After the discovery of a Higgs boson

Transcription

1 After the discovery of a Higgs boson Heidi Rzehak Albert-Ludwigs-Universität Freiburg 27 November 2014

2 Discoveries at the LHC Expectations (Lindau Nobel Laureate Meeting 2008): t Hooft: A Higgs, or more Gross: A super world Veltman: The unexpected [see: After the discovery of a Higgs boson Heidi Rzehak 27 November 2014

3 Discoveries at the LHC... I I I I Nov HCP 2011: Exclusion of a wide Higgs mass range, some theorists thought: complete exclusion until the end of 2011

4 Discoveries at the LHC... I I I I Nov Dec HCP 2011: Exclusion of a wide Higgs mass range, some theorists thought: complete exclusion until the end of 2011 ATLAS & CMS report an excess of events: Too early to draw conclusions

5 Discoveries at the LHC... I I I I Nov Dec July 2012 ATLAS & CMS announce the discovery of a Higgs-like particle

6 Discoveries at the LHC... I I I I Nov Dec July Oct HCP 2011: Exclusion of a wide Higgs mass range, some theorists thought: complete exclusion until the end of 2011 ATLAS & CMS report an excess of events: Too early to draw conclusions ATLAS & CMS announce the discovery of a Higgs-like particle Nobel prize: for the theoret. discovery of a mechanism that contributes to our understanding of the origin of mass...

7 Is it the Higgs boson? Mass: free parameter in the Standard Model expectation from precision measurements: O(100 GeV) (e.g. mass of the W boson) CMS: m H = (stat) (syst) GeV ATLAS: m H = ± 0.37 (stat) ± 0.18 (syst) GeV Spin? spin = 1: Landau-Yang theorem: CP? Massive spin particle cannot decay into two photons: Decay into photons observed spin 1 spin = 2: Excluded with > 99% confidence level spin = 0: compatible model dependent CP-even: compatible spin = 0 CP-odd: Exclusion with 98% confidence level

8 Is it the Higgs boson? Couplings? so far compatible with the Standard Model: Measurement of production und decay channels: pp H ZZ, pp H γγ (+ 2 jets) (discovery channels) pp H WW (compatible with SM) pp H ττ (Evidence!) pp H bb... still relatively large errors ( 20 %) not all couplings accessible Signal strengths: ATLAS Prelim. m H = GeV arxiv: H γγ arxiv: µ = H ZZ* 4l µ = ATLAS-CONF H WW* lνlν arxiv: µ = W,Z H bb ATLAS-CONF H ττ +0.4 µ = µ = σ(stat.) σ( sys inc. theory Total uncertainty ±1σ on µ s = 7 TeV Ldt = fb Signal strength (µ) s = 8 TeV Ldt = 20.3 fb )

9 Is it the Higgs boson? Mass: free parameter in the Standard Model expectation from precision measurements: O(100 GeV) (e.g. mass of the W boson) CMS: m H = (stat) (syst) GeV ATLAS: m H = ± 0.37 (stat) ± 0.18 (syst) GeV Spin? spin = 1: Landau-Yang theorem: CP? Othermodels: Higgsmass canbegivenby otherparameters. Massive spin particle cannot decay into two photons: Decay into photons observed spin 1 spin = 2: Excluded with > 99% confidence level spin = 0: compatible model dependent a mixtureof CP-oddand -even? CP-even: compatible spin = 0 CP-odd: Exclusion with 98% confidence level

10 Is it the Higgs boson? Couplings? so far compatible with the Standard Model: Measurement of production und decay channels: pp H ZZ, pp H γγ (+ 2 jets) (discovery channels) pp H WW (compatible with SM) pp H ττ (Evidence!) pp H bb... still relatively large errors ( 20 %) not all couplings accessible Could be affected by an extended Higgs sector or other unknown particles: how much? Signal strengths: ATLAS Prelim. m H = GeV arxiv: H γγ arxiv: µ = H ZZ* 4l µ = ATLAS-CONF H WW* lνlν arxiv: µ = W,Z H bb ATLAS-CONF H ττ +0.4 µ = µ = σ(stat.) σ( sys inc. theory Total uncertainty ±1σ on µ s = 7 TeV Ldt = fb Signal strength (µ) s = 8 TeV Ldt = 20.3 fb )

