Physics at the LHC Lecture 4: Higgs Physics at the LHC. Klaus Mönig, Sven Moch

Transkript

1 Physics at the LHC Lecture 4: Higgs Physics at the LHC Klaus Mönig, Sven Moch Wintersemester 2009/2010 Physics at the LHC Lecture 4-1 Klaus Mönig

2 Physics at the LHC Lecture 4-2 Klaus Mönig Reminder: Higgs mechanism in the Standard Model ( ) Φ1 + iφ One complex Higgs doublet Φ = 2 with vacuum expectation value, v = 246 GeV. ( ) H + iφ 3 0 v Higgs potential V (Φ) = λ(φ Φ v 2 /2) 2 Gauge couplings of Higgs doublet give gauge boson masses: m 2 W = g2 v 2 m 2 4 Z = g2 v 2 4 cos 2 θ W Φ i get absorbed in longitudinal d.o.f. of W,Z One Higgs particle H remains from fluctuations around v Higgs couplings to gauge bosons fixed by gauge boson mass Higgs mass m 2 H = 2λv2 free parameter

3 Physics at the LHC Lecture 4-3 Klaus Mönig Higgs couplings to fermions: c f [ Fl (Φ + v)f r + f r (Φ + v)f l ] Higgs coupling mass Partial widths: Γ(H ff) = N(f) c G µ 4 2π m2 f (m H)m H (1 + δ (f) QCD ) Γ(H V V ) = 3G2 µm 4 Z 16π 3 m HR V (m 2 V /m2 H ) 2Gµ 2(1) 32π m3 H [V = W(Z)] Higgs couplings to photons and gluons via loops

4 ÏÏ Physics at the LHC Lecture 4-4 Klaus Mönig Partial and total widths of a Standard Model Higgs ½ ½¼¼¼ Àµ Î ½¼¼ Ø Ø ¼º½ ½¼ Ê Àµ ¼º¼½ ½ ¼º½ ¼º¼¼½ ¼º¼½ ¼º¼¼¼½ ¼º¼¼½ ¼¼ ¼¼ ½¼¼¼ ¼¼ ¼¼ ¼¼ ½ ¼ ½¼¼ ½¼¼¼ ¼¼ ½¼¼ ½ ¼ Å À Î Light Higgs: b b is dominant Heavy Higgs: Mostly WW and ZZ Higgs width large above WW threshold Å À Î

5 How the Higgs creates mass Physics at the LHC Lecture 4-5 Klaus Mönig

6 Physics at the LHC Lecture 4-6 Klaus Mönig

7 and how it creates itself Physics at the LHC Lecture 4-7 Klaus Mönig

8 Physics at the LHC Lecture 4-8 Klaus Mönig

9 Physics at the LHC Lecture 4-9 Klaus Mönig Theory: Limits on m H No useful lower limit Upper limit from WW scattering: Polarisation vector for longitudinally polarised particles p 2 WW scattering without Higgs violates unitarity at 1.2 TeV W Z,γ W W Z,γ W W W W W Cross section gets regularised by the Higgs m H < 1 TeV

10 Perturbativity and vacuum stability give Higgs-mass limit as a function of the cutoff parameter If the SM is the final theory up to the Planck scale Λ GeV m H GeV Physics at the LHC Lecture 4-10 Klaus Mönig

11 Physics at the LHC Lecture 4-11 Klaus Mönig Experimental: CL s Direct searches at LEP exclude a Higgs below 114 GeV This limit is valid for couplings significantly smaller than in the SM Observed Expected for background LEP m H (GeV/c 2 ) Analyses of electroweak precision data suggest m H < 200 GeV These analyses are only valid in the Standard Model without additional particles coupling to the gauge bosons χ LEP exclusion at 95% CL G fitter SM Theory uncertainty Fit including theory errors Fit excluding theory errors [GeV] M H Aug 08 3σ 2σ 1σ

