"Table 112" of "Measurement of distributions sensitive to the underlying event in inclusive Z-boson production in $pp$ collisions at $\sqrt{s}=7$ TeV with the ATLAS detector"

CERN-LHC. A measurement of charged-particle distributions sensitive to the properties of the underlying event is presented for an inclusive sample of events containing a Z-boson, decaying to an electron or muon pair. The measurement is based on data collected using the ATLAS detector at the LHC in proton--proton collisions at a centre-of-mass energy of 7 TeV with an integrated luminosity of 4.6/fb. Distributions of the charged particle (excluding the two leptons from Z decay) multiplicity and of the charged particle transverse momentum are measured in regions of azimuthal angle delta(phi) = |phi - phi(Z)| defined with respect to the Z-boson direction: - the toward region: |delta(phi)| < 60 degrees - the transverse region: 60 < |delta(phi)| < 120 degrees - the away region: |delta(phi)| > 120 degrees - the trans-max region: one of the two transverse sectors having a maximum scalar sum of transverse momenta of charged particles on event-by-event basis - the trans-min region: one of the two transverse sectors having a minimum scalar sum of transverse momenta of charged particles on event-by-event basis The fiducial volume is defined as follows: - the two oppositely charged leptons from Z decay are required to have pT > 20 GeV, |eta| < 2.4 and 66 < M(ll) < 116 GeV - charged particles are required to have a proper lifetime tau > 0.3*10**-10 sec, be primary (i.e. produced directly in pp interaction or being decay products of prompt particles with the lifetime less than tau), have pT > 0.5 GeV and |eta| < 2.5 The observables: - pT(Z): transverse momentum of the Z-boson - N(ch)/delta(eta)/delta(delta(phi)): number of stable charged particles per eta-phi unit, averaged over eta-phi range, where -2.5 mu+ mu-, e+ e- identification efficiency and Z momentum resolution; background from pileup and final states yielding the same experimental signature as the Z -> mu+ mu-, e+ e- signal. - Published distributions can be directly compared to a particle level MC generator output with the two definitions of Z -> lepton+ lepton- final state (as indicated in the tables): - Born approximation: Z momentum is defined as the sum of leptons' and FSR photons' momenta, in neglect of interference between photon radiation off the leptons and other charged legs in the process. The particle level fiducial volume can be viewed as the one obtained in an imaginary experiment without FSR, e.g., with Z -> nu nubar final state where both leptons have pT>20 GeV and |eta|<2.5. - Dressed leptons: dressed lepton momentum is defined as a sum of the lepton's momentum and the momenta of all photons of non-hadronic origin within DeltaR<0.1 cone around the direction of the lepton. The particle level fiducial volume is defined using dressed lepton momenta. Material referenced as `auxiliary' in the tables is available at https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2011-42/.

CERN-LHC。本研究针对包含衰变为电子（electron）或缪子（muon）对的Z玻色子（Z-boson）的全域事件样本，呈现了对与本底事件（underlying event）性质敏感的带电粒子分布测量结果。本次测量基于大型强子对撞机（Large Hadron Collider, LHC）上ATLAS探测器采集的数据，对应质心系能量为7 TeV的质子-质子碰撞，积分亮度为4.6 fb⁻¹。
测量对象为扣除Z玻色子衰变产生的两个轻子后的带电粒子多重数分布，以及带电粒子横向动量（transverse momentum, p_T）分布，测量区域按相对于Z玻色子方向定义的方位角差值Δφ=|φ - φ_Z|划分为：
- 前向区域（toward region）：|Δφ| < 60°
- 横向区域（transverse region）：60° < |Δφ| < 120°
- 背向区域（away region）：|Δφ| > 120°
- 横极大区域（trans-max region）：在逐个事件层面，两个横向扇区中带电粒子横向动量标量和最大的扇区
- 横极小区域（trans-min region）：在逐个事件层面，两个横向扇区中带电粒子横向动量标量和最小的扇区

本研究定义的fiducial接受体积（fiducial volume）如下：
- Z玻色子衰变产生的两个带异号电荷的轻子需满足p_T > 20 GeV、赝快度|η| < 2.4，且双轻子不变质量66 GeV < M_ll < 116 GeV
- 带电粒子需满足固有寿命τ > 0.3×10⁻¹⁰ s，且为原初粒子（即直接产生于质子-质子碰撞，或是寿命小于τ的瞬态粒子的衰变产物），同时p_T > 0.5 GeV、|η| < 2.5

可观测物理量包括：
- p_T(Z)：Z玻色子的横向动量
- N_ch/Δη/Δφ：单位η-φ空间内的稳定带电粒子数目，在-2.5 < η < 2.5且0 < |Δφ| < π的范围内取平均。测量中已针对e⁺e⁻、μ⁺μ⁻的识别效率以及Z玻色子动量分辨率进行校正，并扣除了来自叠加碰撞（pileup）以及具有与Z→μ⁺μ⁻、e⁺e⁻信号相同实验特征的末态的背景贡献。

已发布的分布结果可直接与粒子级蒙特卡洛（Monte Carlo, MC）发生器的输出进行对比，对比时采用两种Z→轻子+轻子末态的定义（如表中所示）：
1. 玻恩近似（Born approximation）：Z玻色子动量定义为轻子与末态辐射光子（Final State Radiation, FSR）的动量之和，且忽略轻子与过程中其他带电粒子腿之间的光子辐射干涉效应。粒子级fiducial接受体积可视为在不存在末态辐射的假想实验中得到的体积，例如Z→νν̅末态且两个轻子满足p_T>20 GeV、|η|<2.5的情形。
2. 缀饰轻子（dressed lepton）：缀饰轻子动量定义为轻子自身动量，与所有在轻子方向ΔR<0.1锥区内的非强子起源光子的动量之和。粒子级fiducial接受体积采用缀饰轻子动量进行定义。

表格中标记为“辅助材料”的内容可通过以下链接获取：https://atlas.web.cern.ch/Atlas/GROUPS/PHYSICS/PAPERS/STDM-2011-42/。