Split NMSSM with electroweak baryogenesis

In light of the Higgs boson discovery we reconsider generation of the baryon asymmetry in the non-minimal split Supersymmetry model with an additional singlet superfield in the Higgs sector. We find that successful baryogenesis during the first order electroweak phase transition is possible within phenomenologically viable part of the model parameter space. We discuss several phenomenological consequences of this scenario, namely, predictions for the electric dipole moments of electron and neutron and collider signatures of light charginos and neutralinos.


Introduction
Any phenomenologically viable particle physics model should explain the observed asymmetry between matter and antimatter in the Universe.The analysis of the anisotropy and polarization of the cosmic microwave background provided by WMAP collaboration gives the following baryon-to-photon ratio [1] n B n γ = (6.19± 0.14) × 10 −10 .
To generate the baryon asymmetry of the Universe, three Sakharov's conditions should be satisfied [2]: (i) baryon number violation, (ii) C-and CP -violation and (iii) departure from thermal equilibrium.The latter condition can be realized, in particular, during the strong first order electroweak phase transition (EWPT) which proceeds via nucleation and expansion of bubbles of new phase in the hot plasma of the early Universe (for a recent discussion see, e.g., Refs.[3,4]).The baryon number violation during the EWPT happens due to sphaleron processes in symmetric phase, while the CP -violation is induced by the interaction of particles in plasma with the bubble walls.
In the Standard Model of particle physics (SM) the Sakharov's conditions are only partly fulfilled.In particular, baryon number is violated via electroweak sphaleron transitions at high temperatures.At the same time, the electroweak transition in the SM is not the first order phase transition, hence no sufficient departure from thermal equilibrium.And the contribution of CP -violating CKM phases is too small in any case to provide (1).Finally, the electroweak sphalerons in the broken phase are too fast and would wash out any baryon asymmetry generated during the EWPT [5,6].Therefore, electroweak baryogenesis is only possible in SM extensions.These models should contain additional sources of CP -violation.Moreover, if the baryon asymmetry emerges at the electroweak scale, there should be a mechanism making the EWPT to be the strongly first order.A lot of scenarios for baryogenesis during the EWPT have been proposed and studied, see e.g.Refs.[7,8,9,10,11,12,13,14,15].
The Minimal Supersymmetric Standard Model (MSSM) is one of the most elegant ways to extend the SM framework.In particular, the quadratic divergences cancellation and the gauge couplings unification are the major reasons for the interest in supersymmetric models.Moreover, the lightest neutralino is a natural dark matter candidate in the MSSM [16,17].In general, however, the Higgs boson discovery [18,19], and nonobservation of superpartners at the LHC shrinks severely the region of MSSM parameter space.For instance, squarks and gluinos have been searched for at the LHC [20,21], and the lower bounds on their masses have been set at the level of 1-2 TeV.
An attractive MSSM extension with splitted superpartner spectrum (split MSSM) has been proposed in Refs.[22,23].The squarks and sleptons in these scenarios are very heavy, while neutralinos and charginos remain light.Nevertheless, the main advantages of SUSY, i.e. the gauge coupling unification and existence of dark matter candidate, remain intact in this class of models.Remarkably, the absence of FCNC processes [24] is naturally understood within this setup.Unfortunately, the electroweak baryogenesis can not be realized in minimal version of the split SUSY.This can be cured by introducing a gauge singlet superfield to the Higgs sector of the split MSSM [25].The main features of this split Next-to-Minimal Supersymmetric extension of the Standard Model, split NMSSM, are the following.There are two energy scales in the split NMSSM, electroweak M EW ∼ 100 GeV and splitting scale M S M EW .At M EW scale, the spectrum of split NMSSM contains the SM particles, one Higgs doublet H, the higgsino components Hu,d , winos W , bino B, and in addition a singlet complex scalar field N and its superpatner singlino ñ.The sleptons, squarks and four out of seven scalar degrees of freedom in the Higgs sector have masses of order the splitting scale M S .Hence, these particles are decoupled from the spectrum at low energies E < M S .At the same time, interactions of the scalar components of the singlet N with the Higgs boson are described at M EW by a generic potential, which includes trilinear terms.These couplings are capable of strengthening the first order EWPT.In the present paper, we review this scenario in view of the latest experimental results, in particular, the Higgs boson discovery.
This paper is organized as follows.In Section 2 we discuss the structure of split NMSSM.In Section 3, we explore the phenomenologically allowed region of the model parameters consistent with the Higgs boson of mass m H 125 GeV.In Sections 4 and 5 we study the strong first order EWPT and the baryon asymmetry of the Universe, respectively, for the relevant split NMSSM parameter space.In Section 6 we perform an analysis of the electron and neutron EDMs.There we also discuss the spectra of charginos and neutralinos, which can be probed at the LHC experiments.In Appendix A we calculate one-loop renormalization group (RG) corrections to the Higgs boson mass, which are needed to find allowed region of the parameter space in the split NMSSM scenario.In Appendix B the minimization conditions for the split NMSSM effective potential are presented.

