Electron TMDs and Their Theoretical Analysis
Explore the intricate world of Electron Transverse Momentum-Dependent Distributions (TMDs) and their theoretical framework. Delve into TMD structures, correlators in various gauges, and the significance of T-even and T-odd distributions. Discover numerical results, photon TMDs, and insightful conclusions from key scientific studies in the field.
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Presentation Transcript
The electron in three- dimensional momentum space Luca Mantovani 1
Dressed electron! Brodsky, Hwang, Ma, Smith (2000)arxiv:0003082v3 Brodsky, Hwang, Ma, Smith (2000) Hoyer, Kurki (2009) Miller (2014) arxiv:0003082v3 arxiv:0911.3011 arxiv.org:1409.7412 Hoyer, Kurki (2009)arxiv:0911.3011 Miller (2014)arxiv.org:1409.7412 2
WHY ? Dressed electron TMDs Brodsky, Hwang, Ma, Smith (2000)arxiv:0003082 Brodsky, Hwang, Ma, Smith (2000) Hoyer, Kurki (2009) Miller (2014) arxiv:0003082 arxiv:0911.3011 arxiv.org:1409.7412 Hoyer, Kurki (2009)arxiv:0911.3011 Miller (2014)arxiv.org:1409.7412 2
WHY ? Dressed electron TMDs Brodsky, Hwang, Ma, Smith (2000)arxiv:0003082v3 Brodsky, Hwang, Ma, Smith (2000) Hoyer, Kurki (2009) Miller (2014) arxiv:0003082v3 arxiv:0911.3011 arxiv.org:1409.7412 Hoyer, Kurki (2009)arxiv:0911.3011 Miller (2014)arxiv.org:1409.7412 2
Outline Electron TMDs Theoretical framework Numerical Results Photon TMDs Conclusions Bacchetta, Mantovani, Pasquini (2015) arxiv:1508.06964 Bacchetta, Mantovani, Pasquini (2015) arxiv:1508.06964 3
Gauge-invariant correlator: with 6
Feynman gauge Light-cone gauge 7
Gauge photons ?2order, 8
Electron TMDs T-even T-odd Meissner, Metz, Goeke (2000) arxiv.org:0703176 Meissner, Metz, Goeke (2000) arxiv.org:0703176 9
T-odd TMDs of the dressed electron are vanishing! ?2order, 10
Evaluation of 1. LFWF overlap representation Brodsky, Hwang, Ma, Smith (2000) arxiv:0003082v3 Brodsky, Hwang, Ma, Smith (2000) arxiv:0003082v3 11
Evaluation of 2. Feynman diagram approach = = Feynman gauge, with gauge link Light-cone gauge, no gauge link What about the transverse gauge link in LC gauge? 12
Prescription choice for regulariztion Retarted Advanced Principal Value Belitsky, Ji, Yuan (2002) arxiv.org:0208038 Belitsky, Ji, Yuan (2002) arxiv.org:0208038 13
Extra terms from regularization Extra terms from transverse gauge link Retarted Advanced Principal Value The transverse gauge link makes the evaluation of TMDs prescription-independent in the light-cone gauge 14
Results 15
P-wave S-wave 17
Photon TMDs 19
No need for gauge link! are still vanishing T-odd 20
Conclusions TMD of dressed electron for first time; ring-shaped electron Vanishing T-odd TMDs Discussion of gauge-invariance with non-trivial role of gauge link Outlooks Inclusion of end-points Identify observables sensitive to dressed electron TMDs 22
