Karlsruhe, 12/2006. New Methods for New Physics. Tilman Plehn. Supersymmetry. LHC Signals. Masses. Spins. Parameters. Some ideas

Transcription

1 New Methods MPI für Physik & University of Edinburgh Karlsruhe, 12/26

2 Outline TeV scale supersymmetry Supersymmetric signatures at LHC New physics mass measurements New physics spin measurements Supersymmetric parameter studies Under construction

3 TeV scale supersymmetry: 1 Starting from data... H t H W...which seems to indicate a light Higgs [e-w precision data] problem of light Higgs: mass driven to cutoff of effective Standard Model: δm 2 H g2 (2m 2 W + m2 Z + m2 H 4m2 t ) Λ2 easy solution: counter term to cancel loops or new physics at TeV scale: artificial, unmotivated, ugly supersymmetry extra dimensions little Higgs (pseudo Goldstone Higgs) Higgsless, composite Higgs, TopColor, YourFavoriteNewPhysics... typically cancellation by new particles or discussing away high scale beautiful concepts and symmetries problematic to realize at TeV scale new physics models in baroque state [data seriously in the way] Idea of supersymmetry: cancellation of divergences through statistics factor (-1) [ SM fermions to scalar; SM gauge bosons to fermions; SM scalars to fermions]

4 TeV scale supersymmetry: 2 SUSY breaking: (yet) unobserved partners heavy link to BSM dark matter [Falk,...] link to BSM (g 2) µ? [Stöckinger] link to flavor physics and baryogenesis? [Standard Model fine??] mechanism for SUSY masses unknown [soft SUSY breaking mediated somehow?] maximally blind mediation: msugra/cmssm scalars: m, fermions: m 1/2, tri-scalar term: A plus sign(µ) and tan β in Higgs sector alternatives: gauge, anomaly, gaugino mediation? measure spectrum at LHC instead [not a LHC paradigm!] LHC phenomenology: MSSM conjugate Higgs field not allowed give mass to t and b? two Higgs doublets SUSY Higgs alone interesting would be another talk... SUSY partners at LHC spin d.o.f. fermion f L, f R 1/2 1+1 sfermion fl, f R 1+1 gluon Gµ 1 n-2 gluino g 1/2 2 Majorana gauge bosons γ, Z Higgs bosons h o, H o, A o 3 neutralinos χ o i 1/2 4 2 Majorana gauge bosons W ± Higgs bosons H ± 2 charginos χ ± i 1/2 2 4 Dirac graviton G 2 2 gravitino G 3/2 2 tough

5 at LHC: 1 Inclusive: squarks and gluinos at Tevatron squarks, gluinos strongly interacting p p q q, q g, g g [best if m( q) m( g)] cross sections large at hadron colliders decays to jets and LSP g q q, q L q χ 2, q R q χ 1 [additional jets and leptons possible] gaugino mass unification assumed for details experienced in inclusive jets plus LSP ) 2 Squark Mass (GeV/c DØ Run II Preliminary L=31 pb UA1 UA2 DØ IA LEP 1+2 CDF IB DØ IB DØ II no msugra solution m(q ~ )<m( χ1 ) Gluino Mass (GeV/c ) LEP2 χ +/- LEP2 ~ l

6 at LHC: 1 Inclusive: squarks and gluinos at Tevatron squarks, gluinos strongly interacting p p q q, q g, g g [best if m( q) m( g)] cross sections large at hadron colliders decays to jets and LSP g q q, q L q χ 2, q R q χ 1 [additional jets and leptons possible] gaugino mass unification assumed for details experienced in inclusive jets plus LSP ) 2 Squark Mass (GeV/c DØ Run II Preliminary L=31 pb UA1 UA2 DØ IA LEP 1+2 CDF IB DØ IB DØ II no msugra solution m(q ~ )<m( χ1 ) Gluino Mass (GeV/c ) LEP2 χ +/- LEP2 ~ l When will I believe we see SUSY QCD? gluinos Majorana fermions jet in gluino decay q or q final state leptons with both charges like sign dileptons from g g [Barger,...; Barnett,...; Baer,...] g ũ χ + χ µ + g ũ * χ µ

