LHC More than just Discoveries. Tilman Plehn. SUSY parameters. Markov chains. SUSY maps. MPI für Physik & University of Edinburgh.

Transcription

1 LHC More than MPI für Physik & University of Edinburgh Budapest, 6/27

2 Outline Weak Boson Fusion and Supersymmetry Supersymmetric parameter space SUSY parameter maps

3 Weak Boson Fusion and Supersymmetry Supersymmetry or else... Majorana gluino identifiable once seen Majorana neutralinos? Majorana LSP? signature: like sign charginos [Alwall, TP, Rainwater] stable for simplicity chargino kinematics not necessary [SM backgrounds] () visible over backgrounds? (2) distinct WBF signal? [LHC precision physics attempt] [SUSY QCD backgrounds only] long shot, but interesting and not swamped by SUSY-QCD ) /σ dσ/dp T (jet.45 EW(WBF) EW (all) EW (non-wbf) QCD P T (jet ), GeV/c.2 EW(WBF).8 EW (all).6 EW (non-wbf).4 QCD H T, GeV/c /σ dσ/dh T

4 Alternative Hypotheses Like-sign scalars without Majorana neutralinos assume stable charged Higgs (type-ii two-higgs doublet model) H + H same as simple heavy H [TP, Rainwater, Zeppenfeld; Hankele, Klamke, Figy] WBF signal: two key distributions φ jj, p T,j scalars with flat φ jj, similar to fermions Goldstone modes in W coupling to final state fermions: + ( x)2 P T (x, p T ) 2x p 2 T + ( x)2 (pt 2 + ( x) m2 )2 2x p W T 2 ( x)2 P L (x, p T ) x scalars identified by softer p T,j m 2 W ( x)2 (pt 2 + ( x) m2 W )2 x m 2 W p 4 T ) /σ dσ/dp T (jet.9 χ+χ+ WBF H+H+ W +W P T (jet ), GeV/c

5 Alternative Hypotheses Like-sign vectors without Majorana neutralinos problem: define consistent hypothesis to kill start with copy of SM, heavy W, Z, H, f good news: H necessary for unitarity, but irrelevant at LHC transverse type p T,j distribution like charginos vectors identified by Dirac structure s φ jj ) /σ dσ/dp T (jet.9 χ+χ+ WBF H+H+ W +W P T (jet ), GeV/c ) 2, jet /σ dσ/d φ(jet.9 χ+χ+ WBF.8 H+H+.7.6 W +W φ(jet, jet ) 2

6 Alternative Hypotheses Like-sign vectors without Majorana neutralinos problem: define consistent hypothesis to kill start with copy of SM, heavy W, Z, H, f good news: H necessary for unitarity, but irrelevant at LHC transverse type p T,j distribution like charginos vectors identified by Dirac structure s φ jj Role of heavy fermions not part of the naive set of WBF diagrams gauge connected for Standard Model WW production huge effect on transverse momentum and other scaling distributions ) /σ dσ/dp T (jet SM W+W+ W +W + (quark partners) W +W + (only W Z ) ) 2, jet /σ dσ/d φ(jet SM W+W+ W +W + (quark partners) W +W + (only W Z ) P T (jet ), GeV/c φ(jet, jet ) 2

7 Supersymmetric parameter space Skipping masses and edges for today... parameters: weak-scale Lagrangean measurements: masses or edges, branching fractions, rates,... errors: general correlation, statistics & systematics & theory [SM and BSM backgrounds, QCD environment] problem in grid: huge phase space, no local minimum? problem in fit: domain walls, no global minimum? problem in interpretation: marginalization, secondary minima? Ben s and Chris weather forecasts assume it s SUGRA extract m, m /2, A, tan β, sign(µ), y t,... include all indirect constraints Bayesian probability map as of today [Allanach, Lester, Weber] M /2 (TeV) m (TeV) L/L(max)

8 Supersymmetric parameter space Skipping masses and edges for today... parameters: weak-scale Lagrangean measurements: masses or edges, branching fractions, rates,... errors: general correlation, statistics & systematics & theory [SM and BSM backgrounds, QCD environment] problem in grid: huge phase space, no local minimum? problem in fit: domain walls, no global minimum? problem in interpretation: marginalization, secondary minima? Sfitter: TeV-scale MSSM originally purely best-fit search technically painful () grid for closed subset (2) fit of other parameters (3) complete fit measurements conclusive! secondary minima? LHC ILC LHC+ILC SPSa tanβ.22±9..26±.3.6±.2 M 2.45± ±. 2.23±. 2.2 M ±5 fix ± M τl fix ± ± M τr 29.3± ± ± M µl 98.7± ± ± M q3l 498.3± 497.6± ± M t R fix 5 42± ± M br ±3 fix ± Aτ fix -22.4± ± A t -57.8±9-5.95± ± A b ±3563 fix -977±

