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Exploration of the Muon and Light Dark Matter explanations in NA64 with the CERN SPS high energy muon beam
在 CERN SPS 高能量μ子束下,探索 NA64 中的μ子 和轻暗物质解释

\author{ \作者{
Yu. M. Andreevब, D. Banerjee B. Banto Oberhauser J. Bernhard P. Bisio,, N. Charitonidis

R. B. Galleguillos Silva, A. Gardikiotis S. V. Gertsenberger S. Girod, S. N. Gninenko M. Hösgen,

D. V. Kirpichnikovఠ,, M. M. Kirsanove, V. N. Kolosov, V. A. Kramarenkoө,, L. V. Kravchuk

R. Mena Fredes, R. G. Mena Yanssen, L. Molina Bueno M. Mongilloo, D. V. Peshekhonov
V. A. Polyakov B. Radics K. M. Salamatin V. D. Samoylenko, D. A. Shchukin O. Soto,,

P. V. Volkov®, V. Yu. Volkov I. V. Voronchikhin J. Zamora-Saá and A. S. Zhevlakov
P. V. Volkov®, V. Yu. Volkov I. V. Voronchikhin J. Zamora-Saá 和 A. S. Zhevlakov

Authors affiliated with an institute covered by a cooperation agreement with CERN
作者隶属于与 CERN 签署合作协议的机构

CERN, European Organization for Nuclear Research, CH-1211 Geneva, Switzerland
CERN,瑞士日内瓦 CH-1211,欧洲核子研究组织

ETH Zürich, Institute for Particle Physics and Astrophysics, CH-8093 Zürich, Switzerland
ETH 苏黎世理工学院,粒子物理和天体物理研究所,瑞士苏黎世 8093

INFN, Sezione di Genova, 16147 Genova, Italia
INFN,热内瓦分部,意大利热内瓦 16147

Università degli Studi di Genova, 16126 Genova, Italia
热内瓦大学,意大利热内瓦 16126

Authors affiliated with an international laboratory covered by a cooperation agreement with CERN
与欧洲核子研究组织(CERN)合作协议覆盖的国际实验室有关的 作者

Center for Theoretical and Experimental Particle Physics, Facultad de Ciencias Exactas,
理论与实验粒子物理中心,智利圣地亚哥 Exactas 科学学院

Universidad Andres Bello, Fernandez Concha 700, Santiago, Chile
智利圣地亚哥 Fernandez Concha 700 号,安德烈斯贝略大学

Millennium Institute for Subatomic Physics at High-Energy Frontier (SAPHIR), Fernandez Concha 700, Santiago, Chile
智利圣地亚哥费尔南德斯孔查 700 号高能前沿亚原子物理千年研究所(SAPHIR)

Physics Department, University of Patras, 265 04 Patras, Greece
希腊帕特拉斯大学物理系,帕特拉斯 265 04

Universität Bonn, Helmholtz-Institut für Strahlen-und Kernphysik, 53115 Bonn, Germany
德国波恩大学,辐射与核物理赫尔姆霍兹研究所,波恩 53115

Universidad Técnica Federico Santa María and CCTVal, 2390123 Valparaíso, Chile
智利瓦尔帕莱索 2390123 年圣玛利亚联邦理工大学和 CCTVal

Instituto de Fisica Corpuscular (CSIC/UV), Carrer del Catedratic Jose Beltran Martinez, 2, 46980 Paterna, Valencia, Spain
西班牙瓦伦西亚 46980 年帕特尔纳,何塞·贝尔特兰·马丁内斯教授大街 2 号,CSIC/UV 粒子物理研究所

York University, Toronto, Canada
加拿大多伦多约克大学

Departamento de Fisica, Facultad de Ciencias,
物理系,理学院,

Universidad de La Serena, Avenida Cisternas 1200, La Serena, Chile
智利拉塞雷纳大学,Cisternas 大街 1200 号,拉塞雷纳

Johannes Gutenberg Universitaet Mainz, Germany
约翰内斯·古腾堡大学,德国

}
(Dated: January 4, 2024)
(日期:2024 年 1 月 4 日)

Abstract 摘要

We report on a search for a new vector boson performed at the NA64 experiment employing a high energy muon beam and a missing energy-momentum technique. Muons from the M2 beamline at the CERN Super Proton Synchrotron with a momentum of are directed to an active target. A signal event is a single scattered muon with momentum in the final state, accompanied by missing energy, i.e. no detectable activity in the downstream calorimeters. For a total statistic of muons on target, no event is observed in the expected signal region. This allows us to set new limits on part of the remaining parameter space which could provide an explanation for the muon anomaly. Additionally, our study excludes part of the parameter space suggested by the thermal Dark Matter relic abundance. Our results pave the way to explore Dark Sectors and light Dark Matter with muon beams in a unique and complementary way to other experiments.
我们报告了在 NA64 实验中进行的一项寻找新 矢量玻色子的研究,该实验采用高能量的μ子束和缺失能量-动量技术。来自 CERN 超级质子同步加速器 M2 束线的动量为 的μ子被定向到一个活动靶。信号事件是一个在最终态中动量为 的单个散射μ子,伴随着缺失能量,即在下游量热器中没有可检测的活动。对于总共 个靶上的μ子的统计数据,没有观察到预期信号区域中的任何事件。这使我们能够在剩余 参数空间的一部分上设定新的限制,这部分参数空间可能为μ子 异常提供解释。此外,我们的研究排除了热暗物质遗留丰度所建议的参数空间的一部分。我们的结果为探索暗扇区和轻暗物质提供了一条道路,通过μ子束以一种独特和互补的方式进行,与其他实验不同。

