Phenomenological Aspects of SUSY B-L Extension of the SM 1 Shaaban Khalil Centre for Theoretical Physics British University in Egypt

Outline TeV scale B-L: Minimal bottom-up extension of the SM TeV scale B-L: Minimal bottom-up extension of the SM B-L signatures at LHC B-L signatures at LHC Supersymmetric B-L Supersymmetric B-L B-L Right-handed (s)neutrino B-L Right-handed (s)neutrino (s)neutrino correction to lightest Higgs (s)neutrino correction to lightest Higgs Right-sneutrino Dark Matter Right-sneutrino Dark Matter Conclusions Conclusions 2

The SM, based on the gauge symmetry SU(3) C x SU(2) L x U(1) Y, is in excellent agreement with experimental results. Three firm observational evidences of new physics beyond the Standard Model : 1.Neutrino Masses. 2.Dark Matter. 3.Baryon Asymmetry. These three problems may be solved by introducing right-handed neutrinos. The tremendous success of gauge symmetry in describing the SM indicates that any extension of the SM should be through an extension of its gauge symmetry. Introduction 3

TeV Scale B-L The minimal extension is based on the gauge group: G B-L ≡ SU(3) C x SU(2) L x U(1) Y x U(1) B-L This model can account for the light neutrino masses. New particles are predicted: −Three SM singlet fermions (right-handed neutrinos) (cancellation of gauge anomalies). −Extra gauge boson corresponding to B−L gauge symmetry. −Extra SM singlet scalar (heavy Higgs). S.K. (2006) These new particles have Interesting signatures at the LHC. 4

Z B-L Discovery at LHC  The interactions of the Z′ boson with the SM fermions are described by  Branching ratios:  Branching ratios of Z’ → l+l- are relatively high compared to Z’ → qq: 5 Search for Z’ at LHC via dilepton channels are accessible at LHC.

6  In case of g’’ ~ O(0.1) then M Z B-L ~ O(600) GeV.  In LHC, the neutral gauge boson Z B-L can be produced through:  The SM background for this production consists mostly of the Drell-Yan process:  Therefore, one expects a clear peak at M Z B-L boson in the M e+e- distribution. Z B-L Discovery at LHC (Cont.)  Z B −L boson can be discovered in the e+e− decay channel in the mass region 800<M Z < 1000 GeV with an integrated luminosity of 10 fb −1. Emam, Mine (2008) & Moratti et al. (2009)

7 The lightest heavy neutrinos can be (pair) produced at LHC via Z’ B-L exchange. The main decay channel of R pairs is through two W bosons. Signatures for R at the LHC Integrated luminosity ~ 300 fb -1 gives 71 events for the right handed neutrino mass of 200 GeV while it gives 46 events for the right handed neutrino mass of 400 GeV. S.K., Huitu, Okada, Rai (2008) Possible clean signals, which would enable reconstruction of both the R and Z’ B-L masses, are those involving: (i)Two pairs of charged leptons and missing transverse energy. (ii)Three charged leptons, two jets and missing transverse energy.

Higgs Sector  One complex SU(2) L doublet and one complex scalar singlet:  Six scalar degrees of freedom.  Four are eaten by C,Z 0,W ± after symmetry breaking.  Two physical degrees of freedom: φ, χ. S.K., W. Emam (2007) 8  Mass matrix:  Mass eigenstates:  Masses:  Mixing is controlled by 3 :

Higgs Production  The cross section of this process is proportional to the Higgs boson couplings to the heavy quark mass.  In B-L, the production cross section for the light Higgs state is reduced respect to the SM one by a factor ~ cos 2 .  Heavy Higgs production is suppressed by two effects: a small ~ sin 2  and a large m H’ (compared to m H ). 9  At the LHC, the dominant channel for Higgs boson production is due to gluon-gluon fusion.

10  Both Higgs particles tend to decay into the heaviest gauge bosons and fermions allowed by the phase space.  Branching Ratios of Light Higgs are very close to those of SM: Couplings are cancelled in the ratio.  In addition to SM-like decay channels, either or both Higgs bosons can decay in genuine B-L final states, like R and/or Z’ B-L pairs, with sizable rates. This opens up then the intriguing possibility of all the new states predicted by the B-L model being simultaneously detected at the LHC.

Neutrino Masses and Mixing lLlL eReR R  SU(2) L x U(1) Y (2,-1/2)(1,-1)(1,0)(2,-1/2)(1,0) U(1) B-L A type I seesaw can be obtained from: Majorana mass: After B-L symmetry breaking Dirac mass: After Electroweak symmetry breaking Thus:

TeV Scale B-L with Inverse Seesaw Mechanism Type-I seesaw mechanism implies ~ 10 -6, which may be unnatural small. A new modification for TeV scale B-L model, based on the inverse seesaw mechanism, has been recently proposed. If U(1) B-L is spontaneously broken by a SM singlet scalar  with B-L charge =+1. SM singlet fermions S 1 with B-L =+2 and S 2 with B-L =-2 are introduced, an inverse seesaw mechanism may be implemented. 12  The Lagrangian of the leptonic sector in this model is given by S.K. (2010)

 After B-L and EW symmetry breaking, the neutrino Yukawa interaction terms lead to the following mass terms:  Lepton number is broken but a remnant symmetry: (-1) L+S is survived.  After (-1) L+S is broken at much lower scale, a mass term for S 2 is generated. 13 Diagonalization The 9x9 neutrino mass matrix takes the form: Light neutrino mass ~ eV is obtained for a TeV scale M N, if  S << M N. No restriction imposed on the m D.

