Effects of Strong Fields in Ultra-Peripheral and Peripheral A+A Collisions

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 Pb+Pb, 0.49 nb-1 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 0.05 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

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 electromagnetic 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. 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] October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 10 Pair �! and impact parameter B Impact Parameter Dependence 5 STAR gEPA 1 gEPA 2 QED Data Mass Range 80 2 Au+Au UPC 0.4 < Mee < 0.76 GeV/c

+ - (MeV/c)

ñ 2 gg® e e (QED) 0.76 < Mee < 1.2 GeV/c

4 2 + - 70 gg® e e (STARLight) P 2 á 1.2 < Mee < 2.6 GeV/c 3 arXiv : 1910.12400 (mb/(GeV/c)) 60 Au+Au 200 GeV ) - e

+ p > 0.2 GeV/c 2 T,e e

50 |y | < 1; |h | < 1

® ee e

dP g 1

g 2 0.4 < Mee < 0.76 GeV/c 40 ( s

d 0 Zha, W., Brandenburg, J. D., Tang, Z. & 0 0.02 0.04 0.06 0.08 0.1 Xu, Z. Phys. Lett. B 800, 135089 (2020). 30 P (GeV/c) 0 10 20 30 40 b (fm) QED (and gEPA parameterization) describe data Note: gEPA1 vs. gEPA2 : gEPA2 includes Larger ⟨� ⟩ from impact parameter dependence phase term to approximate full QED result not a result of significant photon virtuality

o QED calculation predicts impact parameter dependence → dependence on the overlapping ﬁeld strengths. Can the QED describe the peripheral data? October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 11 3 QED Calculation & Peripheral Data 5

400 400 -2 α Pb + Pb 5.02 TeV 0 - 10%α Pb + Pb 5.02 TeV 10 - 20% α Pb + Pb 5.02 TeV40 - 80% α Pb + Pb 5.02 TeV > 80% d d d d dN dN dN 600 dN 600

350 2 350 2

1 4 < M < 45 GeV/c 1 1 4 < M < 45 GeV/c 1 −1 N µµ data N N µµ data N 10 Au + Au 200 GeV p Au > 4 +GeV/c Au | η200| < 2.4 GeV Au + Au500 200p >GeV 4 GeV/c |η | < 2.4 500 data 300 T,µ µ 300data T,µ µ data 10−2 Centrality: 60 - 80% STARLight 250 Centrality: 60 - 80%QED 250STARLight Centrality:400 60 - 80% STARLightQED 400 gEPA 1 200 200gEPA 1 gEPA 1

dy (GeV/c) gEPA 2 300 gEPA300 2 T 2 gEPA 2 150 150gEPA 2 gEPA 2 QED 100 100QED 200 QED 200 N/dP

2 50 50 100 100

d −2 −3 10 0 0 10 0 0 0 0.005 0.01 0.005 0.01 0.015 0 0.005 0.01 0.005 0.01 0.015 p > 0.2 GeV/c p > 0.2 GeV/c p > 0.2 GeV/c T,e T,e α α T,e α α |y | < 1; |η | < 1 |y | < 1; |η | < 1 |y | < 1; |η | < 1 ee e 10−3 ee e ee e 2 FIG. 3. The distributions of the2 broadening variable, ↵, from the generalized2 EPA approach (gEPA2, dash blue lines) and 0.4 < Mee < 0.76 (GeV/c ) • 0.76Peripheral < Mee < 1.2 data(GeV/c from) both STAR 1.2 < Mee < 2.6 (GeV/c ) QED (solid red line) for muon pairs in Pb+Pb collisions at psNN = 5.02 TeV for di↵erent centrality classes. The results are

10−3 and ATLAS are well described by

0 0.002 0.004 0.006 ﬁltered0 with the0.002 ﬁducial cuts0.004 described in the0.006 text and0 normalized0.002 to unity to facilitate0.004 a direct0.006 comparison with experimental

