NmSuGra, LHC & dark matter Csaba Balazs Emerald Univercity, Land of OZ Balazs, Carter PRD78 055001 (0808.0770) Lopez-Fogliani, Roszkowski, Ruiz de Austri, Varley PRD80 095013 (0906.4911) Balazs, Carter JHEP03 016 (0906.5012) C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 1/33
The idea Constrain the simplest supersymmetric models using experiments Use smart statistics to obtain the maximal info about the model Determine future model detectability based on present data Confirm/rule out the simplest models (and repeat for nsimplest?) C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 2/33
The results (for NmSuGra) There's a beautiful complementarity between the LHC and direct dark matter detection experiments C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 3/33
Outline Next-to-minimal supersymmetric standard model Supergravity Parameter extraction: Reverend Bayes Posterior probabilities: Fryer Occam LHC detectability Dark matter direct detection C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 4/33
Supersymmetric models are robust They explain the origin of naturalness: Higgsinos Ø Higgs mass protected by chiral symmetry (inertial) mass: SUSY breaking & radiative dynamics Ø EWSB tree d m Z & loop corrections Ø m h d 135 GeV light Higgs boson: m h dark matter: conserved R = ( - 1) 3 H B - L L + 2 S Ø LSP is a stable WIMP baryonic matter: baryo- or lepto-genesis Ø baryon asymmetry gauge unification: sparticle loops Ø unification w/ M GUT ~ 10 16 GeV gravity: gauged supersymmetry Ø supergravity and more experimental and theoretical puzzles unanswered by the standard models of particle & astrophysics C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 8/33
The Minimal Supersymmetric Standard Model (MSSM) Minimal particle content: standard fields Ø superfields Supersymmetry & gauge symmetry Ø all interactions Standard electroweak symmetry breaking Ø particle masses Model parameters are the same as in the standard model (with 2 Higgs doublets) Superpotential ` U ` D ` E ` ` ` ` ` ` - y d H ` - y e H ` + m H W MSSM = y u H u ÿ Q d ÿ Q d ÿ L u ÿ H d C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 9/33
The Minimal Supersymmetric Standard Model (MSSM) Minimal particle content: standard fields Ø superfields Supersymmetry & gauge symmetry Ø all interactions Standard electroweak symmetry breaking Ø particle masses Model parameters are the same as in the standard model (with 2 Higgs doublets) Superpotential ` U ` D ` E ` ` ` ` ` ` - y d H ` - y e H ` + m H W MSSM = y u H u ÿ Q d ÿ Q d ÿ L u ÿ H d Supersymmetry fl super-partner masses = particle masses C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 10/33
Supersymmetry breaking However beautiful, attractive and smart SUSY is, she's broken! One of the simplest: minimal supergravity motivated model mSuGra universality at M GUT spin 0 (spartner) masses Ø M 0 M 1 ê 2 spin 1/2 (gaugino) masses Ø all tri-linear couplings Ø A 0 tan b = X H u \êX H d \ vacuum expectation values Ø electroweak symmetry breaking fl m 2 Ø sign( m ) è U è D è E è - y d A 0 H d ÿ Q è - y e A 0 H d ÿ L è + m B H u ÿ H d + hc + MSSM = y u A 0 H u ÿ Q � soft è è è è + M 1 ê 2 l * l † y 2 y i + 1 2 M 0 j i j C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 11/33
Problems with the MSSM m problem ` ` W MSSM m H u ÿ H d unnatural ≠ EW size for m is not justified Little hierarchy problem SUSY stabilizes M EW , by protecting m h against O( M P ) fluctuations m h = cos 2 H 2 b L m Z J log J m SUSY 2 N + J 1 - NN 2 2 2 X t X t 2 + m EW 2 2 2 m t m SUSY 12 m SUSY D m h small if m SUSY ~ m t ¨ EW precision data Ø m SUSY ~ O(1 TeV) Electroweak fine-tuning problem dm Z max i ( 1 ) large in most constrained MSSM scenarios m Z dp i Dark matter fine-tuning problem max i ( 1 d W ) large in most constrained MSSM scenarios dp i W C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 14/33
Singlet extensions of the MSSM Root of the m , hierarchy & fine-tuning problems is the Higgs sector extending the EWSB sector of the MSSM, problems are alleviated ` ` in the (n,N,S)MSSM the W m H u ÿ H d dynamically generated by ` H ` ` W l S u ÿ H d all these fields ( H i and S ) acquire vev.s at the weak scale little hierarchy and fine-tunings are also alleviated ` H ` ` ` 3 Next-to-minimal MSSM: W NMSSM = W MSSM,Y + l S 1 ÿ H 3 S 2 + k mSuGra Ø universality fixes all NMSSM parameters, but l 5 free parameters: M 0 , M 1 ê 2 , A 0 , tan b , l Single parameter extension of mSuGra solving several MSSM problems C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 15/33