14 The scale of B- L symmetry breaking is unknown, ranging from TeV to much higher scales (GUT or Planck NP). In MSSM, the electroweak and SUSY breaking scale are nicely correlated through the mechanism of radiative breaking of the EW symmetry. Radiative corrections may drive the squared Higgs mass from positive initial values at the GUT scale to negative values at the EW scale. The size of the Higgs VEV responsible for the EW breaking is determined by the size of the top Yukawa coupling and of the soft SUSY breaking terms. Analogously, in a SUSY B-L, it is possible to radiatively induce the breaking of B−L having the scale of such breaking directly linked to the soft SUSY breaking scale. B-L Symmetry Breaking Scale

SUSY and B-L Radiative Symmetry Breaking S.K., A. Masiero, 2007 The RGE of relevant scalar masses are: From M X to M W, m 2  1 and m 2  2 are renormalized differently. At O(1) TeV, m 2  1 becomes negative, the minimization condition is satisfied & B-L gauge symmetry is broken. 15 The minimal SUSY version of B-L model has the following superpotential :

SUSY B-L with Inverse Seesaw  The sneutrino mass matrix of one generation is 8x8 matrix, decomposed into 6x6 mass matrix in the basis of and 2x 2 mass matrix of the basis:. 16  In this mode, B-L is spontaneously broken by chiral singlet superfields  1 with a charge = +1 and  2 with −1.  Also three chiral singlet superfields S 1 with charge +2 and three chiral singlet superfields S 2 with charge −2 are considered to implement the inverse seesaw mechanism.  The superpotential of the leptonic sector of this model is  The relevant soft SUSY breaking terms, assuming the usual universality assumptions, are

 If (12) and (23) elements vanish, the sneutrino masses are: 17 B-L Right-Handed Sneutrino where  The sneutrino mass matrix is obtained from the scalar potential that contains sneutrino fields:  The sneutrino mass matrix can be written as a 3x3 matrix, with entries multiplied by the identity 2x2 matrix

(s)Neutrino Correction to Lightest Higgs In MSSM, the mass of the lightest Higgs at one loop is given by 18 This upper limit on the lightest Higgs boson mass barely consistent with experimental data.  The genuine B−L corrections to the lightest SM-like Higgs boson mass can be obtained from one-loop radiative corrections, due to the right- handed neutrinos and sneutrinos,  For stop mass of order TeV, this correction implies that Elsayed, S.K. Moretti, 2011

The one-loop correction in the effective potential is given by the relation: where the supertrace is defined as follow: ΔV, due to one generation of neutrinos and sneutrinos, is given by: Substituting and differentiating gives with 19

for M N [0.4, 2.5] TeV, Y ν [0.1, √(4π)], and cos2θ = 0, lightest Higgs boson massas function of the lightest sneutrino mass is given as follow: B-L (s)neutrino corrections lead to an absolute upper limit on it at around 180 GeV. If the effect of three generations is considered the upper bound reaches 200 GeV. 20

Sneutrino Dark Matter in SUSY B-L  In SUSY B-L, the lightest sneutrino is given by (large tan β and small tan θ limits): 21  In the MSSM, the lightest neutralino is an attractive candidate for cold DM.  The current experimental constraints: LHC limits, WMAP results and CDMS, impose stringent limits on the lightest neutralino even if it consists of gaugino-Higgsino mixture.  The relevant interactions of the B−L right-handed sneutrino are: S.K., Okada, Toma, 2011

22 Possible annihilation channels of sneutrino. 2 nd diagram gives a sub-dominant contribution, however it may be relevant for indirect detection processes. The thermal average annihilation cross section is given with

The sneutrino relic abundance is given by 23

Sneutrino Direct Detection The general form of the elastic scattering cross section between DM sneutrino & nuclei N is given by Where 24 Here M is the the nuclei mass, A and Z are the mass number and the atomic number. The effective Lagrangian parameters b u and b d are defined as

The elastic cross section is quite insensitive to the B−L sneutrino mass. The limits from CDMS II and XENON experiments indicate to a lower-bound of order 3.7×10 −44 cm 2. Thus, our B−L sneutrino DM can be detected in near future. 25  The sneutrino effective interaction is  Thus, the elastic scattering cross section of B−L right-handed sneutrino is given by  The following upper bound on elastic cross section is obtained:

Sneutrino Indirect Detection A huge, unexplained, boost factor must be introduced in order to account for Pamela results. As a result, it is difficult for our B−L sneutrino to explain the controversial results of PAMELA experiment. 26  B−L sneutrino annihilates into ℓ + ℓ - channels,  However, these channels give sub-dominate contribution to the annihilation process.  Therefore, the corresponding annihilation cross section is < 10 −27 cm 3 s −1.

Summary 27  The SM gauge group can be minimally extended by adding U(1) B−L  B-L extension contains (at least) three right handed neutrinos, extra gauge boson, and extra scalar Higgs. Promising signatures at LHC.  SUSY B-L is just as exciting:  It incorporates well known benefits of SUSY models (gauge coupling unification, solution to the hierarchy problem).  It alleviates well known flaws of more minimal SUSY realizations (such an upper limit on the lightest Higgs boson mass barely consistent with experimental data).  The right-handed sneutrino in the SUSY B-L model with inverse seesaw mechanism is also a viable candidate for cold DM.  Like its SM counterpart, right-handed sneutrino can be a long-lived particle and be pair produced at the LHC through Z B-L. Then, it decays into same-sign di- leptons, with a total cross section of order O(1) pb.  This signal is a striking sparticle signature of the SUSY B-L gauged model.

Thank you 28