11 Need for new physics Main question: What is the underlying theory? Reasons to search for beyond the Standard Model Physics From experiments: dark matter matter-antimatter asymmetry in the universe neutrino oscillations From theory: grand unification embedding of gravity Higgs mass M H : sensitive to physics at high energy scales Λ quantum corrections: δm 2 H Λ2 (hierarchy problem)

12 L ± th L 1 γ / ll T ll lγ ll ± ±± L e rd st 1 nd T KK T T T ± χ Z ± 1 ± 1 ± 1-1 ± 1 ± t Status of LHC searches for new physics Exclusions, exclusions,... (but not of everything) Other Excit. ferm. New quarks LQ V' CI Extra dimensions ATLAS Exotics Searches* - 95% CL Lower Limits (Status: May 2013) Large ED (ADD) : monojet + E T,miss L=4.7 fb, 7 TeV [ ] 4.37 TeV M D (δ=2) Large ED (ADD) : monophoton + E T,miss L=4.6 fb, 7 TeV [ ] 1.93 TeV M D (δ=2) Large ED (ADD) : diphoton & dilepton, m γγ M S (HLZ δ=3, NLO) ATLAS L=4.7 fb, 7 TeV [ ] 4.18 TeV UED : diphoton + E Preliminary T,miss L=4.8 fb, 7 TeV [ ] 1.40 TeV Compact. scale R S /Z ED : dilepton, m L=5.0 fb, 7 TeV [ ] 4.71 TeV ll M 2 KK ~ R RS1 : dilepton, m L=20 fb, 8 TeV [ATLAS-CONF ] ll 2.47 TeV Graviton mass (k/m Pl = 0.1) RS1 : WW resonance, m T,lν lν L=4.7 fb, 7 TeV [ ] 1.23 TeV Graviton mass (k/m Pl = 0.1) Bulk RS : ZZ resonance, m lljj L=7.2 fb, 8 TeV [ATLAS-CONF ] 850 GeV Graviton mass (k/m Pl = 1.0) Ldt = ( 1-20) fb RS g tt (BR=0.925) : tt l+jets, m L=4.7 fb, 7 TeV [ ] 2.07 TeV g mass KK tt ADD BH (M TH /M D =3) : SS dimuon, N ch. part. M (δ=6) s = 7, 8 TeV L=1.3 fb, 7 TeV [ ] 1.25 TeV D ADD BH (M TH /M D =3) : leptons + jets, Σp L=1.0 fb, 7 TeV [ ] 1.5 TeV M D (δ=6) Quantum black hole : dijet, F χ (m jj ) L=4.7 fb, 7 TeV [ ] 4.11 TeV M D (δ=6) qqqq contact interaction : χ(m ) L=4.8 fb, 7 TeV [ ] 7.6 TeV Λ jj qqll CI : ee & µµ, m L=5.0 fb, 7 TeV [ ] 13.9 TeV Λ (constructive int.) uutt CI : SS dilepton + jets + E T,miss L=14.3 fb, 8 TeV [ATLAS-CONF ] 3.3 TeV Λ (C=1) Z' (SSM) : m ee/µµ L=20 fb, 8 TeV [ATLAS-CONF ] 2.86 TeV Z' mass Z' (SSM) : m ττ L=4.7 fb, 7 TeV [ ] 1.4 TeV Z' mass Z' (leptophobic topcolor) : tt l+jets, m L=14.3 fb, 8 TeV [ATLAS-CONF ] 1.8 TeV Z' mass tt W' (SSM) : m T,e/µ L=4.7 fb, 7 TeV [ ] 2.55 TeV W' mass W' ( tq, g =1) : m R tq L=4.7 fb, 7 TeV [ ] 430 GeV W' mass W' R ( tb, LRSM) : m L=14.3 fb, 8 TeV [ATLAS-CONF ] 1.84 TeV W' mass tb Scalar LQ pair (β=1) : kin. vars. in eejj, eνjj L=1.0 fb, 7 TeV [ ] 660 GeV gen. LQ mass Scalar LQ pair (β=1) : kin. vars. in µµjj, µνjj L=1.0 fb, 7 TeV [ ] 685 GeV 2 gen. LQ mass Scalar LQ pair (β=1) : kin. vars. in ττjj, τνjj L=4.7 fb, 7 TeV [ ] 534 GeV 3 gen. LQ mass 4 generation : t't' WbWb L=4.7 fb, 7 TeV [ ] 656 GeV t' mass 4th generation : b'b' SS dilepton + jets + E L=14.3 fb, 8 TeV [ATLAS-CONF ] 720 GeV b' mass T,miss Vector-like quark : TT Ht+X L=14.3 fb, 8 TeV [ATLAS-CONF ] 790 GeV T mass (isospin doublet) Vector-like quark : CC, m lνq L=4.6 fb, 7 TeV [ATLAS-CONF ] 1.12 TeV VLQ mass (charge /3, coupling κ qq = ν/m Q ) Excited quarks : γ-jet resonance, m q* mass Excited quarks : dijet resonance, m jet L=2.1 fb, 7 TeV [ ] 2.46 TeV jj L=13.0 fb, 8 TeV [ATLAS-CONF ] 3.84 TeV q* mass Excited b quark : W-t resonance, m Wt L=4.7 fb, 7 TeV [ ] 870 GeV b* mass (left-handed coupling) Excited leptons : l-γ resonance, m L=13.0 fb, 8 TeV [ATLAS-CONF ] 2.2 TeV l* mass (Λ = m(l*)) Techni-hadrons (LSTC): dilepton, m ee/µµ L=5.0 fb, 7 TeV [ ] 850 GeV ρ T /ω T mass (m(ρ /ω T ) - m(π T ) = M ) W Techni-hadrons (LSTC): WZ resonance (lνll), m L=13.0 fb, 8 TeV [ATLAS-CONF ] 920 GeV ρ mass (m(ρ ) = m(π ) = 1.1 m(ρ )) WZ T ) + m W, m(a T Major. neutr. (LRSM, no mixing) : 2-lep + jets L=2.1 fb, 7 TeV [ ] 1.5 TeV N mass (m(w ) = 2 TeV) R 245 GeV Heavy lepton N (type III seesaw) : Z-l resonance, m L=5.8 fb, 8 TeV [ATLAS-CONF ] ±± ±± Zl N mass ( V = 0.055, V µ = 0.063, V τ = 0) H (DY prod., BR(H ll)=1) : SS ee (µµ), m L=4.7 fb, 7 TeV [ ] 409 GeV H mass (limit at 398 GeV for µµ) Color octet scalar : dijet resonance, m jj L=4.8 fb, 7 TeV [ ] 1.86 TeV Scalar resonance mass Multi-charged particles (DY prod.) : highly ionizing tracks L=4.4 fb, 7 TeV [ ] 490 GeV mass ( q = 4e) Magnetic monopoles (DY prod.) : highly ionizing tracks L=2.0 fb, 7 TeV [ ] 862 GeV mass Mass scale [TeV] *Only a selection of the available mass limits on new states or phenomena shown LSP mass [GeV] ± χ - χ production 2 1 CMS Preliminary s = 8 TeV ICHEP 2014 SUS fb SUS fb Observed Expected m ± χ m = m χ 0 = m χ 0 1 ± χ m +m LSP mass [GeV] χ χ (H χ )(W χ ) χ χ (Z χ )(W χ ) ~ + - χ χ ( l L, BF(l l )=0.5 ) ~ χ χ ( l L, BF(l l )=1 ) χ χ ( τν τ ) ~ χ χ ( l R, BF(l l )=1 ) = m χ 0 1 +m H ~ ~ t - t production, CMS Preliminary s = 8 TeV ICHEP 2014 SUS lep (MVA) 19.5 fb ~ 0 0 t t χ / c χ 1 1 SUS lep + 1-lep + 2-lep (Razor) 19.3 fb SUS lep (Razor) + 1-lep (MVA) 19.3 fb ~ SUS3-009 (monojet stop) 19.7 fb ( t c χ ) SUS3-015 (hadronic stop) 19.4 fb m~ - m χ = m t 0 W m~ - m χ = m 0 t Observed Expected stop mass [GeV] neutralino mass = chargino mass [GeV]

