Excited lepton baryogenesis

The excited leptons that share the quantum numbers with the Standard Model leptons but have larger masses are widespread in many promising new physics theories. A subclass of excited leptons that at low energies interact with the SM fermions dominantly through the effective coupling to lepton and fermion-antifermion pair can be referred as leptomesons. I introduce possible generation of the baryon asymmetry of the universe using these new particles. The discussed baryogenesis mechanisms do not contradict to the small neutrino masses and the proton stability, and can be interesting for the collider experiments.


Introduction
In spite of the present success of the Standard Model (SM) several observations indicate its possible nonfundamentality: large number of the SM fermions, their arbitrary masses and mixings, fractional electric charge of quarks, etc. Among the diversity of new physics models the theories of compositeness [1][2][3][4][5][6][7] try to solve these problems by introducing a substructure of the SM particles, which subcomponents are commonly referred as preons [1]. The composite models may include in the particle content radial, orbital, topological, structural, and other excitations of the ground state particles, e.g., an excited lepton that shares leptonic quantum number with one of the existing leptons, has larger mass and no color charge.
Besides the outlined issues on the particles and their interactions that come from the laboratory studies, another opened questions (including the dark matter problem) arise from the astrophysical observations of the universe around us. In particular, our universe appears to be populated exclusively with baryonic matter rather than antimatter [8]. However this baryon asymmetry can not be explained within the Big Bang cosmology and the SM. Possible scenarios of dynamical generation of the baryon asymmetry during the evolution of the universe from a hot early matter-antimatter symmetric stage are referred as the baryogenesis (BG) mechanisms [9,10], and include new physics.
In the next section we discuss one example of the composite models in question. The interactions and the mass bounds for the excited leptons are outlined in section 3, and the new BG scenarios that involve these particles are discussed in section 4. Finally, we conclude in section 5. a e-mail: dmitry.zhuridov@gmail.com

Composite model example
Consider the haplon models [6,11], which are similar to the models with wakems and chroms [12][13][14], and are based on the symmetry SU(3) c × U(1) em × SU(N) h , where the new haplon group SU(N) h has the confinement scale of the order of 0.3 TeV, and denotes, e.g., SU(2) L × SU(2) R . These models contain the two categories of preons (haplons): the fermions α +1/2 and β −1/2 , and the scalars +1/2 and c −1/6 k , where k = r, g, b ("red, green, blue"). Their quantum number assignment is given in Table 1, where Q is the electric charge, C1 is the choice for the SU(3) c representations in Ref. [6] 1 and C2 is an alternative choice [11]. Then the haplon pairs can compose the SM particles as . . , and the new particles, e.g., a scalar leptoquark S +2/3 = ( c k ), and the neutral scalars S 0 = ( ¯ ) and S 0 c = (c kck ). W 3 mixes with the photon γ similarly to the mixing between γ and ρ 0 -meson. H scalar can be a p-wave excitation of the Z, and the second and third generations can be dynamical excitations. Notice that S +2/3 , S 0 c and S 0 states (if their masses are small) may contribute to the low-energy observables, e.g., so-called, XYZ states [16]. 2

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However, new questions arise: Where does this peculiar haplon picture come from? Can it, in turn, result from a substructure of haplons? Consider the two scalar "prepreons" 3 π k andπ k , which are SU(3) triplets and have the electric charges of −1/6 and +1/6, respectively. Then the set of haplons with their electric and C2 color charges can be reproduced by the triples of "prepreons" (πrπḡπ¯b → {α, }, π r π g π b → {β,¯ },π¯i π j π l → c k ), while additional mechanism of spin generation is required. One can think of possible relation of spin to a circular color currents similarly to some discussions in the context of the condensed matter [20] and gravity [21] theories, taking into account that the distribution of matter in a composite state can be imagined (in particular, in the SU(3) Yang-Mills theory) in terms of the wave functions or probability distributions for the effective subcomponents of a finite size [22][23][24]. Then a "spinning" and "nonspinning" states of the same preon (e.g., α and ) may form a supersymmetric multiplet.
Notice that the possibility of multihaplon states such as (βc k¯ c k ), (α¯ βc kβ c k ), etc., gets more points from recent discoveries of the multiquark hadrons [25].

Excited leptons
The excited lepton states defined in the introduction can be particularly important if their masses are smaller than the leptoquark and leptogluon masses, which can be natural due to the absence of the color charge. The contact interactions among the SM fermions f and the excited fermions f * can be generically written as [8] where Λ is the contact interaction scale, g 2 * = 4π, and the new parameter values are usually taken of |η j | ≤ 1.
Assuming nearly maximal couplings of |η j | 1 and the excited fermion masses of M f * Λ, the present lower bounds for Λ/ |η j | ratios are of the order of few TeV [8]. However, if Eq. (1) expresses a "residue" effective interactions between the composites (with respect to the fundamental interactions among their subcomponents) then |η j | couplings can be small, and even the case of M f * Λ < 1 TeV is not excluded for |η j | 1 and Λ/ |η j | >> M f * .
A particular type of excited leptons that at low energies interact with the SM fermions dominantly through the contact terms we refer as leptomesons (LM). 4 The relevant contact terms (with η couplings) can be realized, e.g., through the leptoquark exchange.

Baryogenesis
Possible BG and the dark matter generation by a scalar 4-haplon state was considered in Ref. [11]. In this proceedings we discuss if fermionic LM states can provide a successful BG [27]. Similarly to the sterile neutrino ν R case, depending on the LM properties, deviation from thermal equilibrium can occur at either production or freezeout and decay (compare to the BG via ν R oscillations [28] and the usual leptogenesis [29], respectively). In both scenarios one should replace the Yukawa interactions of ν R by the contact interactions of LMs, which may result in promising effects.

