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BSM physics and Dark Matter


Andrea Mammarella

University of Debrecen

26-11-2013


1 Introduction and motivation

2 Dark Matter

3 MiAUMSSM

4 Dark Matter in the MiAUMSSM

5 Conclusion


Introduction and motivation

Why BSM physics?

Before the sospension of its running LHC has given to us manyinteresting results, as:

Higgs boson discovery

No direct evidence of physics Beyond the Standard Model(BSM)

These results have confirmed the expected structure of the SM,but nonetheless we are going to talk about BSM physics. Thereare two main reasons:

Dark Matter (DM) evidence

SM theoretical problems



Dark Matter evidence

There are many evidences of the existence of DM:

Rotational velocity of galaxies

Analysis of the distribution of mass vs the distance fromcenter in many galaxies

Data on X-ray emitting gases surrounding elliptical galaxies

WMAP data on Cosmic Microwave Background

However there is no way to describe this observations using onlythe SM.



Theoretical problems of the SM

LSM = Lgauge(Ai , ψi ) + LHiggs(Ai , ψi ,Φ)

The two parts of the SM lagrangian are very different:Gauge:

natural

experimentally tested withgreat accuracy

stable with respect toquantum corrections

Higgs:

ad hoc

not yet tested with greataccuracy

not stable with respect toquantum corrections



Higgs Lagrangian

LHiggs = V0 + µ2Φ+Φ− λ(Φ+Φ)2 + YijψiLΨj

RΦ

The Higgs sector is the origin of many problems of the SM:

V0 ⇒ problem of cosmological constant

µ2 ⇒ problem of quadratic divergences

λ⇒ possible internal inconsistencies

Yij ⇒ Flavour problem



Other SM problems

There are other problems in the SM. It does not predict:

neutrino masses

dark energy

matter-antimatter asymmetry

Furthermore, SM does not include the gravity!So there is a clear the necessity to extend the SM.



BSM physics

How can the SM be extended?Obviously nobody has the right answer and in fact there are manypossibilities:

Supersimmetry

GUT

String Theory

4th family of fermions

loop quantum gravity

...



My work

During my PhD and afterwards I have worked on:

selection of observables that can characterize a BSM model

study of these observables

development of tools to perform the requested numericalcalculations

study of a particular BSM model (called MiAUMSSM)


Dark Matter

Dark Matter properties

A model that aim to propose a DM candidate has to satisfy manyconstraint:

DM relic density: Ωh2 ∼ 0.1

DM candidate has to be stable

DM candidate has to be neutral with respectelectro-magnetism

DM candidate should have very weak interactions with theknown particles of the SM


Dark Matter

One possible answer: Supersymmetry

Supersymmetry provides some of the simpler and best motivatedcandidates to describe DM: neutralinos.

Def

Neutralinos are supersymmetric partners of vector bosons

Furthermore: Supersymmetry ⇒ R-parity:SM particles → 1 Superpartners → −1

Because of R-parity the Lightest Supersymmetric Particle (LSP)predicted by supersymmetric theories is stable.


Dark Matter

Dark Matter calculation

ni : number of the i-th relevant particle per unit of volumeAssumption: ni/n = neq

i /neq with n =

∑i ni

Boltzmann equation:

dn

dt= −3Hn − 〈σeff v〉(n2 − (neq)2)

Relevant quantity:

〈σeff v〉 ≡∑

ij

〈σijvij〉neq

i

neq

neqj

neq


Dark Matter

Thermal averaged effective cross section

〈σeff v〉 =

∑ij〈σijvij〉neq

i neqj

n2eq

=A

n2eq

The first term, written explicitly, is:

A =∑

ij

gigj

(2π)6

∫d3~pid

3~pje−Ei/T e−Ej/Tσijvij

neq =∑

i

gi

(2π)3

∫d3~pie

−Ei/T

Where gi are the degree of freedom of the i-th particle, pi and Ei

are its momentum and energy.