13 Hints? Can the discovered particle s couplings give hints about the underlying model? If no beyond Standard Model physics is seen at the LHC: How large can deviations from the Standard Model Higgs couplings be?

14 Hints? Can the discovered particle s couplings give hints about the underlying model? If no beyond Standard Model physics is seen at the LHC: How large can deviations from the Standard Model Higgs couplings be? How well do we need to know these couplings?

15 How large can the deviations be? No totally model independent answer possible: 3 type of models: Mixed-in singlet Higgs boson Composite Higgs model Minimal Supersymmetric Standard Model (MSSM)

16 Higgs couplings in a mixed-in Singlet Model Standard Model (SM) + exotic Higgs boson singlet: Higgs fields mix via operator H SM 2 S 2 [Schabinger, Wells, hep-ph/ ; Bowen, Cui, Wells, hep-ph/ ] 2 CP-even mass eigenstates h, H with couplings 2 g 2 h = c2 h g 2 SM c h = cos θ h θ h = mixing angle g 2 H = s2 h g 2 SM s h = sin θ h Here: h the SM like one H the heavier Higgs boson detectable at the LHC if light enough

17 Higgs couplings in a mixed-in Singlet Model [Gupta, H.R., Wells, arxiv: ] Region of possible LHC detection of the heavy Higgs boson and region allowed by electroweak precision tests in the sh 2-m H plane: s h s = 14 TeV L = 100 fb 1 Detectable Allowed by EWPT max. deviation of Higgs couplings to other particles: g h g SM s2 h 2 6% m H GeV detectability region based on: [Bowen, Cui, Wells, hep-ph/ ; Iordanidis, Zeppenfeld, hep-ph/ ]

18 Higgs couplings in a mixed-in Singlet Model [Gupta, H.R., Wells, arxiv: ] Region of possible LHC detection of the heavy Higgs boson and region allowed by electroweak precision tests in the sh 2-m H plane: s h s = 14 TeV L = 100 fb 1 Detectable Allowed by EWPT max. deviation of the triple Higgs coupling: g hhh g SM hhh = (ch 3 1) v s3 h 18% v m H GeV detectability region based on: [Bowen, Cui, Wells, hep-ph/ ; Iordanidis, Zeppenfeld, hep-ph/ ]

19 Higgs couplings in Composite Higgs Models Model where the SM Higgs like particle is a pseudo-goldstone: SM vector bosons and fermions + strong sector with Higgs multiplet in terms of an effective field theory for a strong interacting light Higgs (SILH) boson [Guidice, Grojean, Pomarol, Rattazzi, hep-ph/ ] two independent parameters: mass of new resonance m ρ decay constant f with m ρ = g ρ f g ρ = coupling of the new resonance Lagrangian: ( ) cy y L SILH = f H f 2 SM H SM f L H SM f R + c S gg (H SM σ I H SM )B µν W I µν + h.c. 4m 2 ρ + c H 2f 2 µ (H SM H SM) µ (H SM H SM) + c 6λ f 2 (H SM H SM) Naive Dimensional Analysis: c H, c y, c S, c 6 : O(1) numbers

