MadDM A computational tool of DM relic abundance and direct detection M. Backovic, F. Maltoni, A. Martini, Mat McCaskey, K.C. Kong, G. Mohlabeng KUBEC International Workshop on Dark Matter Searches 28 August 2014 Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 1 / 32
State of the art The mystery of dark matter Observations galaxies rotational curves. Bullet cluster. Cosmic microwave background : ΩDM h2 = 0.1199 ± 0.0027. Candidates Heavy neutrinos Axions (Peccei-Quinn): CP violation in QCD. LSP (SUSY) : neutralino χ 01, gravitino (supergravity) LKP (Kaluza-Klein) : extra-dimensions theories.... Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 2 / 32
State of the art DM detection opportunities Three possibilities Indirect detection: FERMI-LAT, AMS-02. Direct detection: XENON100, LUX, CDMS. Production at collider: LHC. Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 3 / 32
State of the art Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 4 / 32
State of the art Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 5 / 32
State of the art Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 6 / 32
State of the art Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 7 / 32
State of the art Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 8 / 32
State of the art DM tools in the LHC era Tools darksusy is a popular, although model specific DM tool (JCAP 0407 (2004) 008). SUSY contains a lot of generic DM features like co-annihilations and resonant annihilations => darksusy has a lot of useful technology for DM phenomenology in a generic model. darksusy can be hacked to include other models, but this is not trivial! Many other (model specific) tools exist: Isatools, SSARD, Drees, Roszkowski... Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 9 / 32
State of the art MADGRAPH5 Since 1994, MADGRAPH has grown into a powerful collider phenomenology framework...... but no capability to calculate astrophysical and cosmological signatures in models which contain dark matter candidates. Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 10 / 32
State of the art MadDM First step to extend MadGraph5 capabilities to dark matter phenomenology Built on top of existing MadGraph5 architecture - inherits all of the existing MadGraph structure. MadDM Why MadGraph5? Popular among experimentalists. Novel Python libraries make add-ons easy. MadGraph5_aMC@NLO is an NLO generator (future loop-induced processes). Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 11 / 32
State of the art ATLAS search for DM ATLAS results from a DM search in fat jet + MET channel - constraints on a myriad of effective models. ATLAS used MG for collider analysis, why not add the MadDM output for relic density? Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 12 / 32
MadDM structure Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 13 / 32
MadDM structure Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 14 / 32
MadDM structure Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 15 / 32
MadDM structure example.py #! /usr/bin/env python from init import * from darkmatter_eff import * #Create the relic density object. dm=darkmatter() #Initialize it from the rsxsm model in the MadGraph model folder, #and store all the results in the Projects/rsxSM subfolder. dm.init_from_model( rsxsm, rsxsm_project, new_proj = True) #dm.init_from_model( DM_eff_scalar, DM_eff_scalar, new_proj = True) # Determine the dark matter candidate... dm.finddmcandidate(prompts=false, dm_candidate= ) #...and all the coannihilation partners with the mass splitting # defined by mx0 - mx1 / mx0 < coann_eps. dm.findcoannparticles(prompts = False, coann_eps = 0.1) #Get the project name with the set of DM particles and see #if it already exists. dm.getprojectname() Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 16 / 32
MadDM structure example.py #Generate all 2-2 diagrams. print "Generating annihilation diagrams..." dm.generatediagrams() #Generate the diagrams for direct detection. print "Generating direct detection diagrams..." dm.generatediagramsdirdetect() (NEW feature!!!) #Print some dark matter properties in the mean time. print "------ Testing the darkmatter object properties ------" print "Calc. Omega: "+str(dm._do_relic_density) print "Calc. DD: "+str(dm._do_direct_detection) print "DM name: "+dm._dm_particles[0].get( name ) print "DM spin: "+str(dm._dm_particles[0].get( spin )) print "DM mass var: "+dm._dm_particles[0].get( mass ) print "Mass: "+ str(dm.getmass(dm._dm_particles[0].get( pdg_code )))+"\n" print "Project: "+dm._projectname #Output the FORTRAN version of the matrix elements #and compile the numerical code. dm.createnumericalsession() #Calculate relic density. omega = dm.calculaterelicabundance() print "----------------------------------------------" print "Relic Density: "+str(omega), print "----------------------------------------------" Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 17 / 32
MadDM - relic abundance MadDM v1.0 : relic abundance M. Backovic M. McCaskey K.C. Kong Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 18 / 32
