Hierarchy problem

Simone Gennai, SNS PisaOn Behalf of the CMS Collaboration

Radion searches in CMSRadion searches in CMS

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Hierarchy problemHierarchy problem1 loop corrections to the Higgs mass in

the SM lead to the following result:

Which represents the so called: hierarchy

problem

To avoid fine tuning we need:

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Few ingredients:SUSY (suppress quadratic divergence in favor of logarithmic

divergence )

Extradimensions (however needed in string theory)

…

How to solve the How to solve the problem?problem?

We have to introduce new physics:It must NOT affect too much EWPM

The new physics must cut off the Higgs mass corrections at order of (100 GeV)2

Can lead to unify EW to Gravity, thanks to the

geometry of the extradimensions

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How can ED explain the How can ED explain the hierarchy problem?hierarchy problem?

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Assuming the RS model and representing the 5D graviton field in our

4D world, we obtain spin-2, spin-1 and scalar representation of the graviton.

Here is the radion!

What is the radion?What is the radion?

Cn(y) are the corresponding coefficients of the Fourier expansion in the warped

fifth dimension

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The parameters of the modelThe parameters of the model

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The effect of the mixingThe effect of the mixingThe Higgs boson couplings can change and

thus for some regions in the parameters space the mixing may prevent the 5 sigma discovery

of the Higgs boson (blue region below).

h-> is lost but->ZZ->4l can be seen

m, GeV

->ZZ->4l discoveryno discovery for h->2

Br(hSM->ZZ->4l) ~= Br(->ZZ->4l)

30 fb-1

= 2 TeV, mh = 125 GeV

Observation of X->hh with 30 fb-1 is a hint for radion !

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Final states used in the Final states used in the analysisanalysis

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We have fixed MR = 300 GeV and Mh = 125 GeV and

we made a scan over (, plane.

->hh->hh

In this scenario, it is interested to study the final state where the radion decays in a couple of Higgs bosons.

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->hh->->hh->bbbb

M =300 GeV, Mh=125 GeV

=1 TeV, =-1/3

-> xBR~100 fb

Main background:

•Irreducible: +jj, +cc, +bb

•Reducible:+jjj, jjjj at LOSelection strategy:

•L1 Trigger: double electrons/photons ET>12 GEV

•HLT : double isolated photons ET>14.5 GeV, pixel matching cut

•Off-line:

•2 isolated (calo+tracker) photons ET1,2 >40, 25 GeV

•2 calo jets with ET>30 GeV, ||<2.4

•Tagging at least 1 b jet

•Invariant mass reconstruction

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B j and B j and Signal invariant mass Signal invariant mass

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Di-jet invariant mass:white is bkg, black is signal. (after all selections and b-tagging but before mass windows cut)

invariant mass: Signal is the narrow peak.(after all selections and b-tagging but before mass windows cut)

B j and B j and invariant mass invariant massAt least 1 jet tagged as b jet.

Correction of the direction using the signal vertex

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Radion invariant mass.

Solid: signal+bkg (max. cross section for signal: =1 TeV, =-0.375)

Dashed: bkg only (irreducible one)

After all selections except mass cut selections

After all selections

Radion mass distributionRadion mass distribution

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Radion invariant mass at 5 point, after all selections

Effect of the bkg scale variationEffect of the bkg scale variation

Signal and background efficiency

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Irreducible bkg only + theoretical uncertainties (scale variation of bkg cross section)

Irreducible bkg + reducible bkg (40% of total bkg)*+theoretical uncertainties (scale variation)

Irreducible bkg + reducible bkg (40% of total bkg) + systematics effects on bkg

(*Red. bkg has been assumed from PRELIMINARY inclusive h-> studies by S. Shevchenko)

5 sigma plot5 sigma plot

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->hh->->hh->bb->l bb->l jetjet n bb n bb

In this analysis we suppose to know the Higgs boson mass value.

The Higgs boson discovery can be performed through the ->hh->bb channel

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Kinematic distributionsKinematic distributionsWe require to tag at least 1 b jet (pT jet > 30 GeV).Selection on the transverse invariant mass of lepton+MET and Max pT of b jet

We can reconstruct the nutrinos energy using the collinear approximation

METMET

jetjetleptonlepton

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M

M Mbj

Mbj

nvariant mass distributionsnvariant mass distributions

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• We can select directly in invariant mass of b and tau jets:• 100 < Mbj <150 GeV• 100 < M < 160 GeV

• Then apply the kinematic fit in order to rescale the jet energies, no changes in the angle between jets

• Fit the radion invariant mass distribution of signal+background

Kinematic fitKinematic fit

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Where:m = true mass = reconstructed mass E1,2=rescaled energies= measured energy= Lagrangian multiplierFor what concerns , the energies after the neutrino reconstructions have been used.

The idea is to minimize a Chi-square form:

After some algebra and some assumption on the jet energy resolution we get an approximated formula for the rescaled energies.

Kinematic fit, the Kinematic fit, the implementationimplementation

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Even if the formula used is an approximation, it yieldsvery good results!

Before

kin. fit

After

kin. fit

Effect of the kinematic fitEffect of the kinematic fit

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Two gaussian have been used:Signal: <m> = 300 GeV

= 15 GeVBkg: <m> = 285 GeV

= 45 GeV

Fitting signal+backgroundFitting signal+background

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5% sys.10% sys.

5 sigma plot5 sigma plot

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->hh->bbbb->hh->bbbb

gg-> 100 pb

BR(->hh) 0.24 BR(h->bb) 0.6

gg-> xBR 10 pb

Non-resonant background:

(strongly dependant on btag performances)- QCD multijet production JJJJ (+JJJJJ, +JJJJJJ, …)

(from 2->2 events + ISR, FSR and gluon splitting)

Main Resonant background:

- tt -> 615 pb (NLO 825 pb)- ttjj -> 507 pb - Zbb -> 349 pb

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Level 1: . (Energetic jet trigger Low Lumi)

1 jets ET> 164 GeV in ||<0.8 OR2 jets ET> 129 in ||<0.8 OR3 jets ET> 76 in ||<0.8 OR4 jest ET> 62 in ||<0.8

HLT:at least 4 jets, 2 of which have to be b-tagged (2 trks with SIP2D>2.)

Off line: Invariant mass reconstruction:looking for 2 identical object (Higgs bosons)

minimizing (m(i,j)-m(k,l)) -> mh-rec

over all possible combinationradion mass reconstruction m(i,j,k,l) -> m

Additional request:mh-rec-1.5 < minv(b,b) < mh-rec + 1.5mrec-1.5 < minv(4b) < mrec + 1.5

Trigger and off-line strategyTrigger and off-line strategy

Corresponding to 95% eff on MC jets4 kHz rate (L1)

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4 b final state results4 b final state results

Signal and background distribution have the same

shape. A counting experiment is the only way to extract signal

significance. To still have 5 discovery at the maximal cross section, the

uncertainty on the bkg extrapolationshould be less than 0.1%

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• The process: gg->->hh has been studied. Three different final states have been considered• bb• bb• bbbb

• A radion mass of 300 GeV and a Higgs boson mass of 125 GeV have been considered.

• For ~2 TeV and in the interval [-0.9, -0.4]the h-> is not visible, while the ->hh (and ->ZZ->4l) gives a signal at 5 sigma.

• The bb final state offers the best possibilities to discover both the radion and the Higgs up to ~2.5 TeV, the bb can give robust confirm to the radion discovery up to ~2 TeV. They can be used to distinguish between the SM Higgs and the radion.

• Systematical effects makes the bbbb final state really challenging.

ConclusionsConclusions