20 Higgs couplings in Composite Higgs Models [Gupta, H.R., Wells, arxiv: ] region allowed by electroweak precision tests in the m ρ -g ρ plane: m Ρ TeV g V g V SM 0.05 Not allowed by EWPT g V g V SM 0.08 g V g V SM 0.1 g V g V SM max. deviation: coupling to vector bosons: g V g SM V = c Hξ % coupling to fermions: g f g SM f = c Hξ 2 + c y ξ % 15% c y c H ξ = v 2 gρ 2, m mρ 2 ρ and g ρ mass and coupling of the new resonance

21 Higgs couplings in Composite Higgs Models [Gupta, H.R., Wells, arxiv: ] region allowed by electroweak precision tests in the m ρ -g ρ plane: m Ρ TeV g V g V SM 0.05 Not allowed by EWPT g V g V SM 0.08 g V g V SM 0.1 g V g V SM max. deviation: coupling to gluons: g g g SM g = c Hξ 2 + c y ξ % 15% c y c H coupling to photons: g γ g SM γ g SM g = c Hξ c y ξ % 5% c y c H, gγ SM : loop-induced

22 Higgs couplings in Composite Higgs Models [Gupta, H.R., Wells, arxiv: ] region allowed by electroweak precision tests in the m ρ -g ρ plane: m Ρ TeV g V g V SM 0.05 Not allowed by EWPT g V g V SM 0.08 g V g V SM 0.1 g V g V SM 0.2 max. deviation: triple Higgs coupling: g hhh ghhh SM = 3 2 c Hξ + c 6 ξ % + 15% c 6 c H

23 Minimal Supersymmetric Standard Model (MSSM) MSSM: Extension of the Standard Model (SM) Further symmetry: Supersymmetry (SUSY): Q Boson = Fermion, Q Fermion = Boson Q = supersymmetry generator Recipe: Standard Model particles + 2 nd Higgs doublet (2HDM) (Generation of fermion masses, anomaly cancelations) Superpartners Explicit soft SUSY-breaking many new (complex) parameters (Else: mass superpartner = mass 2HDM-particle exp. excluded) R-Parity: discrete symmetry

24 Higgs couplings in the MSSM MSSM Higgs potential: depends on gauge couplings Particles to be fully identified or discovered: 2 CP-even h, H 1 CP-odd A 2 charged H ± lots of superpartners might be discovered at the LHC depending }on parameters in our case: h is always the SM like Higgs boson otherwise (i.e. H = SM like Higgs boson): h, A or H ± should be discovered at the LHC

25 Higgs couplings in the MSSM [Gupta, H.R., Wells, arxiv: ] h, H, A, H ± discovery potential for s = 14 TeV, L = 300 fb 1 (modeled after figure of [CLIC Conceptual Design Report (2012); ATLAS collaboration, CERN-LHCC-995]) tan β M A /GeV red region: Several of h, H, A, H ± can be discovered green region: Only a single one, h, can be discovered tan β = ratio of the Higgs vacuum expectation values After the discoverymof A a Higgs = mass boson of the Heidi CP-odd Rzehak Higgs boson 27 November 2014

26 Higgs couplings in the MSSM Legend: [Gupta, H.R., Wells, arxiv: ] several h, H, A, H ± discovered only h is discovered: exluded by Br(b sγ) also stop quarks lighter than a 1 TeV stops heavier 1 TeV, but not all heavier than 1.5 TeV stops heavier than 1.5 TeV Scan done using FeynHiggs [Hahn, Heinemeyer, Hollik, H.R., Weiglein, Williams]

27 Higgs couplings in the MSSM Legend: [Gupta, H.R., Wells, arxiv: ] several h, H, A, H ± discovered only h is discovered: exluded by Br(b sγ) also stop quarks lighter than a 1 TeV stops heavier 1 TeV, but not all heavier than 1.5 TeV stops heavier than 1.5 TeV biggest deviation of the SM Higgs coupling to bottom quarks g b /g SM b with g b = g MSSM b M A M Z : g b g SM b g SM b for tan β = 5, up to a 100%. M2 Z M 2 A