BG from LM oscillations
Once created in the early universe neutral long-lived LMs oscillate and interact with ordinary matter. These processes do not violate the total lepton number L tot (for Dirac LMs). However the oscillations violate CP and therefore do not conserve individual lepton numbers L i for LMs. Hence the initial state with all zero lepton numbers evolves into a state with L tot = L + i L i = 0 but L i 0.
At temperatures T Λ the LMs communicate their lepton asymmetry to neutrinos ν and charged leptons through the effective interactions, e.g., B-conserving (and L-conserving for Dirac LMs) vector couplings where ψ = , ν ( = e, µ, τ), the constants (∼) = 4πη can be real, f and f denote either quarks or leptons such that Q f α + Q f c α + Q ψ β = 0, and N is the neutral LM flavor state related to the mass eigenstates N i as N α = n i=1 U α i N i . Suppose that LMs of at least one type N i remain in thermal equilibrium till the electroweak symmetry breaking time t EW at which sphalerons become ineffective, and those of at least one other type N j come out-of-equilibrium by t EW . Hence the lepton number of former (later) affects (has no effect on) the BG. In result, the final baryon asymmetry after t EW is nonzero. At the time t t EW all LMs decay into the leptons and the quarks (hadrons). For this reason they do not contribute to the dark matter in the universe, and do not destroy the Big Bang nucleosynthesis.
The system of n types of singlet LMs of a given momentum k(t) ∝ T (t) that interact with the primordial plasma can be described by the n × n density matrix ρ(t). In a simplified picture it satisfies the kinetic equation [28] i dρ dt where Γ (Γ p ) is the destruction (production) rate, and the effective Hamiltonian can be written aŝ Advances in Dark Matter and Particle Physics Figure 1. Feynman diagrams for the discussed contributions to the CP asymmetry, where the line direction shows either L or B flow, "×" represents a Majorana mass insertion, and the black bulb represents a subprocess (e.g., a leptoquark exchange). whereM 2 = diag(M 2 1 , . . . , M 2 n ) with the masses M i of N i , and V is a real potential.
One of the main features of the discussed BG from LMs is that the 4-particle interaction cross section that contributes to the destruction rate is proportional to the total energy of the process s instead of the inverse proportionality that takes place in the BG from ν R oscillations. Indeed, this cross section can be written as where a, b, c and d denote the four interacting particles ( f , f , ψ and N ), and C = O(1) is the constant that includes the color factor in the case of the interaction with quarks. In result, the interaction rate that equilibrates LMs, is suppressed by (T/Λ) 4 with respect to the Higgs mediated interaction rate in usual BG via ν R oscillations. The conditions that LMs of type N i remain in thermal equilibrium till t EW , while N j do not, can be written as where H(T ) is the Hubble expansion rate. Due to the suppression factor of (T EW /Λ) 4 the successful BG can be realized with the relatively large couplings | | with respect to the sterile neutrino Yukawas of Y ∼ 10 −7 in the BG via ν R oscillations [28]. In particular, for Λ 10 and 30 TeV we have | | 10 −4 and 10 −3 , respectively. Hence the considered BG scenario can be relevant for the LHC and next colliders without unnatural hierarchy of the couplings.

BG from LM decays
Suppose that the neutral LMs are Majorana particles (N = N c ). Consider their out-of-equilibrium, CP-and Lviolating decays in the early universe. The relevant interactions can be written as To be more specific in the following we consider the term where λ i = αR qq U R i is a complex parameter. Consider the interference of tree and one-loop diagrams 5 shown in Fig. 1. The final CP asymmetry that is produced in decays of the lightest LMs N 1 can be non-zero if Im[(λ † λ) 2 1 j ] 0. Using the width [32], the condition for the decay parameter K ≡ Γ 1 /H(M 1 ) > 3 (strong washout regime) translates into the limit of (λ † λ) 11 4 × 10 −7 × Λ 10 TeV The final baryon asymmetry can be written as where n B (n L ) is the baryon (lepton) number density, s is the entropy density, −28/79 is the sphaleron lepton-tobaryon factor, and κ ≤ 1 is the washout coefficient that can be determined by solving the set of Boltzmann equations. The observed baryon asymmetry of the universe of [8] where n γ is the photon number density, can be produced, e.g., for K ∼ 100 with the degeneracy factor of which enters the resonant CP asymmetry of Notice that the discussed effective LM-quark-quarklepton vertex can be realized, e.g., through the exchange of

Neutrino masses
For Majorana LMs the effective terms of (18) can generate the two-loop contributions to the observable light neutrino masses m ν that is illustrated for f = q in Fig. 2, and for a particular model with the leptoquarks in Fig. 3. A simple estimate of this contribution is where m q is the quark mass. Hence the present bound of m ν 2 eV [33] can be easily satisfied.

Conclusion
The two new testable baryogenesis scenarios in the models with excited leptons are introduced, which do not contradict to the observable neutrino masses. First, the BG from LM oscillations may take place for relatively light and long-lived LMs, which do not all decay before t EW . Second, the BG from LM decays can be realized if all LMs decay before t EW . A particular models based on the former (later) BG proposal require detailed study of the neutrino potential (of the Boltzmann equations) to be verified in the future experiments. In both scenarios the baryon number is violated only by the sphaleron processes that does not affect the proton stability. Due to the relatively low temperatures of the discussed BG mechanisms, an analog of the gravitino problem [34,35] does not exist there.