12 Physics at the LHC Lecture 4-12 Klaus Mönig Higgs production at hadron colliders g g t H q q W,Z H gg fusion W,Z Bremsstrahlung t g H q W,Z H g t q W,Z tt fusion WW, ZZ fusion gg fusion produces a Higgs and nothing else in the detector All other graphs have associated particles that help in the tagging

13 Physics at the LHC Lecture 4-13 Klaus Mönig σ (pb) M. Spira et al. NLO QCD gg H qq' HW Higgs production cross section LHC gg,qq Hbb qq Hqq gg,qq Htt qq HZ M H (GeV) σ(pp H+X) s = 14 TeV m t = 175 GeV CTEQ4M gg fusion dominates in both cases At LHC WW-fusion significant, rest small events for 10 5 pb gg h SM qq h SM qq gg,qq _ h SM tt _ gg,qq _ h SM bb _ Tevatron bb _ h SM M h [GeV] SM σ(pp _ h SM +X) [pb] s = 2 TeV M t = 175 GeV CTEQ4M qq _ h SM W qq _ h SM Z At Tevatron WW-fusion and W,Z Bremsstrahlung relevant Total cross section large at LHC, factor 100 smaller at Tevatron

14 Physics at the LHC Lecture 4-14 Klaus Mönig How to discover a signal? Assume background is known from somewhere Number of events follows a Poisson distribution variance σ for mean value n: σ = n For a given mass expect n t = n s + n b events Require that signal is > 5σ above background (corresponds to a probability of 10 7 for a background fluctuation) need significance S = n s / n b > 5 Influence of detector resolution: Gaussian signal with variance σ D over linear background: S 1/ σ D Dependence on Luminosity: S L

15 Physics at the LHC Lecture 4-15 Klaus Mönig Higgs searches at the Tevatron Light Higgs: Main decay to b b Main channel gg H b b hopeless Possible channels WH lνb b, ZH llb b, ZH ννb b, Medium Higgs gg WW lνlν becomes accessible In addition some signal from WH lνlν +... Heavy Higgs (m H > 200 GeV) No chance because cross section too low

16 Physics at the LHC Lecture 4-16 Klaus Mönig Search for gg WW lνlν Many variables with low separation power E.g. leptons correlated because of Higgs spin (=0) Combined with multivariate techniques, here NN Small signal under huge bg, WW and Drell-Yan dominant R for lepton pairs Jets HWW M = 160 GeV/c L = 3.0 fb H 2 10 All S/B ggh W+jets Wγ tt WZ ZZ 10 DY WW Data CDF Run II Preliminary Neural Net output 2 All Jets HWW M H = 165 GeV/c -1 L = 3.0 fb Total Wj Wγ tt WZ ZZ DY WW HWW Data R(ll) NN Output

17 Physics at the LHC Lecture 4-17 Klaus Mönig Results Low mass region dominated by WH lνb b and WH,ZH MET b b Higher masses only H lνlν Exclusion at low masses still around 2 3σ(SM) At 160 GeV < m H < 170 GeV SM-Higgs excluded! CDF limit for the different channels 95% CL Limit/SM LEP Excl. CDF Run II Preliminary, L= fb -1 WWW 2.7 fb -1 Obs WWW 2.7 fb -1 Exp H ττ 2.0 fb -1 Obs H ττ 2.0 fb -1 Exp ZH llbb 2.7 fb -1 Obs ZH llbb 2.7 fb -1 Exp WH+ZH bbmet 2.1 fb -1 Obs WH+ZH bbmet 2.1 fb -1 Exp WH lνbb 2.7 fb -1 Obs WH lνbb 2.7 fb -1 Exp H WW 3.0 fb -1 Obs H WW 3.0 fb -1 Exp Combined Obs Combined Exp 95% CL Limit/SM 10 Tevatron combined limit Tevatron Run II Preliminary, L= fb -1 LEP Exclusion Expected Observed ±1σ Expected ±2σ Expected Tevatron Exclusion SM 1 January 16, m H (GeV/c 2 ) 1 SM March 5, m H (GeV/c 2 )

