Probing Extreme Electromagnetic Fields with the Breit-Wheeler Process Daniel Brandenburg, for the STAR Collaboration (Shandong University & BNL/CFNS) March 3, 2020 36th Winter Workshop on Nuclear Dynamics Puerto Vallarta, Mexico Outline of this Talk 1. Intro: What is the Breit-Wheeler Process? 2. Results from STAR Collaboration 3. Vacuum Birefringence in Extreme Magnetic Fields 4. The Magnetic Field in Heavy Ion Collisions 1. Measuring the “Initial” (� = 0) Magnetic Field 2. Evidence for Long-lived Magnetic Field or Medium Effects? 5. Conclusions 3/3/20 Daniel Brandenburg 2 Fundamental Interactions : Light & Matter � �⋆ �% Photo Electric Effect Bremsstrahlung Compton Scattering 1887 Hertz, Ann Phys 1895 Röntgen, Ann Phys 1906 Thomson, Conduction of (Leipzig) 31, 983 (Leipzig) 300, 1 Electricity through Gases Bethe-Heitler Pair Single Photon Dirac Annihilation Breit-Wheeler Production Annihilation 1934, Klemperer, pair production 1932, Anderson, 1933, Blackett & Proc Camb Phil Predicted 1934 Science 76,238 Occhialini, Proc R Soc 30, 347 Soc Lond A 139, 699 February 5, 2020 Daniel Brandenburg Based on slide by O. Pike 3 The Breit-Wheeler Process : �� → �)�% �- �/ o Breit-Wheeler process is by definition the lowest-order, tree level process o Two diagrams contribute at the lowest-order o t-channel process, specifically note: �+ = �-+ + �/+ February 5, 2020 Daniel Brandenburg 4 Ultra-Peripheral Heavy-Ion Collisions Ultra-relativistic charged nuclei produce highly Lorentz- contracted electromagnetic field Weizäcker-Williams Equivalent Photon Approximation (EPA): � ≈ � → In a specific phase space, transverse EM fields can be quantized as a flux of real photons Weizsacker̈ , C. F. v. Zeitschrift fur̈ Physik 88 (1934): 612 - / / � ∝ �⃗ = �×� ≈ � ≈ � � CD �� ≈ 1 → High photon density Ultra-strong electric and magnetic fields: � ≈ � → Expected magnetic field strength � ≈ ���� − ���� T Skokov, V., et. al. Int. J. Mod. Phys. A 24 (2009): 5925–32 � � Test QED under extreme conditions 3/3/20 Daniel Brandenburg 5 �� → �)�% Process in UPCs ´103 Zero Degree Calorimeter 60 Au+Au UPC Data 1 neutron 50 2 neutrons 40 3 neutrons 4 neutrons 30 Total Fit 20 dN/d(ADC Sum West ZDC) 10 0 200 400 600 800 1000 1200 ADC Sum West ZDC Breit-Wheeler �� → �)�% Mutual Coulomb excitation and pair production process nuclear dissociation • Provides efficient trigger condition →Provides high statistics sample (>6,000 �)�% pairs from data collected in 2010) → Allows for multidifferential analysis February 5, 2020 Daniel Brandenburg 6 Total �� → �)�% cross-section in the STAR Acceptance A Pure QED 2 → 2 scattering : )) 1 arXiv : 1910.12400 %M %M 2 STAR ��⁄�� ∝ � ≈ � Au+Au UPC gg® e+e- (QED) No vector meson production gg® e+e- (gEPA) → Forbidden for real photons with -1 10 gg® e+e- (STARLight) helicity ±1 (i.e. 0 is forbidden) Scale Uncertainty : ± 13% (mb/(GeV/c ) - e ) % + � �� → � � in the STAR Acceptance: -2 e 10 Data : 0.261±0.004 (stat.) ± 0.013 e ® P > 0.2 GeV/c & |he| < 1.0 dM (sys.) ± 0.034 (scale) mb g ee g |y | < 1.0 & P < 0.1 GeV/c STARLight gEPA QED ( s -3 0.22 mb 0.26 mb 0.29 mb d 10 0.5 1 1.5 2 2.5 M (GeV/c2) Measurement of total cross ee section agrees with theory STARLight: S. R. Klein, et. al. Comput. Phys. Commun. 