Antihydrogen production cross-section measurement of charge exchange between in-flight antiprotons from trap and positronium for the GBAR experiment = GBAR 실험을 위한 트랩에서 방출된 비행 반양성자와 포지트로늄 간 전하 교환에 의한 반수소 생성 단면적 측정

국문 초록 (Abstract)

약한 등가 원리(WEP)는 모든 물체가 구성 성분과 관계없이 중력 하에서 동일한 자유 낙하 궤적을 따른다고 명시한다. WEP는 물질에 대해 10−15 정밀도까지 검증되었으나, 반물질에 대한 유효성은 충분히 검증되지 않았다. 유일한 직접 측정은 2023년 ALPHA-g에 의해 수행되었으며, 반수소의 중력 가속도가 0.75±0.13(stat, sys)±0.16(sim)g로 측정되었다. 이는 정상 중력과 일치하지만 큰 불확도를 가진다. GBAR는 극저온 반수소의 자유 낙하를 이용하여 반물질의 중력 가속도를 1% 정밀도로 측정하는 것을 목표로 한다. GBAR의 방법은 공감 냉각을 통해 ∼10 μK까지 냉각할 수 있는 반수소
이온(H+)을 사용한다. 냉각 후 레이저 광탈리로 양전자 하나를 제거하여 정지 상태의 중성 반수소 원자를 방출하고 자유 낙하를 측정한다. H+생성에는 포지트로늄(Ps)과의 두 번의 연속적인 전하 교환 반응이 필요하다: 첫 번째 반응 ¯ p+Ps → H+e−, 두 번째 반응 H+Ps → H++e−. 이 반응들의 단면적은 생성률을 직접적으로 결정하며, 따라서 실험의 실현 가능성을 좌우한다. 본 연구 이전에 첫 번째 반응의 단면적은 10 keV 이하의 반양성자 에너지에서 측정된적이 없었다.이론모델들—수렴밀접결합(CCC),쿨롱-보른근사(CBA), 유니타리화 보른 근사(UBA)—은 최대 단면적이 10 keV 이하에 있다고 예측하지만, 2–3배의 차이를 보인다. 유일한 실험 데이터는 Merrison 등이 11 keV까지 측정한 물질 등가 반응(p+Ps→H+e+)에서 얻어졌으나, 불확도가 너무 커서 모델들을 구별할 수 없었다. 본 논문은 10 keV 이하 에너지에서 전하 교환 반응 ¯ p+Ps→H+e−를 통한 반수소 생성 단면적의 첫 번째 측정을 제시한다. 측정은 2024년 CERN에서 GBAR 협력단에 의해 6.2 keV와 4.2 keV 반양성자를 사용하여 수행되었다. 실험 장치는 페닝 트랩에서 방출된 반양성자와 나노다공성 SiO2 캐비티 타겟에서 생성된 포지트로늄 구름을 결합하였다. 본 연구의 일부로 구축된 반 양성자 트랩은 고밀도의 평행한 빔을 생성하여 캐비티 타겟 사용을 가능하게 하였고, GBAR의 2022년 결과 대비 반수소 검출률을 10배 향상시켰다. 생성된 반수소원자는1.6 m하류의마이크로채널플레이트(MCP)검출기에서검출되었으며, 반응하지 않은 반양성자는 전기장에 의해 편향되었다. 본인의 기여는 반수소 개수 분석을 위한 DBSCAN 클러스터링과 통계적 배경 제거를 이용한 MCP 이미지 분석 개발, 그리고 반양성자 개수 분석을 위한 CMOS 검출기 교정과 MCP 검출 효율을 위한 GEANT4 시뮬레이션 수행을 포함한다. 측정된 단면적은 다음과 같다: • 6.2 keV: σ = (1.325±0.122(stat)+0.114−0.075 (sys))×10−15 cm2• 4.2 keV: σ = (1.030±0.193(stat)+0.138−0.121 (sys))×10−15 cm2 이 결과는 CCC 및 UBA 예측과 일치하며 CBA를 배제한다. UBA와 CCC는 유사한 최대 단면적(각각 14.8과 17.5 πa20, 15%만 차이)을 예측하므로, 본 측정은 GBAR 실험 최적화에 충분한 제약 조건을 제공한다. 이 데이터는 또한 이전에 탐구되지 않은 에너지 영역에서 양자 3체 산란 이론을 검증하는 데 기여한다. 측정된 단면적은 이론적 예측 범위의 낮은 쪽에 위치하여, 효율적인 H+생성을 위해 더 높은 반양성자 및 포지트로늄 밀도가 필요함을 나타낸다. 이를 보완하기위해반양성자축적및트랩내포지트로늄변환기술이개발중이다. 2025년에GBAR는두번째반응(H+Ps→H++e−)에대한데이터를수집하였으며,분석이진행중이다.이두단면적측정은반물질중력측정이라는GBAR의 목표를 향한 실험 최적화를 가능하게 할 것이다.

