Searching for Supersymmetric Higgs Bosons at the LHC

Searching for Supersymmetric Higgs Bosons at the LHC Tilman Plehn CERN Light neutral Higgs: no-lose-theorem Charged Higgs: bottom induced processes Heavy neutral Higgs: decay to two light Higgses

MSSM Higgs Bosons at the LHC ± ± ± = TeV/c MSSM Higgs Sector Softly broken supersymmetric anomaly free theory two doublets, coupling to up and down type fermions five physical states h o, H o, A o, H ± mixing of scalars to mass eigenstates (mixing angle α) more predictive than Standard Model (upper h o mass limit) conveniently expressed as function of m A and tan β v /v Yukawa couplings to H, A, H ± : m b tan β, m t / tan β (large m A ) typically one light, many heavy scalars [Heinemeyer, Weiglein] M Higgs 5 max 45 m h scen., = 5 h 4 H A 35 H +- 3 5 5 FeynHiggs. 5 5 5 5 3 35 4 45 5 M A Find first Higgs boson complete coverage by WBF h τ τ [TP, Rainwater, Zeppenfeld] problem: mass degeneracy [Boos, Djouadi, Mühlleitner, Nikitenko] m h /m h σ/ N (σ.5 GeV for µµ, γγ and σ 5 GeV for ττ) m h 6 5 4 3 9 4 4 4 4 m A m A ( -m h ) 5 5 4 4 3 3 4 4 ( -m h )=3,5, GeV m A 4 m A Tell it is HDM (MSSM?) look for heavy Higgs bosons H, A ττ, µµ inclusive gg H and gg b bh H ± ντ, tb in pp th, W + H, H + H (n.b. SUSY loops) [Hollik et al, Kniehl et al] 5 4 τν qq H th, H ± tb ± th, H τν appearance in SUSY cascades [Datta, Djouadi, Guchait, Moortgat] 3 ± tt, H τν µ A t = - GeV/c = 6 CMS, 3 fb, M TeV/c, M SUSY - = GeV/c no other conclusive way but to find these particles Excluded by LEP 5 5 3 35 4 45 5 55 m A (GeV/c )

5 45 4 35 max m h scen., = 5 h H A H +- M Higgs 3 5 5 FeynHiggs. 5 5 5 5 3 35 4 45 5 M A

5 4 τν ± qq H ±, H ± th th tb ± ±, H τν 3 τν ± tt, H CMS, 3 fb µ = - GeV/c, M - = GeV/c A t = 6 TeV/c, M SUSY = TeV/c Excluded by LEP 5 5 3 35 4 45 5 55 m A (GeV/c )

. Light Neutral Higgs MSSM Higgs bosons in weak boson fusion [TP, Rainwater, Zeppenfeld] SM cross section > 3 pb for light Higgs in qq qqh (tagging jet signature, central decay products, minijet veto) approximate GeV ττ mass reconstruction at high p T,h [K.Ellis] MSSM decoupling region: (a) Higgs mass range after LEP: m Z m h < 35 GeV (b) production cross section: g W W h = sin(β α) (c) branching fraction: BR(h ττ) > BR(H SM ττ) enhancement of rate: pp qqh qqττ h o m h 8 3 6 4 m 8 A sin (β-α).8.6.4. 3 6 4 m 8 A (σ.b) h [fb].4. 3 6 4 m 8 A 3 H o 6 4 3 6 4 m 8 A cos (β-α).8.6.4. 3 6 4 m 8 A (σ.b) H [fb].4. 3 6 4 m 8 A M SUSY = TeV, maximal mixing heavy Higgs production at low m A 5 5 LHC(4fb - ): VV H ττ VV h ττ no lose theorem for MSSM Higgs scalars 5 LEP: e + e Zh 8 4 6 M A Attempts to escape this channel low tan β: forbidden by LEP m A = 9 GeV and m h = 95 GeV: wide open channel for H super large mixing A t > 6 TeV: enhanced WBF W W and γγ rate CP phases in A t : coverage solid [Carena, Ellis, Wagner,...] funny couplings of all kind: again solid [Schumacher] many multiplets: go for WBF W W channel [Alves, Eboli, TP, Rainwater]

h o H o m h 8 6 4 3 8 6 4 m A 3 8 6 4 m A sin (β-α) cos (β-α).8.6.4..8.6.4. 3 8 6 4 m A 3 8 6 4 m A (σ.b) h [fb] (σ.b) H [fb].4..4. 3 8 6 4 m A 3 8 6 4 m A M SUSY = TeV, maximal mixing

