MEASUREMENTS OF ANGULAR DISTRIBUTIONS OF MUONS FROM UPSILON MESON DECAYS IN P P-BAR COLLISIONS AT SQRT(S)=1.96 TEV SUPPLEMENTAL MATERIAL These tables list the coefficients in Eq. (1) determined from the fit applied to Upsilon(1S,2S,3S) states in the Collins-Soper and s-channel helicity frames, along with their statistical and systematic uncertainties. They also include the fitted values of the rotational invariant measured in both frames for each Upsilon(nS) state. The tables are organized and labeled as follows: TABLE [nS]-[i]-[f] : Fitted coefficients TABLE [nS]-LT : Rotational invariant nS = 1S - Upsilon(1S) parameters nS = 2S - Upsilon(2S) parameters nS = 3S - Upsilon(3S) parameters i = 1 - lambda-theta parameter i = 2 - lambda-phi parameter i = 3 - lambda-theta-phi parameter f = CS - Collins-Soper frame f = SH - s-channel helicity frame Column headings are: PTMIN - low range of transverse momentum (GeV/c) PTMAX - high range of transverse momentum (GeV/c) LAMBDA-* - central value from the fit LT-CS - central value of rotational invariant measured in CS frame LT-SH - central value of rotational invariant measured in SH frame +STAT - positive statistical uncertainty -STAT - negative statistical uncertainty SYST - total symmetric systematic uncertainty TABLE 1S-1-CS : Lambda-theta, Upsilon(1S), Collins-Soper frame PTMIN PTMAX LAMBDA-THETA +STAT -STAT SYST 0 2 0.214 +0.144 -0.139 0.052 2 4 -0.002 +0.074 -0.073 0.039 4 6 -0.053 +0.069 -0.068 0.036 6 8 0.030 +0.074 -0.072 0.022 8 12 0.012 +0.053 -0.051 0.020 12 17 0.029 +0.057 -0.055 0.019 17 23 0.033 +0.099 -0.087 0.047 23 40 0.079 +0.212 -0.180 0.020 TABLE 1S-2-CS : Lambda-phi, Upsilon(1S), Collins-Soper frame PTMIN PTMAX LAMBDA-PHI +STAT -STAT SYST 0 2 -0.021 +0.036 -0.039 0.064 2 4 -0.049 +0.015 -0.015 0.022 4 6 -0.069 +0.015 -0.016 0.023 6 8 -0.104 +0.027 -0.029 0.024 8 12 -0.067 +0.030 -0.031 0.018 12 17 -0.015 +0.043 -0.046 0.045 17 23 -0.172 +0.076 -0.088 0.063 23 40 -0.082 +0.103 -0.128 0.085 TABLE 1S-3-CS : Lambda-theta-phi, Upsilon(1S), Collins-Soper frame PTMIN PTMAX LAMBDA-THETA-PHI +STAT -STAT SYST 0 2 0.022 +0.053 -0.053 0.045 2 4 0.021 +0.027 -0.027 0.022 4 6 0.012 +0.031 -0.030 0.016 6 8 -0.077 +0.040 -0.039 0.016 8 12 0.031 +0.035 -0.034 0.010 12 17 0.094 +0.039 -0.039 0.024 17 23 -0.065 +0.056 -0.057 0.025 23 40 -0.011 +0.120 -0.123 0.052 TABLE 2S-1-CS : Lambda-theta, Upsilon(2S), Collins-Soper