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Global polarization signals from hot, dense and whirly QCD matter - - PowerPoint PPT Presentation

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Global polarization signals from hot, dense and whirly QCD matter Malena Tejeda-Yeomans Facultad de Ciencias Universidad de Colima exico a M a (MexNICA Collaboration) A. Ayala, M. Ayala, E. Cuautle, I. Dom nguez, M. Fontaine, I.

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Global polarization signals from hot, dense and whirly QCD matter

Malena Tejeda-Yeomans

Facultad de Ciencias Universidad de Colima M´ exicoa

a(MexNICA Collaboration) A. Ayala, M. Ayala, E. Cuautle, I. Dom´

ınguez, M. Fontaine, I. Maldonado, L. Montano, E. Moreno, P. Nieto, L. Rebolledo, M. Rodr´ ıguez,

  • J. Salinas, L. Valenzuela, C. Zepeda
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FYI

Please check out recent -review- documents/talks

Polarization and Vorticity in the Quark Gluon Plasma, F. Becattini, M. A. Lisa, e-Print: 2003.03640 [nucl-ex]. Chirality and Criticality: Novel Phenomena in Heavy-Ion Collisions, INT Program INT-20-1c, May 11 - June 5, 2020 ! 2nd week: vorticity, polarization, transport, in magnetic fields. Thermal vorticity and spin polarization in heavy-ion collisions, De-Xian Wei, Wei-Tian Deng, and Xu-Guang Huang, Phys. Rev. C 99, 014905 (2019). Vorticity in low-energy heavy-ion collisions, Xian-Gai Deng, Xu-Guang Huang, Yu-Gang Ma, Song Zhang, e-Print: arXiv:2001.01371 (2020).

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 2

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Spintronics: nanotechnology + L exchange

Usual angular-momentum exchange frameworks: magnetization, light polarization but... What about the exchange of angular momentum in the context of -plain and simple- matter mechanical rotation? spin–rotation coupling: intn of mechanical L and electron spin

  • M. Matsuo, J. Ieda, E. Saitoh, S. Maekawa

PRL 106 (2011)

Mechanical Rotation Magnetization

M Ω

Einstein-de Haas Barnett Spin Transfer Torque Spin Pumping Spin Motive Force Spin Current

Js

Spin-Orbit Interaction in the rotating frame

B

Ω

  • vd-

vd+

Ω $ B e’s trajectories EoM sol with 2 cyclotron frequencies. drift ~ v of the up-(down-) e’s parallel to the azimuthal direction

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 3

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Spin hydrodynamic generation (fluid spintronics)

  • R. Takahashi et al. Nature Phys. 12 (2016)

magnetohydrodynamics vs spin hydrodynamics First observation of coupling between the vorticity of a fluid and the spin of the electron The whirly-ness of the fluid generated through shear viscous effects flow field around any point is the vorticity ! (non-rel: ~ ! = 1

2 ~

r ⇥ v)

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 4

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Spin hydrodynamic generation (fluid spintronics)

  • R. Takahashi et. al. Nature Phys 12 (2016)

spin hydrodynamics to generate a voltage spin electrochemical potential for e" and e# µS ⌘ µ" µ# First observation of coupling between the vorticity of a fluid and the spin of the electron: spin–rotation coupling, mechanical rotation gives rise to a gradient of spin voltage which drives a spin current.

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 5

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Hot, dense, whirly QCD matter

“subatomic spintronics”- X. Deng

  • et. al. arXiv:2001.01371

Global Λ hyperon polarization in nuclear collisions: evidence for the most vortical fluid. STAR Collaboration Nature 548 (2017) ω ⇡ (9 ± 1) ⇥ 1021 s−1

  • sys. in T of a factor of 2

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 6

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Hot, dense, whirly QCD matter

STAR Collaboration, Nature 548 (2017)

ω ⇡ (9 ± 1) ⇥ 1021 s1

How whirly is this? superfluid nanodroplets 107 s1 turbulent flow in superfluid He-II 102 s1 rotating, heated soap bubbles used to model climate change 102 s1 supercell tornado cores 101 s1 the Great Red Spot of Jupiter 104 s1 large-scale terrestrial atmospheric patterns 107 105 s1 solar subsurface flow 107 s1

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 7

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Good whirly-ness probe: Λ hyperon