Non-minimal split Supersymmetry
In this Section we discuss the Lagrangian and particle content of the split NMSSM.Above the splitting scale M S , the model is described by generic 4 NMSSM superpotential where Ĥu,d are superfields of the Higgs doublets, N is a chiral superfield singlet with respect to SU (3 The tree level scalar potential of the non-minimal SUSY model can be written as follows where the contribution of D-terms is the same as that in the MSSM, with g and g being SU (2) L and U (1) Y gauge couplings, respectively.The contribution of F -terms derived from superpotential (2) reads Soft supersymmetry breaking terms are described by the potential where A λ,k and m u,d,N are the trilinear couplings and the soft masses of scalars, respectively.Components of the Higgs doublets H u,d and singlet field N in (4), ( 5) are defined by where S and P are the scalar and pseudoscalar parts of the singlet N , correspondingly.We introduce the following notations: tan β ≡ H 0 u / H 0 d , v S ≡ S and v P ≡ P .An explicit analysis of the particle spectrum of the model with the potential (3) is performed in Ref. [25].We nevertheless briefly discuss the particle content of the scalar sector at energies below the splitting scale.There are ten scalar degrees of freedom at the splitting scale M S , coming from (6).It is shown in Ref. [25] that if the soft SUSY breaking parameters Bµ, m 2 d and m 2 u are of order of the squared splitting scale, M 2 S , then two charged Higgses, one pseudoscalar and one neutral scalar Higgs bosons are heavy and thus decoupled from the low energy spectrum, while a fine-tuning is required for the mass of the lightest Higgs boson H and two singlets, S, P to be at the electroweak scale.Three Goldstone modes are eaten by W ± and Z 0 due to the Higgs mechanism.We emphasize that the particle spectrum in the split NMSSM (as well as in any split SUSY model) below M S requires a fine-tuning of the soft dimensionful parameters [25].
Replacing H u → H sin β and H d → H * cos β in (3) we obtain at the splitting scale M S the effective Lagrangian for the relevant at low energy degrees of freedom in the scalar sector of the model (hereafter we omit the corresponding kinetic terms), , where ḡ2 ≡ g 2 + (g ) 2 .The quark-Higgs Yukawa interactions, gaugino couplings and gaugino mass terms are the same as in the minimal split supersymmetry.New part of the Yukawa interactions for Higgsinos Hu,d and singlino field ñ is given by −L Y = −λN Hu Hd − λ sin βH T ( Hd ñ) + λ cos β(ñ Hu )H * − kN ññ + h.c. ( Now we consider the most general scalar Lagrangian at energies below here the quartic couplings λ, κ, κ 1 , κ 2 and λ N at the electroweak scale are related via renormalization group equations to ḡ, λ, k and tan β at the scale M S .Comparing scalar potential (9) with (7) one can obtain the matching conditions for these couplings at the splitting scale M S : We use here the convention g 2 1 = (5/3)g 2 and g 2 = g adopted in Grand Unified Theories (GUT).Note that the couplings proportional to ξ and η in (9) are absent in the effective Lagrangian at M S , but get induced by loop quantum corrections; thus we set the following RG initial condition ξ = η = 0 (12) at the splitting scale M S .Soft fermion masses and Yukawa interactions below M S are described by the Lagrangian where M 2 and M 1 are wino and bino soft mass parameters in SU (2) L and U (1) Y gaugino sectors, respectively.The corresponding matching conditions for Yukawa couplings at the splitting scale M S read gu = g sin β, gd = g cos β, g u = g sin β, Matching equations for the dimensionful couplings in (9) can be found in a similar way.However, for simplicity we take their values directly at electroweak scale rather than solving RG equations for them from M S down to electroweak energies.In order to reduce the number of trilinear couplings we assume that Higgs-scalar (H −S) and Higgs-pseudoscalar (H − P ) mixing terms in their squared mass matrix are equal to zero at the EW energy scale.This implies appropriate relations for the trilinear couplings Ã1 and Ã2 , From the very beginning we admit explicit CP -violation by taking purely imaginary µterm and from largangians ( 9) and ( 7) we relate its value through the following matching condition at neglecting small RG corrections.Let us note that using minimization conditions for the potential ( 9), soft squared masses m 2 , m2 and m2 N can be re-expressed via vevs of the scalar fields, i.e. v, v S and v P .For completeness these relations are presented in Appendix B.
With the all above assumptions, we are left with only seven independent dimensionful parameters of the model at the EW scale In what follows to get numerical results, for concreteness, we set at the EW scale: while scanning over all the other four parameters.We advertise that the two singlet VEVs v S and v P play very prominent role in developing the EWPT, which is discussed below in Section 4.