NmSuGra para count MP Discreet symmetries of super- & Kahler potentials: Z 3 ä Z 2 solve domain wall problem ` H ` ` ` 3 Next-to-minimal MSSM: W NMSSM = W MSSM + l S 1 ÿ H 3 S 2 + k New parameters X S \ , l , k , A l , A k , m S SUSY breaking mSuGra Ø universality: fixes A k = A l = A 0 9 parameters left M 0 , M 1 ê 2 , A 0 , X H 1 \ , X H 2 \ , X S \ , l , k , m S 3 minimization eq. & v 2 = X H 1 \ 2 + X H 2 \ 2 eliminates 4 para & tan b = X H 1 \êX H 2 \ , m = l X S \ exchanges b and m with 2 para Ø 5 free parameters: M 0 , M 1 ê 2 , A 0 , tan b , l Single parameter extension of mSuGra - no new dimensionful para.s C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 16/33
The logic of science: How NOT to discover SUSY A SUSY model parametrized by P = { p 1 , ..., p n } predicts an experimental outcome D = { d 1 , ..., d n } Assume that the LHC measures the predicted D! Ask the simplest question: Has SUSY been discovered? It's (very-very) tempting to answer: Yes! C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 17/33
The logic of science: How NOT to discover SUSY A SUSY model parametrized by P = { p 1 , ..., p n } predicts an experimental outcome D = { d 1 , ..., d n } Assume that the LHC measures the predicted D! Ask the simplest question: Has SUSY been discovered? In reality the answer is: No! Because P fl D does NOT imply D fl P or in terms of conditional probabilities (P|D) ∫ (D|P) where (P|D) is a measure of the plausibility that P is true given D C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 18/33
How to extract parameters The correct relation between conditional probabilities is Bayes theorem: (P|D) (D) = (D|P) (P) (P|D) posterior distribution - this is what we want to know (D) evidence - here only plays the role of normalization (D|P) likelihood function - probability that D is measured given P 2 /2)/ (D|P) = exp( - c i 2 p s i i 2 = ( d i - t i (p i ) ) 2 /( s i ,exp 2 2 ) i=1...N data points c i + s i ,the (P) prior, describes the a-priori (D independent) distribution of P for para extraction have been shown to be close to Jeffrey's C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 19/33
Posterior distributions Marginalized posteriors (p i |D) = Ÿ (P|D) ¤ j ∫ i „ p j i, j = 1, ..., N parameters (p i ,p j |D) = Ÿ (P|D) ¤ k ∫ i, j „ p k i, j, k = 1, ..., N parameters are probability distributions of the parameters Marginalization implements Occam's razor (p i |D) = Ÿ (P|D) ¤ j ∫ i „ p j = Ÿ (D|P) (P)/ (D) ¤ j ∫ i „ p j where 1 = Ÿ (D|P) (P)/ (D) ¤ j „ p j and 1 = Ÿ (P) ¤ j „ p j A model with a fewer parameters has a higher prior density leading to a higher posterior (assuming same likelihood) C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 20/33
Experimental input Experimental data, constraining supersymmetry, available today LEP lower limits on spartner, Higgs masses & cross sections è è (dozens of upper limits - most restrictive m h , m W 1 , m Z 1 ) as for LEP & upper limit on Br( B s Ø l + l - ) Tevatron Br( b Ø s g ), Br( B + Ø l + n l ), D M d , D M s , ... b fact. g m -2 anomalous magnetic moment of muon plays strong role: constraining high M 0 and M 1 ê 2 WMAP WIMP abundance upper limit very important: excluding significant para-space CDMS/Xe WIMP-proton elastic recoil C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 21/33
Probability distributions for input para C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 22/33
Probability maps for input para C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 23/33
Probability maps for input para è coann., h funnels, FP, ... mSuGra features can be identified: t C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 24/33
An old mSuGra movie ... è coann., h funnels, FP, ... mSuGra features: t C. Balázs, Monash U., Melbourne | NmSuGra, LHC & DM.nb Galilei Institute 11 Jun 2010 | page 25/33
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