The decay of a lambda particle in the 32 cm diameter hydrogen bubble chamber (⇡− @ 16 GeV): ⇡− + p ! jets. CERN-EX-11465-1 (1960)

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 8

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Good whirly-ness probe in HICs: Λ hyperon

Particle Data Group:

X mΛ = 1115.683 ± 0.006 MeV

→ lightest hyperon with s content

X ⌧ = 2.632 ± 0.020 ⇥ 10−10 s ⇠ 7.9 cm at c

→ long lifetime: good for tracking

X Γ1(Λ ! p⇡−) = (63.9 ± 0.5)% Γ2(Λ ! n⇡0) = (35.8 ± 0.5)%

→ primary decay channel: good for reconstruction

X parity-violating weak decay

→ decay dist not-isotropic: p going off in the direction of Λ spin

s u u u d d d u W − Λ ⇡− p

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 9

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In this talk:

I will go through recent measurements of global polarization properties of Λs and ¯ Λs and then put forward a two-component model for global Λ/¯ Λ polarization using X centrality dependent model for Λ production in heavy-ion collisions + X relaxation time for quark spin-alignment + thermal vorticity in the hot/dense QGP

“Core meets corona: a two-component source to explain Lambda and anti-Lambda global polarization in semi-central heavy-ion collisions”. MexNICA Collaboration. e-Print: 2003.13757 [hep-ph]

Finally, highlight how this can help us in the upcoming measurements and analysis at MPD-NICA.

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 10

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In this talk:

+

  • +

+

  • =
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Hot, dense, whirly QCD matter in HICs

Non-central collisions have large angular momentum L ⇠ 105~. Shear forces in initial condition introduce vorticity to the QGP. Spin-orbit coupling: spin alignment, or polarization, along the direction of the vorticity - on average - parallel to J.

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 12

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Vorticity from Λ global polarization

Meassurement of angular momentum retained at mid-rapidity. In most central collisions: no initial angular momentum, no polarization.

(GeV)

NN

s 10

2

10 2 4 6 8

Au+Au 20-50%

this study Λ this study Λ PRC76 024915 (2007) Λ PRC76 024915 (2007) Λ

Centrality [%]

20 40 60 80

[%]

H

P

0.5 1 Λ Λ

= 200 GeV

NN

s STAR Au+Au <6 GeV/c

T

|<1, 0.5<p η | STAR Collaboration, Nature 548 (2017); Phys.Rev.C 98 (2018) 014910 Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 13

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Thermal and kinematic vorticity

HIC simulations µ = uµ, uµ = (1, ~ v), = 1/T !µν = 1 2 (@νµ @µν) !µν = 1 2 (@νuµ @µuν)

  • F. Becattini et. al. Eur.Phys.J.C 75 (2015), C 78 (2018)

10000 20000 30000 40000 50000 60000 70000 80000 90000 2 4 6 8 10 12 14 |Jy| (- h units) b (fm)

  • T. Niida, INT 20-1c, Chirality and Criticality: Novel Phenomena in HIC

b ⇠ 5 10 collisions, favor the development

  • f a larger thermal

vorticity ! study non-central collisions

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Vorticity from Λ global polarization

Spin-orbit coupling: spin alignment, or polarization, along the direction of the vorticity - on average - parallel to ˆ J = ˆ b ⇥ ˆ pbeam

  • F. Becattini et al Eur.Phys.J.C 75 (2015); Becattini, Karpenko, Lisa, Voloshin, Phys. Rev. C 95 (2017)

! pp

*

θ * ˆ Jsys

quark-gluon plasma forward-going beam fragment Λ BBC BBC

dN d cos ✓∗ = 1

2

⇣ 1 + ↵H| ~ PH| cos ✓∗⌘ decay parameter ↵Λ = ↵Λ = 0.642 ± 0.013 If ~ PH is independent of momentum + avg over phase space ~ PH|| ˆ J PH ⌘ h ~ PH · ˆ Ji = 8 ⇡↵H ⌦ cos

  • ∗

p J

↵ REP Observable: psNN-averaged polarization measurements of primary hadrons emitted from the fluid proportional to vorticity ! = |~ !| ! = kB T ~ ( ¯ PH + ¯ P ¯

H)

  • ! ! ⇡ (9 ± 1) ⇥ 1021s−1

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 15

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Λ global polarization - models

v-Hydro, partonic/hadronic transport, etc.