Dark Matter

Approximate solution (steps)

The assumption ni/n = neqi /n

eq makes the BE more manageable,but it does not guarantee an analytical solution.The steps to find an approximate solution are:

defining s = S/R3, Y = n/s

defining the adimensional variable x = MLSP/T

choosing a parametrization for the entropy density:s = heff (T ) 2π2

45 T 3

changing variables from t to x (it is possible because T is afunction of t)

finding the point of freeze-out (the temperature of decoupling)

calculate the solution


Dark Matter

Approximate solution (calculations)

Freeze-out: temperature at which the universe expansion outpacesthe reactions among coannihilating particles. Has to benumerically calculated. A good approximation to find it out is:

x−1f = ln

(MLSP

2π3

√45

2g∗GN

)〈σeff v〉x1/2

The result (for weakly interacting particles) is xf ∼ 25.Boltzmann equation:

dY

dx= −MS

x2

√πg∗45G〈σeff v〉(Y 2) (1)


Dark Matter

Approximate solution

The approximate solution of BE is:

ΩLSPh2 =

ρLSP

ρcrit=

MLSPs0Y0

ρcrit

with ρcrit = 3H2

8πG , s0 the entropy density at the present time and:

Y0 ∼(

45G

πg∗

)1/2(∫ Tf

T0

〈σeff v〉dT)−1

Naive rule:

ΩLSPh2 ≈ 3× 10−27cm3s−1

〈σeff v〉


Dark Matter

Coannihilations

Obtaining the right relic density with only one particle interactingimpose strong constraints on its parameters (mass, charges). Thesituation can be more interesting if we have coannihilations:

Definition

Coannihilations are processes of the type ψ1ψ2 → AB that occur ifthe initial particles have “comparable”masses

Examples:


Dark Matter

Coannihilation

Suppose that we have 2 particles coannihilating. The thermalaverage of effective cross section is:

〈σ(2)eff v〉 = 〈σ22v〉

〈σ11v〉/〈σ22v〉+ 2〈σ12v〉/〈σ22v〉Q + Q2

(1 + Q)2

⇒(Ωh2

)(2) '[

1 + Q

Q

]2 (Ωh2

)(1)with Q = neq

2 /neq1

In the same way, for 3 particles coannihilating we have:

〈σ(3)eff v〉 ' 〈σ22v〉Q2

2 + 2〈σ23v〉Q2Q3 + 〈σ33v〉Q23

(1 + Q2 + Q3)2


MiAUMSSM

Ideas and assumptions of MiAUMSSM

The Minimal Anomalous U(1) Minimal Supersymmetric StandardModel is a string inspired model. Its main properties are:

an extra U(1)

Stuckelberg mechanism ⇒ Stuckelberg particle and Stuckelino

extra symmetry is anomalous

Generalized Chern-Simons (GCS) mechanism


MiAUMSSM

Charges

Gauge group:SU(3)× SU(2)× U(1)× U(1)′

SU(3)c SU(2)L U(1)Y U(1)′

Qi 3 2 1/6 QQ

Uci 3 1 −2/3 QUc

Dci 3 1 1/3 QDc

Li 1 2 −1/2 QL

E ci 1 1 1 QE c

Hu 1 2 1/2 QHu

Hd 1 2 −1/2 QHd

Gauge invariance ⇒ QHu , QQ , QL are independent


MiAUMSSM

Stuckelberg interactions

The part of the Lagrangian that involves the Stuckelberg superfieldis:

Laxion =1

4

(S + S† + 4b3V

(0))2∣∣∣∣θ2θ2

−1

4

[2∑

a=0

b(a)2 S Tr

(W (a)W (a)

)+ b

(4)2 S W (1) W (0)

]θ2

+ h.c .

