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 many interesting 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. There are two main reasons: Dark Matter (DM) evidence SM theoretical problems
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 from center 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 only the SM.
Introduction and motivation Theoretical problems of the SM L SM = L gauge (A i, ψ i ) + L Higgs (A i, ψ i, Φ) The two parts of the SM lagrangian are very different: Gauge: Higgs: natural experimentally tested with great accuracy stable with respect to quantum corrections ad hoc not yet tested with great accuracy not stable with respect to quantum corrections
Introduction and motivation Higgs Lagrangian L Higgs = V 0 + µ 2 Φ + Φ λ(φ + Φ) 2 + Y ij ψl i Ψj R Φ The Higgs sector is the origin of many problems of the SM: V 0 problem of cosmological constant µ 2 problem of quadratic divergences λ possible internal inconsistencies Y ij Flavour problem
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.
Introduction and motivation BSM physics How can the SM be extended? Obviously nobody has the right answer and in fact there are many possibilities: Supersimmetry GUT String Theory 4th family of fermions loop quantum gravity...
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 numerical calculations 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 many constraint: DM relic density: Ωh 2 0.1 DM candidate has to be stable DM candidate has to be neutral with respect electro-magnetism DM candidate should have very weak interactions with the known particles of the SM
Dark Matter One possible answer: Supersymmetry Supersymmetry provides some of the simpler and best motivated candidates 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 n i : number of the i-th relevant particle per unit of volume Assumption: n i /n = n eq i /n eq with n = i n i Boltzmann equation: Relevant quantity: dn dt = 3Hn σ eff v (n 2 (n eq ) 2 ) σ eff v ij σ ij v ij neq i n eq n eq j n eq
Dark Matter Thermal averaged effective cross section σ eff v = ij σ ijv ij n eq i n eq j neq 2 = A n 2 eq The first term, written explicitly, is: A = g i g j (2π) 6 d 3 p i d 3 p j e E i /T e E j /T σ ij v ij ij n eq = i g i (2π) 3 d 3 p i e E i /T Where g i are the degree of freedom of the i-th particle, p i and E i are its momentum and energy.
Dark Matter Approximate solution (steps) The assumption n i /n = n eq i /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/R 3, Y = n/s defining the adimensional variable x = M LSP /T choosing a parametrization for the entropy density: s = h eff (T ) 2π2 45 T 3 changing variables from t to x (it is possible because T is a function 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 outpaces the reactions among coannihilating particles. Has to be numerically calculated. A good approximation to find it out is: x 1 f = ln ( M LSP 2π 3 45 2g G N ) σ eff v x 1/2 The result (for weakly interacting particles) is x f 25. Boltzmann equation: dy dx = M S x 2 πg 45G σ eff v (Y 2 ) (1)
Dark Matter Approximate solution The approximate solution of BE is: Ω LSP h 2 = ρ LSP ρ crit = M LSPs 0 Y 0 ρ crit with ρ crit = 3H2 8πG, s 0 the entropy density at the present time and: Y 0 ( ) 45G 1/2 ( Tf ) 1 πg σ eff v dt T 0 Naive rule: Ω LSP h 2 3 10 27 cm 3 s 1 σ eff v
Dark Matter Coannihilations Obtaining the right relic density with only one particle interacting impose strong constraints on its parameters (mass, charges). The situation can be more interesting if we have coannihilations: Definition Coannihilations are processes of the type ψ 1 ψ 2 AB that occur if the initial particles have comparable masses Examples:
Dark Matter Coannihilation Suppose that we have 2 particles coannihilating. The thermal average of effective cross section is: σ (2) eff v = σ 22v σ 11v / σ 22 v + 2 σ 12 v / σ 22 v Q + Q 2 (1 + Q) 2 ( Ωh 2) (2) [ 1 + Q Q ] 2 ( Ωh 2 ) (1) with Q = n eq 2 /neq 1 In the same way, for 3 particles coannihilating we have: σ (3) eff v σ 22v Q 2 2 + 2 σ 23v Q 2 Q 3 + σ 33 v Q 2 3 (1 + Q 2 + Q 3 ) 2
