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BSM physics and Dark Matter
BSM physics and Dark Matter
Andrea Mammarella
University of Debrecen
26-11-2013
BSM physics and Dark Matter
1 Introduction and motivation
2 Dark Matter
3 MiAUMSSM
4 Dark Matter in the MiAUMSSM
5 Conclusion
BSM physics and Dark Matter
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
BSM physics and Dark Matter
Introduction and motivation
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.
BSM physics and Dark Matter
Introduction and motivation
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
BSM physics and Dark Matter
Introduction and motivation
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
BSM physics and Dark Matter
Introduction and motivation
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 and Dark Matter
Introduction and motivation
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
...
BSM physics and Dark Matter
Introduction and motivation
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)
BSM physics and Dark Matter
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
BSM physics and Dark Matter
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.
BSM physics and Dark Matter
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
BSM physics and Dark Matter
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.
BSM physics and Dark Matter
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
BSM physics and Dark Matter
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)
BSM physics and Dark Matter
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〉
BSM physics and Dark Matter
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:
BSM physics and Dark Matter
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
BSM physics and Dark Matter
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
BSM physics and Dark Matter
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
BSM physics and Dark Matter
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
BSM physics and Dark Matter
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
BSM physics and Dark Matter
Dark Matter in the MiAUMSSM
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.
BSM physics and Dark Matter
Dark Matter in the MiAUMSSM
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.
BSM physics and Dark Matter
Dark Matter in the MiAUMSSM
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.
BSM physics and Dark Matter
Dark Matter in the MiAUMSSM
Results
Bino-higgsino NLSP, mass gap 1 % (left) and 5% (right)
Wino NLSP, mass gap 5% (left) and 10 % (right)
BSM physics and Dark Matter
Dark Matter in the MiAUMSSM
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
BSM physics and Dark Matter
Dark Matter in the MiAUMSSM
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 %
BSM physics and Dark Matter
Dark Matter in the MiAUMSSM
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 %
BSM physics and Dark Matter
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
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