Accelerator Searches

Production of Dark Matter Particles

The CMS and ATLAS experiments at the LHC (Large Hadron Collider) in Geneva have collected data from which the currently most constraining collider limits on the pro-duction of dark matter particles can be derived. The LHC is a ring accelerator with two equal energy proton beams which move in opposite directions. At certain points in the collider, the two proton beams are colliding in the center of multi purpose particle detectors. In practice not two protons but two constituents (partons) of the proton, one out of each colliding proton pair, are interacting due to the large collision energies (design center of mass energy 14 TeV). Partons can be quarks of any flavor (but with a dominance of up over down quarks for a proton), antiquarks of any flavor (always less abundant than quarks in a proton) and gluons (large abundance especially at low mo-mentum transfer but less at high momo-mentum transfer due to the ’asymptotic freedom’

(see Peskin and Schroeder [1995]) of the QCD). The method employed to search for signatures of produced dark matter particles is to search for quark-antiquark collisions with large ’missing’, i.e. not detected, energy in the final state from undetected dark matter particles and a single energetic jet or photon from initial state gluon/photon radiation (CMS Col. [2012a], ATLAS Col. [2012a]). The number of detected events with this signature is measured and compared to the number of expected background events, f.i. from quark-antiquark annihilation into neutrinos via Z-boson exchange with initial state radiation. On the other hand, the number of expected signal events can be cal-culated using an effective field theory approach under the assumption that the particle that mediates the annihilation of quark and antiquark to a pair of dark matter particles

3.2 Experimental Situation

Figure 3.4: Spin independent (left panel) and spin dependent (right panel) WIMP-nucleon scattering cross section upper limits derived from a negative search result for the production of WIMP pairs at the LHC from ATLAS, CMS and CDF at Fermilab. Important are the lines corresponding to D1 (scalar) and possibly D5 which holds only for Dirac fermions but not for Majorana fermions (f.i. supersymmetric neutralinos) in the left panel. In the right panel the lines corresponding to D8 (axial vector) are of primary interest.

For comparison the upper limit on the spin dependent WIMP scattering cross section derived from direct detection experiments (XENON100, CDMS, PI-CASSO, SIMPLE) is plotted. The plot is taken from ATLAS Col. [2012a].

is much heavier than the initial state quarks and final state dark matter particles. The most important effective field theory Lagrangian terms that are investigated under the assumption of heavy mediator particles (mass scale M) are a scalar interaction (D1 in the following), a vector interaction (D5 in the following) and an axial-vector interaction (D8 in the following), for the exact definitions see ATLAS Col. [2012a]. The effective interaction terms can be translated to an effective spin independent (D1 and D5) or spin dependent (D8) cross section which can be compared to the corresponding quantities measured in direct detection experiments (see Goodman et al. [2010] for the exact trans-lation). Figure 3.4 shows the result of the corresponding ATLAS search (ATLAS Col.

[2012a]) based on 4.7fb⁻¹data recorded at a center of mass energy of√

s= 7 TeV. Equiv-alent results have been obtained from a CMS analysis (CMS Col. [2012a]). It is seen that the sensitivity of ATLAS to the spin independent cross section is currently worse compared to XENON100 for DM masses larger than ∼10 GeV. For smaller masses, the sensitivity of XENON100 is worse because such small DM masses produce nuclear re-coils which are typically below the XENON100 detection threshold. In comparison with fig. 3.3 it is also obvious that the LHC sensitivity after a currently performed upgrade resulting in an increased center of mass energy and luminosity should be able to test the

Figure 3.5: Velocity averaged annihilation cross section upper limit derived from LHC data by the ATLAS collaboration. The line corresponding to D5 (D8) holds for vector (axial vector) interactions between WIMPs and quarks. For com-parison an upper limit derived from data recorded by the Fermi-LAT exper-iment and the canonical expectation value for a thermal relic WIMP (see eq.

1.4) is shown. The plot is taken from ATLAS Col. [2012a].

DAMA and CoGeNT signal detections which will be very interesting (an improvement of 2 orders of magnitude in sensitivity to the spin independent cross section is within the discovery reach of a similar analysis conducted at√

s= 14 TeV, see Rajaraman et al. [2011]). It will be very challenging for currently debated WIMP models (f.i. inelastic dark matter, see above) that explain the positive DAMA/CoGeNT signal measurements and the constraining upper limits from XENON100 at the same time if the LHC will not detect a signal in the preferred DAMA and CoGeNT spin independent cross section and WIMP mass regions. Figure 3.4 also shows that the sensitivity of collider searches to spin dependent WIMP interactions is by far superior to the sensitivity of current direct detection experiments.

