From high p theory and data to inferring the anisotropy of - PowerPoint PPT Presentation

Shape of the QGP droplet Initial spatial anisotropy is one of the main properties of QGP. A major limiting factor for QGP tomography. Still not possible to directly infer the initial anisotropy from experimental data. 8 18

Shape of the QGP droplet Initial spatial anisotropy is one of the main properties of QGP. A major limiting factor for QGP tomography. Still not possible to directly infer the initial anisotropy from experimental data. Several theoretical studies (MC-Glauber, EKRT, IP-Glasma, MC-KLN) infer the initial anisotropy; lead to notably different predictions. 8 18

Shape of the QGP droplet Initial spatial anisotropy is one of the main properties of QGP. A major limiting factor for QGP tomography. Still not possible to directly infer the initial anisotropy from experimental data. Several theoretical studies (MC-Glauber, EKRT, IP-Glasma, MC-KLN) infer the initial anisotropy; lead to notably different predictions. Alternative approaches for inferring anisotropy are necessary! 8 18

Shape of the QGP droplet Initial spatial anisotropy is one of the main properties of QGP. A major limiting factor for QGP tomography. Still not possible to directly infer the initial anisotropy from experimental data. Several theoretical studies (MC-Glauber, EKRT, IP-Glasma, MC-KLN) infer the initial anisotropy; lead to notably different predictions. Alternative approaches for inferring anisotropy are necessary! Optimally, these should be complementary to existing predictions. 8 18

Shape of the QGP droplet Initial spatial anisotropy is one of the main properties of QGP. A major limiting factor for QGP tomography. Still not possible to directly infer the initial anisotropy from experimental data. Several theoretical studies (MC-Glauber, EKRT, IP-Glasma, MC-KLN) infer the initial anisotropy; lead to notably different predictions. Alternative approaches for inferring anisotropy are necessary! Optimally, these should be complementary to existing predictions. Based on a method that is fundamentally different than models of early stages of QCD matter. 8 18

A novel approach to extract the initial state anisotropy Inference from already available high- p ⊥ R AA and v 2 measurements (to be measured with higher precision in the future). 9 18

A novel approach to extract the initial state anisotropy Inference from already available high- p ⊥ R AA and v 2 measurements (to be measured with higher precision in the future). Use experimental data (rather than calculations which rely on early stages of QCD matter). Exploit information from interactions of rare high- p ⊥ partons with QCD medium. 9 18

A novel approach to extract the initial state anisotropy Inference from already available high- p ⊥ R AA and v 2 measurements (to be measured with higher precision in the future). Use experimental data (rather than calculations which rely on early stages of QCD matter). Exploit information from interactions of rare high- p ⊥ partons with QCD medium. Advances the applicability of high- p ⊥ data. Up to now, this data was mainly used to study the jet-medium interacions, rather than inferring bulk QGP parameters, such as spatial anisotropy. 9 18

A novel approach to extract the initial state anisotropy What is an appropriate observable? The initial state anisotropy is quantified in terms of eccentricity parameter ǫ 2 : dx dy ( y 2 − x 2 ) ρ ( x , y ) ǫ 2 = � y 2 − x 2 � � � y 2 + x 2 � = dx dy ( y 2 + x 2 ) ρ ( x , y ) , � where ρ ( x , y ) is the initial density distribution of the QGP droplet. M. Djordjevic, S. Stojku, M. Djordjevic and P. Huovinen, Phys.Rev. C Rapid Commun. 100, 031901 (2019). 10 18

A novel approach to extract the initial state anisotropy What is an appropriate observable? The initial state anisotropy is quantified in terms of eccentricity parameter ǫ 2 : dx dy ( y 2 − x 2 ) ρ ( x , y ) ǫ 2 = � y 2 − x 2 � � � y 2 + x 2 � = dx dy ( y 2 + x 2 ) ρ ( x , y ) , � where ρ ( x , y ) is the initial density distribution of the QGP droplet. M. Djordjevic, S. Stojku, M. Djordjevic and P. Huovinen, Phys.Rev. C Rapid Commun. 100, 031901 (2019). High- p ⊥ v 2 is sensitive to both the anisotropy and the size of the system. R AA is sensitive only to the size of the system. 10 18

