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A U(1)’ Gauge Mediator

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Aspects of WIMP Dark Matter Searches at Colliders and Other Probes

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Abstract

As we saw in the previous chapters, simplified models are a useful tool to interpret LHC and other experiments’ data in terms of a minimal theory of Dark Matter, which contains only the relevant degrees of freedom that can be probed in our searches.

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Notes

  1. 1.

    The initial configuration \(\chi \chi \) is a CP eigenstate with eigenvalue \(-1\):the DM particles are identical fermions and their wavefunction must be antisymmetric. In the limit of zero velocity \(L=0\) requires an antisymmetric opposite spin configuration corresponding to \(S=0\). Thus the CP eigenvalue of the \(\chi \chi \) is \((-1)^{2L+S+1}=-1\). In the final state \(f\overline{f}\) f and \(\overline{f}\) have opposite chiralities, implying opposite helicities if we neglect the fermion mass \(m_f\), and the total spin along that axis is \(+\)1. Thus the CP eigenvalue for the final state is \((-1)^{2L+S+1}=+1\). CP conservation thus forbids the annihilation of two DM particles into two massless fermions in the limit of zero velocity, if the fermion current preserves chirality (see also [6]).

  2. 2.

    The “Minimal Dark Matter” model of [7, 8] can be seen as a generalization of this scenario to arbitrary representations.

  3. 3.

    This can naturally happen in various scenarios, e.g. split SUSY [9, 10] or recently proposed mini-split, motivated by the 125 GeV higgs [11, 12].

  4. 4.

    The simplest model that could provide a massive Majorana particle interacting with the \(Z'\) could be the following. We use the 2-component notation. We introduce a Majorana fermion \(\psi _0\) and two Weyl fermions \(\psi _1\), \(\psi _2\). \(\psi _1\) and \(\psi _2\) interact with the \(Z'\) with opposite charges, and we write a mass term (\(\psi _{2\,\alpha }\psi _1^\alpha +\) h.c.) that is both gauge invariant and Lorentz invariant. With just one Weyl spinor we would not manage to write a gauge invariant term. (A term like \(\psi _1^\dagger \psi _1\) would violate Lorentz symmetry.) The Lagrangian for these fields would be

    figure a

    where \(\Phi \) is the scalar field responsible of the BEH mechanism in the \(U(1)'\) sector. Notice that the third line, independently from the value of \(y_1\), \(y_2\), prevents us from writing (9.6) in terms of a Majorana spinor \(\left( {\begin{array}{c}\psi _1\\ \psi _2\end{array}}\right) \). Once \(\Phi \) assumes a vev v, the mass matrix for the triplet \((\psi _1,\psi _2, \psi _0)\) is

    figure b

    where M is a mass term for \(\psi _0\) that can possibly appear in (9.6). The diagonalisation of the mass matrix brings to a Majorana massive particle interacting with \(Z'\), which can be close to \(\psi _0\) if \(M, y_i v\ll m\). Notice that the terms proportional to v in (9.7) introduce a splitting in the mass matrix between what could be the L- and R-handed components of a Dirac spinor. Some theories of inelastic dark matter elaborate on the possibility that this mass splitting is small, and the lightest eigenstate could convert into the heavier one via inelastic scattering.

    We conclude by stressing that the vector-like coupling of \(Z'\) to \(\psi _1\) and \(\psi _2\) ensures the cancellation of the gauge anomaly in the diagrams involving these fermions.

  5. 5.

    We remark the following. If the \(Z'\) mass \(m_{Z'}\) is larger than a few TeV, the bounds shown in Fig. 9.3 and the following fall in a region in which the product \(g_{Z'}g_\chi ^{1/2}\) is necessarily \(\gtrsim 1\). This is in contrast with the fact that our \(Z'\) model has a rather large mediator width, and it must be \(g_{Z'}g_\chi ^{1/2} \lesssim 1\) in order to have \(\Gamma _{Z'}\lesssim m_{Z'}\). For this reason, with the present experimental sensitivity the lines of Fig. 9.8 correspond to a realistic physical situation only for \(m_{Z'}\sim \,\mathrm{few\ TeV}\).

  6. 6.

    For instance, Ref. [58] practically exclude an area of \(10^\circ \) from consideration. Similarly, theoretical studies (see e.g. [59]) mask out \(1^\circ \) to \(2^\circ \) around the Galactic Centre. We do not show the Fermi-LAT Galactic Centre bounds on our plots because they are inferior to the Fermi-LAT dSph bounds. It is also worth mentioning that measurements of the dSphs are essentially foregrounds-free, which renders them extremely robust.

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  1. Deutsches Elektronen-Synchrotron, Hamburg, Germany

    Enrico Morgante

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Morgante, E. (2017). A U(1)’ Gauge Mediator. In: Aspects of WIMP Dark Matter Searches at Colliders and Other Probes. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-67606-7_9

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