Dark Sectors (DS) are a promising paradigm to address open questions of the Standard Model (SM) such as the Dark Matter (DM) origin [1]. In this framework, one postulates a new sector of particles below the electroweak scale that are not charged under the SM but could have a phenomenology of their own . In addition to gravity, the interactions between DS states and the SM could proceed through portal mediators [8-12]. If one assumes that DM is made by the lightest stable DS particles, the resulting feeble interaction between the two sectors is compatible with cosmological observations and, thus, would accommodate a solution to the DM problem. DS models became an extremely fertile domain of exploration with many different techniques tackling the very large parameter space of possible DM candidates (see e.g. for recent reviews [13-16]). Models with lepton numbers gauging are very attractive to explain the origin of DM and, at the same time, provide an explanation for the long-standing muon anomaly [17]. The vector boson originates from the broken symmetry and couples directly to the second and third lepton generations, and their corresponding left-handed neutrinos through the coupling . The extension of this model to interactions with DM candidates, being consistent in predicting the observed DM relic density [24-27] , is achieved by adding to the Lagrangian a term of the type with the current and the coupling of the to the DM candidates. In the case
暗物质(DS)是解决标准模型(SM)中的一些未解问题的一个有前途的范式,比如暗物质(DM)的起源[1]。在这个框架中,人们假设在电弱尺度以下存在一个新的粒子部门,这些粒子不受 SM 的电荷影响,但可能有自己的现象学 。除了引力外,DS 状态与 SM 之间的相互作用可以通过门户中介体进行[8-12]。如果假设 DM 是由最轻的稳定 DS 粒子组成的,那么两个部门之间的微弱相互作用与宇宙学观测相一致,因此可以解决暗物质问题。DS 模型成为一个非常富有成果的探索领域,许多不同的技术处理可能的暗物质候选者的非常庞大的参数空间(例如,参见最近的评论[13-16])。具有量子数 的模型非常有吸引力,可以解释暗物质的起源,并同时为长期存在的 μ子异常提供解释[17]。 矢量玻色子源自破缺的 对称性,并直接耦合到第二和第三代轻子,以及它们对应的左手中微子,通过耦合 。将该模型扩展到与 DM 候选相互作用,通过添加一个类似于 的项到拉格朗日量中,以及 的电流和 与 DM 候选的耦合,从而一致地预测观测到的 DM 遗留密度[24-27]。在这种情况下

