Constraints on the axial-vector and pseudo-scalar mediated WIMP-nucleus interactions from PandaX-4T experiment

We present the constraints on the axial-vector and pseudo-scalar mediated WIMP-nucleus interactions from the PandaX-4T experiment, using the data set corresponding to a total exposure of 0.63~tonne$\cdot$year. No significant signal excess is observed, and the most stringent upper limits to date on the spin-dependent WIMP-neutron scattering cross section are set at 90\% confidence level with the minimum WIMP-neutron scattering cross section of 5.8$\times 10^{-42}$\si{\cm^{2}} for WIMP mass of 40~\si{\GeV/}$c^2$. Exclusion limits on the axial-vector and pseudo-scalar simplified models are also derived.

There is plenty of evidence indicating that a large amount of dark matter exists in our universe.However, its nature is still elusive [1].Weakly interacting massive particle (WIMP) is a plausible dark matter candidate which arises naturally derground Laboratory (CJPL) [8,9], is one of the largest xenon TPC experiments with 3.7-tonne of liquid xenon in the sensitive volume.The cylindrical TPC is covered by 24 polytetrafluoroethylene (PTFE) panels on the side and 368 Hamamatsu R11410-23 3-inch photomultiplier tubes (PMTs) on the top and bottom, with four electrodes placed inside to construct the drift and extraction electric field.Once an incoming energetic particle scatters off xenon nuclei or electrons, prompt scintillation light (S1) and ionized electrons are generated, the latter then drift upward to the liquid xenon surface and produce the electroluminescence light (S2) in the gaseous xenon region under the electric fields.Both S1 and S2 are detected by the PMTs, from which the scattering position and deposited energy can be reconstructed.The ratio of S2 to S1 provides powerful signalbackground discrimination.A more detailed description of the PandaX-4T experiment can be found in Refs.[10,11,5].
The PandaX-4T experiment has set stringent constraints on the spin-independent (SI) WIMP-nucleon cross-section upper limits, excluding 3.8 × 10 −47 cm 2 for a WIMP mass of 40 GeV/c 2 at 90% confidence level (C.L.) [5], which is based on an effective field theory (EFT) describing the Dirac fermion WIMP particle interaction with the nucleon.The physics behind the EFT can be revealed from a simplified model, where the interaction is introduced by a mediator with couplings to WIMPs and quarks.A vector or scalar mediator produces the SI WIMP-nucleon interaction.For an axial-vector and pseudo-scalar mediator, the tree-level process yields the spindependent (SD) WIMP-nucleus interaction instead [12,13].Xenon-based experiments are also sensitive to the SD interactions thanks to the significant abundance of odd-A xenon isotopes with non-zero spin (26.4% spin-1/2 129 Xe and 21.2% spin-3/2 131 Xe in natural xenon) [14,15].The XENON1T experiment has pushed down the SD neutron-only cross-section limits to 6.3 × 10 −42 cm 2 for WIMP mass of 30 GeV/c 2 .As for pseudo-scalar mediator, the tree-level SD process has a strong momentum suppression [16,17], there are no effective searches for this pseudo-scalar mediated SD process in direct detection experiments.However, under the simplified model, the next-toleading-order (NLO) loop-level process does not have this suppression and yields a SI process, which allows the direct detection to be able to probe the pseudo-scalar mediator too.In this letter, we present the search results of SD WIMP-nucleus interactions and constraints on the axial-vector and pseudo-scalar mediators, based on the PandaX-4T commissioning run data.
