Tilman Plehn. Mainz 2/2009

Transcription

1 Once we have all Heidelberg Mainz 2/29

2 Outline Effective Standard Model from cascades Interlude: and jets Interlude: spins from jets Underlying parameters TeV-scale MSSM:

3 Effective Standard Model Data vs renormalizable Standard Model dark matter? [only solid evidence for new physics, weak scale?] (g 2) µ? [loop effects around weak scale?] flavor physics? [new operators above 4 GeV?] neutrino masses? [see-saw at GeV?] gauge coupling unification? [something happening above 6 GeV?] gravity? [mostly negligible below 9 GeV] obviously effective theory, cutoff negotiable Problem with fundamental Higgs Higgs introduced for fundamental theory in UV mass driven to cutoff: δm 2 H /m2 H g2 (2m 2 W + m2 Z + m2 H 4m2 t ) Λ2 tuned counter term: fundamental gauge theory betrayed or new physics at TeV scale: supersymmetry extra dimensions little Higgs, Higgsless, composite Higgs... typically cancellation by new states or discussing away high scale beautiful concepts, challenged at TeV scale whatever is there - LHC s job to sort it out H t H W

4 Effective Standard Model in the LHC era Expectations from the LHC find light Higgs? find new physics stabilizing Higgs mass? see dark matter candidate? Particle theory and new physics [Uli Baur s rule: there is always new physics at higher scales ] model independent analyses likely not helpful testing testable hypotheses [theory: e.g. Higgs sector and underlying theory?] discrete hypotheses: spins,... continuous hypotheses: masses,... link to other observations [DM+Tevatron: Hooper, TP, Valinotto] reconstruction of Lagrangian [theory+experiment]

5 Effective Standard Model in the LHC era Expectations from the LHC find light Higgs? find new physics stabilizing Higgs mass? see dark matter candidate? Particle theory and new physics [Uli Baur s rule: there is always new physics at higher scales ] model independent analyses likely not helpful testing testable hypotheses [theory: e.g. Higgs sector and underlying theory?] discrete hypotheses: spins,... continuous hypotheses: masses,... link to other observations [DM+Tevatron: Hooper, TP, Valinotto] reconstruction of Lagrangian [theory+experiment] Special about LHC [except bigger than Tevatron] beyond inclusive searches [that was Tevatron] lots of strongly interacting particles cascade decays to DM candidate general theme: try to survive QCD aim at underlying theory ν ν χ o + 2 χ σ tot [pb]: pp g g, q q, t t, χ 2 o χ +, ν ν, χ o g, χ + q χ + q t t χ o g g g S = 2 TeV q q NLO LO m [GeV]

6 Effective Standard Model in the LHC era Expectations from the LHC find light Higgs? find new physics stabilizing Higgs mass? see dark matter candidate? Particle theory and new physics [Uli Baur s rule: there is always new physics at higher scales ] model independent analyses likely not helpful testing testable hypotheses [theory: e.g. Higgs sector and underlying theory?] discrete hypotheses: spins,... continuous hypotheses: masses,... link to other observations [DM+Tevatron: Hooper, TP, Valinotto] reconstruction of Lagrangian [theory+experiment] Special about LHC [except bigger than Tevatron] beyond inclusive searches [that was Tevatron] lots of strongly interacting particles cascade decays to DM candidate general theme: try to survive QCD aim at underlying theory χ o + 2 χ σ tot [pb]: pp g g, q q, t t, χ o 2χ +, ν ν, χ g, χ q 2o 2o t t ν ν χ 2o q χ 2o g q q g g S = 4 TeV NLO LO m [GeV]

7 from cascades Cascade decays [Atlas-TDR, Cambridge people] if new particles strongly interacting and LSP weakly interacting like Tevatron: jets + missing energy g b b ~ χ o 2 b µ µ µ ~ o χ tough: (σbr) /(σbr) 2 [model dependence, QCD uncertainty] easier: cascade kinematics [ 7 8 events] long chain g b b χ 2 b b µ + µ b b χ thresholds & edges m 2 χ < m 2 m 2 l m 2 l m2 χ µµ < 2 m l m l new physics mass spectrum from endpoints new physics spins from shapes [Barr, Lester, Smillie, Webber; Alves, Eboli, TP;...]

