Transcript Precise predictions for a light Higgs

Precise predictions for a
light Higgs
Giuseppe Degrassi
Università di Roma Tre
I.N.F.N. Sezione di Roma III
SUSY 2005
The 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 l
with l = 1/cw
A strong hint for a light Higgs
60%
P(mH  210 GeV)
P(mH  260 GeV)
5%
1%
P(mH  230 GeV)
5%
P(mH  290 GeV)
1%
Swinging top
Tevatron:
mt 
Run I
(prel. 99)
174.3  5.1
Run I
(fin. 04)
178.0  4.3
Run I-II
(prel. 05)
174.3  3.4
Light Higgs indication reenforced: 95% C.L. 285
Old considerations are back
SM fit is OK (c2/d.of. =18.6/13)
it will improve if hadronic
asymmetries are excluded
mH pushed down,
P(mH  114 GeV) 7%
(depend on ( )had. )
210 GeV
Is an heavy Higgs ruled out?
NO, but we need new physics of a particular kind
that can compensate for the heavy Higgs
ci  0;
To increase the fitted
(smaller
)
)
(
Most sensitive observable
,
:
SM as an effective theory:
linear realization of SU(2)xU(1)
Buchmuller, Wyler (86);
Hall, Kolda (99); Barbieri, Strumia (99);
Han, Skiba (04)
dimension 6 that can relax the Higgs bound:
The other dimension 6 operators should be suppressed!
WHY?
No Higgs scenario:
non linear realization of SU(2)xU(1)
Theory is not renormalizable; cutoff
cutoff is
Kniehl, Sirlin (99);
Bagger, Falk, Swartz (99)

O (TeV) only if K <0
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:
2
H1
2
H2
2
3
m ,m ,m
responsible for EWSB
(m  0)
2
Hi
Spectrum: five physical states.


H
,
H
A
;
neutral CP-even h, H ; neutral CP-odd
charged
Tree-level mass matrix for the CP-even sector:
exploiting the minimization condition for Veff can be
expressed in terms of mA, mZ , tan 
tree
h
m
decoupling limit:
 mZ
;
Radiative corrections to the MSSM
Higgs sector
tree
h
m
 mZ
ruled out by LEP!
Quantum corrections push
mh
above
mZ .
= effective potential approximation
= external momentum contributions
solutions of
SUSY breaking  incomplete cancellation between loop of
particle and susy partners. Main effect: top and stop loops
One-loop corrections to mh :
4
• scale as mt ;
• depend upon
• have a logarithmic sensitivity to the stop masses.
Large tan  scenario:
completely known
Okada, 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: 1s error on mt
and  s (mz ).
tan = 50
tan =1.5
(courtesy of A. Romanino)
Beyond one-loop: MSSM
;
Two-loop: mixing can be important. Full calculation is relevant.
: dominant contributions known (strong and Yukawa
corrections to the one-loop top/bottom term).
,
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)
Dedes, Slavich,
GD (03)
same accuracy for the minimization condition
Dedes, Slavich (03);
Dedes, Slavich, GD (03)
Important issues:
• scheme-dependence of the input parameters;
• hb  mb, large tan  corrections.
Effect of the two-loop corrections
Top
Bottom
mA  120 GeV
Bottom corrections should be treated with same care
in the OS scheme because of large tan  effects.
mb Xb  mb (Ab   tan )   hb v2
Same renormalization condition of the top-stop sector
gives a counterterm contribution that blows up for large
tan 
from Heinemeyer, Hollik,
Rzehak, Weiglein
EPJC 39 (2005) 465
Estimate of higher order corrections
Several public computer codes that include all dominant
two-loop corrections.
Codes employ input parameters defined in different
renormalization scheme (OS, DR )
OS
• FeynHiggs 2.2 (Heinemeyer, Hollik, Weiglein, Hahn)
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)
Scale and scheme dependence
estimate of higher
order effects
Scale dependence in DR
mh
from Allanach et al.
JHEP09 (2004) 044
8-10 GeV
1-3 GeV
Scheme dependence
from Allanach et al.
JHEP09 (2004) 044
1-2 GeV difference
Xt
0,
Xt
max, 4-5 GeV difference
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 Veff (Landau gauge, DR scheme)
• complete two-loop
• Strong and Yukawa corrections in
from Martin
PRD71 (2005) 016012
from Martin
PRD67 (2002) 095012
Two-loop electroweak
corrections
mh
1 GeV, Q  550 GeV
Momentum dependent
effects
mh
0.1-0.2 GeV,
Q  550 GeV
Martin’s results are not implemented in the 4 public
computer codes.
mh estimates
mh
1-2 GeV
mh  1 GeV
mh
1-2 GeV
two-loop electroweak
two-loop momentum-dependent
leading three-loop corrections
Bound on mh
Bound depends on mt and on the chosen range of
the SUSY parameter. Fix mt  178.0 GeV
• assuming relations among the parameters dictated
by an underline theory of SUSY breaking
(mSUGRA, GMSB, AMSB)
mh  130 GeV
(m0 , m1/ 2  1 TeV, |A0|  3 TeV,
•
scanning in a
“reasonable” region of
the parameter space
mh  144 GeV
from Allanach et al.
JHEP09 (2004) 044
mt mt  2 TeV)
1
2
Light Higgs decays
mh  135 GeV
h  WW*  h  bb
Split SUSY: m  10  h  WW* viable
10
MSSM: h  WW* residual
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 NLO
Aglietti, Bonciani,Vicini, GD (04)
Maltoni, GD (04)
MSSM:
possible negative interference
between top and stops
Djouadi (98)
SUSY-QCD at NLO
Harlander, Steinhauser (04)
from Harlander, Steinhauser
JHEP09 (2004) 066
from Djouadi
hep-ph-0503173
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
mh  3 GeV
• 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.