A novel approach to extract the initial state anisotropy What is an appropriate observable? The initial state anisotropy is quantified in terms of eccentricity parameter ǫ 2 : dx dy ( y 2 − x 2 ) ρ ( x , y ) ǫ 2 = � y 2 − x 2 � � � y 2 + x 2 � = dx dy ( y 2 + x 2 ) ρ ( x , y ) , � where ρ ( x , y ) is the initial density distribution of the QGP droplet. M. Djordjevic, S. Stojku, M. Djordjevic and P. Huovinen, Phys.Rev. C Rapid Commun. 100, 031901 (2019). High- p ⊥ v 2 is sensitive to both the anisotropy and the size of the system. R AA is sensitive only to the size of the system. Can we extract eccentricity from high- p ⊥ R AA and v 2 ? 10 18

Anisotropy observable Use scaling arguments for high- p ⊥ ∆ E / E ≈ � T � a � L � b , where within our model a ≈ 1 . 2, b ≈ 1 . 4 D. Zigic et al. , JPG 46, 085101 (2019); M. Djordjevic and M. Djordjevic, PRC 92, 024918 (2015) 11 18

Anisotropy observable Use scaling arguments for high- p ⊥ ∆ E / E ≈ � T � a � L � b , where within our model a ≈ 1 . 2, b ≈ 1 . 4 D. Zigic et al. , JPG 46, 085101 (2019); M. Djordjevic and M. Djordjevic, PRC 92, 024918 (2015) R in AA − R out v 2 ≈ 1 AA = ⇒ R AA ≈ 1 − ξ � T � a � L � b 2 R in AA + R out AA 1 - R AA ≈ ξ � T � a � L � b b ∆ L � L � − a ∆ T v 2 ≈ ξ � T � a � L � b � � 2 2 � T � 11 18

Anisotropy observable Use scaling arguments for high- p ⊥ ∆ E / E ≈ � T � a � L � b , where within our model a ≈ 1 . 2, b ≈ 1 . 4 D. Zigic et al. , JPG 46, 085101 (2019); M. Djordjevic and M. Djordjevic, PRC 92, 024918 (2015) R in AA − R out v 2 ≈ 1 AA = ⇒ R AA ≈ 1 − ξ � T � a � L � b 2 R in AA + R out AA 1 - R AA ≈ ξ � T � a � L � b b ∆ L � L � − a ∆ T v 2 ≈ ξ � T � a � L � b � � 2 2 � T � v 2 � b � L � − a ∆ L ∆ T � ≈ 1 − R AA 2 2 � T � This ratio carries information on the asymmetry of the system, but through both spatial and temperature variables. M. Djordjevic, S. Stojku, M. Djordjevic and P. Huovinen, Phys.Rev. C Rapid Commun. 100, 031901 (2019). 11 18

Anisotropy parameter ς v 2 � b ∆ L � L � − a ∆ T Temperature vs. spatial asymmetry: � ≈ = ⇒ 1 − R AA 2 2 � T � 12 18

Anisotropy parameter ς v 2 � b ∆ L � L � − a ∆ T Temperature vs. spatial asymmetry: � ≈ = ⇒ 1 − R AA 2 2 � T � � � L out � − � L in � v 2 ≈ 1 b − a � � L out � + � L in � ≈ 0 . 57 ς 1 − R AA 2 c ς = ∆ L � L � = � L out � − � L in � � L out � + � L in � 12 18