Predictions for the Higgs boson mass
In this Section we describe the scanning over the set of three dimensionless parameters (tan β, λ, k) fixed at scale M S and calculate the mass of the Higgs boson resonance.We outline the region of model parameter space consistent with the SM-like Higgs boson with mass about 125 GeV.
In our procedure we choose dimensionless couplings of the model at the splitting scale and calculate the value of the Higgs boson mass by solving RG equations at next-toleading order in coupling constants (NLO).We start solving the truncated part of the RG equations from the EW up to the splitting scale for the SM couplings (g , g, g s , y t ), (20) where g s is SU (3) c gauge coupling and y t denotes the top Yukawa coupling.Initial conditions for RG equations for these couplings at the EW scale are taken as follows [24] α s (M Z ) = 0.118 , M Z = 91.19GeV , M W = 80.39 GeV, and y t (m t ) = 0.95.
Next, we use complete set of the RG equations for dimensionless couplings of the split NMSSM Corresponding RG equations can be found in Ref. [25].In order to obtain values of the couplings (21) at low energies, the values of tan β, λ and k are chosen randomly at the splitting scale M S from the following perturbative regions Then we solve the complete set of the RG equations from M S down to the EW scale by using matching condition (10), ( 12), ( 14) and ( 15).This procedure doesn't guarantee the correct value of top Yukawa coupling at low energy y t (M t ).Therefore, we tune y t (M S ) to obtain the value of y t (M t ) within the error bars (for details see A.3 and Refs.[25,26]).We include a part of threshold correction to the Higgs quartic coupling at the splitting scale [27] resulted in the following modification where δ λ is a conversion term from DR to MS renormalization schemes at M S , The remaining part of the threshold correction to λ depends on hierarchy of masses of heavy scalars near the splitting scale and it has not been taken into account.We should keep it in mind when interpreting the results.Next, we calculate the pole mass of the Higgs boson including one-loop threshold corrections at the electroweak scale, see Appendix A  [27].This is attributed to a large quantum correction coming from heavy stops.Now, we require that the pole mass of the Higgs boson (52) and y t at µ = M t fall within the following ranges 125.3 GeV < m pole h < 125.9 GeV, y lower t < y t < y upper t .
Here we use the average value m h = 125.6 ± 0.3 GeV from CMS [18] and ATLAS [19] combined results (for details see, e.g., Ref. [24] and references therein).Lower and upper limits for y t are extracted from Eq. (80) and correspond to M lower t = 172.3GeV and M upper t = 174.1 GeV respectively.In Fig. 2 we show the selected models in (tan β, λ)plane for the values of the splitting scale M S varying from 10 to 20 TeV.One can see that for tan β > 5 parameter λ can take arbitrary values in the allowed perturbative region.For tan β 1 the allowed region shifts to the maximal values of λ which follows from the matching condition (11).We check that λ is in the perturbative regime up to the GUT scale.In addition, as follows from Fig. 2, the phenomenologically possible values of tan β grow with decreasing of the splitting scale M S for λ < 0.4.This is again related to the balance between the tree-level and loop-induced contributions to the Higgs boson mass.The regions where tan β is either large (β → π/2) or small (β → 0) correspond to the decoupling of the second term in (11).We find that for M S → ∞ the allowed regions for tan β and λ shrink to tan β → 1 and λ → 0, respectively.
As it follows from ( 10) and ( 11) the coupling k does not enter the matching condition for λ at M S and we find that the value of the Higgs boson mass in the model is almost independent of the coupling constant k within the perturbative ranges (22).
In what follows, we choose two close benchmark setups for the free parameters The both benchmark models are well inside the allowed regions in Fig. 2. For calculation of the threshold correction the relevant dimensionful parameters are taken to be M 2 = 1 TeV, M 1 = 300 GeV and Im µ = 120 GeV.As it has been found in [25] the resulting baryon asymmetry is directly related to the value of λ.Thus the coupling λ is rather large for both chosen models.The relevant Yukawa and quartic couplings at the electroweak scale, µ = M t = 173.2GeV, are presented in Table 1.Below we use these couplings in the analysis of the strong first order EWPT (Section 4), in the calculation of BAU (Section 5) and to estimate the values of EDMs of the electron and neutron (Section 6).