212 (2017) 258 gEPA & QED : W. Zha, J.D.B., Z. Tang, Z. Xu arXiv:1812.02820 [nucl-th] calculations at ±�� level February 5, 2020 Daniel Brandenburg 7 Toy MC setup ØIn e+e- pair rest frame, the . is defined as the angle between positron momentum and the beam line • The . distribution for the --->e+e- has e+e- pair mass dependence �� �� → �)�%• The ⁄�cos���. distribution for the hadronic �S two-body decay is flat C 1 �� → �)�% : Individual �)/�% preferentially arXiv : 1910.12400 STAR 2 aligned along beam axis [1]: Mee = 2 GeV/c 0.4 Au+Au2 UPC 0.8 (mb) Mee = 1.2 GeV/c - gg2® e+e (XnXn)´0.88 ) / / - Mee = 0.4 GeV/c 4� 4� e 2 + - / / + Isotropic e e / 1 − / sin � cos � + / Mee = 0.01 GeV/c 4� � � ')| 0.3 e � � = 2 + 4 1 − 0.6 q / / / � ® 4� / → 1 − 1 − / cos � NOTE: for virtual photons � g g 0.2 isotropic (flat) distribution 0.4( d|cos( s o Highly virtual photon interactions should d have an isotropic distribution 0.1 0.2 2 0.4 < Mee < 0.76 GeV/c o Measure �S, the angle between the �) and the beam axis in the pair rest frame. 0 0 0 0.2 0.4 0.6 0.8 0 0.5 1 1.5 2 2.5 3 12/6/17 |cos(q')| 3 q for gg->e+e- process [1] S. Brodsky, T. Kinoshita and H. Terazawa, Phys. Rev. D4, 1532 (1971) STARLight: S. R. Klein, et. al. Comput. Phys. Commun. 212 (2017) 258 February 5, 2020 Daniel Brandenburg 8 �� �� → �)�% ⁄���� �S C �� → �)�% : Individual �)/�% preferentially arXiv : 1910.12400 STAR aligned along beam axis [1]: 0.4 Au+Au UPC (mb) gg® e+e- (XnXn)´0.88 ) / / - 4� 4� e + - / / + Isotropic e e / 1 − / sin � cos � + / 4� � � ')| 0.3 e � � = 2 + 4 1 − q / / / � ® 4� / 1 − 1 − / cos � � g g 0.2 ( d|cos( s o Highly virtual photon interactions should d 0.1 have an isotropic distribution 2 0.4 < Mee < 0.76 GeV/c o Measure �S, the angle between the �) and the 0 beam axis in the pair rest frame. 0 0.2 0.4 0.6 0.8 |cos(q')| ⇒Data are fully consistent with �(�) distribution expected for �� → �)�% [1] S. Brodsky, T. Kinoshita and H. Terazawa, Phys. Rev. D4, 1532 (1971) ⇒Measurably distinct from isotropic STARLight: S. R. Klein, et. al. Comput. Phys. Commun. 212 (2017) 258 distribution February 5, 2020 Daniel Brandenburg 9 ) % �� �� → � � ⁄��+ B arXiv : 1910.12400 o High precision data – test theory 5 STAR predictions Au+Au UPC o STARLight predicts significantly 4 gg® e+e- (STARLight) lower ⟨�+⟩ than seen in data 3 arXiv : 1910.12400 (mb/(GeV/c)) ) - e + 2 e ® dP g 1 g 2 0.4 < Mee < 0.76 GeV/c ( s d 0 0 0.02 0.04 0.06 0.08 0.1 P (GeV/c) QED and STARLight are scaled to match measured �(�� → �)�%) STARLight: S. R. Klein, et. al. Comput. Phys. Commun. 212 (2017) 258 QED : W. Zha, J.D.B., Z. Tang, Z. Xu arXiv:1812.02820 [nucl-th] February 5, 2020 Daniel Brandenburg 10 ) % �� �� → � � ⁄��+ B arXiv : 1910.12400 o Data are well described by 5 STAR leading order QED ) % Au+Au UPC calculation (�� → � � ) with + - 4 gg® e e (QED) quasi-real photons + - gg® e e (STARLight) o STARLight predicts significantly 3 arXiv : 1910.12400 (mb/(GeV/c)) lower ⟨�+⟩ than seen in data ) - STARLight calculations do not have e o + 2 centrality-dependent �+ e distribution ® dP g 1 g 2 0.4 < Mee < 0.76 GeV/c ( s o Experimentally investigate d 0 0 0.02 0.04 0.06 0.08 0.1 impact parameter dependence : P (GeV/c) Compare UPC to peripheral ) % → QED and STARLight are scaled to match measured �(�� → � � ) collisions (come back to later) STARLight: S. R. Klein, et. al. Comput. Phys. Commun. 