Anisotropy parameter ς v 2 � b ∆ L � L � − a ∆ T Temperature vs. spatial asymmetry: � ≈ = ⇒ 1 − R AA 2 2 � T � � � L out � − � L in � v 2 ≈ 1 b − a � � L out � + � L in � ≈ 0 . 57 ς 1 − R AA 2 c ς = ∆ L � L � = � L out � − � L in � � L out � + � L in � At high p ⊥ , v 2 over 1 − R AA ratio is dictated solely by the geometry of the initial fireball! Anisotropy parameter ς follows directly from high p ⊥ experimental data! M. Djordjevic, S. Stojku, M. Djordjevic and P. Huovinen, Phys.Rev. C Rapid Commun. 100, 031901 (2019). 12 18

Comparison with experimental data Solid red line: analytically derived asymptote. 13 18

Comparison with experimental data Solid red line: analytically derived asymptote. For each centrality and from p ⊥ ≈ 20 GeV , v 2 / ( 1 − R AA ) does not depend on p ⊥ , but is determined by the geometry of the system. 13 18

Comparison with experimental data Solid red line: analytically derived asymptote. For each centrality and from p ⊥ ≈ 20 GeV , v 2 / ( 1 − R AA ) does not depend on p ⊥ , but is determined by the geometry of the system. The experimental data from ALICE, CMS and ATLAS show the same tendency, though the error bars are still large. In the LHC Run 3 the error bars should be significantly reduced. 13 18

Comparison with experimental data v 2 / ( 1 − R AA ) indeed carries the information about the system’s anisotropy. It can be simply (from the straight line high- p ⊥ limit) and robustly (in the same way for each centrality) inferred from experimental data. 14 18

Eccentricity Anisotropy parameter ς is not the commonly used anisotropy parameter ǫ 2 . To facilitate comparison with ǫ 2 values in the literature, we define: ǫ 2 L = � L out � 2 − � L in � 2 2 ς � L out � 2 + � L in � 2 = 1 + ς 2 = ⇒ M. Djordjevic, S. Stojku, M. Djordjevic and P. Huovinen, Phys.Rev. C Rapid Commun. 100, 031901 (2019). 15 18

Eccentricity Anisotropy parameter ς is not the commonly used anisotropy parameter ǫ 2 . To facilitate comparison with ǫ 2 values in the literature, we define: ǫ 2 L = � L out � 2 − � L in � 2 2 ς � L out � 2 + � L in � 2 = 1 + ς 2 = ⇒ M. Djordjevic, S. Stojku, M. Djordjevic and P. Huovinen, Phys.Rev. C Rapid Commun. 100, 031901 (2019). ǫ 2 L is in an excellent agreement with ǫ 2 which we started from. v 2 / ( 1 − R AA ) provides a reliable and robust procedure to recover initial state anisotropy. 15 18

Eccentricity Anisotropy parameter ς is not the commonly used anisotropy parameter ǫ 2 . To facilitate comparison with ǫ 2 values in the literature, we define: ǫ 2 L = � L out � 2 − � L in � 2 2 ς � L out � 2 + � L in � 2 = 1 + ς 2 = ⇒ M. Djordjevic, S. Stojku, M. Djordjevic and P. Huovinen, Phys.Rev. C Rapid Commun. 100, 031901 (2019). The width of our ǫ 2 L band is smaller than the difference in ǫ 2 values ǫ 2 L is in an excellent agreement with obtained by using different models. ǫ 2 which we started from. Resolving power to distinguish v 2 / ( 1 − R AA ) provides a reliable and between different initial state robust procedure to recover initial models, although it may not be state anisotropy. possible to separate the finer details of more sophisticated models. 15 18

Summary High- p ⊥ theory and data - traditionally used to explore high- p ⊥ parton interactions with QGP, while QGP properties are explored through low- p ⊥ data and corresponding models. 16 18

Summary High- p ⊥ theory and data - traditionally used to explore high- p ⊥ parton interactions with QGP, while QGP properties are explored through low- p ⊥ data and corresponding models. With a proper description of high- p ⊥ medium interactions, high- p ⊥ probes can become powerful tomography tools, as they are sensitive to global QGP properties. We showed that here in the case of spatial anisotropy of QCD matter. 16 18

