THE SEARCH FOR THE HIGGS BOSON AT THE LHC

THE SEARCH FOR THE HIGGS BOSON AT THE LHC Massimiliano Grazzini (INFN, Firenze) Padova, march 22 2007

Outline Introduction Higgs search at the LHC Main production channels Theoretical predictions Higgs search at the Tevatron Conclusions

Introduction The Standard Model (SM) of electroweak interactions is an gauge theory SU(2) L U(1) Y Explicit mass terms for the gauge bosons are forbidden by gauge invariance Left and right-handed fermions couple differently to gauge fields mass terms are forbidden The way out is provided by Spontaneous Symmetry Breaking (SSB): the lagrangian is still invariant but the gauge symmetry is broken by the vacuum

In the minimal version of the SM the SSB is achieved by introducing one complex scalar doublet: Φ = 1 ( ) w1 + iw 2 2 H + iw 3 4 real degrees of freedom L SB = D µ Φ D µ Φ V (Φ Φ) where V has the usual mexican hat form 3 go to give mass to W and Z bosons 1 remains in the spectrum Higgs boson V Φ = 1 2 ( 0 v ) Extensions of the SM may contain more Higgs doublets MSSM: two doublets Φ u, Φ d each with its own vev v u, v d 8 3 = 5 degrees of freedom Two scalars h, H one pseudoscalar, A, one charged H ±

LEP has put a lower limit on the mass of the SM Higgs boson at M H 114.4 at 95% CL Other constraints come from: Triviality Theoretical arguments (or prejudices...) Vacuum stability dλ dt = 3 4π 2 [ λ 2 + 3λh 2 t 9h 4 t + gauge terms ] t = ln Λ/v If Higgs too heavy λ(t) can hit the Landau pole If Higgs too light (and top heavy) h t wins: vacuum instability but......recent lattice simulations do not show the instability! K. Holland, J. Kuti (2003)

Precision electroweak data: radiative corrections are sensitive to the mass of virtual particles H W, Z W, Z M H = 76 +33 24 GeV M H < 144 GeV (95% CL) LEP EWWG, march 2007 Taking into account LEP limit:... but screening effect: the dependence is only logarithmic at one loop (for top quark the dependence is quadratic m top predicted before discovery!) χ 2 6 5 4 3 2 1 Theory uncertainty α (5) α had = 0.02758±0.00035 0.02749±0.00012 incl. low Q 2 data m Limit = 144 GeV M H < 182 GeV (95% CL) 0 MSSM: at tree level M h < M Z Excluded 30 100 300 m H [GeV] Radiative corrections lift up this limit M h < 135 GeV Preliminary

Higgs production at the LHC 10 2 10 gg"h!(pp"h+x)!pb" #s = 14 TeV M t = 175 GeV CTEQ4M g g q t, b gg fusion H 1 W, Z H 10-1 10-2 10-3 10-4 qq _ "HW qq"hqq gg,qq _ "Htt _ 0 200 400 gg,qq _ "Hbb _ 600 qq _ "HZ 800 1000 M H!GeV" M. Spira W, Z q vector boson fusion g Q H g Q associated production with Q Q q W, Z W, Z Large gluon luminosity gg fusion is the dominant production channel over the whole range of M H q associated production with W, Z H

1 10-1 10-2 10-3 bb _ BR(H)! +! " cc _ gg ## Z# WW 50 100 200 500 1000 M H!GeV" ZZ tt - Key point: enormous QCD background σ(gg H b b) 20 pb σ(b b) 500 µb No chance to look at fully hadronic final states For M H < 140 GeV H γγ (BR 10 3 ) For 140 < M H < 180 GeV H W W lνlν M H > 2M Z H ZZ 4l (gold pleated)

H γγ Background very large but the narrow width of the Higgs and the excellent mass resolution expected should allow to extract the signal Background measured from sidebands H W W lνlν No mass peak but strong angular correlations between the leptons V-A interaction: M.Dittmar, H.Dreiner (1996) H scalar l +( ) (anti-) parallel to W +( ) spin charged leptons tend to be close in angle

Theoretical predictions The framework: QCD factorization theorem h 1 x 1 a H Parton distributions h 2 x 2 b X Partonic cross section σ(p 1, p 2 ; M H ) = a,b 1 0 dx 1 dx 2 f h1,a(x 1, µ 2 F ) f h2,b(x 2, µ 2 F ) ˆσ ab (x 1 p 1, x 2 p 2, α S (µ 2 R); µ 2 F ) Precise predictions for σ depend on good knowledge of BOTH ˆσab and f h,a (x, µ 2 F )

gg fusion g The Higgs coupling is proportional to the quark mass t, b H g top-loop dominates It is a one-loop process already at Born level calculation of higher order corrections is very difficult NLO QCD corrections to the total rate computed more than 10 years ago and found to be large They increase the LO result by about 80%! A. Djouadi, D. Graudenz, M. Spira, P. Zerwas (1991) They are well approximated by the large- limit m top S.Dawson (1991) M.Kramer, E. Laenen, M.Spira(1998)