18 Physics at the LHC Lecture 4-18 Klaus Mönig Higgs search at the LHC Easiest channel: H ZZ l + l l + l σ BR 10 fb for m H = 130 GeV Largest background t t WbW b lν lνclν lνc: σ BR = 1300 fb Best handle: lepton isolation and b-tagging Dominant background after selection: ZZ Channel can be used for discovery for 130 GeV < m H < 600 GeV

19 Physics at the LHC Lecture 4-19 Klaus Mönig Discovery channel for light Higgs: H γγ Main backgrounds: reducible irreducible Start with S/B = 10 6 need to reduce background by at least a factor 1000 Strategy: Effective selection of isolated photons (calorimeter granularity) Very good mass resolution (calorimeter energy resolution)

20 Physics at the LHC Lecture 4-20 Klaus Mönig Complication: Experiments have 1 radiation length in from of tracker about 50% of photons convert before they reach calorimeter have to include converted photons to keep high efficiency The final signal is small, however visible with few fb 1 for a light Higgs

21 These two channels are sufficient to discover the Higgs over the fill mass range Physics at the LHC Lecture 4-21 Klaus Mönig

22 Physics at the LHC Lecture 4-22 Klaus Mönig q q W,Z W,Z WW, ZZ fusion The Higgs in the VV-fusion channel H Higgs is colour singlet W-propagator: with t = ( p p ) 2 4pp sin 2 θ 2 1 t m 2 W propagator constant as long as 2p sin θ 2 < m W forward jets should be visible in the detector colour connection between forward jet and proton remnant rapidity gaps between forward jets and Higgs-jets Tag jets Higgs decay products φ η

23 Physics at the LHC Lecture 4-23 Klaus Mönig Largest background is t t Rapidity of tag jet Rapidity separation top Higgs top Higgs Can be separated with rapidity cuts

24 Physics at the LHC Lecture 4-24 Klaus Mönig With transverse mass M T = (E T,ll + E T,miss ) 2 ( p T,ll p T,miss ) 2 a clean signal can be separated

25 Physics at the LHC Lecture 4-25 Klaus Mönig H ττ: τs have large energy Can assume that neutrinos go in direction of visible decay products τ energy can be reconstructed from kinematic constraints This allows H ττ reconstruction in the presence of tagging jets

26 With fusion channel the Higgs discovery will be assured in significantly more channels Physics at the LHC Lecture 4-26 Klaus Mönig

27 Minimum luminosity needed for a Higgs discovery/exclusion Physics at the LHC Lecture 4-27 Klaus Mönig

28 Physics at the LHC Lecture 4-28 Klaus Mönig Higgs properties LHC has discovered a particle compatible with a Higgs, what can be measured? Mass: Modes with complete Higgs reconstruction (H γγ, H ZZ 4l) allow mass measurement with 0.1% precision. Spin: Coupling Hvv forbidden if H has spin 1 and v is massless vector particle (e.g. g or γ) (angular momentum conservation and Pauli principle) visibility of H γγ or gg H excludes spin 1

29 Physics at the LHC Lecture 4-29 Klaus Mönig If H ZZ 4l is visible spin/cp can be obtained from decay angle distributions: Take H ZZ 2e2µ Add CP odd coupling to SM coupling with strength tanξ/m 2 V Most backgrounds can be suppressed by cuts Can distinguish the extreme cases

30 Physics at the LHC Lecture 4-30 Klaus Mönig The width of the Higgs For a light Higgs the width is much smaller than the detector resolution If m H > 2m W the width gets much larger and can be measured For m H > 200 GeV a precision < 10% is possible

31 Physics at the LHC Lecture 4-31 Klaus Mönig Higgs couplings σ BR Γ prodγ dec Γ H Ratios of production rates measure ratios of partial widths Can obtain ratios of decay widths with > 10% accuracy

32 Physics at the LHC Lecture 4-32 Klaus Mönig For absolute partial widths need additional assumptions. Precisions of couplings depend on assumptions Minimal assumption Γ V < Γ SM V V = W,Z Again precision > 10 20% Better precision with additional assumptions