Strong first order EWPT
In this Section we revisit the results of Ref. [25] for the strongly first order electroweak phase transition in the split NMSSM within the region of the parameter space favored by the measured value of the Higgs boson mass (m h 125 GeV).Let us consider the effective potential at finite temperature T [28] T .
Here V (1) T is the thermal contribution given by where sum goes over all species in the hot plasma (see, e.g., Eq. ( 85)), and where the upper and lower signs correspond to bosons and fermions respectively.In order to avoid baryon number washout after the phase transition the condition v c /T c > ∼ 1.1 has to be satisfied [29] (see also recent revised discussion in [30]).Here v c is the Higgs VEV at the critical temperature T c .We define T c as a temperature at which one bubble of the broken phase begins to nucleate within a causal space-time volume of the Universe.The latter is determined by the Hubble parameter H(T ) as The bubble nucleation rate in a unit space-volume has the form where S 3 = S 3 (T ) is the free energy of the critical bubble at a given temperature Here h(r), S(r) and P (r) are the radial configurations of the scalar fields, which minimize the functional S 3 .Therefore, the probability that the bubble is nucleated inside a causal volume reads The first bubble nucleates when P ∼ 1, which yields a rough estimate for the nucleation criterion S 3 (T )/T ∼ 4 ln , where T is a typical temperature of order the electroweak energy scale, T M EW .More accurate calculation reveals [31] S 3 (T c )/T c 135. ( We recall that singlet VEVs v S and v P are the input parameters of our model.The vacuum (v, v S , v P ) is the global minimum of the effective potential V ef f T =0 in the broken phase (see discussion in Appendix B).At the finite temperature T = 0, this broken minimum is shifted due to the termal corrections (28) In order to find numerically the profile of the critical bubbles, we use the method described in [32,33] and later modified in Ref. [25].The procedure can be summarized as follows.Firstly, for given values of v S , v P and T we find numerically the nearest minima of the effective potential V ef f T in the symmetric (0, S s , P s ) and broken (v c , S c , P c ) phases.For technical reason, we shift the effective potential by a constant to set V ef f T (0, S s , P s ) = 0. Secondly, we construct an anzats for the bubble wall configurations which interpolate between these two minima at the temperature T .Next, using this anzats as the first approximation we numerically find the absolute minimum of the functional where E h (r), E S (r) and E P (r) are the equations of motion for the bubble wall profiles Note that the critical bubble obeys the following boundary conditions (h(r), S(r), P (r)) r=∞ = (0, S s , P s ), dh dr , dS dr , dP dr r=0 = (0, 0, 0).
In Fig. 3 we show dependence of the critical scalar fields on the radial coordinate for the selected benchmark models at their critical temperatures.The corresponding values of the relevant physical parameters are shown in Table 2.All dimensionful parameters in Table 2  P in the broken and in the symmetric phases.This will be the source of CP -violation for generation of the baryon asymmetry during the EWPT.  1 and 2.