T T 2T 2 data. TheQED measurements calculation from ATLAS [25] are also plotted for comparison. P (GeV/c) P2 (GeV/c)2 P2 (GeV/c)2 • ATLAS has newer high precision 2 ⌫ FIG.Physics 1. Letters The B P800 distributions(2020) 135089 of electron-positronlution.data It pair should production be noted within that ⇡↵ the STARP /M acceptancell in a de- for theliding mass nucleiregions maintain 0.4 0.76 their velocities (a (ki ui⌫ ) ? 2 ' ? (left panel), 0.76 1.2(middlepanel),and1tector.2 setup2.6GeV where/c the(right sagitta panel) of a in particle 60 80% trajectory Au+Au is collisionsfunction) at psNN to=200GeV. simplify the calculation. In central TheOctober STAR 22, 2020 measurements [24] and calculationsDaniel Brandenburgmuch from larger | BNL gEPA1,(CFNS) than / SDU the gEPA2, e↵ect of QED multiple and STARLight scattering in [15] the12 are alsocollisions, plotted for where comparison. the photon flux are generated See text for details of the models. detector material and from resolution of the experimen- predominantly by the participant nucleons, charge tal measurements, as is the case for the STAR Detector stopping may be an important correction to the within the measured kinematic range. The measured ↵ initial electromagnetic fields. distributions show broadening in hadronic Pb+Pb colli- and the subsequent result reads: sions with respect to UPCs.lowest Figure order 3 shows is the ↵ dis- omission of higher order contribution and multiple • pair production: tributions from our calculations in Pb+Pb6 collisions at d P (~q) 4 4 We1 have ignored2 higher-order corrections in both psNN = 5.02 TeV for di↵erent centrality classes. The re- 4 4 2 2 2 2 3 3 =(Z↵) 2 6the initial electromagneticd q1 field [10] and Sudakov Z e dw1 dw2 d k1 d k2 sultsF ( arek1 filtered) with the fiduciald cuts:p+dpTµp > 4 GeV/c, (2⇡) 2✏+2✏ = 16 ? ? e↵ect [33], Z which should be quite small in the low 2 2 2 and ⌘µ2 < 2.4, and normalized to facilitate a direct com- 1 (4⇡) w1 w2 (2⇡) (2⇡) |k1| F (N0)F (N1)F (N3)F (N4)[NP0Nand1N3 smallN4]↵ range. It has been pointed out that Z parison with experimental(6) data from ATLAS. The mea- ? 2 2 1 there may be significant multiple pair production F ( k2) 2 2 surements from ATLAS [25] can be wellTr described(p + m by)[N the u/ (p q + m)u/ + k k (w ,w ) / 2D 1 / in/ the1 same event2 [36],(8) which may complicate the 2 1 2 gEPA2 1 and2 QED calculations within⇥ uncertainties.{ ⇥ k2 ? ? 1 calculation1 and measurement. There have been proposals in theN literatureu/ (q regardingp + m)u/ ](p m)[N u/ 2X 2 /1 /+ 1 /+ 5D 2 possible final-state e↵ects to explain the P broadening. final-state e↵ects of magnetic field deflection and ? •1 Two such proposals are that the(p/ broadening/q /q is+ duem) tou/ + N5X umultiple/ (/q + Coulomb/q p/ scattering: where (w1,w2) is the cross-section averaged over the 1 1 1 1 + deflection by the residual magnetic field trapped in an The STAR and ATLAS collaborations have demon- scalar and pseudoscalar polarization. This is exactly the + m)u/ ] , electrically conducting QGP [24, 37] or due2 } to multiple strated that it is possible to identify and measure EPA expression commonly used in the literatureCoulomb and scattering used in the hot and dense medium [25, the Breit-Wheeler process accompanying the cre- in comparison to recent experiments [6].33]. The All the spectral proposed mechanismswith including this study ation of QGP. This opens new opportunity using shape [15, 33], which is insensitive to therequire collision extraordinarily cen- strong electromagnetic2 fields, an this2 process as a probe of emerging QCD phenom- interdisciplinary subject of intenseN0 = interestq1,N1 across= many[q1 (p+ + p )] , trality, is the result of integrating over the whole impact ena [8]. scientific communities. There are a few assumptions2 and 2 parameter space as shown in Eq. 31 to Eq. 32 [9] and N3 = (q1 + q) ,N4 = [qIn+( summary,q1 p+ wep study)] , the impact-parameter depen- caveats in our calculation which deserve further studies: 2 2 dence of the Breit-Wheeler process in heavy-ion collisions subsequently inserting an impact-parameter dependent N2D = (q1 p ) + m , continuous charge distribution without point-like within the framework of the(9) external QED field and the photon flux (w1,w2,b), as shown in Eq.• 36 to 43 in 2 2 structure: N2X = (q1 p+) + m , approximations used to arrive at the Equivalent Photon Ref. [9]. Approximation, and with a full QED calculation based on It has been shown [38, 39] that the substructures of2 2 N5D = (q1 + q p ) + mtwo, lowest-order Feynman diagrams. We further demon- We have also performed a QED calculationprotons at leading- and quarks in nuclei and their fluctuations can significantly alter the electromagnetic field in-2 strate2 that the P spectrum from the STARLight model order based on Ref [30, 31] and extended its original cal- N = (q + q p ) + m , ? 5X 1 + calculation used by the recent comparisons as a baseline culation to all impact parameters as a functionside the of nucleus the at any given instant. This should result in an observable e↵ect deserving further the- results from averaging over the whole impact parameter transverse momentum of the produced pair. The lowest- where p+ and p are the momenta of the created lep- oretical and experimental investigation. The e↵ect space and is therefore by definition independent of impact order two-photon interaction is a second-order process tons, the longitudinal componentsparameter. of Ourq1 are model given results by can qualitatively describe is most prominent in central1 collisions where the with two Feynman diagrams contributing, asATLAS shown results in haveq10 large= uncertainties[(✏+ + ✏ )+ and where(p+z + pbothz)], theq1Pz =broadeningq10/, ✏+ observedand at RHIC as well as the 2 ? Fig. 2 of Ref. [30, 31]. Similarly, the straight-lineSTAR approx- currently lacks✏ theare necessary the energies statistics of the for a producedacoplanarity leptons, broadening and m observedis the at the LHC. It provides measurement. mass of lepton. In the calculationa practical of P (~q procedure), the traces for studying and the Breit-Wheeler pro- imation for the incoming projectile and target nuclei is cess with ultra-strong electromagnetic fields in a control- applied as in the case of all EPA calculations.projectile Otherwise, and targetmatrices nuclei maintain have been the same handled ve- bylable the fashion. Mathematica This outcome package indicates that the broaden- a full QED calculation of the di↵erential• cross-sectionlocity vector beforeFeynCalc and after collision: [34]. The multi-dimensionaling originates integration predominantly is per- from the initial electromag- with two photons colliding to create two leptonsThe has very been first assumptionformed in with Eq. 1 is the that Monte both col- Carlonetic (MC) field integration strength that routine varies significantly with impact calculated. Following the derivation of Ref. [30, 31], the VEGAS [35]. cross section for pair production of leptons is given by The gEPA1 and QED calculations are shown in Fig. 1 as dash-dotted and solid lines, respectively, together with experimental data points and the STARLight calcula- 6 ~ 6 2 d P (b) 2 d P (~q) 2 iq~ ~b tions. It is clear that there is a di↵erence between the = d b 3 3 = d q 3 3 d be · , (7) d p+d p d p+d p gEPA1 and the QED calculations. The most striking Z Z Z di↵erence is in the P spectral shape. The QED curves describe the spectra quite? well with a smooth distribution d6P (q~) and the di↵erential probability 3 3 in QED at the d p+d p of the cross-section increasing from high to low P ,but ? Low pT enhancement in peripheral Pb-Pb collisions at sNN = 5.02 TeV QED Calculation & Peripheral Data