As for axial-vector couplings to quarks and WIMPs, the WIMP-nucleus SD cross-section can be evaluated from chiral effective field theory (EFT) [18,19,20], which is related to the total spin expectation values of the protons and neutrons in the nucleus in the limit of zero momentum transfer.Therefore, a common practice is to consider two special cases where the WIMPs couple only to protons or to neutrons.The corresponding scattering cross-section is expressed as below, where N denotes the proton (p) or neutron (n), µ N is the reduced mass for WIMP scattering off the nucleon,µ A is the reduced mass of WIMP and the target nucleus, S N (q 2 ) is the structure factor for "proton-only" or "neutron-only" cases [18].Due to the cancellation between spins of nucleon pairs, the SD crosssection with a nucleus is dominated by the unpaired nucleon, which is neutron for 129 Xe and 131 Xe.It should be noticed that the cross-section of the "proton-only" case is significantly enhanced due to chiral two-body currents involving the exchange of a pion.The differential event rate for the WIMP SD interaction can be then written as [21,22] where m χ and ρ χ are the WIMP mass and local density respectively, σ A is the WIMP-nucleus cross-section, η is the mean inverse speed of WIMP velocity distribution.It is recommended that ρ χ = 0.3 GeV/(c 2 •cm 3 ) and the WIMP motion obeys the standard halo model [23].Explicitly, the most probable velocity of WIMP in Maxwellian distribution v 0 = 238 km/s, the galactic escape velocity v esc = 544 km/s and the Earth velocity v E = 254 km/s are adopted in this analysis.The typical event rate as a function of the nuclear recoil energy is shown in Fig. 1.Both the SD "proton-only" and "neutron-only" recoil energy spectra are plotted in addition to the SI case for the WIMP mass of 40 GeV/c 2 and 400 GeV/c 2 , with the detection efficiency [5] overlaid.We use the same data set and selections as the WIMP SI analysis [5].In brief, the S1 signal region of interest requires the S1 in the range of 2 to 135 photoelectron(PE) in the fiducial volume, and the S2 signal collected in the bottom PMT array (S2 b ) is adopted to avoid bias from PMT saturation.The data is divided into five subsets, according to the detector status.The background models also inherit from Ref. [5] and the detailed values can be found in the Table II of Ref. [5].The total live time is 86.0 days and the resulting exposure is 0.63 tonne•year.
The 90% confidence level (C.L.) upper limit of SD WIMPnucleon cross-section as a function of WIMP mass is calculated, utilizing the same statistical inference (profile likelihood ratio) in Ref. [5,23].The results are shown in Fig. 2, for "neutron-only" and "proton-only" interaction respectively.Selected previous experiment results are also plotted for comparison.In the WIMP mass above 6 GeV/c 2 region, our most stringent upper limit for "neutron-only" interaction is 5.8×10 −42 cm 2 for a WIMP mass of 40 GeV/c 2 .For the "proton-only" interaction, the minimal excluded cross-section is 1.7×10 −40 cm 2 for 40 GeV/c 2 WIMP mass.Recently, the LZ experiment released its first result on the SD WIMP-nucleon interaction [24], which extends the excluded SD parameter space further.
To explore the physics behind the WIMP-nucleon interaction, we consider the simplified model with a mediator.The axial-vector mediator couples to all quark flavors equally with one unique coupling constant g q , and thus it yields isoscalar couplings to neutrons and protons.In this model, there are four free parameters: WIMP mass m χ , mediator mass m V , the coupling of the mediator to WIMP g χ and the coupling of the mediator to quark g q .Following the Ref. [25], both the tree-level amplitudes and the loop-level amplitudes are calculated, and the latter is negligible.The cross-section is given in Ref. [26,25] with the form where couplings g q = 0.25 and g χ = 1 are adopted as a benchmark scenario.Based on this model, the signal energy spectra are generated and the same analysis method is applied.The 95% C.L. exclusion limit on mediator mass as a function of WIMP mass is obtained, as shown in Fig. 3, with a comparison with other direct detection experiments [27,15].In addition, the renormalization group evolution (RGE) effect is considered to account for the corrections from the mediator mass scale to the nuclear scale in direct detection [28].The limit on the mediator mass with RGE effect is also shown in Fig. 3.The maximum excluded mass of an axial-vector mediator is 825 GeV/c 2 .
Constraints on the mediators are also provided by collider experiments such as the ATLAS and CMS at the Large Hadron Collider (LHC) [29,30], with the benchmark models summarized in Refs.[31,26,32].This result is complementary to that obtained from the collider experiment in the WIMP mass region above several hundred GeV/c 2 .
Figure 3: PandaX-4T 95% C.L. exclusion limit on the mediator mass for a simplified isoscalar model with an axial-vector mediator and a Dirac WIMP, where the coupling constants g q and g χ are 0.25 and 1, respectively.RGE effect is considered in the signal rate calculation, shown as a solid red line.The limit without RGE effect is shown as a dashed red line.The results from other direct detection experiments, XENON1T [15] and PICO-60 [27], and collider experiments, ATLAS [29] and CMS [30], are overlaid for comparison.
