Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

Transcription

1 Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

2 Neutral Higgs Production - Status and Tools: Sven Heinemeyer, IFCA (CSIC, Santander) Wuppertal, 03/ My motivation and focus. MSSM issues 3. gg φ, φ = h, H, A 4. b b φ, φ = h, H, A Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

3 Neutral Higgs Production - Status and Tools: Sven s view (Michael s view later) Sven Heinemeyer, IFCA (CSIC, Santander) Wuppertal, 03/ My motivation and focus. MSSM issues 3. gg φ, φ = h, H, A 4. b b φ, φ = h, H, A Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

4 1. My motivation and focus Supersymmetry (SUSY) : Symmetry between Bosons Fermions Q Fermion Boson Q Boson Fermion Simplified examples: Q top, t scalar top, t Q gluon, g gluino, g each SM multiplet is enlarged to its double size Unbroken SUSY: All particles in a multiplet have the same mass Reality: m e mẽ SUSY is broken via soft SUSY-breaking terms in the Lagrangian (added by hand) SUSY particles are made heavy: M SUSY = O(1 TeV) Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

5 Supersymmetry: Motivation The SM is in a pretty good shape. Why MSSM? (Is it worth to double the particle spectrum?) 1.) Stability of the Higgs mass against higher-order corr..) Unification of gauge couplings: Not possible in the SM, but in the MSSM (although it was not designed for it.) 3.) Spontaneous symmetry breaking via Higgs mechanism is automatic in SUSY GUTs 4.) SUSY provides CDM candidate 5.)... 1/α i Unification of the Coupling Constants in the SM and the minimal MSSM log Q 1/α i /α 1 1/α MSSM 10 1/α [Amaldi, de Boer, Fürstenau 9] 10 log Q Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

6 Supersymmetry: Motivation The SM is in a pretty good shape. Why MSSM? (Is it worth to double the particle spectrum?) 1.) Stability of the Higgs mass against higher-order corr..) Unification of gauge couplings: Not possible ini will theconcentrate SM, but inon SUSY 60 because: the MSSM (although I might 50 it know wasanot few things about the MSSM, designed for it.) and I know much less about the SM... 3.) Spontaneous symmetry breaking via Higgs mechanism is automatic in SUSY GUTs 4.) SUSY provides CDM candidate 5.)... 1/α i Unification of the Coupling Constants in the SM and the minimal MSSM log Q 1/α i /α 1 1/α MSSM 10 1/α [Amaldi, de Boer, Fürstenau 9] 10 log Q Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

7 The Minimal Supersymmetric Standard Model (MSSM) Superpartners for Standard Model particles [ ] [ ] u, d, c, s, t, b e, µ, τ L,R [ũ, d, c, s, t, b ] L,R [ẽ, µ, τ ] L,R L,R [ νe,µ,τ ] L ] [ νe,µ,τ L Spin 1 Spin 0 g W ±, H ± }{{} γ, Z, H 0 1, H0 }{{} Spin 1 / Spin 0 g χ ± 1, χ 0 1,,3,4 Spin 1 Enlarged Higgs sector: Two Higgs doublets focus here! Problem in the MSSM: many scales Problem in the MSSM: complex phases Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

8 Enlarged Higgs sector: Two Higgs doublets H 1 = H = H1 1 H1 H1 H = = v 1 + (φ 1 + iχ 1 )/ φ 1 φ + v + (φ + iχ )/ V = m 1 H 1 H 1 + m H H m 1 (ǫ abh a 1 Hb + h.c.) physical states: h 0, H 0, A 0, H ± Goldstone bosons: G 0, G ± + g + g (H 1 H 1 H H ) + g H 1 H }{{ 8 }}{{} gauge couplings, in contrast to SM Input parameters: (to be determined experimentally) tan β = v, MA v = m 1 (tan β + cot β) 1 Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

9 Enlarged Higgs sector: Two Higgs doublets with CP violation H 1 = H = H1 1 H1 H1 H = = v 1 + (φ 1 + iχ 1 )/ φ 1 φ + v + (φ + iχ )/ e iξ V = m 1 H 1 H 1 + m H H m 1 (ǫ abh a 1 Hb + h.c.) physical states: h 0, H 0, A 0, H ± + g + g (H 1 H 1 H H ) + g H 1 H }{{ 8 }}{{} gauge couplings, in contrast to SM CP-violating phases: ξ, arg(m 1 ) can be set/rotated to zero Input parameters: (to be determined experimentally) tan β = v v 1, M H ± Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