7 at LHC: 2 New physics at the LHC (1) possible discovery signals for new physics, exclusion of parameter space (2) measurements (3) parameter studies CMS g(3) ~ miss E T (1 fb -1 ) L dt = 1, 1, 1, 3 fb -1 A =, tanβ= 35, µ > miss E T (3 fb -1 ) h(123) m 1/2 (GeV) one 2 TH q(5) ~ h(11) EX Ωh 2 =.15 Ωh 2 =.4 g(5) ~ 5 Ωh 2 = 1 q(1) ~ q(2) ~ q(15) ~ g(15) ~ g(2) ~ miss E T (1 fb -1 ) miss E T (1 fb -1 ) g(1) ~ g(25) ~ q(25) ~ cosmologically plausible region Fermilab reach: < 5 GeV m (GeV) one one one DD_211 Catania 18

8 at LHC: 2 New physics at the LHC (1) possible discovery signals for new physics, exclusion of parameter space (2) measurements masses, cross sections, decays (3) parameter studies MSSM Lagrangean, SUSY breaking approach independent of new physics model Some SUSY signals [NLO: Prospino2] jets and /E T : pp q q, g g, q g funny tops: pp t 1 t 1 like sign dileptons: pp g g [ g ũū χ + 1 dū or g ũ u χ 1 du] tri-leptons: pp χ 2 χ 1 [ χ 2 l l χ 1 l l; χ 1 χ 1 l ν] inclusive: similar to Tevatron exclusive: enough events for studies at LHC χ 2o χ 1+ σ tot [pb]: pp g g, q q, t 1t 1, χ 2 o χ 1+, ν ν, χ 2o g, χ 2o q t 1t 1 ν ν χ 2o q χ 2o g q q g g S = 14 TeV NLO LO m [GeV]

9 New physics mass measurements: 1 b b µ µ Spectra from cascade decays decay g b b χ 2 b b µ + µ b b χ 1 cross sections some 1 pb [more than events] thresholds & edges [m ll 2 < (m2 χ 2 detector resolution, calibration, systematic errors, shape analysis, cross sections as input? [better not via Z or to τ] m 2 l )(m2 l m2 χ 1 )/m 2 l ] spectrum information from decay kinematics [Hinchliffe,...;Allanach,...; not only SUSY: Reece & Meade] dσ/dm ll (Events/1fb -1 /.375GeV) g (a) m ll (GeV) b ~ χ 2 o µ ~ χ 1 o dσ/dm llq (Events/1fb -1 /5GeV) (b) m llq (GeV) dσ/dm lq (Events/1fb -1 /5GeV) 2 1 dσ/dm lq (Events/1fb -1 /5GeV) (c1) High m lq (GeV) (c2) Low m lq (GeV) dσ/dm llq (Events/1fb -1 /5GeV) dσ/dm zq (Events/1fb -1 /5GeV) (d) m llq (GeV) (e) m zq (GeV)

10 2 1 1 New Methods New physics mass measurements: 1 b b µ µ Spectra from cascade decays decay g b b χ 2 b b µ + µ b b χ 1 cross sections some 1 pb [more than events] thresholds & edges [m ll 2 < (m2 χ 2 detector resolution, calibration, systematic errors, shape analysis, cross sections as input? [better not via Z or to τ] m 2 l )(m2 l m2 χ 1 )/m 2 l ] spectrum information from decay kinematics [mass differences with smaller errors] g b ~ χ 2 o µ ~ χ 1 o Gluino mass from kinematic endpoints b L in chain, all jets b-tagged [Gjelsten, Miller, Osland] most of time: cascade assumption correct gluino mass to 1% m χ1 m~ l R m χ2 [theoretically defined?] m~ - m q L χ1 - m χ l R m~ - m χ m χ b ~ 1 - m m g ~ m~ - m b 1 χ1 m~ - m g χ1 m~ q L m~ g m~ b Sparticle masses and mass differences [GeV]