• Similar measurement by ALICE in 70 − 90% central collisions • Excess• Low atstatistics very low p T→in �the mass range 2 1.1distribution < mee < 2.7 GeV/ favorsc . QED calculation over traditional • ConsistentEPA with coherent photo-production

• More differential studies: - event plane angle - sensitivity to magnetic field

ALICE Preliminary from QM19

02.June.2020, HP2020 Daiki Sekihata (CNS, the University of Tokyo) 20

October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 13 ⟨QED!core⟩ Calculationvs. neutron & multiplicity CMS UPC Data

-3 PbPb 5.02 TeV (1.5 nb-1) 1.6 ´10 CMS Preliminary • CMS measured � for various 1.5 |y | < 2.4 µµ impact parameter ranges by pµ > 3.5 GeV, |hµ| < 2.4 T tagging the neutron emission

ñ 1.4 8 < Mµµ < 60 GeV

core • Acoplanarity shows impact a á 1.3 parameter dependence in UPC – purely initial state effect 1.2 STARlight

1.1 0n0n 0n1n 0nXn 1n1n 1nXn XnXn • QED calculation also describes this data well, core ØStrong neutron multiplicity dependence of ⟨) see⟩ arxiv:2006.07365 • DeviationShuai Yang, from CMS constant: Preliminary 5.7 from4 HP2020 • b dependence of initial photon pT 6/2/20 Shuai Yang, Hard Probes 2020 18 October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 14 [1] STAR, Phys. Rev. Lett. 121 (2018) 132301 " # [2] S. R. Klein, et. al, Phys. Rev. Lett. 122, (2019), 132301 �� → � � : UPC vs. Peripheral [3] ATLAS Phys. Rev. Lett. 121 (2018) , 212301 Characterize diﬀerence in spectra via ⟨� ⟩ ´10-3 UPC Au+Au 60-80% Au+Au ) �� (MeV/c) arXiv : 1910.12400 -1 5 STAR 1.4 QED Data Au+Au: Measured 38.1 ± 0.9 50.9 ± 2.5 UPC 1.2 4 37.6 48.5 60 - 80% ((GeV/c) QED ) 1 - e (mb/(GeV/c))

+ � range (fm) ≈ 20 ≈ 11.5 − 13.5 ) - 3 e e

+ 0.8 ® e dy

g ® 0.6 g o Leading order QED calculation of

2 dP

g �� → � � describes both spectra (±1�) N(

0.4 2 ( d s 1 0.4 < M < 0.76 GeV/c2 d ee Best ﬁt for spectra in 60-80% collisions found for 0.2 o QED: Scaled by 0.88 QED shape plus 0

UPC: 0 0.02 0.04 0.06 0.08 0.1 14 ± 4 (stat.)±4 (syst.) MeV/c broadening P (GeV/c) 60-80%: o Proposed as a probe of trapped magnetic ﬁeld or Coulomb scattering in QGP [1-3]

QED describes �� spectra in terms of the initial fields! Maybe there is still room for final state effects – test with new ATLAS results (QM19)

October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 15 Connection to the Initial Magnetic Field Magnetic ﬁeld strength and arXiv : 1910.12400 spatial distribution: • Impact parameter dependence of � • Amplitude of azimuthal angular modulation

QED calculations for Breit-Wheeler (�� → �� ) process that use the field map (to the right) describe data ±1�

Peak value for single ion: � ≈ 0.8 ×10 Tesla ≈ 10,000× stronger than Magnetars October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 16 Transverse linearly polarized photons

• Lorentz contraction of EM fields → Quasi-real photons should be linearly polarized in transverse plane (� ⊥ � ⊥ �) • Polarization vector : aligned radially with the “emitting” source • Well defined in the photon position eigenstates • In general event average, washes out polarization effects, since � is random Monday, October 5, 2020 Daniel Brandenburg 17 Transverse linearly polarized photons

��

� � Δ�[�, �]

• Angle between photon polarizations depends on location of produced pair

Monday, October 5, 2020 Daniel Brandenburg 18 Transverse linearly polarized photons

� � � �

Δ�[�, �]

• Angle between photon polarizations depends on location of produced pair

Monday, October 5, 2020 Daniel Brandenburg 19 Experimental Signature of Vacuum Birefringence Optical Theorem

