Effects of Strong Fields in Ultra-Peripheral and Peripheral A+A collisions Daniel Brandenburg Brookhaven National Lab(CFNS ) : Goldhaber Fellow RHIC & AGS Users’ Meeting 2020 October 22nd, 2020 (via ZOOM) Motivation for Directly Measuring the Magnetic Field DK, L.McLerran, H.Warringa NPA‘0 Predicted emergent magnetohydrodynamical Chiro-genesis in Heavy Ion Collisions phenomena of Quantum Chromodynamics oManifestations require ultra-strong magnetic fields oE.g. Chiral Magnetic Effect oMajor goal of RHIC heavy-ion program o Dedicated Isobar run in 2018 Dima Kharzeev’s Quark Matter 2019 talk: K.Fukushima, DK, H.Warringa, “Chiral magnetic effect” PRD’08 October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 2 Ultra-Relativistic Heavy-Ion Collisions Ultra-relativistic charged nuclei produce highly Lorentz contracted electromagnetic field � ≈ � �� ≈ 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 � ≈ � Study unique features of QED under extreme conditions � � October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 3 Photon-Photon fusion (Breit-Wheeler Process) Weizsäcker, C. F. v. Zeitschrift für Physik 88 (1934): 612 Weizäcker-Williams Equivalent Photon Approximation (EPA) → In a specific phase space, transverse EM fields can be quantized as a flux of real photons Photon number density related to field strength (Poynting Vector) ( * * � ∝ �⃗ = �×� ≈ � ≈ � )! Traditional EPA calculations (e.g. STARLight[1]) Photon-photon fusion into lepton anti-lepton pair have predicted cross section correctly for decades Characterized by �!�" pair → so what is new? with very small �� [1] S. R. Klein, et. al. Comput. Phys. Commun. 212 (2017) 258 October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 4 Photon-Photon fusion (Breit-Wheeler Process) Weizsäcker, C. F. v. Zeitschrift für Physik 88 (1934): 612 Weizäcker-Williams Equivalent Photon Approximation (EPA) → In a specific phase space, transverse EM fields can be quantized as a flux of real photons What’s new? 1. Pair �- shows impact parameter dependence → Sensitivity to the field mapping 2. Azimuthal angle correlation in daughter leptons → Quantum position-momentum correlations Use these to experimentally constrain the initial Photon-photon fusion into lepton anti-lepton pair EM fields Characterized by �!�" pair with very small �� October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 5 Surprising result in Peripheral Collisions ! " ! " STAR Measurement of � � at low �� ATLAS Measurement of � � at small acoplanarity 10 s 600 2 α Centrality: 60-80% 0.4-0.76 GeV/c N 2 -2 d d 0 - 10 % 0.76-1.2 GeV/c ´ 10 10 - 20 1%�� 20 - 40 % 40 - 80 % -1 Solid: Au+Au 200 GeV 10 2 -4 s Open: U+U 193 GeV 1.2-2.6 GeV/c ´ 10 1 ATLAS Pb+Pb data ) N Au+Au Cocktail � �� 400 -1 10-3 sNN = 5.02 TeV > 80% data -1 Pb+Pb, 0.49 nb 10-5 ((GeV/c) STARlight + 200 T data overlay 10-7 dN/dp 0 10-9 pe >0.2 GeV/c, |he|<1, |yee|<1 0 0.005STAR 0.01 T0.015 0 0.005 0.01 0.015 0 0.005 0.01 0.015 0 0.005 0.01 0.015 10-11 0 0.2 0.4 α 0.6 0.8 1 α α α s 80 p (GeV/c) A T N d d 0 - 10 % 10 - 20 % 20 - 40 % 40 - 80 % ! " s � Pairs with small acolanarity � − � � 1 Strong excess at low $ over hadronic $ N 60 Pb+Pb data � ATLAS � = 1 − ∝ cocktail observed in peripheral collisions (proxy to pair $) observed � � in peripherals = collisions 5.02 TeV > 80% data 40 NN -1 [1] STAR, Phys. Rev. Lett. 121 (2018) 132301 [2] ATLAS,Pb+Pb, Phys 0.49. Rev. nb Lett. 121, 212301 (2018)STARlight + 20 →Photon-photon fusion even in peripheral collisions with hadronic overlap?data overlay 0 0 0.05 0.1 0 0.05 0.1 0 0.05 0.1 0 0.05 0.1 A A A A October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 6 Surprising result in Peripheral Collisions ! " ! " STAR Measurement of � � at low �� ATLAS Measurement of � � at small acoplanarity - s 600 10 1 α gg®ee (Zha et al.) N Centrality: 60-80% d e gg®ee (Zha et al.) with EM d p0>0.2 - 10GeV/c % 10 - 20 1%�� 20 - 40 % 40 - 80 % T gg®ee (STARlight) e ee s ) -2 |h |<1, |y |<1 1 10 -2 ATLAS Pb+Pb data N STAR � �� 400 s = 5.02 TeV > 80% data -3 NN 10 (a) (b) -1 2 2 Pb+Pb, 0.49 nb 0.4-0.76 GeV/c 0.76-1.2 GeV/c STARlight + dy) ((GeV/c) 0 0.002 0.004 0.006 0.008 200 2 T 2 p2 ((GeV/c)Au+Au )200 GeV p2 ((GeV/c)2) T U+U 193 GeV T data overlay 70 -3 N/(dp 10 2 60 d 0 50 (MeV/c) ñ 2 T (c) p 40 0 0.005 0.01 0.015á 0 0.005 (d) 0.01 0.015 0 0.005 0.01 0.015 0 0.005 0.01 0.015 1.2-2.6 GeV/c2 -4 30 10 0 0.002 0.004 0.006 α 0.5 1 1.5 2 2.5 α α α s 80 2 2 2 p ((GeV/c) ) Mee (GeV/c ) A N T d d 0 - 10 % 10 - 20 % 20 - 40 % 40 - 80 % ! " s � Pairs with small acolanarity � − � � 1 Strong excess at low $ over hadronic $ N 60 Pb+Pb data � ATLAS � = 1 − ∝ cocktail observed in peripheral collisions (proxy to pair $) observed � � in peripherals = collisions 5.02 TeV > 80% data 40 NN -1 [1] STAR, Phys. Rev. Lett. 121 (2018) 132301 [2] ATLAS,Pb+Pb, Phys 0.49. Rev. nb Lett. 121, 212301 (2018)STARlight + 20 →Photon-photon fusion even in peripheral collisions with hadronic overlap?data overlay 0 Traditional EPA calculation cannot describe �� or � distribution 0 0.05 0.1 0 0.05 0.1 0 0.05 0.1 0 0.05 0.1 A A A A October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 7 Is the broadening due to final state, medium effects? 