28 Higgs couplings in the MSSM Legend: [Gupta, H.R., Wells, arxiv: ] several h, H, A, H ± discovered only h is discovered: exluded by Br(b sγ) for large tan β and light stops, enhancement by b contributions b : tan β enhanced contribution due to [Carena, Garcia, Nierste,Wagner, hep-ph/ ] also stop quarks lighter than a 1 TeV stops heavier 1 TeV, but not all heavier than 1.5 TeV stops heavier than 1.5 TeV Φ u b2 b1 g b b

29 Higgs couplings in the MSSM overall behaviour similar for g τ /gτ SM, no τ contributions included for tan β > 20 and heavy stops: maximal deviation of 10 %. Maximal deviations for coupling to Z or W : g V /g SM V < 1 % Maximal deviations for coupling to top quarks: g t /g SM t 3 %

30 Higgs couplings in the MSSM [Gupta, H.R., Wells, arxiv: ] Devation of the triple Higgs coupling in the MSSM: Use same approximation for Higgs boson mass and triple coupling! Here: renormalization-group improved corrections of the eff. potential, incl. some 2-loop terms [Carena, Espinosa, Quiros, Wagner, hep-ph/ ] relaxed Higgs mass constraint: g hhh /ghhh SM 15% strict Higgs mass constraint: g hhh /ghhh SM 4% m t 1 < 1.0 TeV 1.0 TeV m t 1 < 2.5 TeV lighter stop mass m t TeV

31 Remark: Higgs signal strengths applied For example: CL Excluded Regions CMS LEP Fit to Higgs Data tan Β A [D Agnolo, Kuflik, Zanetti, arxiv: ]

32 Summary table of coupling deviations How large can the maximal deviations from the SM Higgs couplings be if no new physics is discovered by the LHC? The answer in the context of 3 different models: hvv h tt h bb hhh Mixed-in Singlet 6% 6% 6% 18% Composite Higgs 8% tens of % tens of % tens of % MSSM < 1% 3% 10%, 100% 2%, 15% tan β > 20 no superpartners all other cases

33 Recap 1: Higgs bosons and their masses In the Standard Model: There exists only one Higgs boson. The Higgs boson mass is a free parameter. In extensions of the Standard Model: Several Higgs bosons might exist. The Higgs boson masses can depend on other parameters of the theory, e.g. in the MSSM.

34 Recap 2: Particle content of the MSSM (2HDM)-Particle Quarks Leptons Gauge bosons Higgs boson s Superpartner Squarks Sleptons Gauginos Higgsinos mix Charginos Neutralinos Constraints from direct searches one way to circumvent constraints: larger SUSY masses Constraints from indirect probes e.g. Higgs boson mass

35 MSSM Higgs masses at tree-level not all independent (2 free parameters, 4 masses) often: Mass M A or M H ± (and tan β) as free parameter tan β = v 2 v 1 : ratio of the Higgs vac. expect. values lightest Higgs boson: h Upper theoretical Born mass bound: M h M Z = 91 GeV with quantum corrections of higher orders: M h 140 GeV dependent on the MSSM parameters

36 Why a precise Higgs mass prediction? Needed as consistent input for the calculation of cross sections and decay widths in the MSSM experimental measured value constraint on viable MSSM parameter space A precise theoretical prediction is needed to fully exploit this constraint: M exp. H < 1 GeV vs M theory H 3 GeV expected: LHC: M exp. H = 200 MeV ILC: M exp. H = 50 MeV

37 Contributions to the Higgs boson masses Born propagator: Quantum corrections: t t t i h h h g +... h h h t t t j i p 2 Mh 2 One-loop level O(α t ): Two-loop level O(α t α s ) α t (top Yukawa coupl.) 2 i p 2 (M 2 h + M2 h ) Additionally, mixing at loop level: h t i t j H