Breit-Wheeler Process

Light-by-Light Scattering Recently realized, Δ� = �∥ − � ≠ 0 leads to a ��(��) modulation in polarized �� → � � [1] The corresponding vacuum LbyL scattering[2] displays a ��(��) modulation [1] C. Li, J. Zhou, Y.-j. Zhou, Phys. Lett. B 795, 576 (2019) [2] Harland-Lang, L. A., Khoze, V. A. & Ryskin, M. G. Eur. Phys. J. C 79, 39 (2019). Δ� = Δ� � + � , � − � ≈ Δ� � + � , � October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 20 [1] C. Li, J. Zhou, Y.-j. Zhou, Phys. Lett. B 795, 576 (2019) Birefringence of the QED Vacuum QED calculation: Li, C., Zhou, J. & Zhou, Y. Phys. Rev. D 101, 034015 (2020). Polarized �� → �� leads to cos 4Δ� 1000 0.45 < M < 0.76 GeV/c2 modulations due to quantum space- / 20) 900 ee STAR p momentum correlations[1] Au+Au UPC Au+Au 60-80% ´ 0.5 � = 200 GeV Total Cross-section Measured STARLight800 gEPA QED Fit: C´( 1 + A cos 2Df + A cos 4Df ) ± 1 s 2Df 4Df Δ� = Δ� �0.261+ � 0.004, � (stat.)− � 700 + ± ( e e)mb 0.013 (syst.) 0.034 (scale) 0.22counts / ( 0.26 0.29 ! ≈±Δ� � + � ±, � 600 Ultra-Peripheral Peripheral HHICs Differential Quantities Total Cross-section Measured STARLight gEPA QED 500 Quantity Measured QED 2/ndf Measured QED 2/ndf 0.261 0.004 (stat.) 400 + ± ( e e)mb 0.013 (syst.)A4 (%)0.034−� (scale)(%) 0.2216 16.8.8 ±2.52.5 2216 0.26.5 18.8 0.29 / 16 27 6 39 10.2 / 17 ! ± | |± ± ± 300

Ultra-PeripheralA2 (%) 2.0Peripheral Peripheral2.4 0 (60 HHICs− 18.880%) / 16 6 6 0 10.2 / 17 Differential Quantities | | ± ± 200 MeasuredP QED2 (MeV/2Quantityc/)ndf Measured 38.1 0.9 37.6 QED —2/ndf 50.9 2.5 48.5 — h ?i ± ±100 + - q Polarized gg ® e e (QED) arXiv : 1910.12400 A (%) 16.8 2.5 22 18.8−� / 16(%) 2727 6± 6 3934.5 10.2 / 17 | 4| ± Table 1: The top row reports± the total measured cross-section within STAR acceptance for + 0 p p e e in (XnXn) events compared with three theory calculations. The lower rows report Df = f - f A (%) 2.0 2.4! 0 18.8 / 16 6 6 0 10.2 / 17 2 ee e | 2| ± measurements of and ± P 2 from UPCs and peripheral HHICs with the corresponding → First Earthh ?i-based observation (�. �� level) of vacuum birefringence P 2 (MeV/c) 38.1 0.9theory 37.6 calculations — where 50.9q applicable.2.5 The 48.5 uncertainties — reported here are the statistical and h ?i ± October 22, 2020± Daniel Brandenburg | BNL (CFNS)2 / SDU 21 q systematic uncertainties added in quadrature. The theory calculations for the P are from h ?i Table 1: The top row reports the totalRef. ( measured24). The QED cross-section calculations within for the STAR modulations acceptance arefor provided by Ref.q (13). + e e in (XnXn) events compared with three theory calculations. The lower rows report ! measurements of and P 2 from UPCs and peripheral HHICs with the corresponding h ?i theory calculations whereq applicable. The uncertainties reported here are the statistical and 2 systematic uncertainties added in quadrature. The theory calculationsSource of for the P are from 2 Distribution h ?i Fit Result /ndf Ref. (24). The QED calculations for the modulations areContamination provided by Ref.q (13).

0 + M ⇢ e e 0.36 1.2 (% of total ) 106 / 98 ee ! ± + ! e e 0.17 0.35 (% of total ) 106 / 98 ! ± + Source of e e +20.57 0.24 (% of total ) 104 / 98 Distribution Contamination Fit Result! /ndf± + 0 + cos ✓0 Isotropic e e +0.9 1.7 (% of total ) 7.7 / 12 M ⇢ e e | 0.36| 1.2 (% of total ) 106 / 98± ee ! ± + P (60 80%) Broadening 14 4 (stat.) 4 (syst.) (MeV/c) 3.4 / 6 ! e e ? 0.17 0.35 (% of total ) 106± / 98 ± ! ± + Table 2: The result from fits to various possible sources of contamination. For each source, the e e +0.57 0.24 (% of total ) 104 / 98 ! given distribution± was fit to the combination of the Breit-Wheeler shape and the listed contam- 2 +ination shape. The /ndf of each fit is also shown. cos ✓0 Isotropic e e +0.9 1.7 (% of total ) 7.7 / 12 | | ± P (60 80%) Broadening 14 4 (stat.) 4 (syst.) (MeV/c) 3.4 / 6 ? ± ± 24 Table 2: The result from fits to various possible sources of contamination. For each source, the given distribution was fit to the combination of the Breit-Wheeler shape and the listed contamination shape. The 2/ndf of each fit is also shown.

