Report of the fit

Fit summary

Description: MAP21 pion TMDs3
Minimiser: minuit
Random seed: 5814
Maximum values allowed for q_T / Q: 0.3 + 0.6/ Q ]
Percentile cut: 8
Parameterisation: MAPTMDPion3
Initial parameters fluctuations: True
Explicit formula:

f_{\rm NP}(x,\zeta, b_T)= \exp \left( g_{1\pi}(x) b_T^2 / 4 \right) \exp\left[- g^2_2 \log\left(\frac{\zeta}{Q_0^2}\right) b_T^2/4 \right]g_{1\pi}(x) = N_{1\pi} \frac{x^{\sigma_{\pi}}(1-x)^{\alpha^2_{\pi}}}{\hat{x}^{\sigma_{\pi}}(1-\hat{x})^{\alpha^2_{\pi}}}Q_0^2 = 1\;{\rm GeV}^2\hat{x} = 0.1 t_0 prescription: False
## Theory summary

Collinear PDF set: MMHT2014nnlo68cl member 0
Collinear pion PDF set: xFitterPI_NLO_EIG member 0
b^* prescription: bstarmin
Perturbative order: N3LL
Reference value of the fine-structure constant: \alpha(Q = 91.1876\;{\rm GeV}) = 0.00776578395589 (running True)

Global statistical estimators

N_{rep} = 201
\chi_{0}^2 = 1.5455
\chi_{mean}^2 = 1.5509
\langle\chi^2\rangle \pm \sigma_{\chi^2} = 1.5746 \pm 0.0349
\langle E \rangle \pm \sigma_{E} = 2.5298 \pm 0.2367

Parameters

Parameter	Central replica	Average over replicas	Fixed
N_{1\pi}	0.46913915	0.46515638 \pm 0.11839214	False
\sigma_\pi	4.0378396	4.49853325 \pm 2.24574404	False
\alpha_\pi	4.3688834	4.39661602 \pm 1.33581571	False

Fit properties

Table of \chi^2’s

Central-replica \chi^2’s:
Experiment	Number of points	\chi_{D}^2	\chi_{\lambda}^2	\chi^2
E537_Q_4.0_4.5	6	0.604	0.773	1.377
E537_Q_4.5_5.0	7	1.147	1.549	2.696
E537_Q_5.0_5.5	8	1.223	1.01	2.233
E537_Q_5.5_6.0	7	1.733	0.699	2.432
E537_Q_6.0_6.5	9	1.038	0.377	1.415
E537_Q_6.5_7.0	9	0.926	0.179	1.105
E537_Q_7.0_7.5	7	0.82	0.156	0.976
E537_Q_7.5_8.0	6	0.751	0.16	0.911
E537_Q_8.0_8.5	2	0.687	0.04	0.727
E537_Q_8.5_9.0	3	0.412	0.04	0.452
E615_Q_4.05_4.50	7	0.706	1.453	2.158
E615_Q_4.50_4.95	8	0.57	1.175	1.745
E615_Q_4.95_5.40	8	0.128	1.321	1.45
E615_Q_5.40_5.85	9	0.135	1.271	1.406
E615_Q_5.85_6.75	9	0.187	1.442	1.629
E615_Q_6.75_7.65	10	0.157	1.45	1.607
E615_Q_7.65_9.00	12	0.357	1.436	1.793
E615_Q_11.70_13.05	11	0.364	0.355	0.719
Total	138	0.633	0.912	1.545

Mean-replica \chi^2’s:
Experiment	Number of points	\chi_{D}^2	\chi_{\lambda}^2	\chi^2
E537_Q_4.0_4.5	6	0.593	0.727	1.32
E537_Q_4.5_5.0	7	1.149	1.523	2.672
E537_Q_5.0_5.5	8	1.23	0.999	2.229
E537_Q_5.5_6.0	7	1.693	0.701	2.395
E537_Q_6.0_6.5	9	1.036	0.381	1.417
E537_Q_6.5_7.0	9	0.932	0.183	1.115
E537_Q_7.0_7.5	7	0.827	0.158	0.985
E537_Q_7.5_8.0	6	0.766	0.161	0.926
E537_Q_8.0_8.5	2	0.712	0.042	0.754
E537_Q_8.5_9.0	3	0.416	0.04	0.456
E615_Q_4.05_4.50	7	0.813	1.508	2.321
E615_Q_4.50_4.95	8	0.599	1.131	1.73
E615_Q_4.95_5.40	8	0.248	1.278	1.526
E615_Q_5.40_5.85	9	0.167	1.24	1.407
E615_Q_5.85_6.75	9	0.198	1.422	1.62
E615_Q_6.75_7.65	10	0.151	1.453	1.603
E615_Q_7.65_9.00	12	0.31	1.454	1.764
E615_Q_11.70_13.05	11	0.367	0.356	0.723
Total	138	0.645	0.905	1.551

Average-over-replicas \chi^2’s:
Experiment	Number of points	\chi^2
E537_Q_4.0_4.5	6	1.445 \pm 0.154
E537_Q_4.5_5.0	7	2.736 \pm 0.147
E537_Q_5.0_5.5	8	2.267 \pm 0.086
E537_Q_5.5_6.0	7	2.469 \pm 0.099
E537_Q_6.0_6.5	9	1.448 \pm 0.049
E537_Q_6.5_7.0	9	1.132 \pm 0.035
E537_Q_7.0_7.5	7	0.999 \pm 0.032
E537_Q_7.5_8.0	6	0.928 \pm 0.022
E537_Q_8.0_8.5	2	0.742 \pm 0.036
E537_Q_8.5_9.0	3	0.457 \pm 0.006
E615_Q_4.05_4.50	7	2.193 \pm 0.157
E615_Q_4.50_4.95	8	1.754 \pm 0.111
E615_Q_4.95_5.40	8	1.478 \pm 0.091
E615_Q_5.40_5.85	9	1.444 \pm 0.053
E615_Q_5.85_6.75	9	1.67 \pm 0.05
E615_Q_6.75_7.65	10	1.637 \pm 0.041
E615_Q_7.65_9.00	12	1.823 \pm 0.078
E615_Q_11.70_13.05	11	0.722 \pm 0.006
Total	138	1.575 \pm 0.035

TMDs in k_T space

TMD PDFBEAM of the d at Q = 2 GeV and x = 0.05

TMD PDFBEAM of the d at Q = 2 GeV and x = 0.1

TMD PDFBEAM of the d at Q = 2 GeV and x = 0.2

TMD PDFBEAM of the d at Q = 10 GeV and x = 0.05

TMD PDFBEAM of the d at Q = 10 GeV and x = 0.1

TMD PDFBEAM of the d at Q = 10 GeV and x = 0.2

Data-theory comparison

E615_Q_11.70_13.05 data-theory comparison