11 New physics mass measurements: 2 Squarks and gluinos always with many jets cascade studies sensitive to jet simulation? matrix element g g+2j and ũ L g+2j [p T,j > 1 GeV] Pythia shower tuned at Tevatron QCD no killer for decay analyses [TP, Rainwater, Skands] [the heavier the better] σ [pb] t t 6 g g ũ L g σ j σ 1j σ 2j dσ/dp T [pb/gev] dσ/dp T [pb/gev] LHC: Susy-MadGraph 2 Pythia: p T (power) 2 p T (wimpy) Q 2 (power) Q 2 (wimpy) Q 2 (tune A) LHC: sps1a mod Susy-MadGraph 2 Pythia: p T (power) 2 p T (wimpy) Q 2 (power) Q 2 (wimpy) Q 2 (tune A) p T,j (pp tt j) p T,j 5 GeV η j <5, R jj >.4 K Pythia =1.8 p T,j (pp ũ L ũ L j) p T,j 5 GeV η j <5, R jj >.4 K Pythia =1.25 max p T,j (pp tt jj) p T,j 5 GeV max p T,j (pp ũ L ũ L jj) p T,j 1 GeV min p T,j (pp tt jj) p T,j 5 GeV min p T,j (pp ũ L ũ L jj) p T,j 1 GeV GeV

12 New physics mass measurements: 2 Squarks and gluinos always with many jets [TP, Rainwater, Skands] cascade studies sensitive to jet simulation? matrix element g g+2j and ũ L g+2j [p T,j > 1 GeV] Pythia shower tuned at Tevatron QCD no killer for decay analyses [the heavier the better] σ [pb] t t 6 g g ũ L g σ j σ 1j σ 2j SUSY plus jets: complex final states [Smadgraph: Cho, Hagiwara, Kanzaki, TP, Rainwater, Stelzer] Majoranas and fermion number violation in Madgraph tested set of Feynman rules [4+ processes: Madgraph - Whizard (Reuter) - Sherpa (Schumann)] implemented in Madevent [Alwall, Maltoni: Louvain group] publicly available:

13 New physics spin measurements: 1 All new physics is hypothesis testing assume squark cascade observed strongly interacting scalar? q µ µ q ~ χ 2 o µ ~ χ 1 o straw-man model where squark is a fermion: universal extra dimensions [Appelquist, Cheng, Dobrescu; Cheng, Matchev, Schmaltz; spectra degenerate ignore; cross section larger ignore] Squark slepton cascade [Smillie, Webber, Athanasiou, Lester] decay chain q χ 2 l χ 1 trick 1: compare with KK q, Z, l, γ trick 2: invariant angles bm = m jl /m max jl most promising [Barr] typically largest pp q g trick 3: production asymmetry q : q 2 : 1 A = [σ(jl + ) σ(jl )]/[σ(jl + ) + σ(jl )] or spin or both? [Arkani-Hamed,...] masses from kinematic endpoints [use m lj, m ll, m jll...] spins from distributions between endpoints [endpoints identical in SUSY and UED]

14 New physics spin measurements: 2 Back to sign of SUSY QCD like sign dileptons indicate Majorana fermion? always like sign dileptons from bosonic gluon show gluino fermionic compare with usual straw man [UED Madgraph: Alves] g b b µ µ b ~ χ 2 o µ ~ χ 1 o

15 New physics spin measurements: 2 Back to sign of SUSY QCD like sign dileptons indicate Majorana fermion? always like sign dileptons from bosonic gluon show gluino fermionic compare with usual straw man [UED Madgraph: Alves] dσ/dm bl ± [fb/gev] dσ/dm bl ± [fb/gev].4 SUSY bl - all cuts bl m ± bl [GeV].4 UED bl - all cuts bl +.2 Gluino bottom cascade [Alves, Eboli, TP] m bl ± [GeV] decay chain like for gluino mass compare with first KK g, q, Z, and l (1) replace initial state asymmetry by b vs. b asymmetry to write down: A = [σ(bl + ) σ(bl )]/[σ(bl + ) + σ(bl )] [still visible after cuts and smearing] independent on production channels (2) purely hadronic m bb [sensitive to gluino boost] masses and spins accessible in decays at LHC A ± = (σ(bl + )-σ(bl - ))/sum A ± = (σ(bl + )-σ(bl - ))/sum A ± = (σ(bl + )-σ(bl - ))/sum.5 SUSY(e ~ +µ ~ +τ ~ ) UED(e (1) +µ (1) +τ (1) ) SPS1a L = 6 fb -1 Mass Spectrum all cuts SUSY(e ~ +µ ~ +τ ~ ) UED(e (1) +µ (1) +τ (1) ) m bl ± [GeV] SPS1a L = 6 fb -1 Mass Spectrum basic cuts q ~ g ~ sample g ~ g ~ sample UED m bl ± [GeV] SPS1a L = 2 fb -1 Mass Spectrum all cuts m bl ± [GeV]