212 (2017) 258 QED : W. Zha, J.D.B., Z. Tang, Z. Xu arXiv:1812.02820 [nucl-th] 11/05/19 Daniel Brandenburg 11 Classical Electromagnetism • Maxwell’s equations are linear ØSuperposition principle holds 1 �/ �ℒfghiijfhg ℒ = − �/ � = � = �l� fghiijfhg / �� 2�l � 1 �ℒfghiijfhg � = � � = − �l �� → Unique speed of light in vacuum: - � = = 299792458 m/s qDCD February 5, 2020 Daniel Brandenburg 12 Quantum Electrodynamics Three important discoveries that alter the classical picture: o Einstein’s energy-mass equivalence: � = ��/ o Uncertainty principle: Δ�Δ� ≥ ℏ/2 Einstein o Existence of positron : Dirac predicts negative electron energy states (1928), Anderson discovered positron in 1932 Anderson February 5, 2020 Daniel Brandenburg 13 Quantum Electrodynamics Three important discoveries that alter the classical picture: o Einstein’s energy-mass equivalence: � = ��/ o Uncertainty principle: Δ�Δ� ≥ ℏ/2 Einstein o Existence of positron : Dirac predicts negative electron energy states (1928), Anderson discovered positron in 1932 → Vacuum fluctuations o 1936: Euler & Heisenberg present modified Lagrangian | | / - z / }~ z / z ℒz{ = | − � + | − � + 7 ⋅ � + ⋯ /CD f CD f f Anderson oNon-linear → Superposition principle is broken! NB: in 1951 Shwinger derived the Lagrangian within QED formalism February 5, 2020 Daniel Brandenburg 14 Vacuum Magnetic Birefringence - � = BUT � ≠ � and � ≠ � qC ∥ + ∥ + Light behaves as if it is traveling through a medium with an index of refraction �ƒhf ≠ 1 Guido Zavattini ICNFP2019 February 5, 2020 Daniel Brandenburg 15 wikipedia Optical Birefringence Birefringent material: Different index of refraction for light polarized parallel (�∥) vs. perpendicular (�+) to material’s ordinary axis → splitting of wave function when �� = �∥ − �+ ≠ � Birefringent Material Linearly polarized (vertical) Ordinary ray Extra-ordinary ray Linearly polarized (horizontal) February 5, 2020 Daniel Brandenburg 16 Vacuum Birefringence Vacuum birefringence : Predicted in 1936 by Heisenberg & Euler. Index of refraction for � interaction with �-field depends on relative polarization angle i.e. �� = �∥ − �+ ≠ � Empty space + R. P. Mignani, et al., Mon. Not. Roy. Astron. Soc. 465 (2017), 492 Ultra-strong Magnetic Field Linearly polarized (vertical) Linearly polarized (horizontal) February 5, 2020 Daniel Brandenburg 17 Birefringence of the QED Vacuum Vacuum birefringence : Index of refraction Feynman Diagram for Vacuum Birefringence for � interaction with �-field depends on relative polarization angle i.e. �� = �∥ − �+ ≠ � � from � Lorentz contraction of EM fields → Quasi-real photons should be linearly polarized (� ⊥ � ⊥ �) Recently realized that a consequence of Probe � Observed � ) % �∥ − �+ ≠ � in �� → � � collisions is a ��� ��� modulation [3] between the pair momentum and the daughter momentum. ����(�) = transmission process �� → �� ����(�) = absorption process �� → �)�% (diagram cut) Can we observe vacuum birefringence [1]S. Bragin, et. al., Phys. Rev. Lett. 119 (2017), 250403 [2]R. P. Mignani, et al., Mon. Not. Roy. Astron. Soc. 465 (2017), 492 in ultra-peripheral collisions? [3] C. Li, J. Zhou, Y.-j. Zhou, Phys. Lett. B 795, 576 (2019) February 5, 2020 Daniel Brandenburg 18 [1] C.