Precise predictions for a light Higgs

Giuseppe DegrassiUniversità di Roma Tre

I.N.F.N. Sezione di Roma III

SUSY 2005The Millennium Window to Particle Physics

Durham 18-23 July 2005

Summary

The nineties legacy: a light Higgs. How solid is the evidence for a light Higgs?

Recent SUSY results for a light Higgs on:

• Mass determination• Production

Conclusions

The LEP legacy

SM Higgs: HZZ coupling = gMZ with = 1/cw

A strong hint for a light Higgs

60%

HP(m 210 GeV) 5%

HP(m 260 GeV) 1% HP(m 230 GeV) 5%

HP(m 290 GeV) 1%

Swinging top

Tevatron: Run I Run I Run I-II (prel. 99) (fin. 04) (prel. 05)

174.3 5.1 178.0 4.3 174.3 3.4tm

Light Higgs indication reenforced: 95% C.L. 285 210 GeV

Old considerations are back

SM fit is OK (2d.of. =18.6/13) it will improve if hadronic asymmetries are excluded

Hmpushed down,

HP(m 114 GeV) 7%

(depend on )had. ( )

NO, but we need new physics of a particular kind that can compensate for the heavy Higgs

Is an heavy Higgs ruled out?

To increase the fitted :(smaller )

Most sensitive observable

,0;ci

( )

Buchmuller, Wyler (86);Hall, Kolda (99); Barbieri, Strumia (99);Han, Skiba (04)

dimension 6 that can relax the Higgs bound:

SM as an effective theory:linear realization of SU(2)xU(1)

The other dimension 6 operators should be suppressed!WHY?

No Higgs scenario:non linear realization of SU(2)xU(1)

Kniehl, Sirlin (99);Bagger, Falk, Swartz (99)

Theory is not renormalizable; cutoff

cutoff is (TeV) only if K <0O

It is not easy to find models that give K<0

What we learnt from the nineties

• Mechanism of EWSB with a light Higgs are clearly favored.

• The success of the SM fit places strong constraint on new physics.

• New physics of the decoupling type ( ) avoids “naturally” ( ) the SM fit constraints (SMFC).

• Non decoupling physics can exist, i.e. effects that do not vanish as . However it needs same “conspiracy” to pass the SMFC.

Supersymmetry

• Is a NP of the decoupling type. No problem with the SMFC.

• Predicts the quartic Higgs coupling. A light Higgs must be in the spectrum.

• Favors the gauge coupling unification.

• Has a dark matter candidate.

• It has to be broken.

Higgs sector of the MSSM

Two SU(2)xU(1) doublets:

Higgs potential:

23

22 ,,21mmm HH responsible for EWSB )0( 2

iHm

Spectrum: five physical states. neutral CP-even neutral CP-odd charged; , Hh ;A HH ,

Tree-level mass matrix for the CP-even sector:exploiting the minimization condition for can be expressed in terms of

effVtan , , ZA mm

Zh mm tree

decoupling limit: ;

Radiative corrections to the MSSM Higgs sector

Zh mm tree ruled out by LEP!

Quantum corrections push above .

hm Zm

= effective potential approximation

= external momentum contributions

solutions of

SUSY breaking incomplete cancellation between loop ofparticle and susy partners. Main effect: top and stop loops

One-loop corrections to : hm4tm• scale as ;

• depend upon• have a logarithmic sensitivity to the stop masses.

Large tan scenario:

completely knownOkada, Yamaguchi, Yanagida (91);Ellis, Ridolfi, Zwirner (91);Haber, Hempfling (91);Chankowski et al. (92);Brignole (92).........

Beyond one-loop: Split SUSY

Around TEV spectrum: SM + gauginos + higgsinos. Sfermions are very heavy.Mixing is unimportant No bottom corrections. The logarithmic correction is very large. It has to be resummed via Split-RGE. Gauge effects can be relevant.

Barbieri, Frigeni, Caravaglios (91);Okada, Yamaguchi, Yanagida (91);Carena et al. (95-96, SubHPole)....

band: 1 error on and .

tm( )s zm

tan = 50

tan =1.5

(courtesy of A. Romanino)

Beyond one-loop: MSSM

: dominant contributions known (strong and Yukawacorrections to the one-loop top/bottom term).

