Top quark decay to a 125 GeV Higgs in the BLMSSM

In this paper, we calculate the rare top quark decay t → ch in a supersymmetric extension of the Standard Model where baryon and lepton numbers are local gauge symmetries. Adopting reasonable assumptions on the parameter space, we find that the branching ratios of t→ch can reach 10−3, which could be detected in the near future.


Introduction
The top quark plays a special role in the Standard Model (SM) and holds great promise in revealing the secret of new physics beyond the SM. The currentlyrunning Large Hadron Collider (LHC) is a top-quark factory, and provides a great opportunity to seek out rare top-quark decays. Among those rare processes, the flavor-changing neutral current (FCNC) decays t→ch deserve special attention, since the branching ratios (BRs) of these rare processes are strongly suppressed in the SM. In addition, ATLAS and CMS have reported significant excess events which are interpreted to be probably related to a neutral Higgs with mass m h 0 ∼124-126 GeV [1,2]. This implies that the Higgs mechanism to break electroweak symmetry possibly has a solid experimental cornerstone.
In the framework of the SM, the possibility of detecting FCNC decays t→ch is essentially hopeless, since tree level FCNC involving quarks are forbidden by the gauge symmetries and particle content [3,4]. In particular, it has recently been recognized that the BRs of the processes are much smaller [5,6] than originally thought [7], being less than 10 −13 . In extensions of the SM, the BRs for FCNC top decays can be orders of magnitude larger. For example, the authors of Ref. [8] study the t → ch process in the framework of the minimal supersymmetric extension of the Standard Model (MSSM), which includes the leading set of supersymmetric QCD and supersymmetric electroweak contributions, and get Br SUSY−EW (t → ch) ∼ 10 −8 and Br SUSY−QCD (t→ch)∼10 −5 . A new study of this process in the MSSM is discussed in Ref. [9]; with tanβ=1.5 or 35 and the mass of SUSY particles about the 1 or 2 TeV scale, the authors get a maximum branching ratio for t → ch of 3×10 −6 , which is much smaller than previous results obtained before the advent of the LHC.
Physicists have been interested in the MSSM [10-13] for a long time. However, since there is an asymmetry between matter and antimatter in the universe, baryon number (B) should be broken. In addition, since heavy majorana neutrinos contained in the seesaw mechanism can induce tiny neutrino masses [14,15] to explain the results obtained in a neutrino oscillation experiment, the lepton number (L) is also expected to be broken. A minimal supersymmetric extension of the SM with local gauged B and L (BLMSSM) is therefore more favoured [16,17]. Since the new quarks predicted by this model are vector-like with respect to the strong, weak and electromagnetic interactions, to cancel anomalies, one obtains that their masses can be above 500 GeV without assuming large couplings to the Higgs doublets in this model. Therefore, there are no Landau poles for the Yukawa couplings here.
In the BLMSSM, B and L are spontaneously broken near the weak scale, proton decay is forbidden, and the three neutrinos get mass from the extended seesaw mechanism at tree level [3,4,16,17]. Therefore, the desert between the grand unified scale and the electroweak scale is not necessary, which is the main motivation for the BLMSSM.
The CMS [18] and ATLAS [19] experiments at the LHC have searched for many possible MSSM signals and set very strong bounds on the gluino and squark masses with R-parity conservation. However, in the BLMSSM, the predictions and bounds for the collider experiments should be changed [16,17,20]. In addition, lepton number violation could be detected at the LHC from the decays of right-handed neutrinos [3,4,21], and we can also look for baryon number violation in the decays of squarks and gauginos [22]. Since there are some exotic fields, and there exist couplings between exotic quarks, exotic scalar quarks and SM quarks in the superpotential, this will cause flavor changing processes, so the BRs for FCNC top decays can be orders of magnitude larger than in the SM.
In this paper we analyze the corrections to the topquark decay t→ch in the BLMSSM. This paper is constructed as follows. In Section 2, we present the main ingredients of the BLMSSM. In section 3, we present the theoretical calculation of the t→ch processes. Section 4 is devoted to the numerical analysis, and our conclusions are summarized in Section 5.