다국어 초록 (Multilingual Abstract)

The Weak Equivalence Principle (WEP) states that all bodies follow the same free-fall trajectory under gravity, independent of their composition. While WEP has been verified for matter to 10−15 precision, its validity for antimatter remains poorly tested. The only direct measurement, by ALPHA-g in 2023, found the gravitational acceleration of antihydrogen to be 0.75±0.13(stat, sys)± 0.16(sim)g—consistent with normal gravity but with large uncertainty. GBAR aims to measure the gravitational acceleration of antimatter with 1% precision using ultra-cold antihydrogen in free fall. GBAR’s approach uses antihydrogen ions (H+), which can be sympathetically cooled to ∼10 μK. After cooling, laser photodetachment removes one positron, releasing a neutral antihydrogen atom at rest for free-fall measurement. Producing H+ requires two sequential charge exchange reactions with positronium (Ps): first ¯ p+Ps→H+e−, then H+Ps→H+ +e−. The cross-sections of these reactions directly determine the production rate and thus he feasibility of the experiment. Before this work, the cross-section for the first reaction had never been measured below 10 keV antiproton energy. Theoretical models—Convergent Close- Coupling (CCC), Coulomb-Born Approximation (CBA), and Unitarized Born Approximation (UBA)—predict the maximum cross-section lies below 10 keV
but disagree by factors of two to three. The only experimental data came from the matter-equivalent reaction (p+Ps→H+e+) measured by Merrison et al. down to 11 keV, with uncertainties too large to distinguish between models. This thesis presents the first cross-section measurement of antihydrogen production from the charge-exchange reaction ¯ p+Ps → H+e− at energies below 10 keV. The measurement was performed by the GBAR collaboration at CERN in 2024 using antiprotons at 6.2 keV and 4.2 keV.
The experimental setup combined antiprotons from a Penning trap with a positronium cloud generated in a nanoporous SiO2 cavity target. The antiproton trap, commissioned as part of this work, produced a dense and parallel beam that enabled use of the cavity target and increased antihydrogen detection rate by a factor of 10 compared to GBAR’s 2022 result. Produced antihydrogen atoms were detected by a microchannel plate (MCP) detector 1.6 m downstream, while unreacted antiprotons were deflected by an electric field. My contributions include developing MCP image analysis using DBSCAN clustering with statistical background subtraction for antihydrogen counting, and performing GEANT4 simulations for CMOS detector calibration for antiproton counting and MCP detection efficiency. The measured cross-sections are: • 6.2 keV: σ = (1.325±0.122(stat)+0.114 −0.075 (sys))×10−15 cm2 • 4.2 keV: σ = (1.030±0.193(stat)+0.138 −0.121 (sys))×10−15 cm2. These results are consistent with CCC and UBA predictions while ruling out CBA. Since UBA and CCC predict similar maximum cross-sections (14.8 and 17.5 πa20 , respectively, differing by only 15%), this measurement provides sufficient constraints for GBAR’s experimental optimization. The data also contribute to testing quantum three-body scattering theory in this previously unexplored energy regime. The measured cross-section is on the lower side of the theoretical range, indicating that higher antiproton and positronium densities will be needed for efficient H+ production. Techniques such as antiproton stacking and in-trap positronium conversion are under development to compensate. In 2025, GBAR collected data for the second reaction (H+Ps→H+ +e−); analysis is ongoing. Together, these cross-section measurements will enable precise optimization of the GBAR experiment toward its goal of measuring antimatter gravity.