Two-loop: mixing can be important. Full calculation is relevant.;

Dedes, Slavich,GD (03)

same accuracy for the minimization conditionDedes, Slavich (03); Dedes, Slavich, GD (03)

Important issues: • scheme-dependence of the input parameters;• , large tan corrections.b bh m

, , , Heinemeyer, Hollik, Weiglein (98);Espinosa, Zhang (00);Slavich, Zwirner,GD (01)

Espinosa, Zhang (00);Brignole, Slavich,Zwirner, GD (02)

Brignole, Slavich, Zwirner, GD (02);Heinemeyer, Hollik,Rzehak, Weiglein (05)

Effect of the two-loop corrections

Top Bottom

120Am GeV

Bottom corrections should be treated with same carein the OS scheme because of large tan effects.

Same renormalization condition of the top-stop sectorgives a counterterm contribution that blows up for largetan

b b b b b 2m X m (A tan ) h v

from Heinemeyer, Hollik,Rzehak, Weiglein EPJC 39 (2005) 465

Several public computer codes that include all dominant two-loop corrections. Codes employ input parameters defined in different renormalization scheme (OS, )DR

Estimate of higher order corrections

OS• FeynHiggs 2.2

DR (possibility of input parameters via RG evolution from a set of high-energy boundary conditions)• SoftSusy 1.9 (Allanach) • SPheno 2.2 (Porod)• Suspect 2.3 (Djoudi, Kneur, Moultaka)

(Heinemeyer, Hollik, Weiglein, Hahn)

Scale and scheme dependence estimate of higher order effects

Scale dependence in DR

hm

8-10 GeV 1-3 GeV

from Allanach et al. JHEP09 (2004) 044

Scheme dependence

from Allanach et al. JHEP09 (2004) 044

0, 1-2 GeV diff erence

max, 4-5 GeV diff erence t

t

X

X

Towards a complete two-loop calculation

The presently available public codes do not include:

• electroweak contributions in •

Recent progress: (S.P. Martin (02-05))

• complete two-loop (Landau gauge, DR scheme)

• complete two-loop

• Strong and Yukawa corrections in

effV

Two-loop electroweak corrections

1 GeV, Q 550 GeVhm

from MartinPRD67 (2002) 095012

from MartinPRD71 (2005) 016012

Momentum dependenteffects

0.1-0.2 GeV,

Q 550 GeVhm

Martin’s results are not implemented in the 4 public

computer codes.

1-2 GeVhm

1 GeVhm

two-loop electroweak

two-loop momentum-dependent

leading three-loop corrections

hm estimates

1-2 GeVhm

Bound on hm

Bound depends on and on the chosen range ofthe SUSY parameter. Fix

tm

130 GeVhm

• assuming relations among the parameters dictated by an underline theory of SUSY breaking (mSUGRA, GMSB, AMSB)

2

0 1/ 21

0( , 1 TeV, |A | 3 TeV, 2 TeV)t t

m m m m

• scanning in a “reasonable” region of the parameter space

144 GeVhm

from Allanach et al. JHEP09 (2004) 044

178.0 eV Gtm

Light Higgs decays

135 GeVhm h WW* h bb

Split SUSY: viable 10 10 h WW*m

MSSM: residualh WW*

Light Higgs production

gg h

largest and best known process

SM: QCD at NNLO

Djouadi, Graudens, Spiras, Zerwas (91-95);Harlander, Kilgore (01-02);Catani, de Florian, M. Grazzini (01)Anastasiou, Melnikov (02);Ravindran, Smith, van Neerven (03)

EW at NLOAglietti, Bonciani,Vicini, GD (04)Maltoni, GD (04)

MSSM:

possible negative interferencebetween top and stops

Djouadi (98)

from Djouadihep-ph-0503173

SUSY-QCD at NLO

from Harlander, SteinhauserJHEP09 (2004) 066

Harlander, Steinhauser (04)

Conclusions

• New value of the top mass strengthens the indication for a light Higgs (but a heavy Higgs is not ruled out, although it needs some “conspiracy” to survive)

• The determination of the mass of the light neutral Higgs in the MSSM has become very precise

• A Split SUSY Higgs can be detected via h W W*

• The gluon fusion production cross-section is now available at the NLO in the SUSY contribution.

3 GeVhm