A supersymmtric extension of the SM where B and L are local gauge symmetries
The local gauge B and L is based on the gauge group In the BLMSSM, to cancel the B and L anomalies, the exotic superfields should include the new quarksQ 4 ,Û c 4 ,D c 4 , Q c 5 ,Û 5 ,D 5 , and the new leptonsL 4 ,Ê c 4 ,N c 4 ,L c 5 ,Ê 5 ,N 5 . In addition, the new Higgs chiral superfieldsΦ B andφ B acquire nonzero vacuum expectation values (VEVs) to break the baryon number spontaneously, and the super-fieldsΦ L andφ L acquire nonzero VEVs to break the lepton number spontaneously. The model also introduces the superfieldsX,X to avoid stability for the exotic quarks. Actually, the lightest superfields could be a candidate for dark matter. The properties of these superfields in the BLMSSM are summarized in Table 1, where B 4 and L 4 stand for the baryon and lepton number of exotic quark and lepton superfields. In our case we will take B 4 =L 4 = 3 2 [23].
In the BLMSSM, the superpotential is written as [23,24] where W MSSM is the MSSM superpotential, and the concrete forms of W B , W L and W X are We can see that since W X contains superfields X and Q 5 (U 5 , D 5 and X ) which couple to all generations of SM quarks, FCNC processes can be generated.
Correspondingly, the soft breaking terms L soft are generally given as with L MSSM soft representing the soft breaking terms of the MSSM, and λ B , λ L being gauginos of U (1) B and U (1) L , respectively.
To break the local gauge symmetry The mass matrices of the Higgs, exotic quarks and exotic scalar quarks were obtained in our previous work [23]; here, we list some useful results.
In four-component Dirac spinors, the mass matrix for exotic charge-2/3 quarks is which can be diagonalized by the unitary transformations giving Similarly, the concrete expressions for 4 × 4 mass squared matrices M 2 t of exotic charge-2/3 scalar quarks t T = (Q 1 4 ,Ũ c * 4 ,Q 2c * 5 ,Ũ 5 ) are given in appendix B of Ref. [23]; these can be diagonalized by the unitary transformationt Using the scalar potential and the soft breaking terms, the mass squared matrix for X,X can be written as where In addition, the four-component Dirac spinor X is defined as X =(ψ X ,ψ X ) T , with the mass term μ X X X.
The flavor conservative couplings between the lightest neutral Higgs and charge-2/3 exotic quarks are with α defined as The couplings between the lightest neutral Higgs and exotic scalar quarks are with ξ S uij and ξ S dij as defined in Appendix C of Ref. [23].
In the mass basis, we obtain the couplings of quarkexotic quark and the X as and the couplings between up type quarks and the superpartners t , X are

Theoretical calculation of the t → ch process
In this section, we present one-loop radiative corrections to the rare decay t→ch in the BLMSSM. For this process, it is convenient to define an effective interaction vertex [8]: where p is the momentum of the initial top quark, p is the momentum of the final state charm quark, and the form factors F L , F R follow from an explicit calculation of vertices and mixed self-energies, with Here the analytical expressions of the MSSM F MSSM L,R can be found in Ref. [8]. Since the SM contribution is very small, about 10 −13 [7], we ignore the SM form factors. In the following, we will discuss the contributions of the BLMSSM F BLMSSM L,R in detail. The relevant one-loop vertex diagrams of the BLMSSM are drawn in Fig. 1. We can see that the FCNC transitions of new physics are mediated by the exotic up type quark t , the neutral scalar particle X i and their superpartners t , X. The contribution to the form factors can be obtained by direct calculation.
In the equations below, m t , m X , m t , m X denote the mass of the exotic quarks t , the mass of the scalar particle X i , and the mass of their superpartners t , X respectively. B i , C ij are the coefficients of the Lorentz-covariant tensors in the standard scalar Passarino-Veltman integrals (Eq. (4.7) in Ref. [25]), and can be calculated using 'LoopTools'.
In Fig. 1(a), when one-loop diagrams are composed by the neutral scalar particles X i and charge-2/3 new quarks t , the contributions to the form factors F a L and F a R are formulated as with the Passarino-Veltman integrals and the relevant coefficients In Fig. 1(b), when the one-loop diagrams are composed by the superpartners t and X, F b L and F b R are formulated as with 073101-4 and the relevant coefficients are In Fig. 2 we present the relevant self-energy diagrams of the rare decay t→ch in the BLMSSM. As in Ref. [8], it is convenient to define the following structure: Here, the factor m t is inserted only to preserve the same dimensionality for the different Σ [8]. The effective interaction vertex of the mixed self-energy diagrams can be taken as the following general form in terms of the various Σ.
Comparing with Eq. (16), the corresponding contribution to the form factors F L and F R is transparent. Using the couplings above, we can get the Σ of the self-energy diagrams in Fig. 2(a) as where B 0,1 are the two-point functions. Similarly, the Σ of the self-energy diagrams in Fig. 2(b) have the form:

