J. KalinowskiU(1) extended SUSY Model supersymetryczny z dodatkową grupą U(1) Jan Kalinowski we współpracy z. S.Y. Choi, H.E. Haber i P.M. Zerwas hep-ph/ Seminarium Fizyki Wysokich Energii, 30 kwietnia 2007

J. KalinowskiU(1) extended SUSY Plan seminarium Motywacja wyjścia poza MS Motywacja wyjścia poza MSSM Model z dodatkową symetrią U(1) Sektor Higgsa Sektor neutralin przykład 2x2 Trochę fenomenologii Podsumowanie

J. KalinowskiU(1) extended SUSY Motivation – origin of mass ? In the SM:  one Higgs doublet  the potential  if (why?) and (why?) then EWSB: = v = 246 GeV  4 dof => 3 massive gauge bosons M W =M Z cos  W = gv/2  one physical Higgs boson m 2 H =  v 2 /2  but  m 2 H ~   => hierarchy problem

J. KalinowskiU(1) extended SUSY MSSM medication  two Higgs doublets  the superpotential  nice feature: radiative EWSB  min. cond.    negative Higgs searches => little fine tuning In the MSSM the hierarchy is stabilised:  but why  ~ EW scale? => the  problem

J. KalinowskiU(1) extended SUSY Beyond MSSM  NMSSM: promote to vev of some scalar field S  tan  =5 Bastero-Gil, Hugonie, King, Roy, Vempati 2000 New term increases the Higgs mass - allows lighter stops reducing fine tuning  But broken Z3 symmetry => cosmological domain-wall problem

J. KalinowskiU(1) extended SUSY  Another way to avoid axion is to promote PQ to the U(1) gauge symmetry  Gauge group USSM=SU(3)xSU(2)xU Y (1) x U X (1)  New scalar S and gauge B’ superfields axion eaten-up by a massive Z’ gauge boson  new fermions are needed to cancel anomalies – assume heavy USSM = a LE subset of E 6 SSM of King, Moretti, Nevzorov hep-ph/

J. KalinowskiU(1) extended SUSY Kinetic term mixing gauge kinetic term for B and B’ l can be converted to canonical form the U(1) part of the covariant derivative => effective Q’ x charge l gaugino masses:

J. KalinowskiU(1) extended SUSY Higgs sector Two iso-doublets H u, H d and one scalar S l After spontaneous EW + U(1) X symmetry breaking by the doublet higgsino mass and higgsino-singlino mass terms are generated l physical Higgs bosons: three neutral scalars two charged one neutral pseudoscalar

J. KalinowskiU(1) extended SUSY Higgs sector hep-ph/ , hep-ph/ The USSM Higgs h 1 mass bound l NMSSM USSM

J. KalinowskiU(1) extended SUSY Neutralino sector In thebasis, the neutralino mass matrix: where and Higgs U(1) x charges

J. KalinowskiU(1) extended SUSY Diagonalizing M 6 For small mixing between and - diagonalize first 4x4 and 2x2 blocks - perform block-diagonalization where - eigenvalues only shifted

J. KalinowskiU(1) extended SUSY How to solve for neutralino masses The neutralino mass term in the Lagrangian Original fields Physical fields where we require Mathematically this is the Takagi diagonalization of a general complex symmetric matrix (singular value decomposition)

J. KalinowskiU(1) extended SUSY Takagi diagonalization Physical masses are not eigenvalues; they are singular values and in general cannot be found by a similarity transformation. We want to solve (to simplify notation ) To compute singular values Hermitian, can be diagonalized in the standard way singular values: but U can be found this way only in some particular cases

J. KalinowskiU(1) extended SUSY Takagi diagonalization Example: Singular value 1 is doubly-degenerate But =1, i.e. does not specify U Theorem: for any complex symmetric n x n matrix there exists a unitary matrix such that with real, non-negative

J. KalinowskiU(1) extended SUSY (if = 0, up to a phase) Proof can be rewritten as Denoting k-th kolumn of U by we have Any non-degenerate => unique up to a sign Any degenerate => invariant subspace take any orthonormal set of

J. KalinowskiU(1) extended SUSY By construction Algorithm for constructing U: rewrite as can be diagonalized by an orthogonal transformation If is eigenvalue with eigenvector, then is eigenvalue with eigenvector = Therefore has equal number of positive and negative eigenvalues and even number of zero eigenvalues. 1) take eigenvectors corresponding to positive 2) for m=0, are linearly dependent Recipe for constructing U:

J. KalinowskiU(1) extended SUSY Example Consider The eigenvalues of M are degenerate and zero, and M has only one eigenvector ~ (1, i ). Thus M cannot be diagonalized by a similarity transformation. But M has two non-degenerate singular values: 0 and 2 since = Solving we find check:

J. KalinowskiU(1) extended SUSY Neutralino sector of U(1) extended SUSY In thebasis, the neutralino mass matrix: where and Higgs U(1) x charges

J. KalinowskiU(1) extended SUSY Real symmetric M 6 can always be diagonalized For small mixing between and - diagonalize first 4x4 and 2x2 blocks the diagonal elements can be of both signs - perform block-diagonalization: mixing between MSSM and new states important if

J. KalinowskiU(1) extended SUSY Illustrative example Evolution of the neutralino mass spectrum as a function of We take a scenario with At M’ 1 =0, the 4’ and 5’ states have negative eigenvalues

J. KalinowskiU(1) extended SUSY Neutralino production in e+e- l via s-channel Z, Z’ and t-,u-channel selectron Z, Z’ => mass eigenstates Z 1, Z 2 with mixing angle l Z exchange: selectron exchange:

J. KalinowskiU(1) extended SUSY Neutralino production in e+e- E cm =800 GeV in our scenario The presence of ~1 TeV Z 2 strongly affects cross sections e.g. for M 1 ’=0 although masses of are as in MSSM

J. KalinowskiU(1) extended SUSY Neutralino decays Phenomenology changes significantly: only selected examples  Cascade decays - c.f. LHC celebrated case  also possible but

J. KalinowskiU(1) extended SUSY Neutralino decays  Radiative decays - important in cross-over zones e.g. near M’ 1 =2.6 TeV 4’-5’ zone

J. KalinowskiU(1) extended SUSY Summary  USSM – a well motivated and interesting scenario  new states: scalar Higgs, Z’ and two neutralinos  Here exploratory studies of the USSM neutralino sector  neutralino sector quite complicated  in a weakly coupled regime under good theoretical control  production and decay processes analysed  phenomenology at e+e- and LHC quite different  a systematic survey needs more detailed analyses  cosmological implications => work in progress