wimpydd is hosted by Hepforge, IPPP Durham

## Examples

Here we show some selected examples that illustrate results user can obtain using WimPyDD.

### Nuclear response functions

• Description
Nuclear response functions $$W^{00}_{\Phi^{\prime\prime}}$$ for the isotopes of xenon.

• Code
• plot_w_functions.py

• Reference
• The phenomenology of nuclear scattering for a WIMP of arbitrary spin [arXiv:2102.09778]

### Differential rate and integrated signal

• Description
Differential rate $$dR/dE_R$$ for NaI (no detector response) and binned rate in DAMA-LIBRA $$S^{(0)}_{[E_1^{\prime},E_2^{\prime}]}$$ (including detector response).

• Code
• plot_diff_rate_s0.py

• Reference
• Similar plots for COSINE-100 experiments can be found in JCAP 06 (2019) 048 [arXiv:1904.00128]

### Binned yearly modulation amplitudes

• Description
Binned yearly modulation amplitudes $$S^{(1)}_{[E_1^{\prime},E_2^{\prime}]}$$ in DAMA-LIBRA (including detector response) for the effective Hamiltonian $${\cal H}=\sum_{\tau=0,1} c_9^{\tau}(m_\chi,\sigma_{ref},r) {\cal O}_{9}^{\tau}$$ and the best-fit values of the parameters.

• Code
• plot_modulation_amplitudes_c9.py

• Reference
• DAMA/LIBRA-phase2 in WIMP effective models,JCAP 07 (2018) 016 [arXiv:1804.07528]

• Description
Binned yearly modulation amplitudes $$S^{(1)}_{[E_1^{\prime},E_2^{\prime}]}$$ in DAMA-LIBRA (including detector response) for the effective Hamiltonian $${\cal H}=\sum_{\tau=0,1} \left[ c_4^{\tau} {\cal O}_{4}^{\tau}+c_5^{\tau} {\cal O}_{5}^{\tau}+c_6^{\tau} {\cal O}_{6}^{\tau} \right]$$ and values of the parameters that minimize the tension with DAMA-LIBRA.

• Code
• plot_modulation_amplitudes_c4_5_6.py

• Reference
• Probing DAMA/LIBRA data in the full parameter space of WIMP effective models of inelastic scattering, Phys.Rev.D 99 (2019) 10, 103019 [arXiv:1902.09121]

### XENON1T exclusion plots

• Description
Estimation of the XENON1T exclusion (90% C.L.) plot for the effective spin-independent Hamiltonian $${\cal H}=\sum_{\tau=0,1} c_1^{\tau} {\cal O}_{1}^{\tau}$$ in terms of the WIMP-nucleon cross section $$\sigma_{\cal N}=c_{\cal N}^2 \frac{\mu_{\chi{\cal N}}^2}{\pi}$$, with $$c_{\cal N}=c_1^p=c_1^n$$, $$c_1^0=c_1^p+c_1^n$$, $$c_1^1=c_1^p-c_1^n$$ and $$\mu_{\chi{\cal N}}$$ the WIMP-nucleon reduced mass.

• Code
• plot_SI_xenon_1t_exclusion_plot.py

• Reference
• Present and projected sensitivities of Dark Matter direct detection experiments to effective WIMP-nucleus couplings, Astropart.Phys. 109 (2019) 50-6 [arXiv:1805.06113]

• Description
Estimation of the XENON1T exclusion plot (90% C.L.) for the effective spin-independent Hamiltonian $${\cal H}=\sum_{\tau=0,1} c_1^{\tau} {\cal O}_{1}^{\tau}$$ in terms of the effective scale $$M$$, with $$c_1^p=c_1^n=\frac{1}{M^2}$$ (experimental lower bond on $$M$$)

• Code
plot_SI_xenon_1t_exclusion_plot_effective_scale.py

• Reference
• Similar plots for different relativistic models can be found in, Astropart.Phys. 114 (2020) 80-91 [arXiv:1810.00607]

• Description
Estimation of the XENON1T exclusion plot (90% C.L.) for Anapole dark matter with Hamiltonian $${\cal H}=\sum_{\tau=0,1} c_8^{\tau} {\cal O}_{8}^{\tau} + c_9^{\tau} {\cal O}_{9}^{\tau}$$ in terms of reference cross section $$\sigma_{ref}$$.

• Code
• plot_anapole_xenon_1t_exclusion.py

• Reference
• Anapole Dark Matter after DAMA/LIBRA-phase2, JCAP 11 (2018) 040 [arXiv:1808.04112]

### Inelastic scattering

• Description
Constraints on WIMP-nucleon scattering (90% C.L.) for XENON1T and PICO60 experiments for spin-independent inelastic dark matter. The color bands signify the uncertanities in the WIMP escape velocity.

• Code
• plot_inelastic_scattering_exclusion.py

### Velocity distribution

• Description
$$\eta^{(0)}$$ is the time averaged part of the velocity integral $$\eta=\int_{v>v_{min}}f(v)/v~d^3v$$, as a function of $$v_{min}$$ i.e. $$\eta(v_{min})=\eta^{(0)}(v_{min})+\eta^{(1)}(v_{min}){\rm cos}[\omega(t-t_0)]$$.

• Code
• plot_eta0_vmin.py

• Description
$$\eta^{(1)}$$ is the modulated part of the velocity integral $$\eta=\int_{v>v_{min}}f(v)/v~d^3v$$, as a function of $$v_{min}$$ i.e. $$\eta(v_{min})=\eta^{(0)}(v_{min})+\eta^{(1)}(v_{min}){\rm cos}[\omega(t-t_0)]$$. Here $$\omega=2\pi$$/yr and $$t_0$$ is the time of maximal signal (used $$t_0=2$$ June).

• Code
• plot_eta1_vmin.py

• Description
Triaxial velocity distribution defined in N.W. Evans, C.M. Carollo and P.T. de Zeeuw, Mon. Not. R. Astron. Soc. 318, 1131 (2000) given by a Maxwellian with velocity dispersions:
$$v^2_r=\frac{v^2_0p^{-4}}{(2+\delta)(1+q^{-2}-p^{-2})}$$
$$v^2_{\phi}=\frac{v^2_0(2q^{-2}-p^{-2}}{2(1+q^{-2}-p^{-2})}$$
$$v^2_{\theta}=\frac{v^2_0(2-p^{-2})}{2(1+q^{-2}-p^{-2})}$$
in the radial directions of the Galactic reference frame. The quantity delta is a free parameter that quantifies the degree of anisotropy of the velocity dispersion tensor.
The parameters p and q parameterize the gravitational triaxial potential.

• Code
• plot_triaxial_model.py

• Reference
• Triaxial haloes and particle dark matter detection [arXiv:astro-ph/0008156]
Effect of the galactic halo modeling on the DAMA-NaI annual modulation result: An extended analysis of the data for weakly interacting massive particles with a purely spin-independent coupling [arXiv:hep-ph/0203242]