Direct detection detection of recoil nuclei after interaction of DM particle in large underground scale detector. DAMA, CDMS, ZENON... experiments.

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1 Direct detection in micromegas. Direct detection detection of recoil nuclei after interaction of DM particle in large underground scale detector. DAMA, CDMS, ZENON... experiments. DM velocities are about velocity of Sun v~ c. For M A ~ Mcdm ~ 100GeV transfer momenta are about 2 v Mcdm M A / (M A +Mcdm) ~ 100MeV ~ 0.5 fm -1 WIMP nucleon elastic cross sections can be calculated in the limit of zero momentum transfer. The cross sections for scattering on nuclei are obtained from the WIMP nucleon cross sections after folding in the nuclei form factors. So, we consider CDM-nucleons elastic amplitudes in v=0 limit and apply them to nuclei case taking into account nuclei form factors. All details are here: Belanger,Boudjema,Pukhov,Semenov arxiv:

2 DM -nucleon collision at v=0 Because of nucleon has spin ½ we have 2 types of spin operators at v=0 limit: spin dependent and spin independent. In QFT such operators can be even or odd respect to particle antiparticle transformation. These operators are the same for nucleons and quarks.

3 Two problems: 1) find effective Lagrangian at quark level 2) Transform quark effective Lagrangian into nucleon one. The first problem is solved by calculation of matrix elements:

4 S is complete matrix element MicrOMEGAs calls CalcHEP with -blind option to create new model with effective operators and calculates interference terms of matrix elements. Note: one has to take into account twist=2 operators. It is done automatically. See details in arxiv:

5 From quark effective operators to nucleon one For SD amplitudes we need sdff <N q-bar γ 5 γ μ q N> = sdff < N γ 5 γ μ N> They are well known from spin physics. In micromegas they are presented by global parameters pvectorffpd Axial-vector form factor for quark in proton PVectorFFPu PVectorFFPs pvectorffnd Axial-vector form factor for quark in neutron pvectorffnu pvectorffns

6 For SI interactions m q <N q-bar q N> = siff M N <N N> SiFF presents contribution of quark q into nucleon mass. They also are global parameters of micromegas ScalarFFPd Scalar form factor for quark in proton ScalarFFPu ScalarFFPs ScalarFFNd Scalar form factor of d in neutron ScalarFFNu ScalarFFNs Problem: too large s-quark FF. It is obtained by π-n scattering. Lattice calculations still do not produce robust result...

7 Heavy quarks form factors: SD case : negligible result of QCD calculations. SI case : can be calculated in QCD! Nucleon mass can be expressed in terms of anomaly of trace of energy-momentum tensor. To find heavy quark contribution to we compare formulas for nf and nf+1

8 Box diagrams with heavy quarks ====> By Dress andnojiri We have universal solution for the case of fermion dark matter and scalar squarks double FeScLoop(double sgn, double mq,double msq,double mne)

9 micromegas routines for calculation of DM nucleon amplitudes double pasi[2] ; // pasi[0] spin-independent amplitude for DM -proton scattering // pasi[0] spin-independent amplitudes for anti-dm proton scattering double pasd[2] // the same for spin dependent double nasi[2], nasd[2]; // the same for DM neutron scattering. qbox =NULL; // for tree level calculations qbox=fescloop; // for loop improved calculations. nucleonamplitudes(qbox,pasi,pasd,nasi,nasd); Amplitudes normalization: For Spin Independent case Cross section [GeV -2 ] = A 2 /4π (Mcdm *M N ) 2 /(Mcdm+M N ) 2 For Spin Dependent case Cross section [GeV -2 ] = 3 A 2 /4π (Mcdm *M N ) 2 /(Mcdm+M N ) 2

10 Interaction with nuclei Spin independent amplitude SD form factor defined by Fermi nucleus distribution. Strong enhancement for large A. Spin dependent form factor if defined by 3 functions because in general Jp proton spin Jn spin of nucleons are not collinear. Squared amplitude in proportion to were

11 DM nucleus scattering in micromegas cross section nevents=nucleusrecoil( Maxwell, // velocity distribution 73, // atomic number Z_Ge, // electric charge J_Ge73, // nucleus spin S00Ge73,S01Ge73,S11Ge73, // SD form factors FeScLoop, // for Box calculation DndE // spectrum array ); Return value number of events in 1kg for day. Number of events in some energy interval in KeV cutrecoilresult(dnde,10,50)); To see plot on the screen displayrecoilplot(dnde,"distribution of recoil energy of 73Ge",0,199);

12 See list of available form SD form factors in file sources/micromegas.h These form factors are result of calculations. V. A. Bednyakov and F. Simkovic, Phys. Part. Nucl. 36 (2005) , [hep-ph/ ].

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14 Direct detection in micromegas. Isothermal model. Rotation velocity in our Galaxy V R =220 km/s for distance 4-20 kpc. Rsun = 8kpc. Suppose V R =Const always and only DM contributes to Gravitation potential. When G M(R)/ R 2 = V R 2 /R ρ(r)= V R 2 / ( 4 π G R 2 ) It gives estimation ρ(rsun) = 0.5 GeV/cm 3 We can expect ρ( v, r) dv 3 dr 3 = F( v 2 /2 + φ(r)) dv 3 dr 3 φ(r) = V 2 R log(r) V 2 R / ( 4 π G R 2 )= dv 3 F( v 2 /2 + V 2 R log(r) ) F(φ) = C exp (- 2 /V 2 R φ) - Boltzmann distribution. So, velocity distribution is