목차 (Table of Contents)

• Abstract i
• Chapter I Introduction 1
• Section 1.1 Antimatter 1
• Section 1.1.1 Theoretical Prediction — The Dirac Equation 1
• Section 1.1.2 Experimental Discovery 2
• Section 1.2 Motivations for Antimatter Research 3
• Section 1.2.1 CPT Symmetry 3
• Section 1.2.2 Matter-Antimatter Asymmetry 4
• Section 1.2.3 Gravity: The Least Measured Property 5
• Section 1.3 Antimatter and Gravity 5
• Section 1.3.1 Weak Equivalence Principle 5
• Section 1.3.2 WEP Tests on Matter 6
• Section 1.3.3 WEP Tests on Antimatter 6
• Section 1.4 The GBAR Experiment 8
• Section 1.4.1 Principle 8
• Section 1.4.2 Antihydrogen Ion Production 9
• Section 1.4.3 Cooling and Free Fall 10
• Section 1.4.4 Precision Goals 10
• Section 1.5 Antihydrogen Production Cross-Section 12
• Section 1.5.1 Importance for GBAR 12
• Section 1.5.2 Prior Experimental Status 12
• Section 1.5.3 Theoretical Models 13
• Section 1.5.4 This Thesis 14
• Section 1.6 Thesis Scope and Outline 14
• Chapter II GBAR 17
• Section 2.1 Antihydrogen ion Production Scheme 17
• Section 2.1.1 First reaction: p̄ + Ps → H̄ + e⁻ 17
• Section 2.1.2 Second reaction: H̄ + Ps → H̄⁺ + e⁻ 21
• Section 2.2 Experimental setup 21
• Section 2.2.1 Antiproton beamline 22
• Section 2.2.2 Positron beamline 32
• Section 2.2.3 Reaction chamber and after 37
• Section 2.2.4 H̄⁺ cooling 42
• Section 2.2.5 Free fall chamber 45
• Chapter III Antiproton trap 49
• Section 3.1 Principle of Penning-Malmberg Trap 49
• Section 3.1.1 Canonical Angular Momentum and Plasma Confinement 52
• Section 3.1.2 Application to GBAR 54
• Section 3.2 Radial Compression by Rotating Wall 55
• Section 3.2.1 Motivation and Physical Principle 55
• Section 3.2.2 Compression Mechanism via Canonical Torque 56
• Section 3.2.3 Compression Regimes 57
• Section 3.2.4 Sympathetic Compression of Antiprotons 59
• Section 3.3 Control system 60
• Section 3.3.1 Hardware 60
• Section 3.3.2 Software 63
• Section 3.4 Operation 69
• Section 3.4.1 Electron Pre-loading and Synchrotron Cooling 69
• Section 3.4.2 Capturing antiproton 71
• Section 3.4.3 Sympathetic Cooling of antiproton 72
• Section 3.4.4 Compression 74
• Section 3.4.5 Extraction and Acceleration 82
• Chapter IV Antihydrogen cross-section measurement at GBAR 87
• Section 4.1 Experimental setup 87
• Section 4.1.1 Antiproton trap 88
• Section 4.1.2 Cavity target 89
• Section 4.1.3 Deflector 90
• Section 4.1.4 Detector scheme 90
• Section 4.1.5 Run Type 96
• Section 4.2 Background Estimation 99
• Section 4.2.1 Antiproton Background 99
• Section 4.2.2 Positron and Positronium Background 100
• Section 4.3 Principle of Cross-Section Determination 102
• Chapter V Analysis 105
• Section 5.1 Overview 105
• Section 5.1.1 Data selection 105
• Section 5.1.2 Number of antiproton 108
• Section 5.1.3 Number of ortho-Positronium 111