16 Supersymmetric parameters: 1 Theory output from LHC: SUSY parameters parameters: weak-scale Lagrangean [Sfitter: Lafaye, TP, Rauch, Zerwas; Fittino; Arkani-Hamed,...] measurements: masses or edges branching fractions cross sections errors: general correlation, statistics & systematics & theory problem in grid: huge phase space, local minimum? problem in fit: domain walls, global minimum? First go at problem ask a friend how SUSY is broken msugra/cmssm fit m, m 1/2, A, tan β, sign(µ), y t,... no problem, include indirect constraints [Ellis, Heinemeyer, Olive, Weiglein,..] probability map as of today [Allanach, Lester, Weber] best fit from LHC/ILC measurements SPS1a LHC LHC ILC LHC+ILC masses edges m m 1/ tan β A

17 Supersymmetric parameters: 1 Theory output from LHC: SUSY parameters parameters: weak-scale Lagrangean [Sfitter: Lafaye, TP, Rauch, Zerwas; Fittino; Arkani-Hamed,...] measurements: masses or edges branching fractions cross sections errors: general correlation, statistics & systematics & theory problem in grid: huge phase space, local minimum? problem in fit: domain walls, global minimum? MSSM instead of msugra/cmssm (1) grid for closed subset (2) fit of other parameters (3) complete fit LHC+ILC perfect [Weiglein etal] too few measurements? secondary minima?... [TP, Lafaye, Zerwas] LHC ILC LHC+ILC SPS1a tanβ 1.22± ±.3 1.6±.2 1 M ± ± ± M ±15 fix ± M τl fix ± ± M τr 129.3± ± ± M µl 198.7± ± ± M q3l 498.3± ± ± M t R fix 5 42± ± M br ±113 fix ± Aτ fix -22.4± ± A t -57.8± ± ± A b ±3563 fix -977±

18 Supersymmetric parameters: 2 Bayes theorem and new physics [Allanach, Roszkowski] Pythia/Herwig/Sherpa: data given the model: p(d m) theorist s prejudice: model p(m) model extraction: p(m d) = p(d m) p(m)/p(d) [p(d) through normalization] given measurements: (1) compute probability map p(m d) of parameter space (2) rank local maxima Weighted Markov chains [scanning algorithm for many dimensions: Rauch & TP] classical: produce representative set of spin states compute average energy based on this reduced sample map (chain) based on probability of a state expensive energy function on sample BSM physics: produce map p(m d) of parameter points evaluate same probability from (binned) density [Allanach,...; Baltz,...; Roszkowski,...] phase space MC approach: weighted chain [two bins with p 1 : 1 with 2 or 11 points] already for msugra/cmssm: MC resolution not sufficient use additional probability maximization to rank maxima

19 Supersymmetric parameters: 2 Bayes theorem and new physics [Allanach, Roszkowski] Pythia/Herwig/Sherpa: data given the model: p(d m) theorist s prejudice: model p(m) model extraction: p(m d) = p(d m) p(m)/p(d) [p(d) through normalization] given measurements: (1) compute probability map p(m d) of parameter space (2) rank local maxima Toy model [Rauch & TP] test function V ( x) in 5 dimensions [general high dimensional extraction tool] Sfitter output #1: probability map Sfitter output #2: list of local maxima [best fit] x x 1

20 Supersymmetric parameters: 2 Bayes theorem and new physics [Allanach, Roszkowski] Pythia/Herwig/Sherpa: data given the model: p(d m) theorist s prejudice: model p(m) model extraction: p(m d) = p(d m) p(m)/p(d) [p(d) through normalization] given measurements: (1) compute probability map p(m d) of parameter space (2) rank local maxima msugra/cmssm with LHC measurements SPS1a kinematic edges with free m t as of yesterday: Sfitter probability maps [Lafaye, TP, Rauch, Zerwas] m 1/ e+9 1e+8 1e+7 1e m 1/ e+9 1e+8 1e+7 1e m m

