& Tech Note: Jin Huang (M.I.T.), Yi Qiang (JLab) Hall A Analysis Workshop Dec 8, JLab
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1 & Tec Note: ttp:// Jin Huang (M.I.T., Yi Qiang (JLab Hall A Analysis Worksop Dec 8, JLab
2 Wat are Azimutal Asymmetries TMD & SIDIS Definition Related Experiments Extracting Azimutal Asymmetries Binning and Fitting A Maximum Likeliood Metod Systematic Uncertainties Spin Flips Angular Acceptance Summary Jin Huang <jinuang@mit.edu> Hall A Analysis Worksop
3 TMD & SIDIS Definition Related Experiments Jin Huang Hall A Analysis Worksop 3
4 TMDs link Intrinsic motion of partons Parton spin Spin of te nucleon Probes orbital motion of quarks troug quark transverse momentum distribution in DIS Nucleon -> Plate L = r p? 0 Transverse motion A new pase of study, fast developing field Great advance in teories (models, factorization, Lattice... Not measured until recent years Semi-Inclusive DIS (SIDIS: HERMES, COMPASS, JLab,... p-p(p_bar process (Drell-Yan, adron prod, jets : FNAL, BNL,... Jin Huang <jinuang@jlab.org> Hall A Collaboration Meeting 4
5 Nucleon Polarization Nucleon Spin Quark Spin Un-Polarized Quark polarization Longitudinally Polarized Transversely Polarized U f 1 = 1 = Boer-Mulder L g 1 = Helicity 1L = Worm Gear 1T = T f 1T = Sivers g 1T = Worm Gear 1T = Transversity Pretzelosity : Contribute to inclusive DIS (quark mass ignored Jin Huang <jinuang@jlab.org> Hall A Collaboration Meeting 5
6 k q, Q xp k P /z W Access to new TMDs not accessible in inclusive DIS (m quark =0 Variables: x, q, Q, z, W, W P W Jin Huang <jinuang@jlab.org> Hall A Collaboration Meeting 6
7 Boer-Mulder Worm Gear Transversity Sivers Pretzelosity Helicity Worm Gear f 1 = 1 = 1L = 1T = f 1T = 1T = g 1 = g 1T = d dxdyd dzd dp { F UU, T cos( F S S [ sin( F [ sin( F sin( ( F sin(3 F S S L T L T [ e [ e... S S S 1 F 1 cos( UU S... sin( UL sin( S UL LL...]...] sin( S UT... sin(3 S UT...] cos( F xyq S y (1 cos( S LT...]} Unpolarized Polarized Target Polarized Beam and Target S L, S T : Target Polarization; e : Beam Polarization Jin Huang <jinuang@jlab.org> Hall A Collaboration Meeting 7
8 q q T T UU LT s s s D g F F d d d d d d A s s 1 1, cos( cos( LT 1 cos( Example: is extractable from Double Beam-Target Spin Asymmetry (DSA in wit transversely polarized target: A LT Define Asymmetry: Ten LNS Student Seminar Jin Huang <jinuang@mit.edu> 8...] cos( 1 [ cos(, S LT S e T T UU S F S F dp dzd dxdyd d e e π X n LT g T F S 1 cos(...] [cos( 1 cos( S LT S e S T A d
9 Hall A 6GeV Neutron Transversity Transversely polarized 3 He target, Polarized Beam Single Target Spin Asymmetry, A UT Probing TMDs : Sivers, Collins & Pretzelosity Double Spin Asymmetry, A LT Probing worm-gear TMD: g1t Hall A 1GeV SIDIS Programs Neutron Transversity wit SoLID/Super-Bigbite New proposal: SIDIS asymmetries wit long. pol. 3 He Hig precision and large acceptance Jlab Hall B, COMPASS, HERMES Azimutal Asymmetries are Popular Observable for Many Oter Experiments Jin Huang <jinuang@mit.edu> Hall A Analysis Worksop 10
10 A Maximum Likeliood Metod A Binning and Fitting Metod Jin Huang <jinuang@mit.edu> Hall A Analysis Worksop 11
11 Input: Pysics events Eac event provide as set of azimutal angles Full Azimutal Yield Luminosity Azimutal Acceptance (Partial Target Polarization Modulation Function Ex. A=cos(φ -φ S Azimutal Asymmetry Structure Function & TMDs Jin Huang <jinuang@mit.edu> Hall A Analysis Worksop 1
12 1. Make fine bins on Azimutal Distributions. Form spin asymmetry witin eac bin Tecniques to suppress yield drift: Local pair metod: See X. Qian s tesis 3. Fit wit modulation functions over all bins and extract: Angular Modulation Uncertainty Correlation Difficult for binning if stat. is low Azimutal Distribution Jin Huang <jinuang@mit.edu> Hall A Analysis Worksop 13
13 Maximum likeliood Estimation (MLE is a popular statistical metod providing estimates for te model s parameters MLE is No binning, more stable at low stat. asymptotically unbiased its bias -> zero as te sample size increases asymptotically efficient Low mean squared error wit te MLE asymptotically normal Gaussian interpretation for te results Jin Huang <jinuang@mit.edu> Transversity Collaboration Meeting 14
14 MLE yield estimation expression is simple: effective carge (life time, target density corrected Comparing wit min-ci fit min-ci results is a weigted sum: Jin Huang <jinuang@mit.edu> Transversity Collaboration Meeting 15
15 min-ci sow bias wen statistics of eac bin is low (<10 Similar situation for angular binned fitting Extracted yield /real Wit min-ci bias From PD Tesis, Yi Qiang Jin Huang Transversity Collaboration Meeting 16
16 Define matrixes Sum over all events: A Function of polarization and azimutal angle Corrections related to luminosity asym. And acceptance to be discussed Te estimator for azimutal asymmetry: Covariance Matrix: uncertainty & correlations Ignore Hig Order Terms Jin Huang <jinuang@mit.edu> Hall A Analysis Worksop 17
17 Example: two-modulation case, no corrections F [ [ P P Covariant Matrix: A A 1 1 A ] ] [ P A A1 ] [ P A ] V ε If are cross-talk between modulations due to limited azimutal acceptance: [ P A1 A ] 0 Ten Uncertainty F Correlation Coefficient uncertainty for eac asymmetry is larger Non-zero correlation between extracted asymmetries Jin Huang <jinuang@mit.edu> Hall A Analysis Worksop 18
18 Results are consistent Jin Huang Hall A Analysis Worksop 19
19 500 separate simulations wit SIMC For eac data, extract asym and err Histogram results Verified bot calculations Input asymmetry to simulation Fit (Gauss Error Ellipse (68%, 95%, 99.7% Jin Huang Hall A Analysis Worksop 0
20 More stat. in eac data set ~= Transversity pion data Jin Huang Hall A Analysis Worksop 1
21 Normalization correction A CP, suppressed wit Spin/elicity flip suppression Luminosity Asym. Symmetric Acceptance Suppression integral of acceptance angular function Contamination of oter modulation terms Terms not included in te fitting Contamination ratio can be estimated wit bot metods Jin Huang <jinuang@mit.edu> Hall A Analysis Worksop
22 Metods for extracting SIDIS azimutal asymmetries are discussed, wit consideration of Spin/elicity flip Incomplete azimutal acceptance Normalization corrections: Luminosity, DAQ Life time, etc. Stable at low stat. Transversity results sown tomorrow! (K. Allada Metods can be used for 1GeV SIDIS experiments Tese are generic metod Studies of oter process wit needs of extracting azimutal asymmetries Jin Huang Hall A Analysis Worksop 4
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