Numerical analysis
In the general case, the partial widths of the t → ch process are [8] where λ(x 2 , y 2 , z 2 ) = (x 2 −(y+z) 2 )(x 2 −(y−z) 2 ) is the usual Källen function, and as mentioned in Eq. (17), +F SM L,R . To compute the branching ratio, we take the SM charged-current two-body decay t→bW to be the dominant t-quark decay mode, which has Γ (t → bW + )= 1.466|V tb | 2 . The branching ratio can be approximated by To reduce the number of free parameters in our numerical analysis, the parameters are adopted as in Ref. [23,24]. With this choice, it is easy for the 2×2 CP -even Higgs mass squared matrix to predict the lightest eigenvector with a mass of 125.9 GeV, and the choice also fits the behavior of h→γγ and h→VV * (V= Z, W) well [23]: choosing m Z B = 1 TeV, μ B = 500 GeV, λ Q = 0.5, and A BQ = 1 TeV. We plot in Fig. 3 the BRs of t → ch versus mQ 4 , with the solid line, dashed line and dotted line corresponding to λ 1 = λ 2 =0.6, 0.4 and 0.2 respectively. We can see that the BRs decrease as mQ 4 runs from 700 GeV to 1300 GeV, and increase when λ 1 = λ 2 increases, because mQ 4 is the mass parameter of the exotic scalar quarks, and λ 1 , λ 2 are proportional to the coupling coefficient. In addition, when mQ 4 1100 GeV, the BRs tend to the results of the MSSM.  In Fig. 4, we plot the variation of Br(t → ch) with m Z B , adopting mQ 4 = 790 GeV, μ B = 500 GeV, λ Q = 0.5, A BQ = 1 TeV, and with λ 1 = λ 2 = 0.6 (solid line), λ 1 = λ 2 = 0.4 (dashed line), and λ 1 = λ 2 = 0.2 (dotted line). We can see that the BRs decrease as m Z B runs from 800 GeV to 1100 GeV, since m Z B contributes to the mass matrix of exotic squarks, and increase when λ 1 = λ 2 increases. When λ 1 = λ 2 = 0.6 or 0.4, Br(t → ch) is of the order of 10 −4 ; when λ 1 = λ 2 =0.2, Br(t→ch) is of the order of 10 −5 .
We assume mQ 4 = 790 GeV, m Z B = 1 TeV, λ Q = 0.5, and A BQ = 1 TeV. We plot in Fig. 5 the BRs of t → ch versus μ B , with the solid line, dashed line and dotted lines corresponding to λ 1 = λ 2 =0.6, 0.4 and 0.2 respectively. We can see that the BRs increase as μ B runs from 300 GeV to 600 GeV, since μ B is inversely proportional to the mass of the exotic squarks.  Choosing mQ 4 =790 GeV, m Z B =1 TeV, μ B =500 GeV and A BQ = 1 TeV, we draw the variation of Br(t → ch) with λ Q in Fig. 6 for λ 1 = λ 2 = 0.6,0.4 and 0.2 respectively. We can see that the curve first increases and then decreases, but not significantly, since λ Q contributes both to the mass of exotic squarks and to the coupling coefficient.

Summary
The LHC is a top-quark factory, and provides a great opportunity to seek out top-quark decays, with earlier work showing that the channel t→ch could be detectable, reaching a sensitivity level of Br(t→ch)∼5×10 −5 [26,27]. In the SM, however, the branching ratio of the process is so small, Br(t→ch)∼ 10 −13 [8], which is too small to be measurable in the near future.
In this work, we study the rare top decay to a 125 GeV Higgs in the framework of the BLMSSM. Adopting reasonable assumptions on the parameter space, we present the radiative correction to the process in the BLMSSM, and draw some of the relationships between the BRs and new physics parameters. We find that the branching ratio of t→ch can reach 10 −3 , so this process could be detected in the near future at the LHC.
In addition, the author of [28] gives an estimated upper limit of Br(t→ch)<2.7% for a Higgs boson mass of 125 GeV, by combining the CMS results from a number of exclusive three-and four-lepton search channels. AT-LAS find the limit of Br(t→ch)<0.83% at 95% C.L. by searching for t → ch, with h → γγ, intt events [29,30]. Our numerical evaluations indicate the BRs are highly dependent upon the parameters λ 1,2 , the values of which can have a sizeable effect on Br(t → ch). Considering the experiment upper bounds from CMS and ATLAS, the parameters λ 1,2 should not be too large under our assumptions of the parameter space.
As we can see above, the t→ch process may be found in the near future, and further constraints on BLMSSM can be obtained from more precise determinations.