24 4

The numerical results for the computed azimuthal asymmetries forthedifferent collisions species and centralities are presented in Figs.2 and 3. Here the azimuthal asymmetries, i.e. the average value of cos 4φ are defined as, dσ cos 4φ d . . cos(4φ) = dP.S. P S (9) ⟨ ⟩ dσ d . . ! dP.S. P S We compute the asymmetry! for two deferent centrality classes as well as for the UPC and the tagged UPC cases. The corresponding impact parameter range for a given centrality class is determined using the Glauber model(see the review article [47] and references therein). For the UPC, the asymmetry is averaged over the impact parameter range [2RA, ]. However, STAR experiments at RHIC measure pair production cross section together with the double electromagnetic∞ excitation in both ions. Neutrons emitted at forward angles by the fragmenting nuclei are measured, and used as a UPC trigger. Requiring lepton pair to be produced in coincidence with Coulomb breakup of the beam nuclei alters the impact parameter distribution compared with exclusive production. In order to incorporate the experimental conditions in the theoretical calculations, one can define a ”tagged” UPC cross section, ∞ 2 2π b⊥db⊥P (b⊥)dσ(b⊥, ...) (10) "2RA where the probability P (b⊥) of emitting a neutron from the scattered nucleus is often parameterized as [48],

3 3 −5 Z (A Z) −5 Z (A Z) P (b⊥)=5.45 10 − exp 5.45 10 − (11) ∗ A2/3b2 − ∗ A2/3b2 ⊥ # ⊥ $ As a matter of fact, the mean impact parameter is dramatically reduced in interactions with Coulomb dissociation. We plot the cos 4φ asymmetry for electron pair production at mid-rapidity as the function of the total transverse momentum q⊥ at the center mass energy √s = 200 GeV in Fig.2. The general trend is that the asymmetry increases when the impact parameter decreases. The overall q⊥ and b⊥ dependent behavior of the asymmetry for the diﬀerent collision species(Au and Ru) are similar, except for that the curves are slightly more ﬂat for the smaller nucleus. The asymmetry reaches a maximal value of 17%–22% percent around q⊥ 30 MeV for the centrality classes [60%-80%], [80%-99.9%],Connection and the tagged to UPC. the For theInitial unrestrictedMagnetic UPC, the as≈ymmetry Field is roughly twice smaller than that in the tagged UPC. The results obtained for di-muon production in Pb-Pb collisions at LHC energy shown in Fig.3 are ratherMagnetic close to these field at RHICstrength energy. and spatial distribution: Li, C., Zhou, J. & Zhou, Y. Phys. Rev. D 101, 034015 (2020). • Illustration to show that Δ�[�, �] changes with � EPA two photon overlap probability More likely � ≈ 20 fm

less likely

More likely

less likely • Amplitude of cos 4Δ� modulation is quite sensitive ! " �→ , to field distribution φ q⊥ Caveat: These do not include integrated s FIG. 2: Estimates of the cos 4 asymmetry as the function of forover the kinematics, diﬀerent only meant centralities as illustration at √ =200GeV.Theelectron and positron rapidities and transverse momenta are integrated over the regions [-1,1], and [0.2 GeV, 0.4 GeV]. The asymmetries October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 22 in Au-Au collisions and Ru-Ru collisions are shown in the leftplotandtherightplotrespectively.

III. CONCLUSIONS

We study the impact parameter dependence of the cos 4φ azimuthal asymmetry for purely electromagnetic lepton pair production in heavy ion collisions at low q⊥. This asymmetry arises from the correlation between the polarization vector of the electric field coherently generated by a fast moving heavy ion and the associated equivalent photon’s transverse momentum. Such correlation reflects the nature of the boosted Coulomb potential. We found that the azimuthal asymmetry has a strong b⊥ dependence. To be more specific, the asymmetry decreases with increasing Summary 1. Many recent exciting developments in photo-processes 2. Experimental & theoretical advances → connection to initial EM field strength & distribution 3. First Earth-based evidence of vacuum birefringence : • Observed by STAR (6.7�) via angular modulations in linear polarized �� → �� process 4. Experimental evidence that HIC produce the strongest magnetic fields in the Universe ≈ 10!" Tesla - over an extensive spatial distribution

A lot more work needed to further constrain magnetic ﬁeld topology and to test for possible medium eﬀects – Exciting opportunities lie ahead

October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 23 Additional Slides

October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 24 [1] STAR, Phys. Rev. Lett. 121 (2018) 132301 10-1 Long-lived Magnetic Field? Centrality: 60-80% gg®ee (Zha et al.) gg®ee (Zha et al.) with EM pe >0.2 GeV/c T gg®ee (STARlight) e ee ) 10-2 |h |<1, |y |<1 ⃗ -2 � = � � + �⃗ ×� STAR � -3 10 (a) (b) 0.4-0.76 GeV/c2 0.76-1.2 GeV/c2

dy) ((GeV/c) 0 0.002 0.004 0.006 0.008

2 T 2 p2 ((GeV/c)Au+Au )200 GeV p2 ((GeV/c)2) T U+U 193 GeV T 70 -3 N/(dp 10 2 60 d 50 (MeV/c) ñ Assumptions: 2 T (c) p 40 á (d) 1.2-2.6 GeV/c2 1. Used STARLight �Spectra 10-4 30 ± 0 0.002 0.004 0.006 0.5 1 1.5 2 2.5 2. All � traverse 1 fm through � ≈ 2 2 2 p ((GeV/c) ) Mee (GeV/c ) 10T (�� ≈ 30 MeV/�) T October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 25 PHYSICAL REVIEW LETTERS 122, 132301 (2019)

