Photon production induced by magnetic fields in HICs: photon yield - PowerPoint PPT Presentation

Photon production induced by magnetic fields in HICs: photon yield and elliptic flow. Luis A. Hernandez September 11, 2017 Instituto de Ciencias Nucleares, UNAM. 1 / 23 �

Outline 1 Motivation 2 Production of γ ′ s . 3 Results 4 Conclusion 2 / 23 �

Motivation Thermal photon puzzle. J-F Paquet et al. ,Phys. Rev. C 93 , (2016) 044906

Motivation Thermal photon puzzle. J-F Paquet et al. ,Phys. Rev. C 93 , (2016) 044906 3 / 23 �

Motivation Thermal photon puzzle. J-F Paquet et al. ,Phys. Rev. C 93 , (2016) 044906 Data status of direct photons. Excess at low p t . Data/model comparisons. New processes to explain the excess. 3 / 23 �

Motivation Data vs Models 2014 O. Linnyk, E. L. Bratkovskaya and W. Cassing, Prog. Part. Nucl. Phys. 87 (2016) 50-115. Transport model: O. Linnyk, E. L. Bratkovskaya and W. Cassing, Phys. Rev. C 89 , 034908 (2014). Fireball model: H. van Hees, C. Gale and R. Rapp, Phys. Rev. C 84 , 054906 (2011). Hydro model: C. Shen, U. W. Heinz, J.-F. Paquet and C. Gale, Phys. Rev. C 89 , 044910 (2014). 4 / 23 �

Motivation Update Data vs Models 2016 PHENIX compared to models. C. Shen, arXiv:1601.02563. 5 / 23 �

Motivation Conditions for a new mechanism to pro- duce γ ’s By Chun Shen We compute the production of prompt photons from the perturbative fusion of low momentum gluons coming from the shattered glasma. 6 / 23 �

Motivation Magnetic fields in HICs. R. Snellings, J. Phys. 13 , (2011) 055008 V. Voronyuk et al. ,Phys. Rev. C 83 , 054911 (2011) V. Skokov, A. Y. Illarionov and V. Toneev, D. E. Kharzeev, L. D. McLerran and H. J. Warringa, Nucl. Phys. A Int. J. Mod. Phys. A 24 , 5925 (2009) 803 , 227 (2008) 7 / 23 �

Motivation Nonequilibrate gluons. Over-occupied initial state called the glasma . Saturation effects → times of order τ s ∼ 1 / Λ s Λ s ≡ saturation scale. ∆ τ s ≃ 1 − 1 . 5fm By Larry McLerran, ISMD2008 8 / 23 �

Production of γ ′ s . Photons from magnetic fields. Trace anomaly converts energy-momentum of gluon bulk into photons. G. Basar, D. Kharzeev and V. V. Skokov, Phys. Rev. Lett. 109 , 202303 (2012). Photon emission by quarks synchrotron radiation. K. Tuchin, Phys. Rev. C 91 , 0124902 (2015). 9 / 23 �

Production of γ ′ s . Gluon fusion induced by eB The quark propagator is written in its coordinate space representation as d 4 p ( 2 π ) 4 e − ip · ( x − x ′ ) S ( p ) , S ( x , x ′ )=Φ( x , x ′ ) � where � x Φ( x , x ′ )=exp { i | q f | x ′ d ξ µ [ A µ + 1 2 F µν ( ξ − x ′ ) ν ] } , the Schwinger phase factor. 10 / 23 �

Production of γ ′ s . Strong magnetic fields. The translational invariant part of the propagator is written in terms of Landau levels, since the strength of the magnetic fields is dominant, therefore we consider the Lowest Landau Level (LLL) or at most the first Landau Level (1LL) p 2 | qf B | � p � ⊥ − S LLL ( p ) O + = − 2 ie � , p 2 � p 2 � � � � ⊥ − 1 − 2 p 2 e | qf B | S 1LL ( p ) � p � O + ⊥ − � p � O − = � + 4 � p ⊥ . p 2 � � − 2 | q f B | | q f B | with O ± � = [ 1 ± ( sign ( q f B )) i γ 1 γ 2 ] / 2 11 / 23 �

Production of γ ′ s . Notation B = B ˆ z . Vector potential A µ = B 2 ( 0 , − y , x , 0 ) ( symmetric gauge ). p µ ⊥ ≡ ( 0 , p 1 , p 2 , 0 ) , p µ � ≡ ( p 0 , 0 , 0 , p 3 ) , p 2 ⊥ ≡ p 2 1 + p 2 2 and p 2 � ≡ p 2 0 − p 2 3 , therefore p 2 = p 2 � − p 2 ⊥ . 12 / 23 �

Production of γ ′ s . The amplitude for the process. � � d 4 r d 4 s d 4 t � d 4 xd 4 yd 4 z M = − ( 2 π ) 4 ( 2 π ) 4 ( 2 π ) 4 e − it · ( y − x ) e − is · ( x − z ) e − ir · ( z − y ) e − ip · z e − ik · y e iq · x × � � � iq f γ α iS ( s ) ig γ µ t c iS ( r ) ig γ ν t d iS ( t ) × Tr � � � iq f γ α iS ( t ) ig γ ν t d iS ( r ) ig γ µ t c iS ( s ) + Tr Φ( x , y )Φ( y , z )Φ( z , x ) ǫ µ ( λ p ) ǫ ν ( λ k ) ǫ α ( λ q ) × Three steps. Compute: Product of Schwinger phase factors/integrals over the space-time points. 1 Tensor structures. 2 Integrals over the momenta. 3 13 / 23 �

Production of γ ′ s . Computing process

Production of γ ′ s . Computing process

Production of γ ′ s . Computing process

Production of γ ′ s . Computing process 14 / 23 �

Production of γ ′ s . Computing process to be continued... 14 / 23 �

Production of γ ′ s . Photon production probability. � � 1 1 M| 2 = ( 2 π ) 4 δ ( 4 ) ( q − k − p ) V τ s | � |M| 2 , 4 4 pol pol Average over the initial gluons. V τ s is the space-time volume Explicitly � �� � |M| 2 = q 2 f α em α 2 q 2 � � � 1 s ω 2 p + 3 ω 2 q 2 ⊥ ω 2 p + ω 2 ⊥ exp − k − ω p ω k . k ( 2 π ) ω 2 q f B ω 2 4 q q pol We have already used that the p µ p ) = ( ω p /ω q ) q µ , = ω p ( 1 , ˆ produced photon needs to move in the original gluon’s direction. k µ ω k ( 1 , ˆ k ) = ( ω k /ω q ) q µ . = 15 / 23 �

Production of γ ′ s . Invariant photon momentum distribution. � � d 3 p d 3 k dN mag χ V ∆ τ s ω q = n ( ω p ) n ( ω k ) d 3 q 2 ( 2 π ) 3 ( 2 π ) 3 2 ω p ( 2 π ) 3 2 ω k � ( 2 π ) 4 δ ( 4 ) ( q − k − p ) 1 |M| 2 . × 4 pol , f High occupation gluon number Three flavours. η n ( ω ) = e ω/ Λ s − 1 . n ( ω ) , distribution of gluons. χ , overlap region (semicentral η high gluon occupation factor. collision). Λ s the saturation scale We introduced a flow velocity factor, that is, ω p , k → ( p , k ) · u . With � u µ = γ ( 1 , β ) and γ = 1 / 1 − β 2 16 / 23 �

Production of γ ′ s . Elliptic flow coefficient The azimuthal distribution with respect to the reaction plane can be given in terms of a Fourier decomposition as � � ∞ � dN mag = N mag 1 + 2 v n ( ω q ) cos( n φ ) , d φ 2 π i = 1 with total number of photons, N mag is � d 3 q dN mag N mag = ( 2 π ) 3 d 3 q Elliptic flow coefficient dN mag ( ω q ) + dN direct mag d ω q ( ω q ) v d ω q ( ω q ) v direct ( ω q ) 2 2 v 2 ( ω q ) = , dN mag d ω q ( ω q ) + dN direct d ω q ( ω q ) 17 / 23 �

Results γ ’s invariant momentum distribution α s = 0 . 3, Λ s = 2 GeV, η = 3, ∆ τ s = 1 . 5 fm, R = 7 fm, β = 0 . 25 and Figure: Difference between PHENIX photon invariant χ = 0 . 8 momentum distribution [ 1 ] and direct (points) or direct minus prompt (zigzag) photons from [ 2 ] [ 1 ] A. Adare et al. [PHENIX Collaboration], Phys. Rev. C 91 , 064904 (2015). [ 2 ] J.-F. Paquet, C. Shen, G. S. Denicol, M. Luzum, B. Schenke, S. Jeon, C. Gale, Phys. Rev. C 93 , 044906 (2016). 18 / 23 �

Results γ ’s invariant momentum distribution ( β = 0 ) Figure: Difference between PHENIX photon invariant momentum distribution [ 1 ] and direct (points) or direct minus prompt (zigzag) photons from [ 2 ] [ 1 ] A. Adare et al. [PHENIX Collaboration], Phys. Rev. C 91 , 064904 (2015). [ 2 ] J.-F. Paquet, C. Shen, G. S. Denicol, M. Luzum, B. Schenke, S. Jeon, C. Gale, Phys. Rev. C 93 , 044906 (2016). 19 / 23 �

Results Coefficient v 2 Figure: Harmonic coefficient v 2 , using the direct photon result of [ 1 ] together with our calculation, also compared to PHENIX data [ 2 ] [ 1 ] J.-F. Paquet, C. Shen, G. S. Denicol, M. Luzum, B. Schenke, S. Jeon, C. Gale, Phys. Rev. C 93 , 044906 (2016). [ 2 ] A. Adare et al. [PHENIX Collaboration], Phys. Rev. C 94 , 064901 (2016). 20 / 23 �

Results Coefficient v 2 ( β = 0 ) Figure: Harmonic coefficient v 2 , using the direct photon result of [ 1 ] together with our calculation, also compared to PHENIX [ 2 ] [ 1 ] J.-F. Paquet, C. Shen, G. S. Denicol, M. Luzum, B. Schenke, S. Jeon, C. Gale, Phys. Rev. C 93 , 044906 (2016). [ 2 ] A. Adare et al. [PHENIX Collaboration], Phys. Rev. C 94 , 064901 (2016). 21 / 23 �

Conclusion Summary In a semi-central HICs, a magnetic field of a large intensity is produced. When eB is the most intense are also the scales associated to the production of a large number of small momentum gluons. eB provides the mechanism to allow that gluons fuse and convert into photons in excess over other well studied mechanisms. eB also provides an initial asymmetry for the development of an azimuthal anisotropy quantified in terms of a substantial v 2 (particularly at low photon momenta). 22 / 23 �

Thank you!!! Enjoy your stay in Tlaxcala!!! 23 / 23 