8 2 Once we have all from cascades Cascade decays [Atlas-TDR, Cambridge people] if new particles strongly interacting and LSP weakly interacting like Tevatron: jets + missing energy g b b ~ χ o 2 b µ µ µ ~ o χ tough: (σbr) /(σbr) 2 [model dependence, QCD uncertainty] easier: cascade kinematics [ 7 8 events] long chain g b b χ 2 b b µ + µ b b χ thresholds & edges m 2 χ < m 2 m 2 l m 2 l m2 χ µµ < 2 m l m l new physics mass spectrum from endpoints new physics spins from shapes [Barr, Lester, Smillie, Webber; Alves, Eboli, TP;...] Gluino decay [Gjelsten, Miller, Osland, Raklev...] only b jets [otherwise dead by QCD] m χ m~ l R m χ2 no problem: off-shell [Catpiss] m~ - m q L χ no problem: jet radiation? [later] gluino mass to % - m χ l R m~ - m χ m χ b ~ - m m g ~ m~ - m b χ m~ - m g m~ b χ m~ q L m~ g Sparticle masses and mass differences [GeV]

9 2 Once we have all from cascades Cascade decays [Atlas-TDR, Cambridge people] if new particles strongly interacting and LSP weakly interacting like Tevatron: jets + missing energy g b b ~ χ o 2 b µ µ µ ~ o χ tough: (σbr) /(σbr) 2 [model dependence, QCD uncertainty] easier: cascade kinematics [ 7 8 events] long chain g b b χ 2 b b µ + µ b b χ thresholds & edges m 2 χ < m 2 m 2 l m 2 l m 2 χ µµ < 2 m l m l new physics mass spectrum from endpoints new physics spins from shapes [Barr, Lester, Smillie, Webber; Alves, Eboli, TP;...] Gluino decay [Gjelsten, Miller, Osland, Raklev...] only b jets [otherwise dead by QCD] m χ m~ l R m χ2 no problem: off-shell [Catpiss] m~ - m q L χ no problem: jet radiation? [later] gluino mass to % but why physical masses? - m χ l R m~ - m χ m χ b ~ - m m g ~ m~ - m b χ m~ - m g m~ b χ m~ q L m~ g Sparticle masses and mass differences [GeV]

10 Interlude: and jets Bored without a collider: solving old MSSM problems problematic general ansatz: 6 6 squark mass matrix flavor violation: K -K mixing, etc CP violation in flavor sector flavor-violating decays: b sγ electric dipole moments... well-known problem for squark sector [include 5 citations here] Solution via symmetries [Kribs, Poppitz, Weiner] continuous global symmetry R[θ] = + [Hall & Randall] chiral superfield Φ (+) = φ (+) + θ χ () + θθ F ( ) vector superfield V () = θσ µ (+) θa µ i θ θθλ (+) + θθ θ θ D () /2 superpotential R[ R d 2 θw (+2) ] = forbidden soft-breaking terms φ 3, φ φ 2, λ λ allowed soft-breaking terms φ 2, φ φ, λψ no Majorana masses, no A terms, no µ term... [Majorana neutrino okay] gluino mass via additional state [chiral superfield, sgluon lowest state, weak sector ugly] at least proof of power of symmetries

11 Interlude: and jets Testable at the LHC L m g g G m 2 g G2 2gm g G q T q sgluon G integrated out for supersoft SUSY breaking [Fox, Nelson, Weiner] G-G-g coupling tree level G-g-g coupling loop-induced m g /mg 2 G-q-q coupling loop-induced m g m q /mg 2 pair production, decay to top quark [TP, Tait] Like-sign top quarks [preliminary numbers] production determined by QCD [always same at LHC] incoming partons: steep drop for large masses decay through G t q, tq leptonic decays: no background also LHC physicists being bored σ tot (pp/pp GG/G+X) [pb] no cuts, no decay LHC pairs - -2 LHC single -3-4 Tevatron m G [GeV]

12 Interlude: and jets Testable at the LHC L m g g G m 2 g G2 2gm g G q T q sgluon G integrated out for supersoft SUSY breaking [Fox, Nelson, Weiner] G-G-g coupling tree level G-g-g coupling loop-induced m g /mg 2 G-q-q coupling loop-induced m g m q /mg 2 pair production, decay to top quark [TP, Tait] Likely bad ideas [Tait & TP; Alwall, Maltoni, de Visscher; TP, Rainwater, Skands] sgluon identification? hadronic W reconstruction? top 4-momentum measurement? decay jet or QCD radiation? collinear initial state radiation [p T,j < M hard ] proper description: CKKW/MLM [in MadEvent] N jet dependent on hard scale N jet dependent on p T,j QCD under control /σ tot dσ/dn jet (tt /GG+jets) jet radiation p T > 3 GeV GG 6 GeV tt GG 3 GeV N jet