Baryon asymmetry
In this Section we discuss the baryon asymmetry created during the EWPT in the hot electroweak plasma.We will closely follow Ref. [34].To the linear order in chemical potentials µ i , the particle asymmetry number density for i-th component of plasma reads as where k i equals 2 and 1 for massless boson and fermion degree of freedom, respectively.For nonrelativistic particle with mass m i , the parameter k i is suppressed by factor exp(−m i /T ).
It is convenient to introduce the following notations: , and similar ones for the corresponding chemical potentials.We emphasize that the densities n i are local quantities and through the parameters in (37) depend on z + v w t, where z is the coordinate perpendicular to the bubble wall, and v w is the wall velocity.The baryon number conservation implies the following relation In diffusion equations we take into account scattering processes involving the top Yukawa coupling y t QtH with the rate Γ Y , strong sphaleron transitions with the rate Γ ss = 6κ ss 8 3 α 4 s T , Higgs boson self interactions with rate Γ H .We also include the rate Γ m for top quark mass interactions and the rates Γ u,d for Higgs-gaugino-higgsino interactions.In addition, we take into account the Higgsino flipping interaction μ Hu Hd which has the rate Γ µ .Following Ref. [34], we write down the set of diffusion equations in the large tan β which are written for combinations of the Higgs bosons and higgsino densities n h = n H + n Hu + n Hd and n H = n H + n Hu − n Hd .Here the prime and double prime denote the first and second derivatives with respect to variable z.In equations ( 38)-( 41), we set Γ μ ≡ Γ µ + Γ d , statistical factors are defined by and CP -violating sources S u and S d are discussed below in due course.We assume that the diffusion coefficients D q are the same for all quarks, and D h are the same for all Higgs bosons and higgsinos.Using the approach advocated in Ref. [35], we eliminate n T and n Q from Eqs. ( 38)-( 41) by substituting the relations which follow from the assumption that both the top Yukawa interactions and the strong sphalerons are in equilibrium.The resulting equations for n H and n h are collected in Ref. [25].It follows from (42), that the left-handed fermion density can be recasted in the following form The statistical factors are k Q = 6, k T = 3, k B = 3, k H = 4, k Hu = k Hd = 2 and hence the constant A t is equal to zero [36].It was shown in Ref. [37], that one-loop corrections to statistical coefficients k i give non-zero value of A t , namely The baryon asymmetry obeys the following equation [35] where Γ ws = 6κ ws α 5 w T is the weak sphaleron rate with κ ws = 20 ± 2 [38].The relaxation coefficient R is given by [39] R = 5  4 n F Γ ws , and n F is the number of generations, n F = 3.Here the domain z < 0 corresponds to the symmetric phase.The solution to Eq. ( 45) reads In the split NMSSM, CP -symmetry gets violated spontaneously while the bubble walls expand in the hot plasma.Indeed, the main source of CP -violation is associated with the complex chargino mass matrix where we define the spatially-dependent effective higgsino mass parameter as follows In the above expressions, h(z), S(z) and P (z) are the kink approximations of the bubble walls [35] here v c , S c and P c are the critical values of the scalar fields (see, e.g.Table 2), ∆S ≡ S c −S s and ∆P ≡ P c −P s .We set velocity of the bubble wall equal to v w = 0.1, the coefficient α is taken to be 3/2.The bubble wall width L w may be chosen in the range 5/T c < L w < 30/T c consistent with the special study [11] and the WKB thick-wall restriction, L w T c > 1.Following Ref. [11], we define the rates in Eqs.(38)(39)(40)(41) as with θ being the step function, and choose the diffusion coefficients in the form D q = 6/T and D h = 110/T .We use the expressions for CP -violating sources S d and S u from Ref. [11] and numerically solve the set of diffusion equations for n h (z) and n H (z).Then, we calculate the asymmetry of left fermions using Eq. ( 43) and by evaluating the integral (46) we obtain the baryon asymmetry generated during EWPT.
Let us consider the baryon-to-entropy ratio ∆ B = n B /s with the entropy density  2 and 1.
where g ef f is the effective number of relativistic degrees of freedom at T c .In Fig. 4 we show dependence of the baryon asymmetry ∆ B /∆ 0 on gaugino mass M 2 for different values of the wall thickness: namely, we take L w = 7/T c and L w = 5/T c for Setup 1 and 2, respectively.The value ∆ 0 = 8.3 × 10 −11 corresponds to n B /n γ = 6.2 × 10 −10 consistent with present measurements (1).It follows from Fig. 4 that baryon asymmetry ∆ B is of order ∆ 0 for large M 2 > ∼ 1 TeV.In this case, the heaviest chargino χ + 2 (wino-like) decouples from the plasma, |m χ + 2 | M 2 , and the lightest chargino (higgsino-like) acquires the mass |m χ + 1 |, which is determined by the effective μ(z)-parameter in (48).Thus, the baryon asymmetry is generated due to the spontaneous CP -violation in the broken (and symmetric) phase.Detailed calculation of CP -violating sources [11] reveals that S u and S d gain contributions which are proportional to the second derivative of Im μ(z) with respect to z coordinate.This means that baryon asymmetry ∆ B /∆ 0 is rather sensitive to the effective parameter, Im(μ ) ∼ κ∆P/L 2 w .
In our numerical analysis, we tune the wall thickness L w to obtain ∆ B /∆ 0 ∼ 1 as M 2 → ∞.At the same time from the very beginning we choose sufficiently large coupling κ (by taking large λ) and pseudoscalar VEV gradient ∆P = P c − P s and large value of tan β.These features select models which are interesting for the realistic electroweak baryogenesis.As we will see in Section 6 the latter condition is also preferred by present electron's EDM constraints.From Fig. 2 we see that large values of λ and tan β require moderate value of the splitting scale M S , which hardly can be larger than 12 − 15 TeV.
In our analysis we can evaluate the baryon asymmetry in the limit n h n H , following the approach, presented in Ref. [40].In this approximation the set of diffusion equations (38)(39)(40)(41) reduces to a single equation on n h , and baryon asymmetry ratio, ∆ B /∆ 0 , can be estimated analytically.In the limit when heaviest chargino decoupled, For L w = 5/T c , T c = 80 GeV and m χ + 1 = 239 GeV this yields ∆ B /∆ 0 ≈ 10.An orderof-magnitude discrepancy between the numerical, ∆ B /∆ 0 ≈ 1, and analytic results (51), is due to the approximations which have been made for solving equation for n h in the analytically approach.Let us note that here we estimate baryon asymmetry originated from chargino sector only.CP -violating sources from neutralino sector can change the calculated value of the asymmetry by a factor of order one.