Summary High- p ⊥ theory and data - traditionally used to explore high- p ⊥ parton interactions with QGP, while QGP properties are explored through low- p ⊥ data and corresponding models. With a proper description of high- p ⊥ medium interactions, high- p ⊥ probes can become powerful tomography tools, as they are sensitive to global QGP properties. We showed that here in the case of spatial anisotropy of QCD matter. By using our dynamical energy loss formalism, we showed that a (modified) ratio of R AA and v 2 presents a reliable and robust observable for straightforward extraction of initial state anisotropy. 16 18

Summary High- p ⊥ theory and data - traditionally used to explore high- p ⊥ parton interactions with QGP, while QGP properties are explored through low- p ⊥ data and corresponding models. With a proper description of high- p ⊥ medium interactions, high- p ⊥ probes can become powerful tomography tools, as they are sensitive to global QGP properties. We showed that here in the case of spatial anisotropy of QCD matter. By using our dynamical energy loss formalism, we showed that a (modified) ratio of R AA and v 2 presents a reliable and robust observable for straightforward extraction of initial state anisotropy. It will be possible to infer anisotropy directly from LHC Run 3 data: an important constraint to models describing the early stages of QGP formation. This demonstates the synergy of more common approaches for inferring QGP properties with high- p ⊥ theory and data. 16 18

Acknowledgements The speaker has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 725741) 17 18

Backup v 2 / ( 1 − R AA ) with full 3+1D hydro DREENA Flatness still observed. Further research is ongoing. 18 / 18

Accelerating longitudinal expansion of resistive relativistic-magneto-hydrodynamics M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She Universita degli Studi di Torino INFN sezione di Torino Frontiers in Nuclear and Hadronic Physics 2020 GGI, Florence, Italy Feb 24 - March 06 M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 1 / 22

Overview Relativistic Magneto-hydrodynamics in heavy ion collisions(RMHD) 1 Accelerating Longitudinal fluid 2 Results and discussion 3 M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 2 / 22

RRMHD RMHD equations The coupled RMHD equations are d µ T µν = 0 , T µν = T µν matt + T µν EM d µ F µν = − J ν , ( d µ J µ = 0) , J µ = ρ u µ + σ µν e ν d µ F ∗ µν = 0 , e µ = F µν u ν , b µ = F ∗ µν u ν Where ρ (Here is zero) is electric charge density. Note that d µ is covariant derivative . In the case of finite and homogeneous electrical conductivity σ ij = σδ ij , For the Resistive RMHD we can re-write the energy and Euler equations as follow: D ǫ + ( ǫ + P )Θ = e λ J λ , ( D = u µ d µ , Θ = d µ u µ ) , ( ǫ + P ) Du α + ∇ α P = F αλ J λ − u α e λ J λ . M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 3 / 22

RMHD Ideal RMHD in magnetized Bjorken model In co-moving frame : u µ = (1 , 0 , 0 , 0) (1) And one assume magnetic field is located in the transverse direction b µ = (0 , b x , b y , 0) (2) According to Bjorken flow ( v z = z t ) D = ∂ τ , Θ = 1 τ . Finally energy density and magnetic field are given by ǫ c b ( τ ) = b 0 ( τ 0 ǫ ( τ ) = τ 4 / 3 , τ ) (3) V. Roy et al, Phys. Lett. B, Vol. 750, (2015) Gabriele Inghirami et al, Eur. Phys. J. C (2016) 76:659. M. Haddadi Moghaddam et al, Eur. Phys. J. C (2018) 78:255. M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 4 / 22

(1+1)D Longitudinal expansion with acceleration We can parameterize the fluid four-velocity in (1+1)D as follows u µ = γ (1 , 0 , 0 , v z ) = (cosh Y , 0 , 0 , sinh Y ) , (4) where Y is the fluid rapidity and v z = tanh Y . Besides, in Milne coordinates ( τ, x , y , η ), one can write � cosh( Y − η ) , 0 , 0 , 1 � γ [1 , 0 , 0 , 1 u µ = τ sinh( Y − η ) = ¯ τ ¯ v ] , (5) where γ = cosh( Y − η ) , ¯ ¯ v = tanh( Y − η ) . (6) By using this parameterization one obtains γ ( ∂ τ + 1 D = ¯ τ ¯ v ∂ η ) (7) v ∂ τ Y + 1 Θ = ¯ γ (¯ τ ∂ η Y ) (8) M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 5 / 22

