TeV $\gamma$-rays and the largest masses and annihilation cross sections of neutralino dark matter

Motivated by the interpretation of the recent results on the TeV gamma radiation from the galactic center, including the new 2004 HESS data, as a by-product of dark matter particles annihilations, we address the question of the largest possible neutralino masses and pair-annihilation cross sections in supersymmetric models. Extending the parameter space of minimal models, such as the mSUGRA and the mAMSB scenarios, to general soft supersymmetry (SUSY) breaking Higgs masses gives access to the largest possible pair annihilation rates, corresponding to resonantly annihilating neutralinos with maximal gaugino-Higgsino mixing. Adopting a model-independent approach, we provide analytical and numerical upper limits for the neutralino pair annihilation cross section. A possible loophole is given by the occurrence of nonperturbative electroweak resonances, a case we also consider here. We then show that a thorough inclusion of QCD effects in gluino (co-)annihilations can, in extreme scenarios, make neutralinos with masses in the hundreds of TeV range, well beyond the $s$-wave unitarity bound, viable dark matter candidates. Finally, we outline the ranges of neutralino masses and cross sections for models thermally producing a WMAP relic abundance, thus providing reference values for “best case” indirect SUSY dark matter detection rates.

Figure 1

The minimal ${\chi }^2$ resulting from fits to the 2003 HESS data (left panel), and to the full $2003+2004$ HESS data set (right panel) on the gamma-rays flux from the galactic Center, as a function of the annihilating dark matter particle mass, for different final state channels (see the text for details), including, as a thick black line, the “best spectral function” case. The two horizontal lines in each panel indicate the 90% and 95% C.L. exclusion limits corresponding to the set of data under consideration.

Figure 2

Iso-confidence-level contours of “best spectral functions” fits to the Cangaroo-II and to the 2003 and 2004 HESS data, in the plane defined by the annihilating particle mass and by the quantity ($\sigma J$), defined in Eq. (3).

Figure 3

Confidence level contours in the $(⟨\sigma v,J⟩)$ plane, for the full HESS data set. The upper $x$-axis indicates the “boost factor”, with respect to the NFW halo profile, i.e. $J/J_{\mathrm{NFW}}$. The red arrows indicate the values of $J$ for a sample of viable Milky Ways halo profiles. In the upper right panel we show the confidence level regions on the $(m_{\chi },(\sigma J))$ plane for the $2003+2004$ HESS data, in the “best spectral functions” approach.

Figure 4

(Left panel): Points, in the mSUGRA parameter space at $A_0=0$ and at $m_{\chi }=m_{{\tilde{\tau }}_1}$ , giving ${\Omega }_{\chi }{h}^2=0.13$, i.e. the largest possible neutralino masses in the stau coannihilation region, for positive (solid blue line) and negative (dashed red line) $\mu$. (Right panel): Points, in the mSUGRA parameter space at $A_0=0$ and at $m_{\chi }=m_A/2$, giving ${\Omega }_{\chi }{h}^2=0.13$, i.e. the largest possible neutralino masses in the funnel region, for positive (solid blue line) and negative (dashed red line) $\mu$.

Figure 5

The pair annihilation cross sections of the largest mass neutralinos in the mSUGRA and mAMSB models giving a WMAP neutralino relic density. The shaded areas correspond to the 90% C.L. contours for the Cangaroo-II data (left, gauge bosons final state case) and for the HESS data (right, best spectral function case, the gauge boson final state being ruled out, see Fig. 1, right), for a NFW profile (upper shaded areas) and for the adiabatically contracted N03 profile (lower shaded areas). The upper (lower) dotted lines correspond to extrapolations of the cross section of mAMSB (HB/FP region of mSUGRA) neutralinos giving a relic abundance outside the $2\mathrm{\text{−}}\sigma$ WMAP range.

Figure 6

(Left): Curves of isorelic abundance for neutralinos in the mSUGRA model with nonuniversal Higgs masses, in the $(m_A,\mu )$ plane. The green shaded area corresponds to the $2\mathrm{\text{−}}\sigma$ WMAP range. (Right): Curves of isocross section for neutralinos in the mSUGRA model with nonuniversal Higgs masses, in the $(m_A,\mu )$ plane. The gray (green) shaded area corresponds to the $2\mathrm{\text{−}}\sigma$ WMAP range, while the light gray (yellow) shaded area indicates the reach of stage-3, ton-sized direct detection experiments.

Figure 7

As in Fig. , but for neutralinos in the mAMSB model with general soft supersymmetry breaking Higgs masses.