EDM constraints and light chargino phenomenology
In this Section we address some phenomenological implementation of the results discussed above.To begin with, we emphasize that current constraints on electric dipole moments of the electron and neutron provide strong limits for CP -violating physics in the split NMSSM.There are three relevant contributions to the EDM of electron or light quark [41,44], are the partial EDMs of fermion (lepton or quark), related to the exchange of Hγ, HZ and W + W − bosons, respectively.General expressions for the electron's EDM d e and neutron's EDM d n were derived in Ref. [44].The values of d e and d n depend on chargino, m χ + i (i = 1, 2), and neutralino, m χ 0 j (j = 1, 5), masses as well as their mixing matrices6 .
The most stringent upper limit on EDM of the electron, |d e /e| < 8.7×10 −29 cm at 90% CL, was obtained by ACME collaboration [45].The current bound on neutron's EDM is |d n /e| < 3.0 × 10 −26 cm at 90 % CL [46].In order to perform the numerical analysis for EDMs, we randomly scan over the following parameter space 0 < M 1 , M 2 < 1000 GeV.In Fig. 5 we show dependence of |d e /e| on the lightest chargino mass m χ + 1 .One can see from the left panel of Fig. 5 that chargino masses in the ranges 225 GeV < m χ + 1 < 239 GeV and 220 GeV < m χ + 1 < 235 GeV are allowed for the Setup 1 and 2, respectively.We check that all these points correspond to large (about 1 TeV) values of M 2 and hence allow for correct value of the BAU.The numerical results for neutron EDM are shown on right panel of Fig. 5.One can see from Fig. 5 that predictions for the neutron EDMs satisfy the current experimental bound in all selected models.For the Setup 1 we present  1 and 2.
an examples of chargino and neutralino mass spectra which are consistent with the EDM bounds in Fig. 5 for M 1 = 300 GeV and M 2 = 1 TeV GeV, m χ 0 2 = 220.5 GeV, m χ 0 3 = 268.0GeV, m χ 0 4 = 341.9GeV, m χ 0 5 = 1006.9GeV.We find in this case, that LSP is singlino-like state with the mass m χ 0 1 = 133.9GeV.The dominant decay channel of the lightest chargino is χ + 1 → χ 0 1 W + , which can be used to test split NMSSM model.In our analysis, we checked that the models satisfying EDM bounds are in agreement with the present CMS [47] and ATLAS [48] limits on charginoneutralino production at LHC without light sleptons.Therefore, the split NMSSM is a phenomenologically viable and cosmologically attractive model which can be probed at the LHC run with pp collision energy of 13 TeV (and 14 TeV).