10 t/ b sector of the MSSM: (scalar partner of the top/bottom quark) Stop, sbottom mass matrices (X t = A t µ /tan β, X b = A b µ tan β): M t = M t L + m t + DT t 1 m t X t m t X t M t R + m t + DT t θ t m t m t M b = M b L + m b + DT b 1 m b X b θ b m b 1 0 m b X b M b R + m b + DT b 0 m b mixing important in stop sector (also in sbottom sector for large tan β) soft SUSY-breaking parameters A t, A b also appear in φ- t/ b couplings SU() relation M t L = M b L relation between m t 1, m t, θ t, m b 1, m b, θ b Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

11 . MSSM issues: (Higgs) cross section calculation at the LHC: σ(pp X) = ij dx 1 dx f i (x 1, µ f ) f j (x, µ f )ˆσ(ij X) PDFs (x 1, :) momentum fraction carried by the incoming quarks, gluons universal for SM and MSSM ˆσ : partonic cross section, calculated perturbatively different in SM and MSSM Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

12 Gluon-Fusion: g g t t t H +... SM: input: SM Higgs mass (free parameter) SM (fermion) masses SM couplings (at the appropriate scale) more in Michael s view? output: SM amplitude, cross section Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

13 Now for the MSSM: Input parameters: M A and tan β all other masses and mixing angles are predicted! Tree-level result for m h, m H : m H,h = 1 [M A + M Z ± (MA + M Z ) 4MZ M A cos β m h M Z at tree level Huge higher-order corrections: [G. Degrassi, S.H., W. Hollik, P. Slavich, G. Weiglein 0] M h < 135 GeV ] (most) Higgs masses and couplings are not free parameters Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

14 Propagator/Mass matrix at tree-level: q m A q m H q m h Propagator / mass matrix with higher-order corrections ( Feynman-diagrammatic approach): M hha (q ) = q m A + ˆΣ AA (q ) ˆΣ AH (q ) ˆΣ Ah (q ) ˆΣ HA (q ) q m H + ˆΣ HH (q ) ˆΣ Hh (q ) ˆΣ ha (q ) ˆΣ hh (q ) q m h + ˆΣ hh (q ) ˆΣ ij (q ) (i, j = h, H, A) : renormalized Higgs self-energies ˆΣ Ah, ˆΣ AH 0 CPV, CP-even and CP-odd fields can mix complex roots of det(m hha (q )): M h i (i = 1,,3): M = M imγ Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

15 Higgs couplings, tree level: g hv V = sin(β α) g SM HV V, V = W ±, Z g HV V g hb b, g hτ + τ = cos(β α) g SM HV V g haz = cos(β α) g cos θ W = sin α cos β gsm Hb b,hτ + τ g ht t = cos α sin β gsm Ht t g Ab b, g Aτ + τ = γ 5 tan β g SM Hb b g hb b, g hτ + τ : significant suppression or enhancement w.r.t. SM coupling possible also here: large higher-order corrections! Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

16 Example for large higher-order corrections in the MSSM: gg h γγ can be strongly suppressed gluophobic Higgs scenario [M. Carena, S.H., C. Wagner, G. Weiglein 0] Strong suppression of gg h γγ possible over the whole parameter space (not realized in msugra/cmssm, GMSB, AMSB,... ) Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

17 Another issue: external (on-shell) Higgs bosons Examples for external (on-shell) Higgs bosons (φ = h 1, h, h 3 ): Higgs production: q g t t φ q W φ g t q W q Higgs decays: b W γ φ b φ W W γ important to ensure on-shell properties of external Higgs boson Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

18 Correct on-shell amplitude with external Higgs h i : [M. Frank, T. Hahn, S.H., W. Hollik, H. Rzehak, G. Weiglein, K. Williams 06] ( ) A(h i ) = Z i Γhi + Z ij Γ hj + Z ik Γ hk Zi : ensures that the residuum of the external Higgs boson is set to 1 Z ij : describes the transition from i j Z i = [ 1 + (ˆΣ eff ii ) (M i ) ] 1, Zij = ij(p ) ii (p ) p =M i ˆΣ eff ii (p ) = ˆΣ ii (p ) i ˆΓ ij (p )ˆΓ jk (p )ˆΓ ki (p ) ˆΓ ki (p )ˆΓ jj (p ) ˆΓ ij (p )ˆΓ kk (p ) ˆΓ jj (p )ˆΓ kk (p ) ˆΓ jk (p ) ˆΓ(p ) = imhha (p ) (p ) = ( Γ(p ) ) 1 m i : tree-level masses M i : higher-order corrected masses Written more compact with the Z matrix : Z ij = Z i Z ij Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