13 Interlude: and jets Testable at the LHC L m g g G m 2 g G2 2gm g G q T q sgluon G integrated out for supersoft SUSY breaking [Fox, Nelson, Weiner] G-G-g coupling tree level G-g-g coupling loop-induced m g /mg 2 G-q-q coupling loop-induced m g m q /mg 2 pair production, decay to top quark [TP, Tait] Likely bad ideas [Tait & TP; Alwall, Maltoni, de Visscher; TP, Rainwater, Skands] sgluon identification? hadronic W reconstruction? top 4-momentum measurement? decay jet or QCD radiation? collinear initial state radiation [p T,j < M hard ] proper description: CKKW/MLM [in MadEvent] N jet dependent on hard scale N jet dependent on p T,j QCD under control /σ tot dσ/dn jet (tt /GG+jets) jet radiation p T > 5 GeV GG 6 GeV tt GG 3 GeV N jet

14 Interlude: and jets Testable at the LHC L m g g G m 2 g G2 2gm g G q T q sgluon G integrated out for supersoft SUSY breaking [Fox, Nelson, Weiner] G-G-g coupling tree level G-g-g coupling loop-induced m g /mg 2 G-q-q coupling loop-induced m g m q /mg 2 pair production, decay to top quark [TP, Tait] Likely bad ideas [Tait & TP; Alwall, Maltoni, de Visscher; TP, Rainwater, Skands] sgluon identification? hadronic W reconstruction? top 4-momentum measurement? decay jet or QCD radiation? collinear initial state radiation [p T,j < M hard ] proper description: CKKW/MLM [in MadEvent] N jet dependent on hard scale N jet dependent on p T,j QCD under control /σ tot dσ/dn jet (tt /GG+jets) jet radiation p T > GeV GG 6 GeV GG 3 GeV tt N jet

15 Interlude: spins from jets Illustrating useful jets: spin of LSP [Alwall, TP, Rainwater] Majorana LSP with like-sign charginos? hypotheses: like sign charginos (SUSY) like sign scalars (scalar dark matter) like sign vector bosons (little Higgs inspired) chargino decay/kinematics not used u u W + χ W + d χ + χ + d WBF : two key distributions φ jj, p T,j [like H ZZ 4µ or WBF-Higgs] distinct WBF signal? [p T,j m W, forward jets] visible over backgrounds? [SUSY QCD backgrounds dominant] toy model, but 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, jet /σ dσ/d η(jet EW(WBF) EW (all) EW (non-wbf) QCD η(jet, jet ) 2

16 Interlude: spins from jets Like-sign scalars or fermions? charged Higgs in 2HDM H + H same as simple H [TP, Rainwater, Zeppenfeld; Hankele, Klamke, Figy] W radiated off quarks [Goldstone coupling to Higgs] + ( x)2 P T (x, p T ) 2x ( x)2 pt 2 P L (x, p T ) x m 2 W p 4 T scalars with softer p T,j ) /σ dσ/dp T (jet.9 χ+χ+ WBF H+H+ W +W P T (jet ), GeV/c

17 Interlude: spins from jets Like-sign scalars or fermions? charged Higgs in 2HDM H + H same as simple H [TP, Rainwater, Zeppenfeld; Hankele, Klamke, Figy] W radiated off quarks [Goldstone coupling to Higgs] + ( x)2 P T (x, p T ) 2x scalars with softer p T,j ( x)2 pt 2 P L (x, p T ) x m 2 W p 4 T Like-sign vectors or fermions? little Higgs inspired start with copy of SM, heavy W, Z, H, f [H necessary for unitarity, but irrelevant at LHC] Lorentz structure reflected in angle between jets vectors with peaked φ jj ) 2, jet /σ dσ/d φ(jet.9 χ+χ+ WBF.8 H+H+.7.6 W +W φ(jet, jet ) 2

