Beyond Effective Field Theory for Dark Matter Searches at the LHC

TL;DR

The paper tackles the validity of interpreting LHC monojet dark matter searches with EFT when a mediator exists, focusing on vector and axial-vector interactions. It uses a simplified UV-complete model with an $s$-channel mediator to compare with the EFT and identifies three regions in the $(m_{\rm DM}, m_{\rm med})$ plane where the EFT is valid, conservative, or overly strong, providing practical rules of thumb. Key findings include that EFT is reliable only for $m_{\rm med} > 2.5$ TeV and perturbative couplings ($m_{\rm DM} < 800$ GeV), with mediator widths generally $\Gamma > m_{\rm med}$, and that relic density constraints restrict $m_{\rm DM}$ to roughly $170$–$520$ GeV in the heavy-mediator regime. The work demonstrates complementarity with direct detection and proposes reporting limits in the $(m_{\rm DM}, m_{\rm med})$ plane to enable robust cross-checks across search strategies.

Abstract

We study the validity of effective field theory (EFT) interpretations of monojet searches for dark matter at the LHC for vector and axial-vector interactions. We show that the EFT approach is valid when the mediator has mass m_med greater than 2.5 TeV. We find that the current limits on the contact interaction scale Lambda in the EFT apply to theories that are perturbative for dark matter mass m_DM < 800 GeV. However, for all values of m_DM in these theories, the mediator width is larger than the mass, so that a particle-like interpretation of the mediator is doubtful. Furthermore, consistency with the thermal relic density occurs only for 170 <m_DM < 520 GeV. For lighter mediator masses, the EFT limit either under-estimates the true limit (because the process is resonantly enhanced) or over-estimates it (because the missing energy distribution is too soft). We give some `rules of thumb' that can be used to estimate the limit on Lambda (to an accuracy of about 50%) for any dark matter and mediator masses from knowledge of the EFT limit. We also compare the relative sensitivities of monojet and dark matter direct detection searches finding that both dominate in different regions of the m_DM-m_med plane. Comparing only the EFT limit with direct searches is misleading and can lead to incorrect conclusions about the relative sensitivity of the two search approaches.

Figures (7)

• Figure 1: Left panel: A comparison of our $90\%$ CL limit (red solid) and the CMS $90\%$ CL limit (blue dashed) on the contact interaction scale $\Lambda$ as a function of $m_{\rm{DM}}$ for the axial-vector operator. The agreement is better than $5\%$. Right panel: A comparison of our $90\%$ CL limit (solid) and the CMS $90\%$ CL limit (dashed) for a vector interaction as a function of mediator mass $m_{\rm{med}}$. The blue and red lines correspond to the limit for $m_{\rm{DM}}=50$ GeV, $\Gamma= m_{\rm{med}}/3$ and $m_{\rm{DM}}=500$ GeV, $\Gamma= m_{\rm{med}}/10$ respectively, where $\Gamma$ is the mediator width. The agreement is typically better than 15% in both cases. An exception is at the peak of the resonance, where our more fine-grained scan better resolves the peak.
• Figure 2: Left panel: The monojet process from a $q\bar{q}$ initial state in the EFT framework. The contact interaction is represented by the shaded blob. Details of the particle mediating the interaction do not have to be specified. Right panel: This shows a UV resolution of the contact interaction for an (axial)-vector mediator $Z^{'}$, exchanged in the $s$-channel. The momentum transfer through the $s$-channel is denoted by $Q$.
• Figure 3: Left panel: The 90% CL limit on $\Lambda$ as a function of $m_{\rm{med}}$ for our axial-vector simplified model with $m_{\rm{DM}}=250$ GeV. Right panel: The ratio of the inclusive cross-sections in the EFT to the simplified model. In both panels, three distinct regions of parameter space are marked: In Region I, the EFT and simplified model calculation agree at the level of 20% or better; in Region II, the simplified model cross-section is larger than the EFT cross-section owing to a resonant enhancement; and in Region III, the simplified model cross-section is smaller than the EFT cross-section. In the left panel we consider two mediator widths $\Gamma$. The grey shaded regions indicate that the boundary between the regions is weakly dependent on $\Gamma$.
• Figure 4: The solid red line indicates the minimum coupling $\sqrt{g_q\,g_{\chi}}$ in order that the CMS EFT limit on $\Lambda$ applies to the simplified model. The perturbative limit on the couplings (4$\pi$) is indicated by the dashed black line. The EFT limits apply to perturbative theories for $m_{\rm{DM}}<800$ GeV. The mediator width $\Gamma$ equals its mass $m_{\rm{med}}$ when $\sqrt{g_q\,g_{\chi}}$ takes the values indicated by the dotted blue line. The EFT limits only apply to theories where $\Gamma>m_{\rm{med}}$, so the mediator may not be identified as a particle. The green dot-dashed line indicates the coupling $\sqrt{g_q\,g_{\chi}}$ where the relic density matches the observed value. This occurs in the range $170\lesssim m_{\rm{DM}}\lesssim520$ GeV.
• Figure 5: Left panel: The differential cross-section with respect to $Q$, the momentum transfer through the $s$-channel, or equivalently, the (unobservable) invariant mass of the dark matter pair. The dotted blue and solid red lines are for $m_{\rm{med}}=100$ GeV and 1000 GeV respectively and the resonant peak at $Q=m_{\rm{med}}$ is clearly observable. The double dotted black line shows the EFT cross-section with $\Lambda=1000$ GeV. No resonant peak is observed in the EFT limit and the cross-section extends to much larger values of $Q$. Right panel: The missing energy distribution for the same mediator masses and couplings as the left panel. The MET distribution for $m_{\rm{med}}=100$ GeV is much softer so that fewer events pass the CMS $\rm{MET}>400$ GeV cut, leading to a weaker limit on $\Lambda$. In both panels, we have fixed $g=g_q=g_{\chi}$ and $m_{\rm{DM}}=10$ GeV.