Conclusion
In this paper we revisit scenario of non-minimal split supersymmetry with possibility of realistic electroweak baryogenesis.It is a realization of split supersymmetry in the framework of NMSSM and contains at the electroweak scale, apart from minimal split supersymmetry particle content, singlet scalar and pseudoscalar states.We observed that within the phenomenologically allowed domain of the parameter space with the mass of the Higgs boson equal to 125 GeV it is possible to find particular models in which the strongly first order electroweak phase transition can be realized and moreover the needed amount of the baryon asymmetry of the Universe is generated.These models predict existence of light chargino state required for successful baryogenesis.We also find relatively light LSP with large admixture of singlino like state.Therefore, it can be considered as a potential dark matter candidate as suggested in Ref. [25].Predictions for the electric dipole moment of electron in these models are found to be about or somewhat larger than 2 − 3 • 10 −29 e cm which is only by factor 3-4 smaller than the current upper limit on this quantity.This makes the searches for EDMs a promising tool to probe the split NMSSM.
The work was supported by the RSF grant 14-22-00161.
A One loop corrections to Higss mass in split NMSSM In this appendix we calculate one-loop RG corrections to the mass of Higgs boson in split NMSSM scenario following Refs.[26,50].In particular, in Ref. [50] the radiative corrections to the Higgs mass were calculated in the NMSSM in Ref. [50], while they were derived explicitly in split MSSM in Ref. [26].However, split MSSM computations [26] can be straightforwardly extended to the split NMSSM case by taking into account the radiative corrections from scalars, charginos and neutralinos, where (m tree h ) 2 = λ(µ)v 2 is the three level Higgs boson mass at µ scale (dimensional renormalization scale in MS scheme); the remnant one-loop corrections in (52) are defined below in Sections A.1 and A.2.We use the experimental value of the Higgs pole mass (52) to plot the figures for the allowed region of split NMSSM parameters in the main text.
A.1 Tree level potential of scalar sector in the broken phase Applying the general results of Ref. [50] we rewrite (9) in the broken phase, where we denote perturbations of the scalar fields about the vacuum as (φ 1 , φ 2 , φ 3 ) = (h, S, P ).Then, substituting (53) into (9) and using minimization conditions (88-89) at the tree level, one can obtain The quartic and trilinear couplings which are relevant for the calculation of the Higgs boson self energy and tadpoles in the scalar sector of the split NMSSM can be written as The parameters of the scalar squared mass matrix read One should diagonalize its 2 × 2 submatrix for the singlets m 2 φ i φ j , with i, j = 2, 3, since off-diagonal mixings of φ 2 and φ 3 with the Higgs field φ 1 are set to be zero (61) (see also discussion before Eq. ( 16)).We denote the singlet eigenstates by h i and diagonalize m 2 φ i φ j by an orthogonal matrix R ij , such that The couplings that enter the calculation of the Higgs boson mass radiative corrections can be expressed as Following the prescription of Ref. [50] we write down one-loop contribution of the scalar singlets to the Higgs boson mass The loop functions A 0 (m) and B 0 (p, m 1 , m 2 ) depend on the renormalization scale µ and can be written in the form where C U V = 1/ − γ E + ln 4π, f B (x) = ln(1 − x) − x ln(1 − x −1 ) − 1 with A simplified formula for B 0 (p 2 , m 1 , m 2 ) at p 2 = 0 read [51], where M = max(m 1 , m 2 ) and m = min(m 1 , m 2 ).