18 Interlude: spins from jets Like-sign scalars or fermions? charged Higgs in 2HDM H + H same as simple H [TP, Rainwater, Zeppenfeld; Hankele, Klamke, Figy] W radiated off quarks [Goldstone coupling to Higgs] + ( x)2 P T (x, p T ) 2x scalars with softer p T,j ( x)2 pt 2 P L (x, p T ) x m 2 W p 4 T Like-sign vectors or fermions? little Higgs inspired start with copy of SM, heavy W, Z, H, f [H necessary for unitarity, but irrelevant at LHC] Lorentz structure reflected in angle between jets vectors with peaked φ jj Heavy fermions in little Higgs models part of unitary UV completion [Englert, Zeppenfeld] huge effects on distributions [at low scales] more like strongly interacting W s ) /σ dσ/dp T (jet SM W+W+ W +W + (quark partners) W +W + (only W Z ) P T (jet ), GeV/c

19 Underlying parameters From kinematics to weak scale parameters parameters: weak-scale Lagrangian [Fittino; : Lafaye, TP, Rauch, Zerwas] measurements: better edges than masses, branching fractions, rates,... [NLO, of course] flavor, dark matter, electroweak constraints,... errors: general correlation, statistics & systematics & theory [flat theory errors!] problem in grid: huge phase space, no local maximum? problem in fit: domain walls, no global maximum? problem in interpretation: bad observables, secondary maxima? Probability maps of new physics [Baltz,...; Roszkowski,...; Allanach,...; ] want to evaluate probability of model being true p(m d) can compute fully exclusive likelihood map p(d m) over m [tough] additional LHC challenge: remove poor directions [e.g. endpoints vs rates] Bayesian: p(m d) p(d m) p(m) with theorists bias p(m) [cosmology, BSM] frequentist: best fitting point max m p(d m) [flavor] LHC era: () compute high-dimensional map p(d m) (2) find and rank local best-fitting points (3) predict additional observables

20 Markov chains Define set of representative points in new physics space measure of representative : likely to agree with data [Markov chain] evaluate any function over chain () probability to agree with data weighted Markov chains [Rauch & TP; Ferrenberg & Swendsen] P bin(p ) = N P N i= /p (2) Higgs mass from LEP and DM relic density LHC rates from LEP and DM relic density dark matter detection from LEP and/or LHC... anything possible and well defined [but better not screw up technically]

21 Markov chains Define set of representative points in new physics space measure of representative : likely to agree with data [Markov chain] evaluate any function over chain () probability to agree with data weighted Markov chains [Rauch & TP; Ferrenberg & Swendsen] P bin (p ) = N P N i= /p (2) Higgs mass from LEP and DM relic density LHC rates from LEP and DM relic density dark matter detection from LEP and/or LHC... anything possible and well defined [but better not screw up technically] Bayesian probabilities vs profile likelihood [Allanach, Cranmer, Lester, Weber; Roszkowski,...] Which is the most likely parameter point? How does dark matter annihilate/couple? m (TeV) M /2 (TeV) L/L(max)

22 Correlations and errors Toy model: MSUGRA map from LHC [LHC endpoints with free y t ] model unrealistic but useful testing ground [will do anything for citations] weighted Markov chains: several times faster output #: fully exclusive likelihood map output #2: ranked list of local maxima strong correlation e.g. of A and y t [including all errors ] correlations and secondary maxima significant [ ] m t 2 χ 2 m m /2 tan β A µ m t 9.3e A

23 Correlations and errors Toy model: MSUGRA map from LHC [LHC endpoints with free y t ] model unrealistic but useful testing ground [will do anything for citations] weighted Markov chains: several times faster output #: fully exclusive likelihood map output #2: ranked list of local maxima strong correlation e.g. of A and y t [including all errors ] correlations and secondary maxima significant [ ] A word on errors central values secondary locally statistical errors Gaussian systematic errors Gaussian, correlated theory errors flat RFit scheme [CKMFitter, profile likelihood inspired] χ 2 = 2 log L = χ T d C χ d 8 >< d i d i < σ (theo) i χ d,i = D d i d i σ (theo) i >: Dσ (exp) d i d i > σ (theo), i i C i,i = C i,j = C j,i =.99 σ(l) i σ (l) +.99 σ (j) σ (j) j i j σ (exp) i σ (exp) j

24 Correlations and errors Toy model: MSUGRA map from LHC [LHC endpoints with free y t ] model unrealistic but useful testing ground [will do anything for citations] weighted Markov chains: several times faster output #: fully exclusive likelihood map output #2: ranked list of local maxima strong correlation e.g. of A and y t [including all errors ] correlations and secondary maxima significant [ ] A word on errors central values secondary locally statistical errors Gaussian systematic errors Gaussian, correlated theory errors flat theory error sizeable SPSa theo exp zero expnocorr zero theo exp zero theo exp gauss theo exp flat masses endpoints m m / tan β A m t errors mean: endpoints instead of masses