As for the pseudo-scalar mediator scenario, one gaugeinvariant and ultra-violet-complete extension of the simplified model is the Two-Higgs-Doublet-Model-Plus-Pseudo-Scalar (2HDM+a) model, as recommended by the LHC DM Forum [31].It contains five Higgs bosons: a light CP-even boson, h, a heavier CP-even boson, H, a CP-odd boson, A, and two charged bosons, H ± , where the lighter CP-even boson h can be identified with the Standard Model Higgs boson.A CP-odd pseudo-scalar mediator, a, is postulated with Yukawa-couplings to both the SM fermions and the Dirac fermion WIMPs, and mixes with the pseudo-scalar A with a mixing angle θ .However, with a pseudo-scalar mediator, the amplitudes of tree-level SD contribution are momentum-suppressed [16,17].There-Figure 4: The upper panel is the triangle diagram of scattering between WIMPs and quarks in 2HDM+a model [33], where a i, j represents the mediator a/A.The lower panel is the corresponding box diagrams in 2HDM+a model [33].
fore, the dominant processes are from the loop-level diagrams which give the SI interactions instead.The loop-level diagrams of interactions between WIMPs and quarks are shown as Fig. 4, and the amplitudes can be calculated from the effective Lagrangian following Ref.[17,12,33].
This model contains 14 independent parameters: the masses of Higgs bosons m h , m H , m A , and m H ± ; the mass of the mediator m a ; the WIMP mass m χ ; the Yukawa coupling strength between the mediator and the WIMP, g χ ; the electroweak vacuum expectation value (VEV), v; the ratio of the VEVs of the two Higgs doublets, tan β ; the mixing angles of the CP-even and CP-odd weak eigenstates, α and θ , respectively; and the three quartic couplings between the scalar doublets and the mediator (λ P1 , λ P2 , λ 3 ).In this letter, the following values of these parameters are adopted as suggested in Ref. [31]: With these parameters and signal rate calculation following Ref.[33], the 95% C.L. exclusion limit on the pseudoscalar mediator mass m a as a function of the WIMP mass is shown in Fig. 5, where the maximal excluded mediator mass is 106 GeV/c 2 .Since the major contribution to the WIMPnucleon scattering is from NLO processes in this scenario, the limits are much weaker than the axial-vector case, leaving a large parameter space viable for WIMPs.
PandaX-4T direct detection and collider search complement each other for this 2HDM+a model, as illustrated in Fig. 6, where the pseudo-scalar mass m a is fixed at 250 GeV/c 2 as the collider search adopts.The exclusion limit is expressed in terms of the ratio of the excluded cross-section (σ ) to the nominal cross-section of the model (σ theory ) calculated with the benchmark parameters.For m a = 250 GeV/c 2 , the predicted thermal relic density as a function of WIMP mass in the 2HDM+a model [34] is also shown in Fig. 6, which indicates that only the WIMP mass range around 125 GeV/c 2 or above 180 GeV/c 2  is allowed.Compared with the results from ATLAS experiment [34], PandaX-4T experiment has much a stronger sensitivity to WIMPs with mass above 180 GeV/c 2 .
In conclusion, this letter presents new constraints on the axial-vector and pseudo-scalar mediated WIMP-nucleus interactions from the PandaX-4T commissioning data of 0.63 tonne•year.The most stringent constraints to date on the mediator mass are set at 90% confidence level are set for the axialvector and pseudo-scalar simplified models, taking into account both the tree-level and loop-level processes.The maximum excluded mass of an axial-vector mediator is 825 GeV/c 2 and that of a pseudo-scalar mediator is 106 GeV/c 2 .Direct detection and collider search are complementary to each other and the combination of these two directions covers a much larger parameter space of WIMPs and mediators.In addition, the upper limits on the conventional spin-dependent WIMP-nucleon scattering cross-section are derived, with the minimum value of 5.8 × 10 −42 cm 2 and 1.7 × 10 −40 cm 2 for neutron-only and proton-only interactions respectively.The PandaX-4T experiment continues taking physics data and will scan unexplored parameter space further.

Figure 1 :
Figure 1: Nuclear recoil energy spectra for the scattering of WIMP on PandaX-4T detector.The SI, SD proton-only, and SD neutron-only are illustrated in blue, green and red curves with σ = 10 −41 cm 2 respectively.The dashed and solid curves represent the 40 GeV/c 2 and 400 GeV/c 2 WIMPs respectively.The detection efficiency of the PandaX-4T experiment is plotted in a dotted curve with the corresponding axis on the right.

Figure 6 :
Figure 6: PandaX-4T 95% C.L. normalized exclusion limit (red solid) for pseudo-scalar mediator model as a function of WIMP mass.The green bandshows the ± 1σ sensitivity band.The normalized limit is expressed in terms of the ratio of the excluded cross-section to the nominal cross-section of the model.The 95% C.L. from ATLAS[34] (orange solid) is also shown for comparison.The relic density (blue dashed) for each WIMP mass[34] is overlaid and described by the right blue axis, based on the parameters shown in (4).