Relevant diagrams generated:

⇒ Cα(i , j)γ5[γµ, γν ]ikµ


MiAUMSSM

Neutralinos mass matrix

The neutralinos mass matrix in the MiAUMMSM (at the treelevel) is:

MN =

MS2 2

√2g0b3 0 0 0 0

. . . M0C2δ + M1S

2δ 0 0 −g0vdQHu g0vuQHu

. . . . . . M1 0 −g1vd2

g1vu

2. . . . . . . . . M2

g2vd2 −g2vu

2. . . . . . . . . . . . 0 −µ. . . . . . . . . . . . . . . 0


Dark Matter in the MiAUMSSM


There are two possibilities:

no mixing between the extra U(1) and the MSSM sector inthe neutralino mass matrix (i.e. QHu = 0)

mixing between the extra U(1) and the MSSM sector in theneutralino mass matrix

We are interested in a LSP that comes from the extra U(1) sectorin order to study the peculiarities of this model.We can consider the LSP alone and the LSP with coannihilations.This LSP can be called XWIMP (eXtra Weakly Interacting MassiveParticle), while an LSP from the MSSM sector is called WIMP.



No coannihilations

The main contribution is:

This interaction is proportional toC 2

A << g21 , g

22 .

So the naive rule of the DMabundance says that this crosssection cannot give the rightanswer.

We have to conclude that an XWIMP alone can not satisfy theconstraints on DM.



No mixing, coannihilations

There are two subcases:

N=2LSP ∼ stuckelino-primeino mixNLSP ∼ bino-higgsino mix

N=3LSP ∼ stuckelino-primeino mixNLSP ∼ wino-higgsino mixNNLSP ∼ chargino

Remembering Q = neq2 /n

eq1 and using the standard (and usually

very good) approximation:

neqi = gi (1 + ∆i )

3/2e−xf ∆i with ∆i = (mi −m1)/m1

it is evident that the mass gap between the coannihilating particleis very important.



Results

Bino-higgsino NLSP, mass gap 1 % (left) and 5% (right)

Wino NLSP, mass gap 5% (left) and 10 % (right)



Mixing, coannihilations

In this case the coannihilating particles could be of extra U(1)origin, of MSSM origin, or a mix of the two.This situation is so complicated that there is no possibility ofanalytical calculation, so we use DarkSUSY. We have modifed theDarkSUSY package to perform numerical simulations in ourextended model:

added the variables from the anomalous extension:MS ,M0,QHu ,QQ ,QL

changed the model-setup routines:

model defining routinesneutralinos mass routinesinteraction routines

changed the cross-section calculation routines



Results (NLSP∼ bino)

200 400 600 800 1000 1200

200

400

600

800

1000

1200

MS

M0

20 40 60 80 100 120 140500

550

600

650

700

750

800

850

MS

Msq

20 40 60 80 100 120 140500

550

600

650

700

750

800

850

MS

M0

IW h2MWMAP

IW h2MWMAP

3Σ

IW h2MWMAP

5Σ

IW h2MWMAP

10Σ

First image: LSP relic density with respect toMS and M0 for mass gap 5 %

Second image: Zoom of the first image

Third image: LSP relic density with respectto MS and M0 for mass gap 10 %



Results (NLSP∼ Wino)

0.082

0.094

0.11

0.127

0.139

1000 1200 1400 1600 1800 2000350

352

354

356

358

360

362

364

Μ

M2

0.082

0.094

0.11

0.127

400 500 600 700 800 900 1000

800

1000

1200

1400

1600

1800

2000

MA

Msq

IW h2MWMAP

IW h2MWMAP

3Σ

IW h2MWMAP

5Σ

IW h2MWMAP

10Σ

Left image: LSP relic density with respect to µ and M2 formass gap 10 %

Right image: LSP relic density with respect to MA0 and msq

for mass gap 10 %


Conclusion

Conclusion

Hopefully in this seminar i have shown:

that SM cannot be the ultimate particle theory for many(theoretical and experimental) reasons

that DM has many properties experimentally verified

that supersymmetric theories are one of the best way todescribe DM (and to solve many other SM problems)

that there is a well defined procedure to calculate the relicdensiy of a certain particle

the definition and the ideas of MiAUMSSM

that DM study can impose constraints over BSM models

bsm physics and dark matter - · pdf filematter-antimatter asymmetry furthermore, sm does not...

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