38 Contributions to the Higgs boson masses Two-point-vertex function: with the matrix: iˆγ(p 2 ) = p 2 M(p 2 ) h ( M 2 M(p 2 )= hborn ˆΣ hh (p 2 ) ˆΣ Hh (p 2 ) ) (CP-conserving case: mixing only ˆΣ Hh (p 2 ) M 2 H Born ˆΣ HH (p 2 ) betw. CP-even Higgs bosons h, H) Calculate the zeros of the determinant of ˆΓ loop-corrected Higgs masses t t h

39 Implications of a GeV Higgs boson (MSSM) Mh/GeV Born 1-loop 2-loop X t /TeV generated using FeynHiggs [Hahn, Heinemeyer, Hollik, H.R., Weiglein, Williams] 1-loop [Frank, Hahn, Heinemeyer, Hollik, H.R., Weiglein] 2-loop O(α {t,b} α s, α 2 {t,b}, α tα b ) [Degrassi, Slavich, Zwirner; Brignole, Degrassi, Slavich, Zwirner; Heinemeyer, Hollik, H.R., Weiglein; Dedes, Degrassi, Slavich], X t = stop mixing parameter A ± 3 GeV mass constrains the parameter space but does not exclude the MSSM. (theory uncertainty 3 GeV) here: no known 3-loop contributions included [Martin; Harlander, Kant, Mihaila, Steinhauser]

40 Higgs boson mass for large stop masses Prediction obtained via Feynman diagrammatic approach: + all log and non-log terms are taken into account at a certain order of perturbation theory - possible appearance of large logs: M h log M S m t M S = m t1 m t2 : SUSY particle mass scale m t1, m t2 : scalar top quark masses m t : top quark mass good prediction for lower SUSY mass scales no reliable prediction for large SUSY mass scales

41 Higgs boson mass for large stop masses Other approach: Renormalization Group Equation (RGE) approach: assume: all SUSY particles are heavy of order M S : above M S : MSSM below M S : Standard Model (as effective theory) match at scale M S : λ MSSM (M S ) = λ Standard Model (M S ) quartic Higgs coupling evolve λ to lower scale using Standard Model running (RGE) the Higgs mass 2 is then M 2 h (m t) = 2λ(m t )v 2 v 174 GeV logs resummed to all orders

42 Advantages Feynman diagrammatic approach: All log- and non-log terms are taken into account at a certain order of perturbation theory: Especially important for lower mass scales Renormalization group equation approach: Resummation of potentially large log-terms: Especially important for larger mass scales Combine both approaches

43 Combination [Hahn, Heinemeyer, Hollik, HR, Weiglein, arxiv: ] [Hahn, Heinemeyer, Hollik, HR, Weiglein] Feynman diagrammatic part: from FeynHiggs Renormalization group equation (RGE) part: quartic Higgs coupling λ 2-loop RGE for running for the strong coupling g s with α s = gs 2 /(4π) [Espinosa, Quiros 91] top Yukawa coupling y t Matching at scale M S = m t 1 m t 2 : λ(m S ) = 3y t 4 8π 2 m t i Xt 2 M 2 S [Carena, Haber, Heinemeyer, Hollik, Wagner, Weiglein, hep-ph/ ] [ 1 X 2 t M 2 S = stop masses ] X t = A t µ cot β = squark mixing parameter leading + next-leading log (ln M S m t ) resummation

44 Combination [Hahn, Heinemeyer, Hollik, HR, Weiglein, arxiv: ] Combination of both approaches: Avoid double counting of logs Subtract logs from the Feynman diagrammatic (FD) result: M 2 h = ( M2 h )FD (X OS t ) ( Mh 2)log (X OS ) + ( Mh 2)RGE (X MS Both approaches use a MS top quark mass FD: X t in on-shell scheme, RGE: X t in MS scheme: Conversion needed: X MS t = X OS t t [ ( 1 + ln M2 S αs mt 2 π 3α )] t 16π t )