The large- m top approximation For a light Higgs it is possible to use an effective lagrangian approach obtained when m top L eff = 1 4 p 1 p 1 Q [ 1 α S 3π H v (1 + ) J.Ellis, M.K.Gaillard, D.V.Nanopoulos (1976) M.Voloshin, V.Zakharov, M.Shifman (1979) ] Tr G µν G µν Known to O(α 3 S) K.G.Chetirkin, M.Steinhauser, B.A.Kniehl (1997) p2 H M >> M Q Effective vertex: one loop less! H p 2 H

gg H at NNLO NLO corrections are well approximated by the large- m top limit This is not accidental: the bulk of the effect comes from virtual and real radiation at relatively low transverse momenta: weakly sensitive to the top loop σh tot reason: steepness of the g (1 x) η gluon density at small x η 5 7 m top NNLO corrections to computed in the large limit Important result but... predictions for more exclusive observables are needed S. Catani, D. De Florian, MG (2001) R.Harlander, W.B. Kilgore (2001,2002) C. Anastasiou, K. Melnikov (2002) V. Ravindran, J. Smith, W.L.Van Neerven (2003) NNLO corrections now implemented for distributions for H γγ FEHIP: gives cross section with arbitrary cuts C. Anastasiou, K. Melnikov, F. Petrello(2005) NEW HNNLO: parton level Monte Carlo generator S. Catani, MG (2007)

Inclusive results at the LHC Inclusion of soft-gluon effects at all orders S. Catani, D. De Florian, P. Nason, MG (2003) For a light Higgs: NNLO effect +15 20 % NNLL effect + 6% Good stability of perturbative result K-factors defined with respect σ LO (µ F = µ R = M H ) µ F (R) = χ L(R) M H 0.5 χf /χ R 2 With and 0.5 χ L(R) 2 but

What is the residual theoretical uncertainty on? Scale dependence σh tot Large m top approximation: It works well BECAUSE the cross section is dominated by soft emission, which is weakly sensitive to the top-loop Message from NLO: use exact Born cross section to normalize the result uncertainty < 5% Parton distributions: at the moment uncertainty in NNLO pdf can be of order 10% An over all accuracy of about 10% can be obtained EW two-loop contributions computed the effect ranges from about 5% to 8% below the WW threshold U. Aglietti, R. Bonciani, G. Degrassi, A. Vicini (2004) G. Degrassi, F. Maltoni (2004)

gg H + jet(s) This channel was proposed as an alternative to the inclusive search for H γγ The reconstruction of the jet allows a better identification of the interaction vertex Background suppression is more efficient These advantages may compensate the loss of events The LO calculation shows that the large approximation works well if both and are smaller than M H q T NLO corrections computed in this limit NB: just a part of NNLO corrections to m top m top S.Abdullin et al. (1998) R.K.Ellis, I.Hinchliffe, M.Soldate, J.J.van der Bij (1988) U. Baur, E.W.Glover (1990) σ tot H D. de Florian, Z.Kunszt, MG (1999) NLO effect large: +60% Scale dependence reduced: from ±35% to ±20% at NLO

gg H with a jet veto S.Catani, D. de Florian, MG (2002) t W b An important background for H W W lνlν is t t and W t leading to high-pt jets in the final state introduce jet veto to cut jets with p T > p veto T Effect of jet veto can be evaluated by subtracting from the inclusive cross section the anti-vetoed cross section obtained from the NLO calculation Impact of higher order corrections reduced

NEW: An NNLO MC for gg H γγ We have implemented the NNLO calculation in a fully exclusive parton level generator including the H γγ decay S. Catani, MG (2007) ecompasses previous calculations in a single stand-alone numerical code it make possible to apply arbitrary cuts Example from CMS TDR: good agreement with Anastasiou et al. p min T p max T > 35 GeV > 40 GeV y < 2.5 Photons should be isolated: total transverse energy in a cone of radius R = 0.3 should be smaller than 6 GeV

...but fixed order calculations may fail!

The transverse momentum (q T ) spectrum A precise knowledge of the q T spectrum may help to find strategies to improve statistical significance The region q T M H where most of the events are expected is affected by large logarithmic contributions of the form that must be resummed to all orders α n S ln 2n M 2 H/q 2 T Resummed calculation at low q T matched to fixed order at large q T with the correct normalization Very stable results G. Bozzi, S. Catani, D. de Florian, MG (2003, 2005) Public program available: HqT http://theory.fi.infn.it/grazzini/codes.html

NEW: inclusion of rapidity dependence Quality of the matching and perturbative stability are confirmed q T Upon integration over we obtain an independent calculation of the NLO and NNLO rapidity distribution

Backgrounds H γγ Background known at NLO (DIPHOX package) T. Binoth et al (2000) Contribution from gg fusion included at N 3 LO Z. Bern et al (2003) H W W lνlν NLO corrections known Soft-gluon effects included Spin correlation effects essential in the φ distribution L.Dixon et al. (1999) J. Campbell, K. Ellis (1999) (no spin corr.) MG (2005) V. Drollinger