(1+1)D Longitudinal expansion with acceleration Non central collisions can create an out-of-plane magnetic field and in-plane electric field. The magnetic field in non central collisions is dominated by the y component which induces a Faraday current in xz plane. We consider the following setup: γ [1 , 0 , 0 , 1 u µ = ¯ τ ¯ v ] , Figure: λ is acceleration parameter. e µ = [0 , e x , 0 , 0] , b µ = [0 , 0 , b y , 0] . M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 6 / 22

(1+1D) Longitudinal expansion with acceleration We summarize the RRMHD align in (1+1D): γ ( − 1) τσ e 2 ( τ∂ τ + ¯ v ∂ η ) ǫ + ( ǫ + P )( τ ¯ v ∂ τ Y + ∂ η Y ) = ¯ x , γ ( − 1) τσ e x b y , ( ǫ + P )( τ∂ τ + ¯ v ∂ η ) Y + ( τ ¯ v ∂ τ + ∂ η ) P = ¯ ∂ τ ( u τ b y + 1 τ e x u η ) + ∂ η ( u η b y − 1 τ e x u τ ) + (1 τ )( u τ b y + 1 τ e x u η ) = 0 , ∂ τ ( u τ e x + (1 τ ) b y u η ) + ∂ η ( u η e x − 1 τ b y u τ ) + (1 τ )( u τ e x + (1 τ ) b y u η ) = − σ e x . M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 7 / 22

We suppose that all quantities are constant in the transverse plane. Hence in order to solve the last two equations, we can write the following Ansatz: e x ( τ, η ) = − h ( τ, η ) sinh( Y − η ) (9) b y ( τ, η ) = h ( τ, η ) cosh( Y − η ) (10) then we have: ∂ τ h ( τ, η ) + h ( τ, η ) = 0 , (11) τ ∂ η h ( τ, η ) + ( στ ) h ( τ, η ) sinh( η − Y ) = 0 (12) and the solutions of the above Equations can be written as: h ( τ, η ) = c ( η ) , (13) τ sinh( Y − η ) = 1 ∂ η c ( η ) c ( η ) , (14) στ � σ 2 τ 2 ( ∂ η c ( η ) 1 c ( η ) ) 2 cosh( Y − η ) = 1 + (15) M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 8 / 22

Analytical Solutions We summarize the solutions for fluid rapidity, four velocity profile and EM fields as follows: Y = η + sinh − 1 ( 1 ∂ η c ( η ) c ( η ) ) , (16) στ � σ 2 τ 2 ( ∂ η c ( η ) 1 u τ = c ( η ) ) 2 , 1 + (17) 1 ∂ η c ( η ) u η = c ( η ) , (18) στ 2 e x ( τ, η ) = − 1 ∂ c ( η ) ∂η , (19) στ 2 � σ 2 τ 2 ( ∂ η c ( η ) b y ( τ, η ) = c ( η ) 1 c ( η ) ) 2 . 1 + (20) × τ The energy and momentum conservation equations are solved numerically. M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 9 / 22

Definition of function c ( η )? converting of the EM fields from Milne to Cartesian coordinates in the lab frame: E L = (sinh( η ) c ( η ) , 0 , 0) , (21) τ B L = (0 , cosh( η ) c ( η ) , 0) (22) τ Observation : 2! η 2 + ... ) is considered. If we choose a constant Where c ( η ) = c 0 (1 + α 2 value for c ( η ) =const, then the flow has no acceleration λ = 1, ( Y ≡ η → ¯ v = 0), the electric field in co-moving frame e x vanishes and τ , ǫ ∝ τ − 4 we have: b y ∝ 1 s = 1 3 if c 2 3 . M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 10 / 22

