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The Higgs sector in theMSSM

Wolfgang Frisch

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Outline

● The Higgs sector in the Standard Model

● Naturalness problem

● Supersymmetry and the MSSM

● The MSSM Higgs sector at tree level

● Decoupling limit

●

Loop corrected Higgs mass● Higgs searches/production at LEP&LH

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●  The Standard model contains one Higgs doublet, that givesmasses to up, down – quarks and leptons.

●   is spontaneously broken down to

electromagnetism

The Higgs sector in the Standard Model

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In the SM, the global fit suggests a light Higgs boson mass

The Higgs sector in the Standard Model

Mass limit from !"

#ncertainties from higher ord

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Naturalness problem Is the Standard Model valid up to the Planck scale ?

Limits on the SM Higgs mass Three Higgs boson mass ranges

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Naturalness problem

$othing restricts the SM to survive up to the "lanck Scale if theHiggs mass is in the region from %&'(%)' *e+. However this isunnatural.

f the cutoff scale - is very high, fine tuning of the Higgs bosonmass is a serious problem. The squared Higgs boson massdepends quadratically on the cutoff scale -.

e need to find a reason to keep the Higgs boson mass light. The mass of the Higgs boson should be located in theelectroweak scale.

dea/ There is a symmetry that protects the Higgs boson fromreceiving too large corrections.

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vector superfield 

 The Higgs boson self(energy 0main contribution comes form top(

loop1

superpartner scalar 

Both contributions cancel if  

e!l fermion "o#$%&'

comple( scalar field "o#$%&'

Supersymmetry

matter superfield

vector boson "o#$%&'

gaugino "o#$%&'

energ! cutoff

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The MSSM

The MSSM is the minimal supers!mmetric e(tension of the SM

Minimal $%)' set of S*S+ generators

Minimal $%&' set of Higgs doublets H1, H2 

Supers!mmetr! is broken in nature

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● Three sources for the Higgs potential in the MSSM

● "terms from the superpotential

● #terms from the superpotential

● Supers!mmetr! breaking Lagrangian

● -lectroeak s!mmetr! breaking . Supers!mmetr! breaking

● /P conserving at treelevel, since all phases can be absorbed

The Higgs potential in the MSSM

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●  Two Higgs doublets are required in supersymmetric theories

to generate mass for both 2up2 type and 2down2 type quarksand charged leptons.

●  The mass eigenstates

Higgs sector at tree-level

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●  The two Higgs fields e3panded in mass eigenstates

●  The angle beta is the ratio of the two +!+s

● n particular

Higgs sector at Tree-level

●  Two additional parameters in the Higgs potential MA,

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● Masses of h', H' are !igenvalues of the following

matri3

●

4lpha is the angle that diagonali5es . 6orm theabove results one obtains

6rom the equation for mh0  one can derive an upper bound to

the light 7" even Higgs boson h'

Higgs sector at tree-level

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mh0  as a function of mA0  and

●

 The SM does not constrain the value of at tree level● Since also the Higgs self(coupling 8 is unknown

● n the MSSM the Higgs self(couplings are related to electroweakcouplings.

Higgs sector at tree-level

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● mh' reaches its upper bound value

Higgs sector at tree-level

Decoupling limit:

● 9ther Higgs bosons become heavy and degenerate in

mass

!mportant parameter in Higgs coupling to"ermion and vector bosons

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● eak boson masses

● *auge bosoncouplings

Higgs couplings to gauge bosons

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● Summary of the Higgs couplings to gauge bosons

Higgs couplings to gauge bosons

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● Couplings relative to SM values

Higgs couplings to fermions

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●

Ma3imal mass of the 7"(even Higgs boson h' at one(looplevel

●   dependence

●  logarithmic sensitivity to stop quark masses

● dependence of Higgs mass on , ma3imal value at

oop-corrected Higgs mass

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● radiative corrections must be considered since, dominant

effects arise from loops involving the &rd generation quarksand squarks and are proportional to large :ukawa couplings

● Squark mi3ing matri3 in interaction eigenstates

● Squark mi3ing parameters

● Squark mi3ing matri3 must be diagonali5ed to describe masseigenstates

oop-corrected Higgs mass

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● Ma3imal Mi3ing vs Minimal Mi3ing

oop-corrected Higgs mass

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oop-corrected Higgs mass

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Higgs searches at L-P● MSSM Higgs production at !"

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Higgs production at HC

● *luon fusion   ● +ector boson fusion● 4ssociated production with

Large to yu#a$a coupling

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;ranching ratio of h0  and H0  for small

MSSM Higgs branching ratios

Hi b hi ti

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 The couplings to down(like fermions are enhanced.

Higgs branching ratios

;ranching ratio of h0  and H0  for large

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Summary

● To Higgs doublets .

● -lectroeak s!mmetr! breaking . S*S+breaking

● *pper mass bound for h0 . one light Higgsboson