3 5 5 LHC(4fb - ): VV H ττ VV h ττ 5 LEP: e + e Zh 8 4 6 M A

. (Heavy) Charged Higgs Most promising channel associated production pp th + X for large tan β decay H ± ντ most promising [Assamagan, Coadou] m b =4.6 GeV /σ tot dσ/d y b (gg b th ). m b =.46 GeV Exclusive production gg bth.5 = GeV = 5 GeV = 5 GeV 3 4 5 6 7 y b.4 /σ tot dσ/dp T,b (gg b th ) collinear bottom jets from gluon splitting, regularized by m b.3.. m b =4.6 GeV = GeV = 5 GeV = 5 GeV experiment: forward jets, p T,b peaked at m b (factor /6 for each tagged b) use bottom inclusive cross section 3 4 5 p T,b check asymptotic cross section behavior dσ/dp T,b p T,b /m T,b inclusive total rate σ log(p max T,b /pmin T,b ) = log(pmax T,b /m b) p T,b dσ/dp T,b (gg b th ) how large logarithms? resum? 3 = GeV =5 GeV m b =4.6 GeV m b =.46 GeV Inclusive process bg th =5 GeV 3 p T,b resum large logarithms log(p T,b /m b ) in exclusive process gg bth equivalent to bottom parton density and inclusive process bg th µ F,b transverse momentum size of bottom parton (µ F,b p max T,b ; usually hard scale µ F,b = M) numerical improvement or overestimate? () check bottom inclusive total rate () check bottom inclusive t, H distributions

m b =4.6 GeV /σ tot dσ/d y b (gg b th ). m b =.46 GeV.5 = GeV = 5 GeV = 5 GeV 3 4 5 6 7 y b.4.3. /σ tot dσ/dp T,b (gg b th ) m b =4.6 GeV = GeV = 5 GeV = 5 GeV. 3 4 5 p T,b

p T,b dσ/dp T,b (gg b th ) = GeV 3 =5 GeV m b =4.6 GeV m b =.46 GeV =5 GeV 3 p T,b

Total Rate: Bottom Factorization Scale... - LHC: gg b th - with P g (x)= - - Q b /(m t + ) Q b /(m t + ) Q b /(m t + )... - - - =5,5, GeV =5 GeV =5 GeV = GeV p T,b /(m t + ) p T,b /(m t + ) p T,b /(m t + ) Perturbative bottom factorization scale from exclusive process two steps: first bottom virtuality Q max b general exclusive process: gg bx M approximate gluon density L = L /x asymptotic behavior M = S σ /Q b σ = σ L 6π S M dq b Q b F (Q b ) F (Q b ) known correction to asymptotic behavior [Boos, TP] dσ/dq b /Q b define Q max b at turning point d F (Q b )/d(log Q b ) = Q max b M/ (hard scale argument Q max b M, not more than that!) x n P (p) (x) Q F = GeV Q F = GeV - - x Second step: transverse momentum p max T,b check explicitly: Q b Q max b also yields p T,b p max T,b translate Q b into p T,b point by point LHC: gg b th - Q b dσ/dq b p T,b dσ/dp T,b p max T,b /Qmax b Q max b /M yields p max T,b Q max b / M/4 LHC: gg b th - with P g (x)=x - Q b dσ/dq b p T,b dσ/dp T,b (numerical study of gg bth : µ F,b M/5) Q b dσ/dq b p T,b dσ/dp T,b So what did we learn from exclusive process? log(p T,b /m b ) after integrating over bottom jet but large logs at maximum log(m/(5m b )) [TP; Maltoni, Willenbrock] hard scale for inclusive process: µ F,b M gg and bg processes: µ F,b M/5 from partonic phase space Total cross section with bottom partons understood

LHC: gg b th - =5,5, GeV Q b dσ/dq b p T,b dσ/dp T,b.. =5 GeV =5 GeV = GeV - Q b /(m t + ) - p T,b /(m t + ) LHC: gg b th - with P g (x)=. Q b dσ/dq b. p T,b dσ/dp T,b - Q b /(m t + ) - p T,b /(m t + ) LHC: gg b th - with P g (x)=x -. Q b dσ/dq b. p T,b dσ/dp T,b - Q b /(m t + ) - p T,b /(m t + )