Initial Condition for Magnetic field In order to fix the constant, c 0 , the initial condition for magnetic field at mid rapidity in the lab frame is considered eB y L ( τ 0 = 0 . 5 , 0) = 0 . 0018 GeV 2 , and coefficient α is selected in order to parameterize the acceleration λ . ∘ 0.0015 ∘ ∘ ∘ ∘ B y ( GeV 2 / e ) ∘ Present work ∘ 0.0010 ∘ ∘∘ ∘ eB y ( τ , η = 0 ) : Init.Con ∘∘∘∘∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ ∘ 0.0005 0.0000 0 1 2 3 4 5 τ Figure: Magnetic field B y at mid-rapidity in the lab frame. U. G¨ ursoy, et al. Phys. Rev. C 98 , 055201 (2018). M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 11 / 22

Longitudinal acceleration λ 1.8 1.8 Η � 0 Τ � Τ 0 Η � 1 Τ � 1 1.6 1.6 Η � 2 Λ � Τ , Η � Λ � Τ , Η � Τ � Τ 1 1.4 1.4 1.2 1.2 1.0 1.0 0.5 1.0 1.5 2.0 2.5 3.0 � 3 � 2 � 1 0 1 2 3 Τ � fm � c � Η Figure: Acceleration parameter λ ( τ, η ) in term of proper time τ (Left) and rapidity η (Right). The coefficients are chosen for α = 0 . 1 , σ = 0 . 023 fm − 1 . At the late time of the expansion λ → 1 and in the both forward and backward rapidity, by increasing the rapidity, the acceleration parameter decreases. M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 12 / 22

Dynamical evolution of electric field e x Η � 0 0.0030 0.004 Τ � Τ 0 Τ � 1 0.0025 Η � � 1 � � e x � Τ , Η � � GeV 2 0.002 Τ � Τ 1 e x � Τ , Η � � GeV 2 Η � � 2 0.0020 e e 0.000 0.0015 0.0010 � 0.002 0.0005 � 0.004 0.0000 0.5 1.0 1.5 2.0 2.5 3.0 � 3 � 2 � 1 0 1 2 3 Τ � fm � c � Η Figure: Electric field e x ( τ, η ) in term of proper time τ (Left) and rapidity η (Right). The coefficients are chosen for α = 0 . 1 , σ = 0 . 023 fm − 1 . M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 13 / 22

Dynamical evolution of magnetic field b y 0.005 Τ � Τ 0 0.0035 Η � 0 0.0030 Τ � 1 0.004 � � b y � Τ , Η � � GeV 2 b y � Τ , Η � � GeV 2 Η � 2 0.0025 e e 0.003 Τ � Τ 1 Η � 3 0.0020 0.0015 0.002 0.0010 0.001 0.0005 0.0000 0.000 0.5 1.0 1.5 2.0 2.5 3.0 � 3 � 2 � 1 0 1 2 3 Τ � fm � c � Η Figure: Magnetic field e x ( τ, η ) in term of proper time τ (Left) and rapidity η (Right). The coefficients are chosen for α = 0 . 1 , σ = 0 . 023 fm − 1 . M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 14 / 22

The energy density ǫ of the magnetized matter 1.0 1.0 � Τ 0 � Τ � 4 � 3 0.8 0.8 Η � 0 Η � 1 Ε � Τ , Η �� Ε 0 0.6 Ε � Τ , Η �� Ε 0 0.6 Τ � Τ 0 Η � 2 Τ � 1 0.4 0.4 Τ � Τ 1 0.2 0.2 0.0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 � 3 � 2 � 1 0 1 2 3 Τ � fm � c � Η Figure: The ratio of energy density ǫ ( τ, η ) /ǫ 0 in term of proper time τ (Left) and rapidity η (Right). The coefficients are chosen for α = 0 . 1 , σ = 0 . 023 fm − 1 . M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 15 / 22