−Su Q;mμ;r PT-broadening effects are sensitive to the electromagnetic W b ; r N γγ b ; r e ð ⊥Þ; 2 property of the quark-gluon plasma, whereas the jet ð ⊥ ⊥Þ¼ ð ⊥ ⊥Þ ðÞ

PT-broadening effects depend on the strong interaction where Su is the Sudakov factor and will be presented below. property. The experimental and theoretical investigations of By setting S 0, one gets back to the results in previous u ¼ both phenomena will deepen our understanding of the hot studies [38–41]. The factor N γγ represents the incoming medium created in these collisions. The clear indication of photon flux overlap, lepton PT-broadening effects from ATLAS and STAR [29,30] should stimulate further study on dijet azimuthal 2 2 i k1 k2 ·r correlations in heavy ion collisions. N γγ b ; r xaxb d k1 d k2 e ð ⊥þ ⊥Þ ⊥ ð ⊥ ⊥Þ¼ ⊥ ⊥ The rest of the Letter is organized as follows. We first γZ γ × fA xa;k1 fB xb;k2 b; 3 study the azimuthal angular correlation for dileptons in ½ ð ⊥Þ ð ⊥Þ ðÞ UPCs in Sec. II. Then, we investigate the medium effects, including the QED multiple scattering effects and the where xa k1=PA and xb k2=PB. To simplify the above expression,¼ we have¼ introduced an impact magnetic effects in Secs. III and IV, respectively. Finally, γ γ Sec. V summarizes the paper. parameter b -dependent photon flux: fAfB b 2 2 ⊥ ½ ¼ Lepton pair production in ultraperipheral heavy ion d b1 d b2 Θ b Nγ b1 ;k1 Nγ b2 ;k2 , where ⊥ ⊥ ð ⊥Þ ð ⊥ ⊥Þ ð ⊥ ⊥Þ collisions.—The leading order production of lepton pairs Θ b denotes the impact parameter constraints for a R ð Þ comes from photon-photon scattering, see, Fig. 1(a). The particular centrality with b⃗ b⃗ 1 − b⃗ 2 , and individual ⊥ ¼ ⊥ ⊥ outgoing leptons have momenta p1 and p2, individual photon flux Nγ b1 ;k1 can be computed separately ð ⊥ ⊥Þ transverse momenta p1 and p2 , and rapidities y1 and y2, [38–42]. Here, the interdependence between the impact respectively. The leptons⊥ are produced⊥ dominantly back to parameter bi and the photon’s transverse momentum back in the transverse plane, i.e., p⃗ p⃗ 1 p⃗ 2 ≪ contribution k⊥ is ignored, which could introduce addi- j ⊥j ¼ j ⊥ þ ⊥j i p1 ∼ p2 . The incoming photons have the tional theoretical⊥ uncertainties. j ⊥j j ⊥j following momenta: k P = s ey1 ey2 P and k 1 p A 2 The Sudakov factor Su starts to appear at one-loop order, −y1 −y2 ¼ ⊥ ð þ Þ ¼ P =ps e e PB, where P represents p1 ∼ where soft photon radiations contribute to the dominant ⊥ ð þ Þ ffiffiffi ⊥ j ⊥j p2 , and the incoming nuclei have per-nucleon momenta logarithms in the kinematics of our interest. The typical j ⊥j ffiffiffi PA and PB. In the Sudakov resummation formalism, the Feynman diagrams for the real photon radiation are shown differential cross section can be written as [37] in Figs. 1(b),1(c). Applying the Eikonal approximation, see, e.g., Ref. [43], we obtain − AB γγ →μþμ 2 dσ ½ d r ip ·r σ ⊥ e W b ; r ; 1 2 2 0 2 ⊥ ⊥ 2p1 · p2 dy1dy2d p1 d p2 ¼ 2π ð ⊥ ⊥Þ ðÞ M 1 r 2 e2 M 0 2; 4 ⊥ ⊥ Z ð Þ ðÞ soft ðÞ j ¼ p1 · ksp2 · ks j j ðÞ where b denotes the centrality at a particular impact ⊥ ¯ 0 2 2 4 where M 0 is the leading order Born amplitude and parameter of AA collisions, σ0 MðÞ =16π Q with ðÞ ¯ 2 2 2 2 2 ¼ j j ks is the soft photon momentum. In the small total trans- M0 4π αe2 t u =tu, Q is the invariant massPHYSICAL for REVIEW LETTERS 122, 132301 (2019) thej leptonj ¼ð pair,Þ t andð uþareÞ the usual Mandelstam variables verse momentum region l p ≪ P , we have the 2 2 following behavior from⊥ ¼ the⊥ above⊥ contribution: for the 2 → 2 process.Qse Inr the∼ 1. coordinate Therefore, we space need which to take into account the ⊥ 2 2 2 2 2 allows one to convenientlymultiple take scattering care of effects. the transverse α=π 1=l ln Q =l mμ , where mμ is the lepton If we compare[1] S. R. Klein, the et. above al, Phys. dipole Rev. Lett. to 122, the (2019),ð QCD 132301Þð dipole ⊥Þ ð ⊥ þ Þ momentum conservation, W b ; r is the combination mass and l is related to ks . In order to derive the one- [49,50], we[2] will ATLAS find Phys. Rev. the Lett. following 121 (2018) , 212301 differences. First,⊥ ⊥ Coulomb Scattering ofthrough incoming photon fluxesQGP consideredð ⊥ ⊥Þ in previous studies loop result for Su, we need to Fourier transform the above because the couplings in QED and QCD are dramatically [38 42] and all order Sudakov resummation (see, e.g., expression to the conjugate r space, and add the virtual – different, this introduces a major difference for the medium ⊥ Refs. [21,22,43]), photon contributions. Because of the lepton mass mμ, the • Charged particles may scatter off charge centersPT-broadening in QGP, effects, in modifying addition to the difference in the primordial pair � ? Sudakov effects mentioned above. Second,cancellation the saturation between the real and virtual diagrams will scales depend on the charge density. Sincedepend only onquarks the relative size of μr c0=r and mμ, where −γE ¼ ⊥ carry electric charge, the QED saturation scalec0 will2e dependwith γEFIG.the 3. Euler Medium’s constant. modifications In the to end, the acoplanarity we find distribution, on the quark density, whereas the QCD saturationat one-loop¼ scale order with[37] different, values of the effective qLˆ . depends on both quark and gluon density. Their densities are proportional to the respective degree of freedoms if we αis too2 Q2 small (few percent of the P -broadening value) to (a) (b) (c) − ln 2 ; μr >mμT; PHYSICAL REVIEW LETTERS 122, 132301 (2019)assume the ratio of the thermal distributions of quarks and 2π μr S have any observational effects. 5 21 u 2 2 m2 FIG. 1. The leading ordergluons: and2 next-to-leadingNf∶16 [51]. Here orderNf QEDis the number of active¼ α MediumQ Q effects:μ Magnetic fields.—ThereðÞ has been a ( − 2π ln 2 ln 2 ln 2 ; μr