45 Combination [Hahn, Heinemeyer, Hollik, HR, Weiglein, arxiv: ] For M A M Z : ˆΣ φuφ u (sin β) 2 M 2 h self energy of the interaction eigenstates φ u φ u couples to up-type quarks Correction can be incorporated into the self energy matrix corrections are also taking into account in the mixing

46 M h [GeV] Results of combination FH295 3-loop 4-loop 5-loop 6-loop 7-loop LL+NLL FeynHiggs X t /M S = 2 X t = M S [GeV] M A = M 2 = µ = 1 TeV, m g = 1.6 TeV, tan β = 10 Comparison of: old FeynHiggs reliable up to M s = O(1TeV) analyt. solution of RGE: 3-loop... 7-loop level: Logs of order O(α t α 2 s, α 2 t α s, α 3 t )... numerical solution: LL+NLL: logs resummed to all orders [T. Hahn, S. Heinemeyer, W. Hollik, H.R., G. Weiglein, arxiv: ]

47 Results of combination M h [GeV] loop, O(α t α s 2 ) 3-loop full LL+NLL H3m FeynHiggs A 0 = 0, tanβ = M S [GeV] Comparison with H3m: [Kant, Harlander, Mihaila, Steinhauser, arxiv: ] 3-loop: O(α t α 2 s ), O(α 2 t α s ), O(α 3 t ), only leading and next-to leading logs single scale M S [Hahn, Heinemeyer, Hollik, HR, Weiglein, arxiv: ] H3m: complete O(α t α 2 s ) result different scales At 2-loop: different ren. schemes CMSSM: m 0 = m 1/2 = GeV, A 0 = 0, tan β = 10, µ > 0, spectra generation with SoftSUSY [Allanach, hep-ph/ ]

48 Complementary: Pure RGE approach Similar findings for large SUSY masses: [Draper, Lee, Wagner, arxiv: ] 1Σ, 2Σ ATLAS CMS LEP exclusion S 2-loop NNLL result 3-loop NNLL result 4-loop NNLL result resummed result Differences: 3-loop running for λ 2-loop matching not yet implemented into a computer code

49 Summary Exciting times: Discovery of a Higgs boson Still exciting: What is its true nature? At the moment: compatible with the Standard Model Constraints on the parameter space of extension of the Standard Model (e.g. coming from the Higgs mass) Precise measurement of its couplings can help with the complete identification of the particle

50

51 How was it discovered? Discovery channels (LHC: p p collider, p = proton): pp H ZZ 4l: pp H γγ: (here: l = µ, µ = muon) g g t t t H Z Z l l l l g g t t H t γ W W W γ

52 How was it discovered? Discovery channels (LHC: p p collider, p = proton): pp H ZZ 4l: pp H γγ + 2 jets: (here: l = µ, µ = muon) g g t t t H Z Z l l l l q q V V H W W q γ W γ q

53 Dependence on the gluino mass M gluino = 1600 GeV M gluino = M S FeynHiggs X t /M S = 2 M h [GeV] X t = M S [GeV] M A = M 2 = µ = 1 TeV, m g = 1.6 TeV, tan β = 10

54 Implications of a GeV Higgs boson (MSSM) Mh/GeV Born 2-loop 1-loop LL+NLL X t /TeV generated using FeynHiggs [Hahn, Heinemeyer, Hollik, H.R., Weiglein, Williams] 1-loop [Frank, Hahn, Heinemeyer, Hollik, H.R., Weiglein] 2-loop O(α {t,b} α s, α 2 {t,b}, α tα b ) [Degrassi, Slavich, Zwirner; Brignole, Degrassi, Slavich, Zwirner; Heinemeyer, Hollik, H.R., Weiglein; Dedes, Degrassi, Slavich] LL+NLL: with resummed logs (stop soft-breaking parameter M SUSY = 1 TeV) [Hahn, Heinemeyer, Hollik, H.R., Weiglein] A ± 3 GeV mass constrains the parameter space but does not exclude the MSSM. (theory uncertainty 3 GeV)