9 New physics parameter spaces [Sfitter: Lafaye, TP, Rauch, Zerwas] always start at exclusive likelihood map p(d m) over m problem: blind directions in m [flavor physics is different] () Bayes theorem: p(m d) = p(d m) p(m)/p(d) [measure theorist s prejudice p(m)] (2) profile likelihood: best-fit point in blind direction [no integration, no pdf] Sfitter: () compute map p(m d) of parameter space (2) rank local maxima (3) do your favorite Bayesian/frequentist dance... Weighted map (chain) based on probability of a state expensive energy function on sample BSM physics: map p(m d) of parameter points evaluate same probability from (binned) density weighted [inspired by weighted Monte Carlo] already for msugra: MCMC resolution not sufficient additional likelihood hill climber to rank maxima

10 New physics parameter spaces [Sfitter: Lafaye, TP, Rauch, Zerwas] always start at exclusive likelihood map p(d m) over m problem: blind directions in m [flavor physics is different] () Bayes theorem: p(m d) = p(d m) p(m)/p(d) [measure theorist s prejudice p(m)] (2) profile likelihood: best-fit point in blind direction [no integration, no pdf] Sfitter: () compute map p(m d) of parameter space (2) rank local maxima (3) do your favorite Bayesian/frequentist dance... Sfitter toy model test function V ( x) in 5 dimensions [general high dimensional extraction tool] Sfitter output #: fully exclusive likelihood map [hard to plot] Sfitter output #2: ranked list of local maxima x V=74.9 ( ) V=59.9 ( ) V=58.2 ( ) V=25. ( ) V=6. ( ) V=2. ( ) x

11 SUSY parameter maps msugra-spsa map with LHC edges kinematic edges with free y b, y t, flat theory errors included Sfitter output #: fully inclusive likelihood map Sfitter output #2: ranked list of local maxima m / e+7 e+6 χ 2 m m /2 tan β A µ m t.3e m

12 SUSY parameter maps msugra-spsa map with LHC edges kinematic edges with free y b, y t, flat theory errors included strong correlation e.g. of A and y t after properly including all (theory) errors points around maximum in m -m /2 plane [left: Bayesian pdf; right: p-likelihood; top: µ < ; bottom: µ > ] m t 8 m t A 2 A m t 8 m t A A

13 SUSY parameter maps msugra-spsa map with LHC edges kinematic edges with free y b, y t, flat theory errors included statistics does not make a difference to you, look at tan β [top: tan β; bottom: B; left: Bayesian pdf; right: p-likelihood].. /χ 2 e-4 /χ 2 e-4 e-6 e-6 e-8 e tan(β) tan(β).. /χ 2 e-4 /χ 2 e-4 e-6 e-6 e-8 e tan(β) tan(β) we can do msugra properly, more observables via brand-new SLHA2

14 SUSY parameter maps MSSM: the real thing nothing but going from 6D to 5D space practically: killing grids, Minuit, laptop analyses, Master Code,... Sfitter outputs # and #2 still the same [weighted Markov chain plus hill climber] p-likelihood or Bayesian probability maps for correlated space [left: Bayesian pdf; right: p-likelihood] 8 e+7 e+6 8 e+7 e+6 M M M M 5 e+7 e+6 5 e+7 e+6 µ µ M M

15 SUSY parameter maps MSSM: the real thing nothing but going from 6D to 5D space practically: killing grids, Minuit, laptop analyses, Master Code,... Sfitter outputs # and #2 still the same [weighted Markov chain plus hill climber] bottom up running of RGE [Sfitter + Kneur] /Mi vs log(q).4 M /2Gen vs log(q) M 3Gen vs log(q) 7 A_3rdGen vs log(q) testing models instead of believing in them

16 LHC will do a great job......but you have to get things right LHC will find signals for TeV scale new physics LHC will study exclusive signals LHC will provide us with mass and many other measurements we have to get the QCD part right we have to get the errors part right we have to get the statistics part right we have to talk to (the right) experimentalists

17