where (away from the near on-shell resonant enhancement ), the relic density is driven by , with the relevant -channel annihilation cross-section scaling as . Below the resonance, , the -channel annihilation is , with .
(远离近似共振增强 )时,遗留密度由 驱动,相关的 -通道湮灭截面按比例缩放为 。在共振点以下, -通道湮灭是 ,具有
Within this framework, the discrepancy between the experimental and SM predicted values can also be explained through loop corrections [5, 4853]. The current bounds for arise from direct searches, sensitive to the kinematically allowed visible decay channel . Neutrino scattering ex- periments and missing energy searches through provide constraints for . The lower bound is set through the contribution to the radiation density of the Universe through , with its value being defined from both the CMB spectrum and the Big Bang nucleosynthesis (BBN) to and .
在这个框架内,实验 和 SM 预测的 值之间的差异也可以通过环修正来解释[5, 4853]。 的当前边界来自于直接搜索,对动力学允许的可见衰变通道 敏感。中微子散射实验 和通过 进行的失能量搜索为 提供了约束。下限是通过 对宇宙辐射密度的贡献设定的,其值是从 CMB 谱 和宇宙大爆炸核合成(BBN) 定义的。
In this Letter, we report on the first results of the NA64 experiment muon program, dubbed NA64 , looking for Dark Sectors weakly coupled to muons. The experimental set-up and working principle are schematically shown in Fig. 1.
在这封信中,我们报告了 NA64 实验μ子计划的第一批结果,代号为 NA64 ,寻找与μ子弱耦合的暗扇区。实验设置和工作原理如图 1 所示。
Figure 1. Schematic illustration of the NA64 set-up. a) The spectrometer in the upstream region is used for identifying incoming muons with momentum . b) The downstream part composed of calorimeters and a second spectrometer measures the momentum of the scattered muons to search for the vector boson production. c) Sketch of the bremsstrahlung-like reaction invisible) of incident muons on the ECAL target.
图 1. NA64 设置的示意图。a)上游区域的谱仪用于识别动量为 的入射μ子。b)由量热器和第二个谱仪组成的下游部分测量散射μ子的动量,以寻找 矢量玻色子产生。c)关于 入射μ子在 ECAL 靶上的类辐射反应 (不可见)的草图。
If a boson exists, it could be produced in the bremsstrahlung-like reaction of a high energy muon scattering off atomic nuclei in a target , followed by its prompt invisible decay invisible, with only in the vanilla model, and additionally, for DM candidates . For a value of one can accommodate in the same parameter space the muon and the DM relic prediction [68]. In the region of interest (below , the branching ratio to DS invisible final states can be assumed to be , while the ones in visible states and neutrinos can be neglected.
如果存在 玻色子,它可能是由高能量μ子在靶 上散射后类辐射反应产生的,随后是其即时不可见衰变 (不可见),在香草模型中仅有 ,另外, 用于 DM 候选 。对于 的一个值,可以在相同的参数空间中容纳μ子 和 DM 残留预测[68]。在感兴趣的区域(低于 ,DS 不可见最终态的分支比可以假定为 ,而可忽略可见状态 和中微子的状态。
The search for signal events is based on a missing energy-momentum technique which consists of the detection of a primary beam muon with a momentum of in the initial state, and a single muon scat- tered off an active target with missing momentum in the final state, accompanied by missing energy, i.e. no detectable electromagnetic or hadronic activity in the downstream calorimeters.
信号事件的搜索基于一种缺失能量-动量技术,其中包括检测具有 动量的初级束缪子在初始状态下,以及一个散射到带有缺失动量 的活动靶上的单个缪子在最终状态下,伴随着缺失能量,即在下游量热器中没有可检测的电磁或强子活动。
The muons are delivered by the M2 beamline at the CERN Super Proton Synchrotron (SPS)[69]. The beam optics comprises a series of quadrupoles focusing the beam before the target with a divergency and . The incoming muon momentum is reconstructed through a magnetic spectrometer (MS1) consisting of three bending magnets (BEND6), together with four micro-mesh gas detectors (Micromegas, ), two straw tubes chambers and six scintillator hodoscopes, the beam momentum stations . The obtained resolution is . The target is an active electromagnetic
缪子由 CERN 超级质子同步加速器(SPS)的 M2 束线提供[69]。束流光学包括一系列四极透镜,在靶前聚焦束流,发散度为 。入射缪子动量通过由三个 弯曲磁铁(BEND6)、四个微网气体探测器(Micromegas, )、两个吸管室 和六个闪烁体闪烁体组成的磁谱仪(MS1)重建,束流动量站 。获得的分辨率为 。靶是一个活跃的电磁体。

calorimeter (ECAL) composed of Shashlik-type modules made of a lead-scintillator resulting in 40 radiation lengths . The ECAL is followed by a large high-efficiency veto counter (VETO) and a 5 nuclear interaction lengths copper-Sc (Cu-Sc) hadronic calorimeter (VHCAL) with a hole in its middle. The outgoing muon momentum is reconstructed through a second magnetic spectrometer consisting of a single 1.4 bending magnet (MS2) together with four gaseous electron multiplier trackers , two additional straw chambers and three Micromegas yielding a resolution of . To identify and remove any residuals from interactions in the detectors upstream MS2 and ensure maximal hermeticity, two large iron-Sc (Fe-Sc) HCAL modules are placed at the end of the set-up together with a UV straw, . The trigger system is defined by a veto counter with a hole and a set of Sc counters before the target, together with two and counters and sandwiching the HCAL modules, shifted from the undeflected beam axis (referred to as zero-line) to detect the scattered muons.
电量计(ECAL)由铅闪烁体模块组成,导致 40 个辐射长度。ECAL 后面是一个大型高效率否决计数器(VETO)和一个 5 个核相互作用长度的铜-闪烁体(Cu-Sc)强子量能器(VHCAL),中间有一个孔。通过第二个磁谱仪重建出射的μ子动量,该磁谱仪由一个单一的 1.4 弯曲磁铁(MS2)以及四个气体电子倍增器跟踪器、两个额外的吸管室和三个微网电离室组成,分辨率为。为了识别和清除上游 MS2 探测器中的任何残留相互作用,并确保最大的全封闭性,两个大型铁-闪烁体(Fe-Sc)HCAL 模块与一个 UV 吸管放置在设置的末端。触发系统由一个带孔的否决计数器和一组靶前的闪烁体计数器定义,以及两个和计数器夹在 HCAL 模块之间,从未偏转的光束轴线(称为零线)偏移,以侦测散射的μ子。
The data were collected in two trigger configurations with different and distances to the zero-line along the deflection axis , namely and with a similar . The corresponding measured rate is and of the calibration trigger coincidences at a beam intensity of spill. In each configuration, we recorded respectively and muons on target (MOT) yielding a total accumulated statistics of MOT.
数据是在两种触发配置