frame PTMIN PTMAX LAMBDA-THETA +STAT -STAT SYST 0 2 -0.591 +0.262 -0.248 0.070 2 4 -0.115 +0.187 -0.181 0.028 4 6 -0.042 +0.169 -0.163 0.062 6 8 -0.194 +0.152 -0.145 0.051 8 12 0.007 +0.112 -0.106 0.029 12 17 -0.041 +0.100 -0.094 0.028 17 23 -0.055 +0.156 -0.126 0.068 23 40 0.151 +0.380 -0.246 0.213 TABLE 2S-2-CS : Lambda-phi, Upsilon(2S), Collins-Soper frame PTMIN PTMAX LAMBDA-PHI +STAT -STAT SYST 0 2 0.200 +0.064 -0.071 0.149 2 4 -0.120 +0.041 -0.042 0.021 4 6 -0.031 +0.034 -0.035 0.033 6 8 -0.038 +0.046 -0.048 0.068 8 12 -0.072 +0.054 -0.058 0.018 12 17 0.041 +0.069 -0.075 0.087 17 23 0.048 +0.101 -0.127 0.083 23 40 -0.175 +0.213 -0.317 0.274 TABLE 2S-3-CS : Lambda-theta-phi, Upsilon(2S), Collins-Soper frame PTMIN PTMAX LAMBDA-THETA-PHI +STAT -STAT SYST 0 2 0.143 +0.104 -0.103 0.069 2 4 0.144 +0.065 -0.065 0.050 4 6 0.051 +0.066 -0.066 0.023 6 8 0.071 +0.078 -0.077 0.039 8 12 0.012 +0.068 -0.067 0.017 12 17 0.126 +0.073 -0.072 0.058 17 23 -0.018 +0.090 -0.090 0.045 23 40 -0.224 +0.147 -0.181 0.166 TABLE 3S-1-CS : Lambda-theta, Upsilon(3S), Collins-Soper frame PTMIN PTMAX LAMBDA-THETA +STAT -STAT SYST 0 2 0.371 +0.501 -0.458 0.109 2 4 -0.659 +0.307 -0.288 0.135 4 6 -0.421 +0.297 -0.284 0.140 6 8 -0.049 +0.270 -0.253 0.044 8 12 -0.286 +0.144 -0.135 0.036 12 17 -0.217 +0.123 -0.111 0.022 17 23 -0.198 +0.182 -0.145 0.056 23 40 0.021 +0.368 -0.257 0.124 TABLE 3S-2-CS : Lambda-phi, Upsilon(3S), Collins-Soper frame PTMIN PTMAX LAMBDA-PHI +STAT -STAT SYST 0 2 0.435 +0.093 -0.108 0.084 2 4 -0.053 +0.065 -0.069 0.234 4 6 -0.114 +0.064 -0.069 0.166 6 8 -0.077 +0.070 -0.077 0.094 8 12 -0.072 +0.073 -0.080 0.022 12 17 0.058 +0.084 -0.094 0.058 17 23 0.085 +0.095 -0.136 0.114 23 40 -0.023 +0.194 -0.270 0.164 TABLE 3S-3-CS : Lambda-theta-phi, Upsilon(3S), Collins-Soper frame PTMIN PTMAX LAMBDA-THETA-PHI +STAT -STAT SYST 0 2 0.052 +0.180 -0.177 0.038 2 4 0.049 +0.110 -0.109 0.122 4 6 0.181 +0.119 -0.117 0.099 6 8 0.289 +0.133 -0.129 0.086 8 12 0.065 +0.093 -0.092 0.025 12 17 0.014 +0.092 -0.091 0.029 17 23 -0.139 +0.081 -0.088 0.088 23 40 -0.216 +0.182 -0.199 0.125 TABLE 1S-1-SH : Lambda-theta, Upsilon(1S), s-channel helicity frame PTMIN PTMAX LAMBDA-THETA +STAT -STAT SYST 0 2 0.008 +0.102 -0.100 0.049 2 4 -0.078 +0.041 -0.040 0.030 4 6 -0.111 +0.044 -0.043 0.029 6 8 -0.125 +0.060 -0.058 0.039 8 12 -0.154 +0.056 -0.055 0.024 12 17 -0.133 +0.082 -0.080 0.036 