If the system is in thermal equilibrium, then equilibrium of spin degrees of freedom (spin and orbital angular momentum)

summary from Xu-Guang Huang (Fudan University) - QM 2019

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 16

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Λ/¯ Λ global polarization from a two-component source

  • A. Ayala, E. Cuautle, G. Herrera, and L. M. Monta˜

no, Phys. Rev. C 65 (2002)

Non-central heavy-ion collision of a symmetric system: Λ/¯ Λs from core via QGP processes Λ/¯ Λs from corona via n + n reactions

+

  • NΛ =

core

z }| { NΛ QGP +

corona

z }| { NΛ REC

Choose reference direction: baryon mom ! || pol perp production plane ! ? pol

Polarization asymmetry -spin alignment asymmetry- of any baryon species produced in high-energy reactions P = N" N# N" + N# N" and N# baryons with spin aligned and opposite to a given direction.

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 17

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Λ/¯ Λ global polarization from a two-component source

Introduce PΛ

REC, PΛ REC polarization in the corona

PΛ =

PΛ

REC+ N↑ Λ QGP−N↓ Λ QGP NΛ REC

! ✓ 1+

NΛ QGP NΛ REC

◆

, where PΛ

REC =

N↑

Λ REC−N↓ Λ REC

N↑

Λ REC+N↓ Λ REC

(1) PΛ =

@PΛ

REC+ N↑ Λ QGP−N↓ Λ QGP NΛ REC

1 A ✓ 1+

NΛ QGP NΛ REC

◆

where PΛ

REC =

N↑

Λ REC−N↓ Λ REC

N↑

Λ REC+N↓ Λ REC

, (2) Approximation PΛ

REC = PΛ REC = 0, reactions in cold nuclear matter are less

efficient to couple spin with angular momentum PΛ = ✓

N↑

Λ QGP−N↓ Λ QGP

NΛ REC

◆ ⇣ 1 +

NΛ QGP NΛ REC

⌘ , PΛ = ✓

N↑

Λ QGP−N↓ Λ QGP

NΛ REC

◆ ⇣ 1 +

NΛ QGP NΛ REC

⌘ . (3)

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 18

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Core features ! NΛ QGP, NΛ QGP

Core reactions are more efficient to align particle spin to global angular momentum, so intrinsic global Λ and Λ polarizations are finite but small z = (N"

Λ QGP N# Λ QGP)

NΛ QGP ¯ z = (N"

Λ QGP N# Λ QGP)

NΛ QGP ' |{z}

NΛ QGP'NΛ QGP

(N"

Λ QGP N# Λ QGP)

NΛ QGP Therefore, Eq. (3) can be written as (we expect z > ¯ z) PΛ = z NΛ QGP

NΛ REC

⇣ 1 + NΛ QGP

NΛ REC

⌘, PΛ = ¯ z NΛ QGP

NΛ REC

⇣ 1 + NΛ QGP

NΛ REC

⌘. (4)

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 19

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Corona features ! NΛ REC, NΛ REC

Cold nuclear matter with p + p-like reactions: s-quark is cheaper than 3 ¯ q’s! Model NΛ REC = wNΛ REC with w = w(psNN) < 1 PΛ = z NΛ QGP

NΛ REC

⇣ 1 + NΛ QGP

NΛ REC

⌘, PΛ = ¯

z w

NΛ QGP

NΛ REC

⇣ 1 + 1

w

NΛ QGP

NΛ REC

⌘, (5) Lets find out about this w = w(psNN)...

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 20

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Corona features

Cold nuclear matter (less dense than core): model as p + p intn Experimental data on the ratio w = NΛ REC/NΛ REC

  • btained from p + p

collisions at different energies w = NΛ REC/NΛ REC is smaller than 1 except for the largest collision energy considered

  • M. Gazdzicki and D. Rohrich, Z. Phys. C 71 (1996); J. W. Chapman et al., Phys. Lett. B 47, 465 (1973); C. H¨
  • hne,

CERN-THESIS-2003-034; J. Baechler et al. (NA35 Collaboration), Nucl. Phys. A 525 (1991); G. Charlton et al., Phys. Rev. Lett. 30 (1973); F. Lopinto et al., Phys. Rev. D 22 (1980); F. W. Busser et al., Phys. Lett. B 61 (1976); D. Brick et al., Nucl. Phys. B 164 (1980);

  • H. Kichimi et al., Phys. Rev. D 20 (1979); S. Erhan, et al. Phys. Lett. B 85 (1979); B. I. Abelev et al. (STAR Collaboration), Phys. Rev.