Figure 3.5 shows a translation of the negative search result obtained from LHC data to the velocity averaged annihilation cross section defined in eq. 1.4. The figure compares the obtained limit onhσviwith a limit derived in an indirect search with the Fermi-LAT detector that is described later in this text. Fermi-LAT performed a search for a

Majo-3.2 Experimental Situation rana WIMP annihilation in outer space where always two WIMPs annihilate dominantly into bottom quarks. The assumptions of the Fermi-LAT search fit well to a search for a supersymmetric neutralino WIMP which is by construction a Majorana particle, i.e.

its own antiparticle. The Fermi-LAT result can be modified to the corresponding result for a Dirac fermion by a multiplication with 2 which is already done in fig. 3.5. This factor two accounts for the fact that a given Dirac WIMP in space cannot annihilate with every other WIMP but on average only with every 2nd WIMP and thus the ex-pected annihilation rate is by a factor of 2 smaller than for Majorana WIMPs which translates approximately to a factor of 2 weaker upper limit onhσvi. To read fig. 3.5 for a supersymmetric WIMP, the line corresponding to D5 is vanishing (Majorana fermions have helicity suppressed vector coupling), the line corresponding to D8 is essentially unaltered (see also Fox et al. [2012]) and the line corresponding to the Fermi-LAT upper limit has to be divided by two. The Fermi-LAT sensitivity to neutralino WIMP is then larger above ∼ 60 GeV than the current LHC sensitivity. Below ∼ 60 GeV the LHC sensitivity is larger, respectively. It can, however, be expected that the LHC sensitivity will improve significantly after the currently performed energy and luminosity upgrade.

Other Collider Searches

Besides the direct production of WIMP particles in collider experiments, there are other methods to possibly gain hints for the existence and nature of WIMP dark matter. The two most important strategies are precision measurements of quantities that are tightly constrained by standard model calculations (f.i. branching ratios or magnetic moments of electrons and muons) and the search for particles whose existence is not predicted by the standard model of particle physics (f.i. an enlarged Higgs sector with more than one Higgs boson as predicted by supersymmetric extensions of the standard model). Devia-tions of measured observables from standard model predicDevia-tions hint obviously towards the interaction not being adequately described by the standard model. In turn, models beyond the standard model of particle physics with enlarged parameter space and parti-cle content are candidates to explain the deviations of observables from standard model predictions. A strong hint for the existence of dark matter particles would be found if a certain candidate model for physics beyond the standard model can be found that is compatible with the measurements and the model does predict the existence of dark matter particles. An incomplete list of three examples of observables that have recently gained particular interest is

• theh→γγbranching fraction for the decay of the Higgs boson (assumed to be the recently discovered boson with ∼ 125 GeV mass, CMS Col. [2012b]). Currently ATLAS observes a branching fraction relative to the standard model prediction of 1.65±0.24_stat ±0.21_sys (presented at Moriond 2013 conference) which is within systematical and statistical errors compatible with the standard model prediction at the ∼2σ level and CMS measures a result compatible with the standard model prediction within 1σ (presented at Moriond 2013 conference).

• The decay of the ’strange B meson’, B_s = (¯bs) consisting of a bottom antiquark and a strange quark into two muons (Bs → µ⁺µ⁻) is almost forbidden in the standard model due to helicity suppression. Hints for the presence of the decay have been recently observed (at ∼3.5σ) and deviations from the standard model prediction have been searched for with LHCb without success (see LHCb Col.

[2013]). Specific regions in the MSSM parameter space were in turn ruled out but

’substantial room for the SUSY parameters’ is left (see Arbey et al. [2013]). The precision measurement of B meson branching fractions is of particular interest for the search for physics beyond the standard model because B mesons have typically a mass that is large enough to open decays into many channels that are suppressed by the standard model but at the same time the mass is small enough to enable production of B mesons at current collider energies.

• The magnetic moment of the muon has been measured to be incompatible with the standard model prediction at the level of∼3σ (see f.i. Jegerlehner and Nyffler [2009]). The measured discrepancy is not yet significant enough to allow a resilient conclusion on its nature but is discussed as one of the most interesting hints for physics beyond the standard model.