Total Rate: QCD Corrections Next-to-leading Order QCD Calculation [TP] leading order uncertainty large for bg th complete set of virtual and real SUSY corrections running Yukawa couplings, everything else misleading N correction +3% 4% perturbatively stable [Zhu] - -.8.6.4..8 N: gb th : gb th : gg b th σ tot (pp th +X) [pb] (m b running mass) m b pole mass 4 6 8 K (pp th +X) = 3 5 µ = 4m av µ = m av µ = m av /4 3 3 4 6 8 Scale Dependence renormalization scale dependence numerically dominant µ R (m t + )/ natural choice [c.f. Higgs decays, Melnikov].8.6.4. µ F =µ R µ R =m av σ tot (pp th +X) [pb] =5 GeV N factorization scale dependene critical only for small µ F µ F (m t + )/5 from exclusive process problem at small scales: bottom induced process not dominant N scale dependence ±% well defined limit µ F m b returns exclusive process gg bth µ F =m av µ/m av Matching at threshold < m t m b : top pair production and Breit Wigner propagator > m t m b : resummed off-shell process double counting of pp t t t( bh ) subtract on-shell top pairs from N bg th process (unique in small width approximation, see SUSY-pairs) - σ sum σ off-shell σ BW σ tot (pp th +X) [pb] = 3 σ incl,n σ incl, consistent matching by simply adding channels 5 t t m = +m b ±Γ 3 4 5

- σ tot (pp th +X) [pb] (m b running mass) m b pole mass - N: gb th : gb th : gg b th 4 6 8.8.6.4..8 K (pp th +X) = 3 5 µ = 4m av µ = m av µ = m av /4 3 3 4 6 8

σ sum σ tot (pp th +X) [pb] = 3 σ off-shell σ incl,n - σ BW σ incl, 5 m t = +m b ±Γ t 3 4 5

.5.5.4. N: µ F =M/5 N: µ F =,GeV.4..6.4. N: µ F =M/5 N: µ F =GeV =5GeV =3 - N: µ F =M/5 N: µ F =,GeV p T,H /σ dσ/dy H =5GeV =3 =5GeV =3 =5GeV =3 3 p T,t.5.5.4. N: µ F =M/5 N: µ F =,GeV.4..4.3.. N: µ F =M/5 N: µ F =GeV - p T,t /σ dσ/dy t /σ dσ/dm th P g (µ F ) /P g (M/5) µ F =M/5 µ F =,GeV 4 5 6 7 m th Distributions for Inclusive Process On to the distributions [Berger, Han, Jiang, TP] bottom parton description appropriate for total rate Higgs and top distributions? bottom partons established for exclusive cross sections? () Test zero transverse momentum approximation bottom partons assuming small p T,b p z,b compare inclusive process and (massless) exclusive ( 3) process (as it is part of N rate) /σ dσ/dp T,H /σ dσ/dp T,t run bottom factorization scale µ F m b switch on/off incoming bottoms, left with gg bth /σ dσ/dm th 4 5 6 7 mth y H x PDF =m th /E coll 4 5 6 7 mth y t slightly harder distributions (due to x dependence of bottom PDF) () Test zero bottom mass approximation agreement exclusive vs. inclusive cross section established check with bottom mass dependent pp bth perfect agreement with exclusive process for small m b very good agreement with physical bottom mass case bottom parton picture altogether appropriate σ incl,n σ excl,.46 σ excl /σ dσ/dp T,t σ excl,qq σ excl,.46 σ excl /σ dσ/dm th σ incl,n σ excl,qq

/σ dσ/dp T,H.5 =5GeV =3.5 N: µ F =M/5 N: µ F =,GeV p T,H.5.5 N: µ F =M/5 N: µ F =,GeV /σ dσ/dp T,t p T,t.4.4. /σ dσ/dy H =5GeV =3. /σ dσ/dy t N: µ F =M/5 N: µ F =GeV - y H N: µ F =M/5 N: µ F =GeV - y t.4 /σ dσ/dm th.4 /σ dσ/dm th P g (µ F ) /P g (M/5). N: µ F =M/5 =5GeV =3 N: µ F =,GeV 4 5 6 7 mth. µ F =M/5 x PDF =m th /E coll µ F =,GeV 4 5 6 7 mth

.6 σ incl,n /σ dσ/dp T,t.4 σ excl,.46 σ excl /σ dσ/dm th.4 σ excl,.46 σ excl =5GeV =3.3. σ incl,n σ excl,qq. σ excl,qq. 3 p T,t 4 5 6 7 m th

SUSY-QCD Corrections SUSY-QCD Loop Contributions [TP; Berger, Han, Jiang, TP] infrared finite but ultraviolet divergent SUSY loop contributions () universal corrections y b /( + b ) [Carena, Garcia, Nierste, Wagner; Guasch, Häflinger, Spira] () remaining explicit SUSY loop diagrams m m / tan β µ ( b ) resum non b a 5 4 477-9.5% 3.% b 4 3 5 535-3.% -.% 45 3 45 53-3.% -.% 3 9 4 633 79-8.8% 3.% 4 4 3 5 389 357-3.% -.4% 5 5 3 5 637 697-7.7%.% m m / tan β µ M M,3 6 5 3 4 476 48 3-9.% 3.% Λ M mes N mes tan β µ 7 4 3 8 3 3 5 36 476-7.8%.5% 8 3 3 5 4 538-7.5%.5% m b corrections dominant for tan β (dependent on sign of µ) explicit loop corrections negligible % for generic msugra