25 TeV-scale MSSM: MSSM map from LHC shifting from 6D to 9D parameter space [killing grids, Minuit, laptop style fits...] Markov chain globally + hill climber locally outputs # and #2 still the same [weighted Markov chain plus hill climber] three neutralinos observed [left: Bayesian right: likelihood] 5 e+8 e+6 µ M

26 TeV-scale MSSM: MSSM map from LHC shifting from 6D to 9D parameter space [killing grids, Minuit, laptop style fits...] Markov chain globally + hill climber locally outputs # and #2 still the same [weighted Markov chain plus hill climber] three neutralinos observed [left: Bayesian right: likelihood] 6e-7.6 5e-7.5 4e-7.4 /χ 2 3e-7 /χ 2.3 2e-7.2 e M M quality of fit not always useful: all the same... µ < µ > M M µ tan β M M µl M µr A t ( ) A t (+) m A m t means probably much more work to do...

27 Beyond the LHC Why theorists involved? want to learn statistics [usually get that badly wrong] theory errors not negligible [rates for focus point scenarios] link with other observations model dependent

28 Beyond the LHC Why theorists involved? want to learn statistics [usually get that badly wrong] theory errors not negligible [rates for focus point scenarios] link with other observations model dependent MSSM parameters beyond LHC remember: unknown sign(µ), believe based tan β from m h LHC rates: tan β from heavy Higgs tough [Kinnunen, Lehti, Moortgat, Nikitenko, Spira] µ 5-5 e+8 e M

29 Beyond the LHC Why theorists involved? want to learn statistics [usually get that badly wrong] theory errors not negligible [rates for focus point scenarios] link with other observations model dependent MSSM parameters beyond LHC remember: unknown sign(µ), believe based tan β from m h LHC rates: tan β from heavy Higgs tough [Kinnunen, Lehti, Moortgat, Nikitenko, Spira] () use current precision on (g 2) µ tan β [ + Alexander, Kreiss] strongly correlated and promising LHC LHC (g 2) SPSa tan β.± 4.5.3± 2.. M 2.± ± M ± ± M ± ± M µl 93.2± ± M µr 35.± ± M q3l 48.4± ± M br 5.7± ± M ql 524.6± ± M qr 57.3± ± m A 46.3±O( 3 ) 4.±O( 2 ) µ 35.5± ±

30 Beyond the LHC Why theorists involved? want to learn statistics [usually get that badly wrong] theory errors not negligible [rates for focus point scenarios] link with other observations model dependent MSSM parameters beyond LHC remember: unknown sign(µ), believe based tan β from m h LHC rates: tan β from heavy Higgs tough [Kinnunen, Lehti, Moortgat, Nikitenko, Spira] () use current precision on (g 2) µ tan β [ + Alexander, Kreiss] strongly correlated and promising (2) use BR(B s µµ) with stop chargino sector [Hisano, Kawagoe, Nojiri] 7% error on f Bs by 25 crucial [Della Morte, Del Debbio; + Jäger, Spannowsky] perturbative effects secondary no theory error BR/BR = 5% true best error best error tan β M A M M M µ M t,r

31 Beyond the LHC Why theorists involved? want to learn statistics [usually get that badly wrong] theory errors not negligible [rates for focus point scenarios] link with other observations model dependent MSSM parameters beyond LHC remember: unknown sign(µ), believe based tan β from m h LHC rates: tan β from heavy Higgs tough [Kinnunen, Lehti, Moortgat, Nikitenko, Spira] () use current precision on (g 2) µ tan β [ + Alexander, Kreiss] strongly correlated and promising (2) use BR(B s µµ) with stop chargino sector [Hisano, Kawagoe, Nojiri] 7% error on f Bs by 25 crucial [Della Morte, Del Debbio; + Jäger, Spannowsky] perturbative effects secondary Renormalization group bottom up SUSY breaking, unification, GUT? [ + Kneur] /M i M M 2 M 3 scale-invariant sum rules? [Cohen, Schmalz] solidly inference from weak scale log(q)

32 Outlook Understanding the TeV scale () look for solid new physics signals (2) measure weak scale Lagrangian (3) determine fundamental physics construct new physics hypotheses compute reliable predictions avoid getting killed by QCD LHC more than a discovery machine!

33