Observation K.J. Eskola and et al, Eur. Phys. J. C 1, 627-632 (1998). P. Bozek, Phys. Rev. C 77, 034911 (2008). Figure: (Left): The initial energy condition for ǫ ( τ 0 , η ) for √ s = 5500 GeV. The dashed curve is Gaussian fit ǫ ( τ 0 , η ) = ǫ 0 exp ( − η 2 2 w 2 ), with w = 3 . 8. (Right): Initial energy density distribution for the ideal fluid hydrodynamic evolution with a realistic EOS (dashed line), for viscous hydrodynamic evolutions (solid lines), and for a relativistic gas EOS (dashed-dotted line). M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 16 / 22

Connection between energy density and electrical conductivity 1.0 1.2 1.0 0.8 � Τ 0 � Τ � 4 � 3 0.8 Σ � 0.043 Ε � Τ ,0 �� Ε 0 0.6 Ε � Τ 0 , Η �� Ε 0 Σ � 0.023 Σ � 0.023 0.6 Σ � 0.033 0.4 0.4 Σ � 0.043 Σ � 0.053 0.2 0.2 0.0 0.5 1.0 1.5 2.0 2.5 3.0 � 3 � 2 � 1 0 1 2 3 Τ � fm � c � Η Figure: The ratio of energy density ǫ ( τ, η ) /ǫ 0 in term of proper time τ (Left) and rapidity η (Right). The coefficients are chosen for α = 0 . 1. It seems that there is a critical upper bound for the electrical conductivity of the matter: σ < 0 . 053 fm − 1 M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 17 / 22

Connection between energy density and parameter α 1.0 1.5 Α � 0.1 Α � 0.09 0.8 � Τ 0 � Τ � 4 � 3 Α � 0.08 1.0 Ε � Τ ,0 �� Ε 0 Α � 0.07 0.6 Ε � Τ 0 , Η �� Ε 0 Α � 0.1 0.4 0.5 Α � 0.07 0.2 Α � 0.06 0.0 0.5 1.0 1.5 2.0 2.5 3.0 � 3 � 2 � 1 0 1 2 3 Τ � fm � c � Η Figure: The ratio of energy density ǫ ( τ, η ) /ǫ 0 in term of proper time τ (Left) and rapidity η (Right). The coefficients are chosen for α = 0 . 1. It seems that there is a critical lower bound for α : α > 0 . 06 M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 18 / 22

Thank You M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 19 / 22

Backup Slides M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 20 / 22

Relativistic MHD Energy-momentum tensor and four vector fields pl = ( ǫ + P ) u µ u ν + Pg µν T µν (23) η − 1 T µν em = F µη F ν 4 F ηρ F ηρ g µν (24) F µν = u µ e ν − u ν e µ + ε µνλκ b λ u κ , (25) F ⋆αβ = u µ b ν − u ν b µ − ε µνλκ e λ u κ (26) Levi - Civita : ε µνλκ = 1 / � − det g [ µνλκ ] , (27) Electric four vector : e α = γ [ v · E , ( E + v × B )] T , ( Cartesian ) (28) Magnetic four vector : b α = γ [ v · B , ( B − v × E )] T , ( Cartesian ) (29) v , � B , � Where � E are measured in lab frame and γ is Lorentz factor. M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 21 / 22

Why to study magnetic field in HIC? Strong magnetic field may produce many effects: 1 The Chiral Magnetic Effect (CME) 2 The Chiral Magnetic Wave (CMW) 3 The Chiral separation Hall effect (CSHE) 4 Influence on the elliptic flow ( v 2 ) 5 Influence on the directed flow ( v 1 ) 6 ... M. Haddadi Moghaddam In Collaboration with: W. M. Alberico, Duan She (School-2020, Florence) arXiv:2002.09752 Feb 24 - March 06 22 / 22