188 L. McLerran, V. Skokov / Nuclear Physics A 929 (2014) 184–190 • Idea: Extremely small �" → easily deflected by relatively small perturbations • Two proposals from different groups: vacuum 1. Lorentz-Force bending due to long-lived magnetic field [1] STAR, Phys. Rev. Lett. 121 (2018) 132301 2. Coulomb scattering through QGP medium [2] S. R. Klein, et. al, Phys. Rev. Lett. 122, (2019), 132301 [3] ATLAS, Phys. Rev. Lett. 121 (2018) , 212301 Fig. 1. Magnetic field for static mediumL. with McLerran, Ohmic V. conductivity,Skokov, Nuclearσ . Physics A 929 (2014) 184–190 Ohm The decay of the conductivity owing to expansion of the medium can only decrease the life- time of the magnetic field and thus will not be considered here. Our simulations are done for Au–Au collisions at energy √s 200 GeV and fixed impact parameter b 6fm.InFig. 1 we October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 8 show time evolution of the magnetic= field in the origin x 0asafunctionoftheelectriccon-= ⃗ = 2 ductivity σOhm.Theresultsshowthatthelifetimeofthestrongmagneticfield(eB > mπ ) is not affected by the conductivity, if one uses realistic values obtained in Ref. [5]. 4. Energy dependence In the previous section, we established that for realistic values of the conductivities the elec- tromagnetic fields in heavy-ion collisions are almost unmodified by the presence of the medium. Thus one can safely use the magnetic field generated by the original protons only. This magnetic field can be approximated as follows 1 cZ eB(t,x 0) , (18) ⃗ = = γ t2 (2R/γ )2 + where Z is the number of protons, R is the radius of the nuclei, γ is the Lorentz factor and, finally, c is some non-important numerical coefficient. We are interested on the effect of the magnetic field on the matter, otherwise the magnetic field does not contribute to photon production. Thus we need to compute the magnetic field at the time tm,characterizingmatterformationtime. 1 On the basis of a very general argument, one would expect that tm aQs− .Hereweassumed that the Color Glass Condensate (CGC) provides an appropriate description= of the early stage of heavy ion collisions, namely Qs ΛQCD;intheCGCframework,owingtothepresenceof only one dimensional scale, the matter≪ formation time is inversely proportional to the saturation scale. We also note that if the formation time for a particle is much less than this, the magnetic field has a correspondingly larger effect, as the magnetic field is biggest at early times. The phenomenological constraints from photon azimuthal anisotropy at the top RHIC energy demand RHIC tm 2R/γRHIC,i.e.a 2RQ /γRHIC.Usingthisrelation,wecanestimatethemagnitudeof ≈ = s Equivalent Photon Approximation • Traditional Equivalent Photon Approximation (EPA) has been used to describe cross section successfully (∼ ±30% level) for years üTake impact parameter (�) into account for photon flux ✗BUT, treats photons as plane waves with � = ��̂ • In this treatment photon �- must result from virtuality → No �-dependenCe on kinematiCs (��, �, etC) • Until recently there was no data to test the validity of these assumptions o E.g. past ATLAS UPC measurements agree with STARLight but resolution effects are significant, obscure the physics o Past STAR measurements – insufficient statistical precision [1] S. R. Klein, et. al. Comput. Phys. Commun. 212 (2017) 258 October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 9 ! " �� �� → � � ⁄��# B o STAR’s excellent �- resolution → 5 STAR directly measure pair �- Au+Au UPC o High precision data – test various 4 gg® e+e- (STARLight) theory predictions/assumptions 3 arXiv : 1910.12400 (mb/(GeV/c)) ) - o STARLight predicts significantly e + 2 lower ⟨�<⟩ than seen in data e ® dP g 1 g 2 0.4 < Mee < 0.76 GeV/c o Is the increased �< observed due to ( s significant virtuality? d 0 0 0.02 0.04 0.06 0.08 0.1 o Let’s look at how the calculation is P (GeV/c) done in the lowest order QED case QED and STARLiGHt are scaled to matcH measured �(�� → �!�") STARLiGHt: S.