132301-4 4

×10−3

1.5 3 > 42 40 27 α < 1.45 Pb + Pb 5.02 TeV Au + Au 200 GeV 10

26 × 2 40 2 8 < Mµµ < 60 GeV/c 0.4 < Mee < 2.6 GeV/c > 1.4 > (MeV) (MeV/c)

38 α 2 T 25 > < p 1.35 p > 3.5 GeV/c |η | < 2.4 2 T p > 0.2 GeV/c |η | < 1.0 T,µ µ 38 T,e e 24 <

1n 0n1n 1n>1n 19 1.05 0n>1n >1n>1n 30 0n>1n >1n>1n 18 1 30 12.5 13 13.5 14 14.5 0.62 0.64 0.66 0.68 0.7 2 2 (GeV/c ) (GeV/c )

2 FIG. 3. (Color online) Left panel: the ↵ and pT of muon pairs within the ﬁducial acceptance as a function of average pair h i h i 2 mass, Mµµ ,for di↵erent UPC centrality classes in Pb + Pb collisions at psNN =5.02TeV.Rightpanel:the p and ↵ h i p h T i h i of electron-positron pairs within the ﬁducial acceptance as a function of average pair mass, Mee ,for di↵erent UPC centrality 2 2 h i p QED Calculations & classesCMS in AuAcoplanarity + Au collisions at psNN =200GeV.The ↵ and pT is extracted for pT < 0.01. core h i h i ⟨! ⟩ vs. neutron multiplicity p −3 -1 ×10 -3 1.5 42 3 ´10 PbPb 5.02 TeV (1.5 nb ) > 40 27

1.6 α

CMS < 1.45 Pb + Pb 5.02 TeV Au + Au 200 GeV 10 Preliminary 2 40 2 26 ×

1.4 8 < Mµµ < 60 GeV/c 0.4 < Mee < 2.6 GeV/c > 1.5 |y | < 2.4 38 (MeV/c) (MeV/c) µµ 25 α > >

ñ 1.4 8 < Mµµ < 60 GeV

1.3 0n0n 1n1n 36 0n0n 1n1n 23 core 36

a 1.25 0n1n 1n>1n 0n1n 1n>1n á 1.3 22 1.2 0n>1n >1n>1n 34 0n>1n >1n>1n 34 21 1.2 1.15 20 STARlight 32 1.1 32 1.1 19 0n0n 0n1n 0nXn 1n1n 1nXn XnXn 1.05 arxiv:2006.07365 30 18 1 30 50 100 20 40 60 ØStrong neutron multiplicity dependence of ⟨)core⟩ (fm) (fm) • Deviation from constant: 5.74 FIG. 4. (Color online) Left panel: the ↵ and p2 of muon pairs within the ﬁducial acceptance as a function of average • b dependence of initial photon pT h i h T i impact parameter, b , for di↵erent UPC centrality classes in Pb + Pb collisions at s =5.02TeV.Rightpanel:the p2 6/2/20October 22, 2020 Shuai Yang, Hard Probes Daniel2020 Brandenburg | BNL (CFNS) / SDU 18 p 27 p NN T and ↵ of electron-positronh i pairs within the ﬁducial acceptance as a function of average impact parameter, b , for di↵erenth i h i 2 2 h i p UPC centrality classes in Au + Au collisions at psNN =200GeV.The ↵ and p is extracted for p < 0.01. h i h T i T p