MadDM - relic abundance MadDM - Relic density calculation In DM model with only one DM particle, the density evolution is described by the rate equation ( dn ( ) ) χ 2 + 3Hn χ = 2 σ eff v nχ 2 nχ EQ, dt with σ eff v N i,j=1 σ(χ i χ j SM)v neq χ i nχ EQ, the equilibrium density (n EQ χ n EQ χ j ) 2, the thermally averaged cross section To obtain DM relic abundance in canonical models, integrate the rate equation from a freeze out time (determined by iteration over the rate equation integration) ( Ωh 2 dx σv ) 1 x 2 x m χ T x f MadDM takes co-annihlation, treshold effects and resonances into account and is also able to deal with non-canonical models! Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 19 / 32
MadDM - relic abundance MadDM - Relic density validation Toy model : Real singlet extension of SM (rsxsm): L DM = m2 2 H H + λ ( ) 2 H δ H + 4 2 H H S 2 + m2 S 2 S2 + λ S 4 S4 Only parameters are mass of DM and coupling to the H boson S H S iδ iδv H S H S Typical DM annihilation diagrams : S H S H S V S f S H H S H H S H S H S H S V S f Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 20 / 32
MadDM - relic abundance Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 21 / 32
MadDM - direct detection MadDM v2.0 : direct detection and DDM M. Backovic M. McCaskey A. Martini F. Maltoni K.C. Kong G. Mohlabeng A. Para J. Yoo Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 22 / 32
MadDM - direct detection MadDM : Direct detection (NEW) Typically v DM 300km/s c Transfer momentum to nuclei is very low 0-momentum transfer approximation. Calculation steps : 1 Lagrangian: extract spin-independent and spin-dependent operators. 2 DM-quarks amplitude computation with MadGraph. 3 DM-nucleon calculation (form factors). 4 DM-nucleus interaction. 5 Direct detection rates. Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 23 / 32
MadDM - direct detection MadDM: operator expansion method We implement an effective Lagrangian (L eff ) including all the effective operators available for DM-quarks interactions for a specific DM spin and for SI (or SD) (similar as micromegas, arxiv:0803.2360) : SI SD DM spin Even Odd 0 2MχΦχΦ χ ( µφχφ ψq ψq i ) χ Φχ µφ χ ψ q γ µ ψq 1 2 ψχψχ ψ q ψq ψ q γµψχ ψq γ µ ψq 1 2MχA χµ Aµ χ (A ψq ψq iλq,o α ) χ µaχ,α Aα χ µa χα ψ q γµψq 1 2 1 ψχγµγ 5 ψχ ψ q γ µ γ 5 ψ ( q ) 6 αa χβ Aχν A χβ αaχν i 3 2 1 2 ψχσµνψχ ψq σµν ψ q (AχµA ) χν A χµ Aχν ψ q σ µν ψq ε αβνµ ψ q γ5 γµψ q Then the trick is to combine L eff to the input model (related to L input ) to get the interference term between the two models : M eff +input 2 = M input 2 + M eff 2 + 2 M eff M input the interference term gives us the right contribution! Already implemented in MadDM Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 24 / 32
MadDM - direct detection DM-nucleus interaction Matrix element qq of quarks in a nucleon state : qq = m p,n fq p,n (light quarks); qq = 2 m p,n f p,n G (heavy quarks) m q 27 m q DM-nucleon couplings: f χ p,n = m p,n q=u,d,s C q fq p,n m q + 2 27 m p,n f p,n G q=c,b,t where C q comes from the projection operator method (and M = C q qq ). Finally, you can compute the cross-section DM-nucleus (SI interactions), σ = Already implemented in MadDM! 4mN 2 m2 χ π ( ) 2 (Af χ p + (A Z)f χ ) 2 n M χ + m N C q m q Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 25 / 32
MadDM - direct detection DM-nucleus interaction Spin dependent case : σ = 16m2 N m2 χ π ( J A + 1 ( ) ) εp 2 Sp a + ε n S A 2 n M χ + m N J A where J A is the spin of the nucleus, Sp,n A are the expectation value of the spin content of the nucleon in a nucleus with A nucleons Already implemented in MadDM! Differential rate : dr = ρ 0σ 0 de r 2m χ mr 2 F (E r ) v min [ ] f(v) dv v Available soon in MadDM! Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 26 / 32
MadDM - direct detection b, t b, t b, t MadDM validations - rsxsm χ H χ χ χ 10-6 Micromegas MadDM 10-6 Micromegas MadDM σ p (pb) proton scalar DM scalar interaction (Higgs portal) σ n (pb) neutron scalar DM scalar interaction (Higgs portal) 10-7 10-7 50 100 150 200 M DM (GeV) 50 100 150 200 M DM (GeV) Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 27 / 32
MadDM - direct detection MadDM validations - Higgs portal (vector DM) Micromegas MadDM Micromegas MadDM 10-5 10-5 σ p (pb) proton vector DM scalar interaction (Higgs portal) σ n (pb) neutron vector DM scalar interaction (Higgs portal) 10-6 50 100 150 200 M DM (GeV) 10-6 50 100 150 200 M DM (GeV) Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 28 / 32
MadDM - direct detection MadDM validations - Axial vector interaction (fermion DM) 0.35 Micromegas MadDM 0.24 Micromegas MadDM 0.23 neutron σ p (pb) 0.3 proton σ n (pb) 0.22 fermion DM axial-vector interaction 0.21 fermion DM axial-vector interaction 0.25 60 80 100 120 140 160 180 200 M DM (GeV) 0.2 60 80 100 120 140 160 180 200 M DM (GeV) Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 29 / 32
MadDM - direct detection MadDM: directional detection R E A D Y Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 30 / 32
MadDM - direct detection MadDM - (near) future plans. Link to Pythia/ GALPROP Currently discussing Database of experimental results (e.g. HiggsBounds) Urgent! MadDM NLO Direct detection Almost finished Indirect detection susy.phsx.ku.edu/~mihailo/ Directional detection Finished, awaiting direct detection module Much effort to integrate NLO tools into MadGraph framework. Web interface Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 31 / 32
MadDM - direct detection MadDM DEMO! Tutorial : http://susy.phsx.ku.edu/~mihailo/tutorial.html Antony Martini (UCL-CP3) MadDM v2.0 28 August 2014 32 / 32