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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
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