Vector boson fusion q W, Z W, Z H Valence quarks pdf peaked around Transverse momentum of final state quarks of order of a fraction of the W(Z) mass x 0.1 0.2 Tends to produce two highly energetic jets with a large rapidity interval between them q Since the exchanged boson is colourless, there is no hadronic activity between the quark jets QCD corrections to the total rate increase the LO result by 5 10% Now implemented for distributions: results are very stable T. Han, S. Willenbrock (1991) T. Figy, C. Oleari, D. Zeppenfeld (2003) J. Campbell, K. Ellis (2003) even if the cross section is almost one order of magnitude smaller than for gg fusion this channel is very attractive both for discovery and for precision measurements of the Higgs couplings

Associated production with a t t pair q g t H g t H LO result known since long time q t g t Z. Kunszt (1984) Important discovery channel in low mass region: H b b triggering on the leptonic decay of one of the top Requires good b-tagging efficiency Relevant also to measure t th Yukawa coupling NLO corrections recently computed by two groups At the LHC they increase the cross section by about Scale uncertainty reduced to about 15% W.Beenakker, S. Dittmaier, B.Plumper, M. Spira, P. Zerwas (2002) S.Dawson, L.Reina (2003) 20%

Associated production with a b b pair In the SM the cross section is very small but it becomes dominant g g b H b in the MSSM at large tan β = v u /v d Already at LO there are large contributions of the form α S log M H /m b originating from the collinear splitting g b b two computational schemes: four-flavour scheme (begins with gg b bh at LO) five-flavour scheme: introduces bottom pdf (begins with b b H at LO) Higher order corrections computed in the two schemes Careful comparison performed in recent years R.Harlander, W.Kilgore (2003) S. Dittmaier, M. Kramer, M. Spira(2003) S.Dawson, C. Jackson, L.Reina, D. Wackeroth (2003) J.Campbell, K. Ellis, F.Maltoni, S. Willenbrock (2003) Initial differences reduced if more consistent comparison is performed

Signal significance 10 2 % L dt = 30 fb -1 (no K-factors) ATLAS H! " " tth (H! bb) H! ZZ (*)! 4 l H! WW (*)! l#l# qqh! qq WW (*) qqh! qq $$ Total significance 10 1 100 120 140 160 180 200 m H (GeV/c 2 ) S.Asai et al. (2004) LO only despite the theoretical efforts of last years! NLO corrections included when available

MSSM Higgs At tree level the MSSM Higgs sector can be described by two parameters: m A and tan β Here only lightest neutral Higgs LHC may miss part of SUSY Higgs spectrum F. Gianotti (2003)

What about the Tevatron? The Tevatron is presently operating at 1.96 TeV 2.5 fb 1 delivered 2 fb 1 on tape 40 pb 1 per week currently delivered 4 8 fb 1 expected by end of 2009 Higgs search very difficult but the machine is now performing well!

Higgs production at the Tevatron 10 2 10 1 10-1 gg"h SM qq"h SM qq!(pp _ "h SM +X)!pb" #s = 2 TeV M t = 175 GeV CTEQ4M qq _ "h SM W As for the LHC gg H b b is ruled out by the huge background 10-2 10-3 10-4 gg,qq _ "h SM tt _ bb _ "h SM qq _ "h SM Z gg,qq _ "h SM bb _ 80 100 120 140 160 180 200 M. Spira M H < 130 GeV M H > 130 GeV M h SM!GeV" pp HW b b lν gg W W lνlν But: H γγ too small to be observed! The lepton gives the necessary background rejection

Thresholds L = 4 fb 1 ) -1 Int. Luminosity per Exp. (fb 10 1 Higgs Sensitivity Study (í03) statistical power only (no systematics) 100 105 110 115 120 125 130 135 140 2 Higgs Mass m H (GeV/c ) SUSY/Higgs Workshop (í98-í99) σ 5! Discovery 3! σevidence 95% CL Exclusion With L = 4 fb 1 the SM Higgs could be excluded up to M H 130 GeV Note that systematical uncertainties could change this picture!

hep-ex/0612044 95% CL Limit / SM 40 35 30 25 20 LEP Excluded Tevatron Run II Preliminary DØ Expected CDF Expected Tevatron Expected Tevatron Observed! Ldt=0.3-1.0 fb -1 15 10 5 0 100 110 120 130 140 150 160 170 180 190 200 2 m H (GeV/c ) Currently a factor of 10 away from M H = 115 GeV Only a factor of 4 away from M H = 165 GeV

Summary After 35 years of SM the Higgs boson has not been found yet LEP has put a lower limit on the mass of the SM Higgs boson at M H 114.4 at 95% CL The Tevatron may have a chance to see a Higgs signal if enough integrated luminosity will be accumulated The SM Higgs can be discovered at the LHC over the full mass range in about one year of run at low luminosity A great effort has been devoted in recent years to improve theoretical predictions for the various production cross sections and also for the corresponding backgrounds This knowledge will be essential to improve search strategies, to fully exploit the various channels in the delicate low mass region and to measure the Higgs couplings