MiAUMSSM Ideas and assumptions of MiAUMSSM The Minimal Anomalous U(1) Minimal Supersymmetric Standard Model is a string inspired model. Its main properties are: an extra U(1) Stückelberg mechanism Stückelberg particle and Stückelino 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) Q i 3 2 1/6 Q Q Ui c 3 1 2/3 Q U c 3 1 1/3 Q D c D c i L i 1 2 1/2 Q L Ei c 1 1 1 Q E c H u 1 2 1/2 Q Hu H d 1 2 1/2 Q Hd Gauge invariance Q Hu, Q Q, Q L are independent
MiAUMSSM Stückelberg interactions The part of the Lagrangian that involves the Stückelberg superfield is: L axion = 1 4 {[ 2 1 4 a=0 ( S + S + 4b 3 V (0)) 2 θ 2 θ 2 Relevant diagrams generated: ] ( b (a) 2 S Tr W (a) W (a)) + b (4) 2 S W (1) W (0) θ 2 + h.c. } C α (i, j)γ 5 [γ µ, γ ν ]ik µ
MiAUMSSM Neutralinos mass matrix The neutralinos mass matrix in the MiAUMMSM (at the tree level) is: MÑ = M S 2 2 2g 0 b 3 0 0 0 0... M 0 Cδ 2 + M 1Sδ 2 0 0 g 0 v d Q Hu g 0 v u Q Hu...... M 1 0 g 1v d 2 g......... M 2 v d 2............ 0 µ............... 0 g 1 v u 2 2 g 2v u 2
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 in the neutralino mass matrix (i.e. Q Hu = 0) mixing between the extra U(1) and the MSSM sector in the neutralino mass matrix We are interested in a LSP that comes from the extra U(1) sector in 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 Massive Particle), while an LSP from the MSSM sector is called WIMP.
Dark Matter in the MiAUMSSM No coannihilations The main contribution is: This interaction is proportional to C 2 A << g 2 1, g 2 2. So the naive rule of the DM abundance says that this cross section cannot give the right answer. We have to conclude that an XWIMP alone can not satisfy the constraints on DM.
Dark Matter in the MiAUMSSM No mixing, coannihilations There are two subcases: N=2 LSP stückelino-primeino mix NLSP bino-higgsino mix N=3 LSP stückelino-primeino mix NLSP wino-higgsino mix NNLSP chargino Remembering Q = n eq 2 /neq 1 and using the standard (and usually very good) approximation: n eq i = g i (1 + i ) 3/2 e x f i with i = (m i m 1 )/m 1 it is evident that the mass gap between the coannihilating particle is very important.
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)
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 of analytical calculation, so we use DarkSUSY. We have modifed the DarkSUSY package to perform numerical simulations in our extended model: added the variables from the anomalous extension: M S, M 0, Q Hu, Q Q, Q L changed the model-setup routines: model defining routines neutralinos mass routines interaction routines changed the cross-section calculation routines
Dark Matter in the MiAUMSSM Results (NLSP bino) 850 1200 1000 800 M 0 600 400 800 750 700 Msq 650 600 850 800 750 700 M 0 650 600 200 550 550 200 400 600 800 1000 1200 M S 500 20 40 60 80 100 120 140 M S 500 20 40 60 80 100 120 140 M S h 2 10Σ WMAP h 2 5Σ WMAP h 2 3Σ WMAP h 2 WMAP First image: LSP relic density with respect to M S and M 0 for mass gap 5 % Second image: Zoom of the first image Third image: LSP relic density with respect to M S and M 0 for mass gap 10 %
BSM physics and Dark Matter Dark Matter in the MiAUMSSM Results (NLSP Wino) 2000 364 10 Σ IW h2 MWMAP 1800 362 0.082 0.139 1600 360 0.127 5Σ M2 358 1200 0.11 354 352 IW h2 MWMAP 1400 Msq 356 0.094 3Σ 0.094 IW h2 MWMAP 1000 0.082 0.11 IW h2 MWMAP 800 350 0.127 1000 1200 1400 1600 1800 2000 400 Μ 500 600 700 800 900 1000 MA Left image: LSP relic density with respect to µ and M2 for mass 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 to describe DM (and to solve many other SM problems) that there is a well defined procedure to calculate the relic densiy of a certain particle the definition and the ideas of MiAUMSSM that DM study can impose constraints over BSM models