Beyond the SM: SUSY. Marina Cobal University of Udine

Transcription

1 Beyond the SM: SUSY Marina Cobal University of Udine

2 Why the SM is not enough The gauge hierarchy problem Characteristic energy of the SM: M W ~100 GeV Characteristic energy scale of gravity: M P ~ GeV Quantum gravity (?) SUSY algebra contains generator of space-time translations Quadratic divergence of the mass of scalar bosons Arbitrary parameters in the SM Electroweak symmetry breaking (EWSB) mechanism

3 Supersymmetry Fermion Boson SUSY at the scale Λsusy : Λ Λ susy susy 1011 GeVin MSSM TeV in GMSB

4 It solves the problem of the ultraviolet divergency of the Higgs mass: huge fine-tuning needed to keep the scalar Higgs mass finite, protecting it from loop corrections: Higgs mass stabilization "m H 2 = # B 2 $ 2 "m H 2 = %# f $ 2 SUSY: motivations J=1 J=1/2 J=0 + + Quadratic divergences with Λ Cancellations are the same if all the particles have the same mass and the same coupling constants A Higgs mass equal or less than1 TeV (as predicted by the MS) requires that SUSY is broken at this scale, that is, particle masses differentiate at this scale: m B2 m F2 < 1 TeV 2 )

5 A (Very) Brief History of SUSY First mathematically consistent formulation was made in the 1970 s by several independent groups Part of superstring theory Current collider studies set limits on the masses of SUSY particles

6 SUSY Algebra Supersymmetry is a symmetry that relates boson to fermion degrees of freedom. The generators of supersymmetry are two component anticommuting spinors, satisfying:

7 SUSY particles

8 Spontaneous symmetry breaking The possible SUSY models depend from the way the symmetry is broken. This can be done in different ways: - Gravity mediated: the lagrangian terms of susy breaking contain superpotential with the gravitons ( e.g. msugra ) - Gauge mediated: the superpotential is built from ordinary gauge - Other scenarios anomalous /exotics: ASMB The spectroscopy and the Number of parameters depend from the model

9 Spontaneous symmetry breaking in SUSY Examples of different spectra in SUSY

10 MSSM SUSY is broken via gravitational interactions of the particles with fields (msugra) The Minimum Supersymmetric Standard Model (MSSM) is the minimal extension of the SM, the one which predicts the minimum spectrum of particles compatible with the existence of SUSY and a reduced number of parameters Coupling constants U(1), SU(2), SU(3) Higgs couplings with fermions Mass terms for the Higgs bosons Mass terms for the gauge bosons (W,Z,g) Mass terms for the scalars (sfermions and charged Higgs) Contribution to the mixing of the left and right handed sfermions Contriibution to the Higgs potential

11 New multiplicative quantum number: R-parity R p = If R is conserved (classic scenario): + 1 SM particles - 1 SUSY particles -the lightest supersimmetric particle (LSP) is stable and neutral -NLSP -> LSP + particelle del MS In MSSM : lightest neutralino LSP: In GMSB: gravitino G ~ χ A stable SUSY-LSP would be a perfect candidate to justify the presence of such a quantity of drak matter in our universe. Universe composition according to the latest measurements 0.03% heavy atoms 0.5 % neutrinos 4.5% barions 25% dark matter 70% dark energy

12 Higgs sector: from SM to MSSM In the Minimal SuperSymmetric Model there are two Higgs doublet (is the minimum number needed to give a mass to the fermions and to the s-fermions) Standard Model 1 Higgs doublet (v) 1 final state H 1 parameter M H radiative corrections: quadratically divergent MSSM 2 Higgs doublets (v 1,v 2 ) 5 final states h, H, A, H +, H- 2 needed parameters: M h, tanβ=v 2 /v 1 finite radiative corrections, but depending from m top, m susys A t A b m

13 Constrained MSSM In the constrained version (CMSSM), the hypothesis is done that at the Plank scale there is just one universal mass parameter for all the gauginos m 1/2, and there is just one mass for the scalars: m 0. Terms of symmetry breaking in SUSY: universal parameters M 1/2 -> M i A µ tanβ Gaugino masses M 1 :M 2 :M 3 =α 1 :α 2 :α 3 Trilinear m 0 Sfermion GUT scale Higgsino mass <H 2 > 0 <H 1 > 0 The full low energy spectrum (the one which can be observed experimentally) of the SUSY particles depends from these parameters and from the coupling constants, and can be evaluated as a function of these input parameters Regions.

14 SUSY strategy searches at LHC If SUSY exists at the EW scale then it will be accessible at the LHC Cascade decays up to LSP 1. Step: Look for deviation of the Standard Model combination of Jets, Leptons, E miss Example: Multijet + E miss T signature T 2. Step: Define the SUSY mass scale with inclusive variables, es. Effective masses 3. Step: Determination of the model parameters Strategy: select particular decay chains and use the kinematics to determine the mass combinations

15 Constrained MSSM The cross sections for the production of s-particles (and then the Physics reach, for a given machine) are reported in the plane (m 0, m 1/2 )

16 SUSY particle production at the colliders 16

17 SUSY particle decays at the colliders Corso SM, Dottorato, XX ciclo 17

18 SUSY at the e+e- colliders e e e e e e e e e e χ χ χi χ j... ~~... ~~ νν... qq ~~... Couple of charginos neutralinos sleptons sneutrinos squark Mass Limits Nothing has been found up to s=208 GeV! m ( 0 χ ) 1 ( + χ ) m m ~ ~ m m q~ 1 ( ν ) ( ) > > 50 GeV/c 90 GeV/c ( ) 2 > GeV/c 2 2 > 100 GeV/c > GeV/c 2 2

19 SUSY candidate E CM =196 GeV M(miss)=148 GeV/c 2 P(μ)=8.5 GeV/c M(hadr)=16 GeV/c 2 e + e - " # + # $ " # 1 0 # 1 0 µ%qq

20 Squarks and gluinos Squarks e gluinos produced through strong processes high x-section d urto Production depends from the squark e sgluinos mass m ~q, ~ g ~ 1 TeV σ ~ 1 pb 10 4 events produced at low L

21 Decay of squarks and gluinos q ~ χ 0 2 χ 0 1 q Z q ~ q χ 0 2 Z χ 0 1 Decays of squarks and gluinos 3 Possible productions: The cascade decays are very complex. The main topology is: Missing transverse energy + Jets at high PT

22 Decay of squarks and gluinos If the R-parity is conserved: jets (many from b quark and tau), isolated and non-isolated leptons and E T miss from - At least 2 acoplanar jets and high Etmiss -up to 4 jets (gluinos) E T > 100, 50, 50, 50 GeV, E miss T > 100 GeV Max effective mass = m_squark (or m_gluino) ( effective mass) No-lepton SM example: msugra m 0 = 100 GeV, m 1/2 = 300 GeV tan β = 10, A 0 = 0, µ > 0 ttbar+jets Z ( νν)+jets W+jets QCD jets All backgrounds SUSY signal (SU3) SUSY LHC reach Squark and Gluino masses 1 fb -1 M ~ 1500 GeV 10 fb -1 M ~ 1900 GeV 100 fb -1 M ~ 2500 GeV TeV-scale SUSY immediately accessible

23 SUSY searches at LHC 14 TeV) Tiypical SUSY event: ET(miss) + jets Up to 1.3TeV: one week Up to 1.8TeV: one month Up to 2.2TeV: one year 3TeV: final limit E T Physics reach at LHC in the (m 0,m 1/2 ) plane 23