SoLID-SIDIS Projection on Measurements of Transversity and Tensor Charge Zhihong Ye, Argonne National Lab SoLID-TMD Workshop at Stony Brooks University 01/28/2016~01/30/2016

Coverage:  Forward Acceptance: Φ: 2π, θ: 8 o o, P: 1.0 – 7.0 GeV/c,  Large Acceptance: Φ: 2π, θ: 16 o -24 o, P: 3.5 – 7.0 GeV/c Coincidence Trigger: Electron Trigger + Hardron Trigger (pions, and maybe kaons) Forward-Angle : Detect electrons & hadrons Large-Angle : Detect electrons only Resolution by GEM: δP/P ~ 2%, θ ~ 0.6mrad, Φ ~ 5mrad Future SoLID-SIDIS Experiments 2

 E (A): SIDIS with Transversely Polarized He3, 90 days  E (A): SIDIS with Longitudinally Polarized He3, 35 days  E (A): SIDIS with Polarized Proton, 120 days 3

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Factor SoLID E (A) (neutron) SBS E (A-) (only neutron) SoLID E , A (proton) CLAS12 C (only proton; conditional approved) TargetsHe3 (“n”) NH3(“p”)HDice (“p”) Polarization (P) 65% 70%60% Dilution-Factor (f) 0.15~ *80% Lumonisity (L) 1.0x10 36 cm -2 s x10 36 cm -2 s x10 35 cm -2 s x10 33 cm -2 s -1 Solid-Angle (Ω e *Ω h ) (θ min =5 o, θ max =35 o )? SIDIS π + Events*P 2 *f M0.21M5.06M3.07M Total Bins (e, π + ) 1014 (Q 2, z, P t, x B ) 120 (z, P t, x B ) For E0=8.8 or 11GeV 617 (Q 2, z, P t, x B ) 1310 (Q 2, z, P t, x B ) Compared with other 12GeV Experiments 5

SoLID bins are to match the SBS and the CLAS12 bins, so they are not optimized for SoLID kinematics Compared with other 12GeV Experiments – 1D Binning  SoLID-SIDIS and SBS-SIDIS are complementary but not direct competing with each other.  SoLID-SIDIS and CLAS12-SIDIS are overall comparable but CLAS12 has only the proton target (and the HDice target still hasn’t been proved to work as expected) vs. SBS vs. SBS (He3, “neutron”) vs. CLAS12 (proton) 6

Impact on Transversity and Tensor Charge Collins Asymmetry: Tensor Charge: Transversity (Z.-B. Kang, A. Prokudin, P. Sun, F. Yuan, Phys. Rev. D 93, ) 7

Impact on Transversity and Tensor Charge Collins Asymmetry: Non-perturbative factors containing the initial conditions of evolution Unpolarized FF Collins FF Transversity Unpolarized PDF A free parameter in the global fit to allow Collins FF to change its shape w.r.t unpolarized FF. (Z.-B. Kang, A. Prokudin, P. Sun, F. Yuan, Phys. Rev. D 93, ) 8

Impact on Transversity and Tensor Charge  For u and d quarks, while anti-quark transversities are set to zero. The global fit to the existing SIDIS and (e+,e-) world data: Plus a covariant error matrix that contains the correlated uncertainties of these parameters (Z.-B. Kang, A. Prokudin, P. Sun, F. Yuan, Phys. Rev. D 93, )  Transversity:  Twist-3 Collins FF:  13 free parameters: 9

Impact on Transversity and Tensor Charge (Z.-B. Kang, A. Prokudin, P. Sun, F. Yuan, Phys. Rev. D 93, ) The global fit to the existing SIDIS and (e+,e-) world data: 10

Impact on Transversity and Tensor Charge Adding the SoLID-SIDIS and CLAS12-SIDIS projected data:  Bayes Reweighting Technique: (N. Sato, J. F. Owens, and H. Prosper, Phys. Rev. D89, (2014), ) Bayes Theorem: Probability density function (pdf) for a model parameter is going to be modified in presence of new data: New pdf (posterior density) Old pdf (prior density) The conditional probability for a data set D (Likelihood function) Normalization The expectation value of a quantity, O, with the new data: The variance (“new errors”) with the new data: Asymmetry of a data-bin w/ the best fit parameters Uncertainty of a data-bin from projections  Generate pseudo-data: (1) Randomly generate a set of these 13 parameters based on the covariant matrix; (2) calculate the asymmetry value of each projected data-bin; (3) Assign the projected statistical error to each bin (4) repeat to generate more pseudo-data sets. 11 Asymmetry of a data-bin w/ the randomly generated parameters

Impact on Transversity and Tensor Charge Adding the SoLID-SIDIS and CLAS12-SIDIS projected data: For a fair comparison, we apply the same technique to predict impacts of SoLID-SIDIS data and the CLAS12-SIDIS data. Only the statistical uncertainties are under consideration. Will add systematic errors of the SoLID-SIDIS system soon (with helps from Tianbo Liu). Overall uncertainties from PDFs, FFs and so on will also be included soon. 12

Impact on Transversity and Tensor Charge  Preliminary Results on the Transversity: Adding the SoLID-SIDIS and CLAS12-SIDIS projected data: Solid proton-pip Solid 3he-pip Preliminary Only show the improvement on the statistical uncertainties which become very tiny They show improvements of different data sets to different flavors along xB The central curve of the d-quark transversity distribution has an offset due to partial sampling of a parameter (see next page) 13

Impact on Transversity and Tensor Charge  Preliminary Results on the Transversity: Adding the SoLID-SIDIS and CLAS12-SIDIS projected data: u-quark parameter sampling d-quark parameters sampling d-quark transversity is offset center because of partial sampling the Nd parameter (generating new results now) 14

Impact on Transversity and Tensor Charge  Preliminary Results on the Tensor Charge: Preliminary Adding the SoLID-SIDIS and CLAS12-SIDIS projected data: CLAS12 results are also available but we will show it later once things are final. Note: This work is still undergoing in collaborating with Kalyan Allada, Alexei Prokudin, Nobuo Sato and Zhihong Ye 15

Summary  Highly rated SIDIS experiments have been approved to measure SIDIS asymmetries with both proton and “neutron” targets at different polarization directions.  The large acceptance and high intensity of the SoLID detector allow us to collect high quality data with great statistics while minimizing the detector-related systematic uncertainties  A quick comparison of SoLID-SIDIS programs with the SBS and CLAS12 SIDIS programs  Global fit won’t be an effective method when we add lots of new data into the fit  With the physics model developed by Kang et. al, we are developing a new TMD extraction techniques based on the Bayes reweight method.  We are evaluating the impact of the projected SoLID-SIDIS data (and projected CLAS12- SIDIS data) to the determination of Transersity and Tensor-Charge 16