction can accommodate with the anomalous magnetic moment of the muon,

where

In this chapter, we review some candidates of new charged particles from BSM physics. After listing some examples of them, the applications to some flavor physics will be discussed focusing on some specific cases. We find it interesting to consider new charged particles which are related to flavor physics in both lepton and quark sectors.

## 2. Some charged particles from beyond the standard model physics

In this section we review some examples of charged particles which are induced from BSM physics.

### 2.1 Charged scalar bosons

Singly charged scalar appears from two-Higgs doublet model (2HDM) [17, 18] in which two

where

where all flavor indices are hidden,

where

where

A doubly charged scalar boson also appears from

where

where

where

where

Note that these charged scalars also contribute to lepton flavor violation processes.

### 2.2 Vector-like leptons

The vector-like leptons (VLLs) are discussed in Ref. [29]. They are new charged particles without conflict of gauge anomaly problem and induce rich lepton flavor physics. To obtain mixing with the SM leptons, the representations of VLL under

where we have suppressed the flavor indices;

with

where the basis is chosen such that the SM lepton mass matrices are in diagonalized form,

Note that the elements of

To diagonalize

where

where

If one sets

### 2.3 Vector-like quarks

Here we consider vector-like triplet quarks (VLTQs) that are discussed in Ref. [30] The gauge invariant Yukawa couplings of VLTQs to the SM quarks, to the SM Higgs doublet and to the new Higgs singlet field are written as

where

The electric charges of

where

### 2.4 Scalar leptoquarks

In this subsection we consider leptoquarks (LQs) which are discussed for example in Refs. [31, 32]. The three LQs are

where the superscripts are the electric charges of the particles. Accordingly, the LQ Yukawa couplings to the SM fermions are expressed as

where the flavor indices are hidden,

The scalar LQs can also couple to the SM Higgs field via the scalar potential, and the cross section for the Higgs to diphoton can be modified in principle. However, the couplings of the LQs to the Higgs are independent parameters and irrelevant to the flavors, so by taking proper values for the parameters, the signal strength parameter for the Higgs to diphoton can fit the LHC data. For detailed analysis see Table 1 in Ref. [31].

Particle type | Examples of application | |
---|---|---|

Charged scalar | Neutrino mass, lepton flavor violation | |

Vector-like lepton | Lepton flavor violation | |

Vector-like quark | Quark flavor physics | |

Scalar leptoquark | Meson decay, lepton flavor violation |

## 3. Examples of applying charged particles to flavor physics

In this section, we review applications of charged particles to flavor physics by considering VLLs and LQs as examples.

### 3.1 Flavor physics from vector-like lepton

Introduction of VLLs contributes to lepton flavor physics via Yukawa interactions discussed in previous section. Here we review the leptonic decay of the SM Higgs and LFV decay of charged lepton as an illustration based on Ref. [29].

#### 3.1.1 Modification to h → τ + τ − branching ratio

From Eq. (18), it can be seen that the modified Higgs couplings to the SM leptons are proportional lepton masses. By comparison with other lepton channels, it can be seen that the

If the SM Higgs production cross section is not changed, the signal strength for

#### 3.1.2 τ → μγ process in vector-like lepton model

In the following, we investigate the contributions of new couplings in Eq. (18) to the rare tau decays and to the flavor-conserving muon anomalous magnetic moment. We first investigate the muon

where

Accordingly, the BR for

We present the contours for

### 3.2 B -meson flavor physics with leptoquarks

This section is based on Ref. [32]. Several interesting excesses in semileptonic

where

#### 3.2.1 Effective interactions for semileptonic B -decay

According to the interactions in Eq. (24), we first formulate the four-Fermi interactions for the

where the indices

With the Yukawa couplings in Eq. (24), the effective Hamiltonian for the

where the Fierz transformations have been applied. By Eq. (31), it can be clearly seen that the quark currents from both the doublet and triplet LQs are left-handed; however, the lepton current from the doublet (triplet) LQ is right(left)-handed. When one includes Eq. (31) in the SM contributions, the effective Hamiltonian for the

where the leptonic currents are denoted by

The effective Wilson coefficients with LQ contributions are expressed as

where

#### 3.2.2 Constraints from Δ F = 2 , radiative lepton flavor violating, B + → K + ν ν ¯ , B s → μ + μ − , and B c → τν processes

Before we analyze the muon

where

In addition to the muon

with

where

Note that

As mentioned earlier, the singlet LQ does not contribute to

where

In addition to the

where

Using

#### 3.2.3 Observables: R D ∗ and R K ∗

The observables of

where

where

and the other form factors are taken to be

The values of

f(0) | 0.67 | 0.67 | 0.69 | 0.76 | 0.69 | 0.66 | 0.62 | 0.68 | 0.68 | 0.33 |

0.57 | 0.78 | 0.56 | 0.57 | 0.58 | 0.78 | 1.40 | 0.57 | 0.64 | 1.46 | |

0.41 | ||||||||||

f(0) | 0.36 | 0.36 | 0.35 | 0.44 | 0.45 | 0.36 | 0.32 | 0.39 | 0.39 | 0.27 |

0.43 | 0.70 | 0.43 | 0.45 | 0.46 | 0.64 | 1.23 | 0.45 | 0.72 | 1.31 | |

0.27 | 0.36 | 0.38 | 0.62 | 0.41 |

According to the form factors in Eqs. (44) and (45), and the interactions in Eqs. (30) and (32), we briefly summarize the differential decay rates for the semileptonic

where the

We note that the effective couplings

where

where

From Eq. (52), the measured ratio

#### 3.2.4 Numerical analysis

After discussing the possible constraints and observables of interest, we now present the numerical analysis to determine the common parameter region where the

The parameters related to the radiative LFV,

where

where

After discussing the constraints and the correlations among various processes, we present the numerical analysis. There are several LQs in this scenario, but we use

According to the relationships shown in Eq. (56),

After studying the muon

Finally, we make some remarks regarding the constraint due to the LQ search at the LHC. Due to the flavor physics constraints, only the

## 4. Conclusions

We have reviewed some charged particles which appear from physics beyond the Standard Model of particle physics. Some possible candidates of them are listed such as charged scalar boson, vector-like leptons, vector-like quarks, and leptoquarks. After showing some properties and interactions of these particles, we reviewed some applications to flavor physics in which lepton flavor physics with vector-like lepton and