def fn(mx, ms, sv):
assert ms > mx
hp = HiggsPortal(mx, ms, 1, 1)
sv_1 = hp.annihilation_cross_sections(
2 * hp.mx * (1 + 0.5 * v_mw**2)
)["total"] * v_mw * sv_inv_MeV_to_cm3_per_s
# Find smallest stheta compatible with <sigma v> for the given
# gsxx_max
stheta_min = np.sqrt(sv / sv_1) / gsxx_max
if stheta_min > 0.999:
return -1e100
stheta_grid = np.geomspace(stheta_min, 0.999, 20)
constr_mins = np.full_like(stheta_grid, np.inf)
gsxxs = np.zeros_like(stheta_grid)
for i, stheta in enumerate(stheta_grid):
hp.stheta = stheta
hp.gsxx = np.sqrt(sv / sv_1) / hp.stheta
gsxxs[i] = hp.gsxx
# Figure out strongest constraint
constr_mins[i] = np.min([fn() for fn in hp.constraints().values()])
# Check if (mx, ms, sv) point is allowed for some (gsxx, stheta) combination
return constr_mins.max()
# %% hidden=true
hp = HiggsPortal(mx=100, ms=1, gsxx=1, stheta=1.)
ms_over_mx = 1.1
if ms_over_mx < 1: # xx->ss
mx_grid = np.linspace(0.1, 1000, 60)
else: # xx->SM
mx_grid = np.linspace(0.1, 500, 60)
ms_grid = ms_over_mx * mx_grid
stheta_grid = np.geomspace(1e-6, 0.999, 50)
# constrs = hp.constrain("ms", ms_grid, "stheta", stheta_grid, "image")
# > 0: allowed, < 0: not allowed.
constrs = {
c: np.full([len(stheta_grid), len(mx_grid)], np.inf) for c in hp.constraints()
}
for i in range(len(stheta_grid)): # stheta
for j in range(len(mx_grid)): # mx, ms
hp.mx = mx_grid[j]
hp.ms = ms_grid[j]
hp.stheta = stheta_grid[i]
for c, fn in hp.constraints().items():
constrs[c][i, j] = fn()
# %% code_folding=[] hidden=true
for (name, constr), color in zip(constrs.items(), mpl_colors):
# if name == "higgs -> invis":
# continue
plt.contourf(
mx_grid, stheta_grid, constr, levels=[-1e100, 0], colors=[color],