EW Naturalness in Light of the LHC Data. Maxim Perelstein, Cornell U. ACP Winter Conference, March

Transcription

1 EW Naturalness in Light of the LHC Data Maxim Perelstein, Cornell U. ACP Winter Conference, March 3

2 SM Higgs: Lagrangian and Physical Parameters The SM Higgs potential has two terms two parameters: Higgs gets a vacuum expectation value, known from e.g. the W mass: The physical Higgs boson mass is Higgs mass at ~6 GeV gives Question for this talk: how natural are these values? Focus on the mass parameter in this talk; quartic also important

3 SM Higgs:Renormalization Higgs mass parameter receives radiative corrections: = Higgs-X coupling constant, = # of d.o.f. in X (X=SM fields) Naturalness: Simple measure of unnaturalness: ( = fine-tuning) An alternative measure (usually agree parametrically, but care is needed):

4 Natural New Physics Scales Hierarchy of SM Higgs couplings TOP HIGGS SU()xU() Gauge Bosons SU(3) Gluons st/nd Gen. quarks, bottom, leptons Cutoff scales required by naturalness are inversely related to the couplings: Top quark: For st, nd gen. quarks, bottom, leptons, this bound is TeV or more.

5 Top Partners Are current experimental bounds on new physics consistent with naturalness? Bounds depend on the specific nature of new physics I will take a bottom-up approach (~simplified model), focusing on the third generation (Higgs+Top+Top Partner) I will consider two well-motivated examples: Spin-/ top partner (a la Little Higgs) Spin- top partner (a la SUSY)

6 Fermionic Top Partner Example : spin-/ top partners ( ) [Berger, Hubisz, MP,5.3] Realization: Little Higgs models L = λ u R V χ L λ fu R U L + h.c. Global SU(3) symmetry (softly broken by quadratic divergence at one-loop: ) enforces cancellation of δµ = 3 λ t m T 8π log Λ m T. Two-parameter model: and

7 Top Partners: FT vs PEW..8 Allowed by PEW Α FT=% m T FT=5% FT=% Pre-LHC: Precision electroweak constraints limit This corresponds to ~% tuning Note: only top-sector included (i.e. assumes other sources of PEW corrections that appear in full LH models are sufficiently suppressed)

8 Top Partners: FT vs LHC Top partner decays: Excluded by CMS search (recast, data)..8 Α.6.4 % FT m T

9 Naturalness and Higgs Couplings Α Α FT=% m T FT=5% FT=% m T Large deviations expected in natural regions of parameter space, due to Higgs compositeness (not loops!) Current Higgs data already puts better bounds than precision electroweak and direct searches!

10 Bosonic Top Partners, a.k.a. Stops Example : spin- top partners A 3-parameter model: h h t It is possible to cancel all Higgs mass instabili t L + + h h h h t R Same as MSSM with everything but decoupled at M>a few TeV [NB: cannot decouple - come back to it later in the talk!] Much recent progress in top-down models realizing such spectra in SUSY Fine-tuning: δm H u 3y ( ) t m 6π Q3 + m t + A Λ c t log m Q 3 + m t c 3 6π ( y t ( m + m m t ) + ( m m ) 4v sin β sin θ t ) log Λ m + m, Fine-tuning is minimal when the messenger scale is as low as possible (model-building issue; probably ~ TeV is the minimum)

11 Stops: Fine-Tuning vs Mass 8 % 8 <% 6 3% 6 4 5% 4 % % % % % 5% 3% No Mixing Maximal Mixing Optimistically assumed ; for higher values, rescale by Note: SUSY models have an additional issue of generating the required Higgs quartic; this is NOT reflected in these plots

12 Fine-Tuning vs Higgs Mass 8. 6 Maximal Mixing MSSM predicts get to 6 GeV at tree level; needs a large stop contribution to fine-tuned at best at ~% level However, small non-minimality can alleviate fine-tuning: new F-term (e.g. NMSSM) or D-term (extra gauge groups) contributions to the quartic NMSSM (extra singlet) only requires -% tuning [Hall, Pinner, Ruderman, ]

13 Stops: LHC Bounds,OM5N5 M-+5N5 56 GeV corresponds to ~5% FT (no mixing, no mass splitting, ) No bounds in special (but pretty broad) regions: Compressed spectrum ( ) Stealthy stop ( ) No bounds if R-Parity is violated (for example, as in MFV-SUSY)

14 Gluinos and Naturalness Rad. corrections to the stop mass also need to be cut off (stop=scalar!) Dominated by QCD; cut off by the gluino naturalness requires (Majorana gluinos, as in MSSM) (Dirac gluinos) [Brust, Katz, Lawrence, Sundrum, ] [Same plot with an on-shell stop?]