17 23 -0.229 +0.131 -0.126 0.076 23 40 -0.213 +0.248 -0.219 0.111 TABLE 1S-2-SH : Lambda-phi, Upsilon(1S), s-channel helicity frame PTMIN PTMAX LAMBDA-PHI +STAT -STAT SYST 0 2 -0.025 +0.037 -0.040 0.068 2 4 -0.044 +0.020 -0.020 0.021 4 6 -0.070 +0.027 -0.028 0.022 6 8 -0.059 +0.035 -0.036 0.017 8 12 -0.022 +0.025 -0.025 0.018 12 17 -0.004 +0.024 -0.025 0.041 17 23 -0.060 +0.032 -0.033 0.025 23 40 0.014 +0.071 -0.078 0.058 TABLE 1S-3-SH : Lambda-theta-phi, Upsilon(1S), s-channel helicity frame PTMIN PTMAX LAMBDA-THETA-PHI +STAT -STAT SYST 0 2 0.054 +0.054 -0.054 0.021 2 4 -0.020 +0.021 -0.021 0.011 4 6 0.009 +0.023 -0.023 0.008 6 8 -0.020 +0.032 -0.032 0.010 8 12 -0.060 +0.028 -0.028 0.012 12 17 -0.020 +0.032 -0.032 0.002 17 23 0.054 +0.049 -0.049 0.016 23 40 -0.046 +0.091 -0.090 0.052 TABLE 2S-1-SH : Lambda-theta, Upsilon(2S), s-channel helicity frame PTMIN PTMAX LAMBDA-THETA +STAT -STAT SYST 0 2 -0.069 +0.201 -0.205 0.046 2 4 -0.287 +0.096 -0.092 0.056 4 6 -0.108 +0.100 -0.093 0.052 6 8 -0.085 +0.123 -0.113 0.070 8 12 -0.179 +0.110 -0.103 0.030 12 17 -0.091 +0.147 -0.141 0.076 17 23 0.057 +0.256 -0.236 0.121 23 40 0.004 +0.393 -0.334 0.165 TABLE 2S-2-SH : Lambda-phi, Upsilon(2S), s-channel helicity frame PTMIN PTMAX LAMBDA-PHI +STAT -STAT SYST 0 2 0.194 +0.068 -0.079 0.132 2 4 -0.063 +0.048 -0.051 0.014 4 6 -0.038 +0.054 -0.059 0.031 6 8 -0.013 +0.067 -0.075 0.059 8 12 -0.017 +0.052 -0.057 0.018 12 17 -0.039 +0.051 -0.052 0.097 17 23 -0.026 +0.060 -0.062 0.051 23 40 0.091 +0.112 -0.114 0.160 TABLE 2S-3-SH : Lambda-theta-phi, Upsilon(2S), s-channel helicity frame PTMIN PTMAX LAMBDA-THETA-PHI +STAT -STAT SYST 0 2 -0.261 +0.127 -0.130 0.015 2 4 0.045 +0.054 -0.053 0.014 4 6 -0.059 +0.051 -0.051 0.014 6 8 -0.083 +0.063 -0.063 0.018 8 12 -0.008 +0.055 -0.055 0.020 12 17 -0.013 +0.063 -0.063 0.013 17 23 -0.148 +0.074 -0.075 0.057 23 40 0.189 +0.131 -0.127 0.091 TABLE 3S-1-SH : Lambda-theta, Upsilon(3S), s-channel helicity frame PTMIN PTMAX LAMBDA-THETA +STAT -STAT SYST 0 2 0.323 +0.381 -0.342 0.115 2 4 -0.190 +0.183 -0.168 0.075 4 6 -0.007 +0.208 -0.183 0.087 6 8 -0.481 +0.139 -0.129 0.134 8 12 0.067 +0.187 -0.172 0.039 12 17 0.143 +0.230 -0.215 0.074 17 23 0.142 +0.365 -0.333 0.124 23 40 0.138 +0.503 -0.420 0.135 TABLE 3S-2-SH : Lambda-phi, Upsilon(3S), s-channel helicity frame PTMIN PTMAX LAMBDA-PHI +STAT -STAT SYST 0 2 0.515 +0.085 -0.099 0.070 2 4 0.002 +0.083 -0.092 0.189 4 6 -0.107 +0.110 -0.128 0.143 6 8 0.139 +0.083 -0.093 0.053 8 12 -0.190 +0.089 -0.098 0.034 12 17 -0.120 +0.075 -0.079 0.059 17 23 -0.076 +0.083 -0.088 0.064 23 40 0.043 +0.128 -0.128 0.116 TABLE 3S-3-SH : Lambda-theta-phi, Upsilon(3S), s-channel helicity frame PTMIN PTMAX LAMBDA-THETA-PHI +STAT -STAT SYST 0 2 0.434 +0.205 -0.197 0.041 2 4 -0.046 +0.097 -0.097 0.019 4 6 0.077 +0.100 -0.100 0.014 6 8 0.050 +0.086 -0.086 0.007 8 12 0.081 +0.095 -0.094 0.021 12 17 -0.004 +0.090 -0.090 0.018 17 23 0.046 +0.120 -0.119 0.039 23 40 -0.287 +0.164 -0.168 0.093 TABLE 1S-LT : Lambda-tilde, Upsilon(1S), Collins-Soper/s-channel helicity frame PTMIN PTMAX LT-CS +STAT -STAT SYST LT-SH +STAT -STAT SYST 0 2 0.149 +0.169 -0.164 0.054 -0.064 +0.140 -0.136 0.057 2 4 -0.143 +0.079 -0.078 0.057 -0.201 +0.054 -0.053 0.036 4 6 -0.244 +0.074 -0.073 0.062 -0.300 +0.056 -0.055 0.044 6 8 -0.255 +0.090 -0.089 0.063 -0.284 +0.084 -0.082 0.060 8 12 -0.176 +0.079 -0.077 0.039 -0.215 +0.077 -0.074 0.042 12 17 -0.016 +0.113 -0.107 0.058 -0.145 +0.102 -0.098 0.059 17 23 -0.412 +0.172 -0.160 0.072 -0.385 +0.157 -0.146 0.084 23 40 -0.153 +0.335 -0.310 0.074 -0.173 +0.363 -0.302 0.117 TABLE 2S-LT : Lambda-tilde, Upsilon(2S), Collins-Soper/s-channel helicity frame PTMIN PTMAX LT-CS +STAT -STAT SYST LT-SH +STAT -STAT SYST 0 2 0.012 +0.427 -0.392 0.086 0.634 +0.424 -0.390 0.118 2 4 -0.423 +0.189 -0.182 0.047 -0.449 +0.125 -0.120 0.048 4 6 -0.132 +0.190 -0.182 0.107 -0.214 +0.131 -0.125 0.076 6 8 -0.296 +0.190 -0.181 0.120 -0.124 +0.178 -0.169 0.101 8 12 -0.196 +0.162 -0.154 0.044 -0.227 +0.156 -0.151 0.056 12 17 0.086 +0.214 -0.197 0.108 -0.201 +0.193 -0.179 0.109 17 23 0.093 +0.381 -0.333 0.116 -0.020 +0.344 -0.302 0.084 23 40 -0.317 +0.575 -0.465 0.111 0.306 +0.585 -0.521 0.093 TABLE 3S-LT : Lambda-tilde, Upsilon(3S), Collins-Soper/s-channel helicity frame PTMIN PTMAX LT-CS +STAT -STAT SYST LT-SH +STAT -STAT SYST 0 2 2.961 +1.499 -1.201 0.113 3.855 +1.753 -1.335 0.571 2 4 -0.776 +0.326 -0.302 0.071 -0.184 +0.256 -0.236 0.093 4 6 -0.688 +0.307 -0.288 0.207 -0.297 +0.245 -0.228 0.131 6 8 -0.260 +0.304 -0.281 0.178 -0.077 +0.288 -0.259 0.174 8 12 -0.467 +0.212 -0.198 0.058 -0.421 +0.206 -0.193 0.070 12 17 -0.047 +0.270 -0.245 0.127 -0.194 +0.250 -0.231 0.128 17 23 0.064 +0.462 -0.399 0.149 -0.081 +0.426 -0.365 0.142 23 40 -0.046 +0.788 -0.562 0.154 0.278 +0.879 -0.616 0.117