Figure 8

(Left): The thermally averaged effective cross section $⟨{\sigma }_{\mathrm{eff}}v⟩(T),$ at a neutralino mass of TeV, for four models (respectively a mAMSB winolike neutralino, a mSUGRA neutralino lying in the HB/FP region, and two resonantly annihilating models at $m_1=\mu$ (mixed bino-Higgsino) and $m_2=\mu$, such that $m_{\chi }=m_A/2$.). (Right): cross sections of resonantly annihilating neutralinos in the $(m_{\chi },⟨\sigma v⟩)$ plane. The (green) strips correspond to models giving a thermal neutralino relic abundance within the $2\mathrm{\text{−}}\sigma$ WMAP range. The (light blue and red) shaded areas refer to the 90% C.L. regions for the Cangaroo-II data and for the $2003+2004$ HESS data, for a NFW profile (two upper shaded areas) and for the adiabatically contracted N03 profile (two lower shaded areas). We assume here that neutralinos pair annihilate with $\mathrm{BR}(b\overline{b})=70\%$ and $\mathrm{BR}({\tau }^{+}{\tau }^{-})=30\%$.

Figure 9

The $⟨\sigma v⟩$ contributing to the continuum gamma-rays yield from neutralino pair annihilations including nonperturbative electroweak effects [16], for a winolike (solid blue line) and for a Higgsinolike (dashed red line) lightest neutralino. The chargino-neutralino mass splitting was computed including loop effects from custodial SU(2)-breaking in the gauge boson sector, i.e. in the limit of heavy sfermions [77]. We also indicate the 90% C.L. regions for the Cangaroo-II data set fit, for neutralinos annihilating into gauge bosons. We recall that the pure gauge bosons final state is excluded by the 2004 HESS data (see Sec. 2).

Figure 10

(Left): the thermally averaged gluino pair annihilation cross section as a function of $m_{\tilde{g}}/T$ (lower $x$ axis) and of $T$ (upper $x$-axis, respectively), for a gluino mass $m_{\tilde{g}}=1\mathrm{TeV}$, assuming a fully perturbative ${\sigma }_P$ , a Sommerfeld-enhanced $E\times {\sigma }_P$ , and a fully nonperturbative annihilation cross section. We also include the $s$-wave unitarity limit [80] (solid black line) and the cross section of a 1 TeV purely winolike neutralino (brown dot-dashed line). (Right): The effective thermally averaged neutralino pair annihilation cross section $⟨\sigma v⟩$ (i.e. including coannihilations) as a function of $m_{\chi }/T$ (lower $x$axis) and of $T$ (upper $x$-axis), for a mSUGRA bino- like neutralino with a 1 TeV mass ($\tan \beta =30$, $m_0=5M_{1/2}$, $\mu >0$, $A_0=0$), without gluino coannihilations (solid black line) and including gluino coannihilations. In the latter case we show the lines corresponding to the four gluino annihilation cross sections scenarios of the left panel, for gluino-neutralino mass splittings such that the resulting final neutralino relic abundance corresponds to the central nonbaryonic dark matter abundance deduced from the WMAP data [1], ${\Omega }_{\chi }{h}^2=0.113$.

Figure 11

Isolevel curves corresponding to given neutralino relic abundance values, in the plane defined by the neutralino mass ($x$-axis) and by the relative gluino-neutralino mass splitting ($y$-axis), for four different gluino pair annihilation scenarios. The green shaded area corresponds to the 95% C.L. range for ${\Omega }_{\chi }{h}^2$, while the area shaded in gray, in the right part of each panel, indicates the region in the plane excluded by Tevatron searches for gluinos [74].

Figure 12

The regions, in the $(m_{\chi },⟨\sigma v⟩)$ plane, populated by supersymmetric models with nonrescaled cross section and arbitrarily low relic abundances (light-blue hatched region) and by models with a WMAP relic abundance or with a rescaled cross section [i.e. if ${\Omega }_{\chi }{h}^2<{\Omega }_{\mathrm{DM}}^{\min }{h}^2$ then $⟨\sigma v\to \sigma v\times ({\Omega }_{\chi }/{\Omega }_{\mathrm{DM}}^{\min }{)}^2$], indicated by dark blue squares. The latter were obtained through a random scan over the general, flavor diagonal and $CP$- conserving, MSSM parameter space. The region lying above the red line produces an excess of $\mathrm{L}{}^6\mathrm{i}$ in the early Universe, if all DM is composed by neutralinos. (Right): same as for the left panel, but for the “supersymmetric factor” $⟨\sigma v⟩/m_{\chi }^2$.

Figure 13

The regions, in the $(m_{\chi },⟨\sigma v⟩)$ plane of supersymmetric models with nonrescaled cross section [light gray (yellow) shaded area] and of models with a WMAP relic abundance or with a rescaled cross section [gray (orange) shaded area] excluded by the Egret data [32] and/or by the 2004 HESS data [21] on the gamma-ray flux from the center of the Galaxy, for three different halo models. The thin dashed lines indicate the shape of the Egret and HESS bounds, for the NFW profile, where one constraint is weaker than the other. We also indicate, again with a thin dashed line and for the NFW profile, the bound resulting from the 2003 HESS data. (Right): same as for the left panel, but for the “supersymmetric factor” $⟨\sigma v⟩/m_{\chi }^2$.