33 Physics at the LHC Lecture 4-33 Klaus Mönig The Higgs in supersymmetric models SUSY needs at least two Higgs-doublets (H 1,H 2 ) to generate masses of down- and up-type particles Physical particles: h = H 2 cosα H 1 sinα H = H 2 sin α + H 1 cosα A CP odd charged Higgses H ± Define tanβ = v 2 v 1 = ratio of expectation values (v v2 2 = v2 SM )

34 Physics at the LHC Lecture 4-34 Klaus Mönig Born Formulae: m 2 h,h = 1 2 m h < m Z m H > m Z m 2 H ± = m 2 A + m2 W [ m 2 A + m2 Z (m 2 A + m2 Z) 2 4m 2 A m 2 Z cos2 2β ] tan 2α = tan 2β m2 A + m2 Z m 2 A m2 Z ( π 2 < α < 0 < β < π 2 ) Higgs sector described by two free parameters

35 Physics at the LHC Lecture 4-35 Klaus Mönig However large radiative corrections: shift of m h up to 130 GeV prediction gets dependent on other SUSY parameters, especially on mixing in stop sector strong dependence on top mass: m h / m t 1 Currently allowed region: m A (GeV/c 2 ) (a) m h -max Theoretically Inaccessible Excluded by LEP tanβ > 2 preferred! m h (GeV/c 2 ) tanβ 10 1 (b) m h -max Excluded by LEP Theoretically Inaccessible m h (GeV/c 2 )

36 Physics at the LHC Lecture 4-36 Klaus Mönig If m A large: β α = π/2 m H m H ± m A Only one light Higgs can be seen Branching ratios: Γ(h V V ) = sin 2 (β α)γ SM (h V V ) Γ(h UU) = cos2 α sin 2 β Γ SM(h UU) Γ(h DD) = sin2 α cos 2 β Γ SM(h DD) For m A large the light Higgs becomes SM like

37 Physics at the LHC Lecture 4-37 Klaus Mönig Heavy Higgses at the LHC For small tanβ (disfavoured by LEP) gg H,A production gets enhanced due to stronger t th coupling H,A t t gets enhanced For large tanβ H,A production from b b-fusion gets enhanced Large branching ratio H ττ Medium tanβ Only SM-like h visible

38 Physics at the LHC Lecture 4-38 Klaus Mönig Visible SUSY-Higgs channels Visible SUSY-Higgses at the LHC H, H _+ h,h,a h,h,a, _+ H h, _+ H h(sm like) h,h h,h, _+ H _+ h,h,a, h, H _+ H At least a SM-like h can always be seen However there is a significant chance that the rest of the SUSY Higgs sector remains invisible This does not include decays into SUSY particles (strongly model dependent!)

39 Physics at the LHC Lecture 4-39 Klaus Mönig Invisible Higgs E.g. in SUSY models it is possible that the Higgs decays into invisible particles (e.g. the LSP) The properties of the VV-fusion process allows even in this case to separate the Higgs from the background (arbitrary) dσ j dp T (arbitrary) jj dσ dm -1 Signal 10 QCDjj Wjj Zjj j P T [GeV/c] 10-1 Signal QCDjj Wjj Zjj (arbitrary) dσ d η (arbitrary) dσ dp TMiss Signal QCDjj Wjj Zjj η Signal 10-1 QCDjj Wjj 10-2 Zjj Mjj [GeV/c ] P TMiss [GeV/c]

40 Physics at the LHC Lecture 4-40 Klaus Mönig This allows to set a limit on ξ 2 = BR(H inv)σ(qq qqh)/σ(qq qqh,sm)) in the range 2 ξ fb fb 95% CL M H [GeV/c 2 ] The Higgs thus cannot be missed because it decays invisible!

41 Physics at the LHC Lecture 4-41 Klaus Mönig Conclusions of lecture 4 A roughly SM like Higgs cannot be missed at the LHC A precise mass measurement is almost included in the discovery Spin and CP properties may be measured to some extend In SUSY the light h will be seen, the rest is questionable