1 where ± the azimuthal angles of the two individual lep- 19 pointed out in Ref. [10], the high-order soft photon ra- 2 tons. This definitions largely avoids the detector induced 20 diation will modify the ↵ distribution, which may com- 3 distortions from poor momentum resolution. Fig. 2 21 plicate these calculations. Fortunately, according to the 4 shows the results of our calculations for ↵ distributions 22 Sudakov resummation approach, the e↵ect is small at low 2 5 of muon pairs in Pb + Pb collisions at psNN = 5.02 23 pair P (large ↵) . In this paper we focus on the pT < ? 6 TeV for di↵erent neutron emission scenarios in UPCs. 24 0.01 range which accounts for the majority of the pro- 7 The results are filtered with the fiducial acceptance de- 25 duction and neglect the Sudakov e↵ect, which should be 8 scribed in the figure and normalized to unity to facilitate 26 studied in future work. 9 a direct comparison with experimental data. The ↵ dis- 10 tribution with no neutron emission from the two nuclei 27 To quantitatively describe the impact parameter de- 11 (labelled as “0n0n” in the figure) have a narrower dis- 28 pendent broadening for lepton pair production in UPCs, 12 tribution comparison to the same distribution for events 29 we employ the QED approach to estimate the mean of 2 2 13 with any number of neutron emission. As expected, the 30 the ↵ and p distributions ( ↵ , and p )versusav- T h i h T i 14 normalized ↵ spectrum becomes broader in the case of 31 erage impact parameter, b , for di↵erent neutron emis- p h i p 2 15 emitting more neutrons, which correspond to smaller im- 32 sion scenarios. Fig. 4 shows the ↵ and p of lepton h i h T i 16 pact parameters. Interestingly, the most probable value 33 pairs as a function of b for di↵erent neutron emission h i p 17 of ↵ distribution is not at zero, and shifts to a higher 34 scenarios. The results are filtered with the fiducial accep- 2 18 value in the collisions with more neutron emission. As 35 tance described in the figure, and the pT range is limited Control “centrality” in UPC

Klein and Steinberg, arXiv: 2005.01872

, where Determine neutron multiplicity

UPC ØBearing analogy to centrality • bXnXn < b0nXn < b0n0n

STARLIGHT only provides a 6/2/20few neutron emission Shuai Yang, Hard Probes 2020 12 ØStraight cut to disentangle neutrons scenarios • 0n0n, 0n1n, 0nXn, 1n1n, 1nXn, XnXn (X≥2) ØFit to estimate purity • 0n and Xn: ~100% • 1n: ~93-95% 6/2/20 Shuai Yang, Hard Probes 2020 16 Leading order "" → $!$"

CMS Preliminary PbPb 5.02 TeV (1.5 nb-1) 103 + - Sum gg ® µ µ 102 Core

Tail |yµµ| < 2.4 µ µ a p > 3.5 GeV, |h | < 2.4 10 T /d

s 8 < Mµµ < 60 GeV 1 )dN s

10-1 (1/N

#."% -2 (#$/&!'&"×$ ) 10 core: "!×$ #," tail: %!×(1 + (%*/%+)×+) 10-3 0 0.05 0.1 0.15 0.2 0.25 a ØDecouple ) spectrum: • Data: ⟨(core⟩ = (1227 ± 7 (stat.) ± 8 (syst.)) × 10-6 • STARlight: 1348 × 10-6 6/2/20 Shuai Yang, Hard Probes 2020 15 Total �� → �!�" cross-section in STAR Acceptance A Pure QED 2 → 2 scattering :

)) 1 arXiv : 1910.12400 2 STAR ��⁄�� ∝ � ≈ � Au+Au UPC gg® e+e- (QED) gg® e+e- (gEPA) No vector meson production -1 10 gg® e+e- (STARLight) → Forbidden for real photons with Scale Uncertainty : ± 13%

(mb/(GeV/c helicity ±1 (i.e. 0 is forbidden) ) - e

+ � �� → � � in STAR Acceptance: -2 e 10 Data : 0.261±0.004 (stat.) ± 0.013 (sys.) e ® P > 0.2 GeV/c & |he| < 1.0

dM ± 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 July 30, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 30 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 �$ two-body decay is flat C 1 �� → �� : Individual �/� preferentially arXiv : 1910.12400 STAR 2 Mee = 2 GeV/c aligned along beam axis [1]: 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 4� 1 − sin � cos � + Mee = 0.01 GeV/c � � ')| 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( o Highly virtual photon interactions should s d have an isotropic distribution 0.1 0.2 2 0.4 < Mee < 0.76 GeV/c o Measure �, the angle between the � and 0 the beam axis in the pair rest frame. 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

July 30, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 31 �� → �"�# ⁄�� $ 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 4� 1 − sin � cos � + � � ')| 0.3 e

� � = 2 + 4 1 − q � 4� ® 1 − 1 − cos �

� g

g 0.2 ( d|cos( o Highly virtual photon interactions should s d 0.1 have an isotropic distribution 2 0.4 < Mee < 0.76 GeV/c o Measure �, the angle between the � and 0 the 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

July 30, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 32 Outline of this talk 1. Introduction and Motivation o Motivation for direct measurement of electromagnetic fields o The extreme EM fields in heavy-ion collisions 2. Heavy ion collisions → QED under extreme conditions • Surprising results in peripheral heavy-ion collisions • Breit-Wheeler pair production & vacuum birefringence 3. A tool for precision mapping of the electromagnetic fields

4. Conclusions

October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 33 October 22, 2020 Daniel Brandenburg | BNL (CFNS) / SDU 34