19 Numerical example for external Higgs bosons: [T. Hahn, S.H., W. Hollik, H. Rzehak, G. Weiglein 07] M SUSY = m g = M = 500 GeV, A t = 1000 GeV, µ = 1000 GeV, M H ± = 150 GeV Γ(h 1 τ + τ ) as a function of φ Xt ϕ Xt Γ(h 1 τ + τ ) / MeV ϕ Xt tan β = 5.0 π π/ 0 π/ π tan β = 15 π π/ 0 π/ π ZHiggs UHiggs(q on-shell) UHiggs(q = 0) full: red solid: Z, approximations: blue solid: U, blue dashed: R deviations at the 5-10% level Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

20 Needed: Input MT 17.7 MB 4.7 MW 80.4 MZ 91.1 MSusy 975 MA0 00 Abs(M_) 33 Abs(MUE) 980 TB 50 Abs(At) -300 Abs(Ab) 1500 Abs(M_3) 975 Computercode Output HIGGS MASSES Mh0 = MHH = MA0 = MHp = SAeff = ZHiggs = \ \ ESTIMATED UNCERTAINTIES DeltaMh0 = DeltaMHH = DeltaMA0 = DeltaMHp = Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

21 Needed: Input MT 17.7 MB 4.7 MW 80.4 MZ 91.1 MSusy 975 MA0 00 Abs(M_) 33 Abs(MUE) 980 TB 50 Abs(At) -300 Abs(Ab) 1500 Abs(M_3) 975 Computercode Codes on the market: Output HIGGS MASSES Mh0 = MHH = MA0 = MHp = SAeff = ZHiggs = \ \ ESTIMATED UNCERTAINTIES DeltaMh0 = DeltaMHH = DeltaMA0 = DeltaMHp = FeynHiggs [T. Hahn, S.H., W. Hollik, H. Rzehak, G. Weiglein] ( CPSuperH [J.S. Lee, A. Pilaftsis et al.] ( Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

22 Short (biased?) comparison: 1) Higgs self-energy correction in the rmssm: CPsH: (leading) log approx. for one-loop approx. for momentum dependence (at one-loop) (leading) log approx. for O ( α s α t, α t ) dependence O(α s α b ): (α s tan β) n resummation FeynHiggs: full one-loop including full complex phase dependence full momentum dependence (at one-loop) full O ( α s α t, α ) t O(α s α b ): (α s tan β) n resummation + subleading terms of O ( α t α b, α b Im ˆΣ included consistently in mass and coupling evaluation ) Higgs self-energy corrections in the cmssm: see back-up 3) OS properties for external Higgs bosons: Only FeynHiggs has the Z matrix ) Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

23 Gluon-Fusion in the MSSM: Additional contribution to gg φ : g t g t t φ + t φ +... g t g t input: SM (fermion) masses SM couplings (at the appropriate scale) MSSM parameters output new input (via FeynHiggs, CPsH,...): MSSM Higgs masses MSSM couplings, Z matrix,... output: MSSM amplitude, cross section How to re-use SM amplitudes? How to include MSSM corrections? Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

24 3. gg φ, φ = h, H, A Q: How to obtain the best MSSM prediction? What can be used from the SM? How to include new MSSM corrections... A: Several methods possible: 0) Full calculation 1) FeynHiggs (old) ) FeynHiggs (new) 3) Michael s proposal 4)... Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

25 0) Full calculation [C. Anastasiou, S. Beerli, A. Daleo 08] [M. Mühlleitner, H. Rzehak, M. Spira 10] (?) NLO QCD calculation(s) How to include more SM results (NNLO top, NLO EW)? How to include MSSM issues? (so far unsolved?) Michael s view? Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

26 1) FeynHiggs (old): A MSSM = top MSSM k NLO t k NNLO t + Rebot MSSM k b,r + Imbot MSSM k b,i + SM MSSM rest + SUSY k SUSY A NNLO SM = top knlo t + SMrest k NNLO t + Rebot k b,r + Imbot k b,i M MSSM = A MSSM M NNLO SM = ANNLO SM σ MSSM = M MSSM M NNLO SM σ NNLO SM k t, k b,r, k b,i from σ LO SM, σnlo SM (top, bottom, top + bottom) Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