C 75 (2007); E. Abbas et al. (ALICE Collaboration), Eur. Phys. J. C 73 (2013).

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PΛ/PΛ in terms of z, ¯ z, w and NΛ QGP/NΛ REC

PΛ = z NΛ QGP

NΛ REC

⇣ 1 + NΛ QGP

NΛ REC

⌘, PΛ = ¯

z w

NΛ QGP

NΛ REC

⇣ 1 + 1

w

NΛ QGP

NΛ REC

⌘

! PΛ/PΛ > 1 for a range of parameter space ! 1/w > 1 amplifying effect X extreme situation ¯ z = z and NΛ QGP/NΛ REC = 1, PΛ/PΛ > 1 for 0 < w < 1 X realistic scenario with ¯ z < z and with NΛ QGP/NΛ REC < 1, PΛ/PΛ > 1 for 0 < w < 0.55 X if NΛ QGP/NΛ REC > 1, PΛ/PΛ > 1 only for 0 < w < 0.25

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 22

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Study Λ/¯ Λ production in QGP vs REC

Do non-central collisions at different energies and impact parameters favor a scenario where NΛ QGP/NΛ REC . 1 and thus PΛ > PΛ?

Average number of strange quarks produced in the QGP scales with the number of participants in the collision

  • J. Letessier, J. Rafelski and A. Tounsi, Phys. Lett. B 389 (1996)

hsi = NΛ QGP = c (Np QGP)2 with 0.001  c  0.005 (6) Λs are not the only strange hadrons produced in the reaction: c = 0.0025 Np QGP = Z d2s np(~ s, ~ b) ✓ 2 6 4

density of participants

z }| { np(~ s, ~ b) nc 3 7 5 (7) nc = 3.3 fm−2 critical density of participants above which the QGP can be produced

  • J. P. Blaizot, J. Y. Ollitrault, Phys. Rev. Lett. 77 (1996)

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 23

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Study Λ/¯ Λ production in QGP vs REC

np(~ s, ~ b) = TA(~ s )[1eNN(psNN)TB(~

s~ b)]+TB(~

s ~ b)[1eNN(psNN)TA(~

s)]

thickness functions TA, TB ~ b along the impact parameter NN nucleon-nucleon xsec

Michael L. Miller et. al. Ann.Rev.Nucl.Part.Sci.57 (2007)

The thickness function TA TA(~ s ) = Z 1

1

⇢A(z,~ s ) dz, Woods-Saxon ⇢A(r) = (1 + e(rRA)/a)1, a = 0.41 fm, RA = 1.1A1/3 fm.

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 24

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Study Λ/¯ Λ production in QGP vs REC

Number of Λs produced in the core NΛ QGP = (0.0025) (Np QGP)2 where Np QGP = Z d2s np(~ s, ~ b) ✓ h np(~ s, ~ b) nc i Number of Λs produced in the corona NΛ REC = Λ

NN (psNN)

| {z }

Λ p+p xsec

Z d2s TB(~ b ~ s)TA(~ s ) ⇥ ✓ h nc np(~ s, ~ b) i

NΛ QGP/NΛ REC > 1 for b . 6 fm NΛ QGP/NΛ REC < 1 for b & 6 fm

Fit to experiment σΛ NN √sNN

  • = C ln √sNN + D, with C = 1.67 ± 0.05 mb and D = −1.60 ± 0.08 mb. D. Brick et al.,
  • Nucl. Phys. B 164 (1980). H. Kichimi et al., Phys. Rev. D 20 (1979). S. Erhan et al., Phys. Lett. B 85 (1979). K. Jaeger et al., Phys.
  • Rev. D 11 (1975). V. Blobel et al. (Bonn-Hamburg-Munich Collaboration), Nucl. Phys. B 69 (1974). D. Drijard et al.

(CERN-Dortmund-Heidelberg-Warsaw Collaboration), Z. Phys. C 12 (1982).

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Intrinsic global polarization from relaxation times

Relaxation time for quark/antiquark spin and thermal vorticity alignment in a quark-gluon plasma at finite temperature and quark chemical potential

  • A. Ayala. D. de la Cruz, L. A. Hern´

andez, and J. Salinas, e-Print: arXiv:2003.06545 [hep-ph]

The interaction between the thermal vorticity and the quark spin is modeled by means of an effective vertex ! Γ ! ⌧ = 1/Γ z = 1 exp (t/⌧) ¯ z = 1 exp (t/¯ ⌧) as functions of the Λ and Λ formation time t within the QGP.