• Section 5.1.4 Number of Antihydrogen 120
• Section 5.1.5 Overlap function 127
• Section 5.1.6 Additional study 128
• Section 5.2 CMOS Detector Calibration Simulation 129
• Section 5.2.1 Simulation 130
• Section 5.2.2 Event Classification 140
• Section 5.2.3 Simulation result 141
• Section 5.2.4 Discussion 143
• Section 5.2.5 Backscattering study 145
• Section 5.2.6 Experimental Method 147
• Section 5.2.7 Fitting and Result 147
• Section 5.2.8 Result 148
• Section 5.2.9 Conclusion 149
• Section 5.3 Antihydrogen MCP Image analysis 149
• Section 5.3.1 Clustering Algorithm: DBSCAN 151
• Section 5.4 Systematic Uncertainty from DBSCAN Cluster Merging 170
• Section 5.4.1 Motivation 170
• Section 5.4.2 Methodology 170
• Section 5.4.3 Results 175
• Section 5.4.4 Discussion 178
• Section 5.5 MCP detection efficiency for Antihydrogen 182
• Section 5.5.1 Simulation 183
• Section 5.5.2 Result 190
• Section 5.5.3 Discussion 192
• Section 5.5.4 Conclusion 194
• Chapter VI Result 197
• Section 6.1 Data Selection 197
• Section 6.1.1 Particle Presence Verification 197
• Section 6.1.2 Event Selection Summary 199
• Section 6.2 Antihydrogen Analysis 202
• Section 6.2.1 Antihydrogen Signal Extraction 202
• Section 6.2.2 Image Analysis Results 206
• Section 6.2.3 Electrical Signal Analysis Results 208
• Section 6.2.4 Corrections 211
• Section 6.2.5 Correlation Between Image and Electrical Signals 214
• Section 6.3 Number of Antiprotons 214
• Section 6.4 Number of ortho-Positronium 217
• Section 6.4.1 Positron Number 218
• Section 6.4.2 o-Ps Fraction 218
• Section 6.4.3 Total o-Ps Number 219
• Section 6.5 Overlap Function 221
• Section 6.5.1 Antiproton Velocity 222
• Section 6.5.2 Cavity Volume 223
• Section 6.5.3 Temporal Overlap Integral 223
• Section 6.6 Cross Section Result 226
• Chapter VII Conclusion and Discussion 229
• Section 7.1 Summary of Results 229
• Section 7.2 Experimental Achievements 230
• Section 7.3 Comparison with Theoretical Models 230
• Section 7.4 Implications for GBAR 232
• Section 7.5 Outlook 233
• Appendix 233
• Appendix I Backscattering of antiprotons on the MCP 235
• Section A.1 GEANT4 predictions of antiproton backscattering 236
• Section A.1.1 Electromagnetic physics list 236
• Section A.1.2 Impact of the material 238
• Section A.1.3 Predicted signal in the CMOS tracker: simplified model 241
• Section A.1.4 Predicted signal in the CMOS tracker: actual model 246
• Section A.2 Dedicated runs on MCP2 253
• Section A.2.1 The measurements 253
• Section A.2.2 Various checks of these data 256
• Section A.3 Fit of the backscattering fraction of antiprotons on MCP2 261
• Section A.3.1 Fit model 263
• Section A.3.2 Results of the fit to the 4 keV + 100 keV data 267
• Section A.3.3 Conclusions 274
• Bibliography 277
• Abstract in Korean 289