3. (Heavy) Neutral Higgs... LHC: gg bb H - LHC: ug b td - -... =3,5,5, GeV - - - m b =.46 GeV m t =75,5, GeV m t =75,5, GeV Bottom induced production of neutral Higgses rate enhanced by tan β gg b bh exclusive versus bg bh inclusive bg bh exclusive versus b b H inclusive appropriate factorization scale µ F,b M/5 = m h /5 check: b b H NN scale dependence [Harlander & Kilgore] µ R,b variation for fixed µ F,b m h /4 well under control µ F,b variation for fixed µ R,b m h almost fixed point..8.6 σ(pp (bb )H+X) LHC M H = GeV.4 N. NN µ R =M H - µ F /M H check: exclusive vs. inclusive total rate [Dittmaier, Spira, Krämer] σ(q q, gg b bh + X) [fb] σ(b b H + X) [fb] M H N NN Tevatron LHC 3.9.7 +3.5 8..4 +3. 8.6 5. +4.7.5 +.3...9 +.9.56.8 +.3.69.6 +..79.3 +. (5.3 +.7.7 ) (7.3 +..6 ) (4.8 +4.3 3. ) (7. +.4.6 ) 4 4.3.4 +.4 8..9 +. 7.4.5 +.4 9.8.4 +. Side remark: single top production qg btq [Willenbrock et al] less steep quark densities, x x Q b dσ/dq b p T,b dσ/dp T,b production above threshold Q max b m t generally p max T,b Q max b / µ F,b m t / covered by quoted theoretical uncertainty Q b dσ/dq b LHC: d g b tu Q b dσ/dq b Q b /m h Q b /m t Q b /m t p T,b /m h p T,b dσ/dp T,b p T,b /m t p T,b dσ/dp T,b p T,b /m t

. σ(pp (bb )H+X) LHC M H = GeV.8.6.4 N. NN µ R =M H - µ F /M H Harlander, Kilgore

Heavy Higgs Decay to Light Higgses SM Higgs pair production at the LHC [Baur, TP, Rainwater] HH 4W : believable detector simulation needed, not hopeless (use m vis to determine λ HHH ) HH b bττ: miracle required HH 4b: several major miracles mandatory TESLA in better shape [Castanier, Gay,... ; Lafaye, Mühlleitner,...] HH b bµµ: at least small miracle would be helpful (might come out of µµ mass resolution) HH b bγγ: some enhancement needed MSSM pair production gg hh [Djouadi, Haber, Zerwas] only way to access tan β < beyond no-lose theorem factor enhancement of cross section HH b bγγ best shot backgrounds hard to compute but under control σ σ(pp hh bb γγ) [fb] =3 - σ SM BR BR(h bb ) - - BR(h γγ) 5σ with 3 fb possible for tan β = 3 - -3 m h =7.5 GeV= / 5 5 3 35 4 45 5 m A

σ BR σ(pp hh bb γγ) [fb] BR(h bb ) =3 - - σ SM BR(h γγ) - - m h =7.5 GeV= / -3 5 5 3 35 4 45 5 m A

Conclusions () One MSSM Higgs guaranteed to be seen stable to variations of MSSM () heavy Higgs bosons necessary to tell it might be the MSSM charged Higgs production with bottom jets understood ( ) N rate for charged Higgs production known: N : inclusive process well defined N : remaining scale uncertainty % N 3 : m b corrections dominant in MSSM for large tan β N 4 : non-factorizable corrections negligible in MSSM (3) neutral Higgs production with b b H understood (4) signal H hh b bγγ for small tan β

m h 6 5 4 9 3 4 4 4 m A 4 m A ( -m h ) 5 4 3 5 4 3 4 4 m A ( -m h )=3,5, GeV 4 m A

x n P (p) (x) Q F = GeV Q F = GeV - - x

.5 σ tot (pp th +X) [pb] =5 GeV N µ F /µ F, =µ R /µ R, µ R =µ R, µ F =µ F, - µ/µ.5. σ tot (pp th +X) [pb] =5 GeV N.5 µ F /µ F, =µ R /µ R, µ R =µ R, µ F =µ F, - µ/µ

LHC: gg bb H =3,5,5, GeV Q b dσ/dq b p T,b dσ/dp T,b.. m b =.46 GeV - Q b /m h - p T,b /m h LHC: ug b td m t =75,5, GeV. Q b dσ/dq b. p T,b dσ/dp T,b - Q b /m t - p T,b /m t LHC: d g b tu m t =75,5, GeV. Q b dσ/dq b. p T,b dσ/dp T,b - Q b /m t - p T,b /m t