  • Theoretical Physics Colloquium ASU, July 1st, 2020

Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 26

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Λ/¯ Λ global polarization from a two-component source

  • Au + Au 20-50% Λ and Λ

polarization from core-corona model bands: Λ and Λ formation time in QGP range 1.5 fm < t < 4.5 fm vs data STAR-BES Nature 548 (2017)

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 27

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What happens for psNN < 7.7 GeV? (NICA, FAIR, RHIC)

At psNN ⇠ 2mN, is L ⇠ 0? Then ! ⇠ 0? Is thermal vorticity well defined?

  • X. Deng, et. al. arXiv:2001.01371 [nucl-th] (UrQMD)

E.E. Kolomeitsev, et. al. Phys. Rev. C 97 (2018) (PHSD)

(GeV)

NN

s 1 2 3 4 5 6 7 10 20 30 40 〉

y

ϖ

  • 〈

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 b=5.0 fm b=8.0 fm b=10.0 fm

Au+Au

5 10 15 20 25

  • 1

1 2 3 4 5 8 9 10 Λ and Λ polarization [%]

t [fm/c]

Λ Λ+res. decays Λ Λ+res. decays STAR exp. Λ STAR exp.Λ

Au+Au @ s

1/2=7.7 GeV, b=7.5fm

|η|<1 |ϖ|<1

If ! / P then polarization is consistent with data.

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 28

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Λ/¯ Λ global polarization from a two-component source

To summarize: in non-central collisions Λ and Λ hyperons can be produced from different density zones within the interaction region: core or corona polarization properties of Λ and Λ differ depending on the region they come from competing production effects: NΛ QGP/NΛ REC > 1 in central to semi-central collisions and NΛ QGP/NΛ REC < 1 in peripheral collisions so global Λ polarization can be larger than the global Λ polarization in peripheral collisions: corona-like in spite of the thermal vorticity-produced, Λ polarization is larger than Λ polarization in the central collisions: core-like in collisions with intermediate to large impact parameters, which correspond to the kind of collisions that favor the development of a larger thermal vorticity, NΛ QGP/NΛ REC . 1 and thus PΛ > PΛ

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 29

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In progress: MexNICA at MPD-NICA

EM field creation in A+A collisions at lower energies and impact on photoproduction, vorticity, hyperon polarization

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 30

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In progress: MexNICA at MPD-NICA - Preliminary

Simulations with UrQMD, PHSD, LAQGSM for A + A at NICA energies to produce and reconstruct hyperons and to simulate the influence of polarization effects: initial conditions, hydro evolution, freeze-out, B-fields, etc. Preliminary, Bi+Bi @ 9 GeV MPDroot-framework - TPC Ivonne Maldondado, MexNICA postdoc, UAS

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 31

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In progress: MexNICA at MPD-NICA - Preliminary

Simulations with UrQMD, PHSD, LAQGSM for A + A at NICA energies to produce and reconstruct hyperons and to simulate the influence of polarization effects: initial conditions, hydro evolution, freeze-out, B-fields, etc. Preliminary, Bi+Bi @ 9 GeV MPDroot-framework - TPC Ivonne Maldondado, MexNICA postdoc, UAS

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 32

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In progress: MexNICA at MPD-NICA - Preliminary

Simulations with UrQMD, PHSD, LAQGSM for A + A at NICA energies to produce and reconstruct hyperons and to simulate the influence of polarization effects: initial conditions, hydro evolution, freeze-out, B-fields, etc. Preliminary, Bi+Bi @ 9 GeV MPDroot-framework - TPC Ivonne Maldondado, MexNICA postdoc, UAS

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 33

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Final remarks

X Heavy-ion physics: electronics ! spintronics X Interesting sources of vorticity: jets, magnetic field X Vorticity and transport mechanisms: viscosity X The role of polarization measurements to study vorticity AND mechanisms/sources X New experiments coming up - NICA, FAIR, RHIC, many

  • pportunities!

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 34

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THANKS

Theoretical Physics Colloquium ASU, July 1st, 2020 Malena Tejeda-Yeomans (U. de Colima) matejeda@ucol.mx 35