Supersymmetry at the LHC What is supersymmetry? Present data & SUSY SUSY at the LHC C. Balázs, L. Cooper, D. Carter, D. Kahawala C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 1/25
What shall we find at the LHC? Experimental data & theoretical hints fl new physics beyond the SM @ LHC The new physics will hopefully explain the origin of mass light Higgs dark matter baryons gauge unification naturalness gravity and more. But... C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 2/25
... we already have theories that explain... well... "everything"! For example: in the supersymmetric framework we can explain the origin of mass: SUSY breaking & radiative dynamics Ø EWSB light Higgs: m tree h d m Z & loop corrections Ø m h d 135 GeV dark matter: conserved R = (-1) 3 HB -LL+2 S Ø LSP stable, neutral WIMP baryons: GUT-, lepto-, baryogenesis Ø baryon-antibaryon asymmetry gauge unification: sparticle loops Ø unification at M GUT ~ 10 16 GeV naturalness: Higgsinos Ø Higgs mass protected by chiral symmetry gravity: gauged supersymmetry Ø supergravity and more. But... C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 3/25
... what are the chances that we confirm, say, SUSY at the LHC??? Surprisingly, this question can be answered Even more surprisingly, this question can be answered quite precisely! But to obtain a quantitative answer, first we have to know what we mean by the theory a bit of statistics what present experiments tell us about the theory what the LHC data might look like I will illustrate this logic using supersymmetry C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 4/25
What do we mean by supersymmetry? Superfields spin Higgs matter force 1 j m y m l m 1 ê 2 j è a y a l è a 0 j y è l Supersymmetry b + 0\ =» y è \, f a +»0\ =» y a \ Q a + ª b - f a +, Q ā ª b + f ā Q a +» y è \ =» y a \, Q ā» y a \ =» y è \ H = 2 i=1 (p i 2 + w 2 x i 2 )/2 = w ([b +,b - ] + {f a +, f ā })/2 = w {Q a +, Q ā }/2 [H, Q a ] = 0 C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 5/25
The MSSM Standard fields Ø superfields Kinetic Lagrangian & gauge interactions super- & gauge symmetry Superpotential W MSSM =-y u H` u ÿ Q` U` + y d H` d ÿ Q` D` + y e H` d ÿ L` E` - m H` u ÿ H` Scalar potential V MSSM = V MSSM (H u, H d,...) No new parameters (compared to the SM with 2 Higgs doublets) Lightest spartner (dark matter) candidates (neutral WIMFs (n,n,u)mssm) spin \ mass M 3ê2 M 1 M 2 M 1 ' m 1 m 2 m S m a è m n è 2 G 3 ê 2 G è 1 B W 0 B' 1 ê 2 B è W è 0 B è ' H è u H è d S è i a è n i 0 H u H d S i a è n i d C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 6/25
Supersymmetry breaking SUSY might be beautiful, attractive and smart, but... she's broken! SUSY breaking is parametrized by the soft Lagrangian all possible term allowed by the symmetries but free of quadratic divergences: soft =-y u A u H u ÿ Q è U è + y d A d H d ÿ Q è D è + y e A e H d ÿ L è E è -mb H u ÿ H d + hc + 1 2 M i l è a è i l ia + 2 mi H i» 2 +m 2 i y è i y è i O(100) soft parameters Top-down approach: msugra (CMSSM), GMSB, AMSB, inomsb,... assumptions: hidden sector, SSB mediation, unification, universality,... scenario is parametrized in terms of a few high (GUT) scale parameters all soft parameters at M EW are determined dynamically by RGE flow Example: msugra M i = M 1ê2, A j = A 0, m i = M 0 m 1, m 2, m, B Higgs potential extrema, v 2 = XH 1 \ 2 + XH 2 \ 2 : tanb & sgn(m) C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 7/25
The statistics bit (that I promised you earlier) Until now, we defined a theory (supersymmetry) and its parameters Now, we assume: the theory is correct & a set of experimental data exists, and define the probability that under these conditions the theoretical parameters have certain values: (parameters theory,data) According to Reverend Bayes (parameters theory,data) = (d t,p)* (p t)/ (d t) (d t,p) = the likelihood that a theory t with parameters p produces data d (p t) = the probability that the parameters have values p in the theory t (d t) = the chance that the set of data d is predicted by a theory t (d p,t) = i exp(-c i 2 /2)/ 2 p s i c i 2 = (d i - t i (p)) 2 /s i 2 In many cases (p t) and (d t) are uniform and then (p t,d) ~ (d t,p) C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 8/25
Likelihood Theoretical parameters (p) are constrained by exp'tal data available today (d i ) for msugra p = {M 0, M 1ê2, A 0, tanb, sign(m)} To quantify experimental constraints we can simply use the log likelihood : c 2 = i d i - t i IpM 2 í s i 2, where i runs over: LEP chargino & Higgs mass Tevatron Br(B s Ø l + l - ) HFAG Br(b Ø s g) g-2 anomalous magnetic moment of m WMAP CDMS neutralino relic abundance spin-independent neutralino-proton elastic recoil C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 9/25
msugra likelihood C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 10/25
msugra likelihood (p t,d) = (d t,p)* (p t)/ (d t) C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 11/25