27 ) FeynHiggs (new): A MSSM = top MSSM k NLO t k NNLO t + Rebot MSSM k b,r + Imbot MSSM k b,i + SM MSSM rest + SUSY k SUSY A NLO SM = top knlo t + SMrest + Rebot k b,r + Imbot k b,i M MSSM = A MSSM M NLO SM = ANLO SM σ MSSM = M MSSM M NLO SM σ NLO SM k t, k b,r, k b,i from σ LO SM, σnlo SM (top, bottom, top + bottom) Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

28 3) Michael s proposal Michael s view :-) Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

29 3) Michael s proposal Michael s view :-) σ MSSM = σ NLO+NNLO? SM,top + σ SM,bot ( ) g MSSM t gt SM ( ) g MSSM b gb SM + σ SM,top bot gmssm t gb MSSM + SUSY? gt SM gb SM Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

30 Pros and cons: By construction: All three versions get the top-bottom (interference) contribution right To be discussed: inclusion of NNLO SM corrections? inclusion of SUSY corrections? interference between SUSY and SM? inclusion of b corrections in b bφ vertex?... Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

31 4. b b φ, φ = h, H, A 4FS vs. 5FS calculations and investigations in the SM more discussions later!? Relevance for MSSM: b bφ coupling can grow with tan β Heavy Higgs bosons can be detected via b b H/A τ + τ... Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

32 Results for neutral heavy Higgs bosons: MSSM Higgs discovery contours in M A tan β plane (Φ = H, A) (m max h benchmark scenario): [CMS PTDR 06] tanβ φ µµ ττ φ eµ φ ττ e+jet φ ττ φ ττ µ+jet -1 jet+jet, 60 fb -1 CMS, 30 fb pp bbφ, φ = h,h,a max m h scenario M SUSY = 1 TeV/c = 00 GeV/c M µ = 00 GeV/c m gluino = 800 GeV/c Stop mix: X = M t SUSY M A,GeV/c Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

33 Differences compared to the SM Higgs: Additional enhancement factors compared to the SM case: b tan β y A b y b 1 + b b t b At large tan β: either H A or h A H + y b tan β 1 + b b = α s 3 π m g µ tan β I(m b 1, m b, m g ) + α t 4 π A t µ tan β I(m t 1, m t, µ) other parameters enter strong µ dependence Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

34 MSSM NLO calculation (5FS): [S. Dittmaier, M. Krämer, A. Mück, T. Schlüter 08] b gives a very good approximation for the SUSY corrections Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

35 MSSM NLO calculation (5FS): [S. Dittmaier, M. Krämer, A. Mück, T. Schlüter 08] b gives a very good approximation for the SUSY corrections FeynHiggs approach: 1. use bbh@nnlo [R. Harlander, W. Kilgore 03] so far: grid in M H and s planned: link bbh@nnlo directly to FeynHiggs. include b corrections ( effective coupling approximation ) 3. include MSSM issues best MSSM prediction? Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

36 Dependence of LHC wedge from b b H/A τ + τ jets on µ: [S.H., A. Nikitenko, G. Weiglein et al. 06] tanβ 50 µ = GeV/c µ = -00 GeV/c tanβ 50 µ = GeV/c µ = -00 GeV/c 40 µ = 00 GeV/c µ = 1000 GeV/c 40 µ = 00 GeV/c µ = 1000 GeV/c CMS, 60 fb pp bbφ ττ j+j mmax h scenario M SUSY = 1 TeV/c M = 00 GeV/c m gluino = 0.8 M SUSY Stop mix: X t = M SUSY CMS, 60 fb pp bbφ ττ j+j no mixing scenario M SUSY = TeV/c M = 00 GeV/c m gluino = 0.8 M SUSY Stop mix: X t = M A,GeV/c M A,GeV/c based on full CMS simulation non-negligible variation with the sign and absolute value of µ ( numerical compensations in production and decay) Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

37 Back-up Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

38 FeynHiggs vs. CPsH in the cmssm (I): Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

39 FeynHiggs vs. CPsH in the cmssm (II): Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,

40 FeynHiggs vs. CPsH in the cmssm (III): Sven Heinemeyer, gg H and q q H at the LHC, Wuppertal,