200227 J.H.Liu Diffusion of heavy quarks in the early stage of High energy nuclear high energy nuclear collisions collisions Classical Yang-Mills fields Junhong Liu 12 Diffusion of heavy quark in in collaboration with S. Plumari, S. K. Das, V. Greco, and glasma M. Ruggieri Summary 1 School of Nuclear Science and Technology, Lanzhou University 2 INFN-Laboratori Nazionali del Sud Florence Italy, February 2020

Table of Contents 200227 J.H.Liu High energy 1 High energy nuclear collisions nuclear collisions Classical Yang-Mills fields 2 Classical Yang-Mills fields Diffusion of heavy quark in glasma Summary 3 Diffusion of heavy quark in glasma 4 Summary

Table of Contents 200227 J.H.Liu High energy 1 High energy nuclear collisions nuclear collisions Classical Yang-Mills fields 2 Classical Yang-Mills fields Diffusion of heavy quark in glasma Summary 3 Diffusion of heavy quark in glasma 4 Summary

Relativistic Heavy Ion Collisions 200227 J.H.Liu High energy nuclear collisions Classical Yang-Mills fields Diffusion of heavy quark in glasma Summary

Collisions process 200227 J.H.Liu initial stage: Glasma model High energy nuclear QGP stage: collisions Classical transport Yang-Mills theory fields Diffusion of Hadron stage: heavy quark in glasma transport Summary theory Hybrid description of Relativistic Heavy Ion Collisions Classical Yang-Mills field + Transport theory

Table of Contents 200227 J.H.Liu High energy 1 High energy nuclear collisions nuclear collisions Classical Yang-Mills fields 2 Classical Yang-Mills fields Diffusion of heavy quark in glasma Summary 3 Diffusion of heavy quark in glasma 4 Summary

Initial condition 200227 J.H.Liu Glasma can be treated as High energy nuclear classical fields due to the collisions large occupation number Classical Yang-Mills fields Diffusion of Initial glasma fields can be heavy quark in glasma computed with the random Summary static sources due to Lorentz Andreas Ipp, David M¨ uller Physics time dilatation Letters B 771 (2017) 74-79 ρ a (x T ) ρ b (y T ) = ( g 2 µ ) 2 δ ab δ (2) (x T − y T ) � � L. D. McLerran and R. Venugopalan, Phys. Rev. D 49, 2233 (1994)

Classical Yang-Mills fields 200227 τ , η coordinates J.H.Liu High energy η = 1 � t + z � � nuclear t 2 − z 2 τ = 2 ln collisions t − z Classical Yang-Mills In this case, CYM will be fields Diffusion of heavy quark in E i = τ∂ τ A i , (1) glasma 1 Summary = τ ∂ τ A η , (2) E η 1 ∂ τ E i = τ D η F η i + τ D j F ji , (3) 1 ∂ τ E η = τ D j F j η . (4)

Numerical results of CYM 200227 J.H.Liu Evolving fields up to 0.4 fm: High energy nuclear collisions Classical Yang-Mills fields Diffusion of heavy quark in glasma Summary J. H. Liu, S. Plumari, S. K. Das, V. Greco, and M. Ruggieri 1911.02480

Table of Contents 200227 J.H.Liu High energy 1 High energy nuclear collisions nuclear collisions Classical Yang-Mills fields 2 Classical Yang-Mills fields Diffusion of heavy quark in glasma Summary 3 Diffusion of heavy quark in glasma 4 Summary

heavy quarks as probes 200227 J.H.Liu Carry negligible color current High energy nuclear Self-interactions occur rarely collisions Probe the very early Classical Yang-Mills evolution of the Glasma fields fields Diffusion of heavy quark in dx i dt = p i glasma (5) Summary E E dp i dt = Q a F a i ν p ν (6) E dQ a = Q c ε cba A b µ p µ (7) dt

Spectrum of heavy quarks 200227 M. Ruggieri and S. K. Das, Phys. Rev. D 98, no. 9, 094024 (2018) J.H.Liu High energy nuclear collisions Classical Yang-Mills fields Diffusion of heavy quark in glasma Summary g 2 µ = 3 . 4 GeV Diffusion results in a shift of traverse momentum of heavy quarks.