Problems with MSSM m problem W m H` 1.H` 2 unnatural EW size for m is not justified Electroweak fine-tuning (little hierarchy) problem tension between a light h 0 and LEP limits on spartner (t è ) masses: electroweak precision data demand m h close to 114.4 GeV, but m h = cos 2 H2 bl m 2 Z + m 2 EW KlogK m 2 SUSY 2 O + X 2 t 2 K1 - m t m SUSY X t 2 2 OO 12 m SUSY m SUSY = m t è1 m t è 2, X t = A t - m cot(b) Dark matter fine-tuning problem f ~ max i ( 1 W dw dp i ) large in most constrained MSSM scenarios --- list your own problems with the MSSM here --- C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 12/25
Singlet extensions of the MSSM Easy to fix these MSSM problems while keeping positive features intact! The root of the m and fine-tuning problems is the Higgs sector extending the EWSB sector of the MSSM, these problems are alleviated in the (n,n,s)mssm the W m H` 1.H` 2 dynamically generated by W l S` H` 1.H` 2 no dimensionful parameters are present in the superpotential all these fields (H i and S ) acquire a vev.s at the weak scale electroweak fine tuning can also be alleviated caveat: new dimensionful soft parameters associated with the singlet it can be argued that the m problem is only deferred to SUSY breaking C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 13/25
NmSuGra Discreet symmetries of super- & Kahler potentials: Z 3 ä Z 2 MP solve domain wall problem Superpotential W = W MSSM +l S` H` 1.H` 2 + k 3 S` 3 Next-to-minimal MSSM Scalar potential V = V MSSM + m S 2» S» 2 + Jl A l SH 1.H 2 + k 3 A k S 3 + h.c.n New parameters XS \, 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 1ê2, A 0, XH 1 \, XH 2 \, XS \, l, k, m S 3 minimization eq. & v 2 = XH 1 \ 2 + XH 2 \ 2 eliminates 4 para & tanb =XH 1 \ ê XH 2 \, m =l XS \ exchanges b and m with 2 para Ø 5 free parameters (and a sign): M 0, M 1ê2, A 0, tanb, l, sign(m) A single parameter extension of msugra, without new dimensionful parameters C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 14/25
NmSuGra likelihood C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 15/25
Role of g m -2 Large contribution to c 2 for high M 0 and M 1ê2 from the muon anomalous magnetic moment when the theoretical error is taken at face value exp Da m = am - SM am = 29.5 ± 8.8ä10-10 3.4 s discrepancy main theoretical uncertainty from measurement of s(e + e - Øg * Øhadrons) optical theorem: hadronic vacuum polarization (HVP) ~ s(e + e - Øg * Øhadrons) the HVP contribution can also be calculated using t decay spectral functions in the past there was a significant discrepancy between the e+e- Ø hadrons and t decay based data most recent calculations of the HVP contribution are in better agreement isospin-breaking corrections reduce the difference between these two sets of data (lowering the t-based determination), and a new analysis of the pion form factor claims that the t and e + e - data are more consistent high precision measurements of BaBar will hopefully, improve the accuracy C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 16/25
The LSP is the lightest neutralino Dark matter Z è 1 = N 11 B è + N 12 W è 3 + N 13 H è 1 + N 14 H è 2 + N 15 S è Z è 1 is mostly bino-like as in msugra, but all type of dark matter occurs: bino-, wino-, higgsino- and singlino-like dark matter All the familiar neutralino (co-)annihilation mechanisms are found: bulk region, focus point type region (1), Higgs resonances (via all five neutral Higgses 2), stau co-annihilation (3), stop co-annihilation (4). C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 17/25
Dark matter C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 18/25
Discovery of NmSuGra A given NmSuGra model point is discoverable at LEP if m h 0 < 114.4 GeV or m W è 1 < 103.5 GeV m h 0 limit is relaxed for non-sm-like Higgses LHC if m g è < 1.75 TeV or m t è1 m t è 2 < 2 TeV this is based on detailed msugra analysis SI CDMS1T if s p Z è 1 (m è Z ) is larger than the estimated 1 ton CDMS limit 1 Assuming this, the bulk of the NmSuGra para-space is discoverable! The remaining para-space is disfavored at more than 99 % confidence level this is dominated by g m - 2 C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 19/25
Discovery of NmSuGra C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 20/25
After the discovery (msugra) C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 21/25
Summary The Bayesian approach allows us to calculate the likelihood of discovery of various parameter regions for any (well defined) theories The constrained models of supersymmetry have been tested and the approach is found to produce roboust results Present experiments prefer moderate values of the dimensionful (N)mSuGra parameters M 0, M 1ê2, and A 0 (at 95 % CL) If M 0, M 1ê2, and A 0 are indeed moderate, then the LHC and a ton equivalent of CDMS is guaranteed to discover (N)mSuGra under the condition that the g m -2 discrepancy prevails The msugra and NmSuGra models can be discovered at the LHC at 95 % CL C. Balázs, Monash U. Melbourne SUSY@LHC.nb Seattle, 23 Sep 2008 page 22/25