21 Supersymmetric parameters: 2 Bayes theorem and new physics [Allanach, Roszkowski] Pythia/Herwig/Sherpa: data given the model: p(d m) theorist s prejudice: model p(m) model extraction: p(m d) = p(d m) p(m)/p(d) [p(d) through normalization] given measurements: (1) compute probability map p(m d) of parameter space (2) rank local maxima MSSM with LHC measurements SPS1a kinematic edges and free m t as of yesterday: Sfitter probability map [Lafaye, TP, Rauch, Zerwas] 1 M( ~ µ R ) e+13 1e+12 1e+11 1e+1 1e µ

22 Under construction: 1 Problems in the spin extraction unclear if information available [top partners: Meade & Reece] model independent spin analysis unlikely advantages of hypotheses testing Matrix element method [CDF, D; McElrath] compute likelihood of top events estimating M 2 maximize likelihood p(d SM, m t ) as function of m t... Statistics: Neyman Pearson lemma assume correct hypothsis m 1 : SUSY cascade assume wrong hypothsis m 2 : UED cascade likelihood ratio p(d m 1 )/p(d m 2 ) most powerful estimator [lowest probability to mistake right for fluctuation of wrong (type-ii error)] probability of event p(d m) M 2 compute maximum statistical significance

23 Under construction: 1 Problems in the spin extraction unclear if information available [top partners: Meade & Reece] model independent spin analysis unlikely advantages of hypotheses testing Matrix element method [CDF, D; McElrath] compute likelihood of top events estimating M 2 maximize likelihood p(d SM, m t ) as function of m t... Statistics: Neyman Pearson lemma assume correct hypothsis m 1 : Higgs signal in WBF H µµ [TP, Rainwater] assume wrong hypothsis m 2 : SM background likelihood ratio p(d m 1 )/p(d m 2 ) most powerful estimator [lowest probability to mistake right for fluctuation of wrong (type-ii error)] probability of event p(d m) M 2 compute maximum statistical significance of WBF H µµ

24 Under construction: 2 Maximum significance for LHC signals example: combined n-event Poisson [p(n s + b) = e (s+b) (s + b) n /n!] p(n s + b) q = log = s + n log p(n b) 1 + s b n j log «X j s j + X j phase space integration over p(d s, b) M s,b 2 [LEP Higgs inspired]! q( r) = σ sl + log 1 + Ms( r) 2 M b ( r) 2 probability distribution function via Fourier transform: ρ s,b (q) compute CL b (q) = R q dq ρ b (q ) [5σ is CL b = ] 1 + s j b j «

25 Under construction: 2 Maximum significance for LHC signals example: combined n-event Poisson [p(n s + b) = e (s+b) (s + b) n /n!] p(n s + b) q = log = s + n log p(n b) 1 + s b n j log «X j s j + X j phase space integration over p(d s, b) M s,b 2 [LEP Higgs inspired]! q( r) = σ sl + log 1 + Ms( r) 2 M b ( r) 2 probability distribution function via Fourier transform: ρ s,b (q) compute CL b (q) = R q dq ρ b (q ) [5σ is CL b = ] 1 + s j b j «Semi realistic results [Cranmer & TP] irreducible & unsmeared Z σ tot = Z dps M PS dσ PS = d r M( r) dσ( r) smearing mµµ width mmeas Z σ tot = d r dr m µµ [unobserved dimensions] Z dr m M( r) dσ( r) W (r m, r m ) acceptance cuts to reduce phase space... [bad measurements] WBF H µµ: 3.5σ in 3 fb 1

26 Under construction: 2 Maximum significance for LHC signals example: combined n-event Poisson [p(n s + b) = e (s+b) (s + b) n /n!] p(n s + b) q = log = s + n log p(n b) 1 + s b n j log «X j s j + X j phase space integration over p(d s, b) M s,b 2 [LEP Higgs inspired]! q( r) = σ sl + log 1 + Ms( r) 2 M b ( r) 2 probability distribution function via Fourier transform: ρ s,b (q) compute CL b (q) = R q dq ρ b (q ) [5σ is CL b = ] 1 + s j b j «Statistics for phenomenologists [Cranmer, TP, Reuter] numerical evaluation instantaneous [sanity check neural nets?] implementation into Whizard on the way cannot tell if a search is possible can tell if a search is impossible

27 New physics at the LHC A lot has been done higher order calculations improved background estimates web based signal event generators mass and spin measurements parameter extraction/probability maps... A lot is still left to do more higher order calculations even better background estimates QCD effects on new physics measurements scans of high dimensional parameter spaces statistics tools for phenomenologists... even exciting times still require some work

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