15 Same-Sign Dilepton Signature of RPV/MFV SUSY [Berger, MP, Saelim, Tanedo,3.46] 7 95 c.l. exclusion limits: CMS SSDL b jets MET search W b l 6 g t/ t b ν 5 SR8. t t s b t mass GeV 4 SR SR6 SR7 g t/ t W s ν l 3 s 8 TeV.5 fb b Gluino mass bound: ~8 GeV g mass GeV Recast of CMS SSDL+b+MET Search

16 Boosting SSDL RPV Search [Berger, MP, Saelim, Tanedo,3.46] Distribution of R 95 exclusion SR8 j SR8 jj t mass GeV 8 6 SR8 SR6 Stop decay products ang. separation 4 s 4 TeV fb g mass GeV or high-mass fat jets required

17 Naturalness and Higgs Couplings Stop loops contribute to Higgs couplings to gluons and photons [MP, Rey-Le Lorier, in progress] Naive correlation: more FT heavier stops more SM-like hgg; can be violated in the presence of large A-terms (negative contr. to hgg!) No Mixing Maximal Mixing

18 Tree-Level Tuning in SUSY So far, we focused on tree vs. loop tuning, which appears in all models In SUSY, there is a separate issue: two distinct tree-level contributions to Naturalness: SUSY-breaking soft mass SUSY-preserving F-term expect light (~ GeV) Higgsinos [GeV]! m" 5 5 CMS Preliminary pp $! "!"!" ±! m "! - m " $ Z! "!" $ W! " ± < m Z - s = 8 TeV, L = 9. fb int 95% C.L. CLs NLO Exclusions Observed lj +3l ± # Expecteded lj +3l ± # Observed 3l only Observed lj only m ±=m [GeV]! "! " theory Minimal (sort of) spectrum 3 [fb] 95% CL upper limit on # [GeV]! m" m~ l CMS Preliminary pp $! "! m " ±! = m " ±!" ±!" $ ~ e & e, µ " & µ, " %& %!" $ ~ e e, µ " µ, " %% ~ + - Br(! " $ l l ) =.5! > m " - s = 8 TeV, L = 9. fb int 95% C.L. CLs NLO Exclusions Observed 3l Expected 3l m ±=m [GeV] ± +.5m "! "! "! =.5m! " theory ± # theory ± # With light sleptons 3 [fb] 95% CL upper limit on #

19 Naturalness and Dark Matter Direct Detection (MSSM) χ χ h : (gz χ g Z χ )(cos αz χ4 + sin αz χ3 ), χ χ H : (gz χ g Z χ )(sin αz χ4 cos αz χ3 ). Generic mixings: χ q (a) h,h χ q Natural cross section (h exchange only): required to get lower x-section! [MP, Shakya, 7.548] (basically fixed)

20 XENON() XENON() XENONT Color-code: purity p = min(f H, F H ). Red Orange Green Cyan [MP, Shakya, 7.548] [Scan: pmssm, no relic density constraint]

21 XENON() XENON() XENONT Color-code: EWSB fine-tuning Red Green Cyan Lower DD cross section means MORE FINE-TUNING! [Scan: pmssm, no relic density constraint, gaugino LSP]

22 Beyond the MSSM [MP, Shakya, 8.833] XENON() XENON() XENON() XENON() XENONT XENONT NMSSM lambda-susy Lower DD cross section means MORE FINE-TUNING!

23 Conclusions Current LHC bounds (direct searches) demand fine-tuning only at -% level, in a bottom-up approach This applies to spin- as well as spin-/ top partners Even less tuned scenarios are still possible in the spin- case: compressed or stealthy spectra, RPV Higgs rate measurements are beginning to have interesting implications for naturalness, with much more to come Dark matter direct detection bounds are beginning to develop a tension with naturalness, in the (N)MSSM context