A.2 Chargino-neutralino sector of split NMSSM
The Lagrangian of interest for chargino/neutralino sector is where Following Ref. [26], let us consider the contribution of chargino and neutralino to the Higgs boson mass at one-loop level, where is the Higgs boson tadpole contribution which involves terms from chargino and and neutralino sector, respectively.The relevant self energies read Σ h , where The last term in Eq. ( 74) is the corrections from the contribution of chargino and neutralino into the W ± boson self-energy

Figure 1 :
Figure 1: Prediction for the Higgs boson mass m h as a function of M S and tan β.We assumed here that the Yukawa top coupling falls within the range y lower t

Figure 2 :
Figure 2: Allowed regions for tan β and λ(M S ) for various values of the splitting scale M S .

Figure 3 :
Figure 3: The critical bubble profile for the parameter set presented in Tables1 and 2. Left and right panels correspond to Setups (1) and (2), respectively.

Figure 4 :
Figure 4: Plot of ∆ B /∆ 0 versus gaugino mass parameter M 2 for the parameter sets presented in Tables2 and 1.

Figure 5 :
Figure 5: Left panel: the EDM of electron versus the lightest chargino mass m χ + 1 .Dotted lines represent the current experimental bound |d e /e| < 8.7 × 10 −29 cm.Right panel: the neutron's EDM with upper limit |d n /e| < 3.0 × 10 −26 cm.The relevant couplings, µ-terms and both singlet VEVs v S and v P at T = 0 are given in Tables1 and 2.

Table 2 :
are in GeV.We observe considerable change in the values of the pseudoscalar field Parameters for the first order EWPT in the split NMSSM.