3.36pt Introduction Exclusive heavy quark photoproduction in UPC - PowerPoint PPT Presentation

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion 3.36pt

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Parton tomography: Wigner distributions in nucleon and nuclear targets Emmanuel G. de Oliveira emmanuel.de.oliveira@ufsc.br UFSC – Federal University of Santa Catarina Florianópolis, Brazil in collaboration with Pelicer, M. R. and Pasechnik, R. 10.1103/PhysRevD.99.034016 [1811.12888] COST Heavy-Ion Workshop, Lund March 1st, 2019

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Distributions Parton correlator and distributions Markus Diehl 1512.01328 � H ( k , P , ∆) = ( 2 π ) − 4 d 4 z e iz · k k − 1 k + 1 2 ∆ 2 ∆ P − 1 P + 1 2 ∆ 2 ∆ p ( P + 1 q ( − 1 2 z )Γ q ( 1 2 z ) | p ( P − 1 � � × 2 ∆) | ¯ 2 ∆) parton correlation function ∆ = 0 H ( k, P, ∆) f ( k, P ) parton correlation function � dk − ξ = 0 FT H ( x, k , ξ, b ) H ( x, k , ξ, ∆ ) GTMD � dk − W ( x, k , b ) Wigner distribution � d 2 k � d 2 k ξ = 0 FT H ( x, ξ, ∆ 2 ) � d 2 b H ( x, ξ, b ) GPD FT f ( x, z ) f ( x, k ) f ( x, b ) impact parameter � distribution dx x n − 1 TMD � d 2 k ξ = 0 � n � � dx x n − 1 k =0 A nk (∆ 2 ) (2 ξ ) k d 2 b GFFs f ( x ) F n ( b ) F n (∆ 2 ) PDF form factor

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Distributions Quark Wigner distribution � dz − d 2 � d 2 � b ⊥ ) = 1 � b ⊥ 2 π e iz − xP + � z ⊥ ( 2 π ) 2 e i � ∆ ⊥ · � z ⊥ · � W ( x , � k ⊥ , � b ⊥ ( 2 π ) 2 e − i � k ⊥ 2 p ( P + ∆ ⊥ 2 ) | p ( P − ∆ ⊥ q ( − z 2 )Γ q ( z � � × 2 ) | ¯ 2 ) Five dimensional distribution. Most complete information for on-shell partons in a Lorentz contracted nucleus. Orbital angular momentum introduces correlations between � k and � b ⊥ : � dx d 2 � k ⊥ d 2 � b ⊥ ( � b ⊥ × � k ⊥ ) W ( x , � k ⊥ , � L z == b ⊥ ) These correlations can contribute to elliptic flow.

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Distributions Gluon Wigner distribution at small x from the dipole cross section � d 2 � � 1 r ⊥ d 2 � � b ⊥ + � � � b ⊥ − � �� b ⊥ r ⊥ r ⊥ e i � ∆ ⊥ · � b ⊥ + i � S ( � k , � k ⊥ · � r ⊥ � � U † ∆ ⊥ ) = N c Tr U ( 2 π ) 4 2 2 k 1 The dipole S -matrix provides information on correlations in k 2 impact parameter space During scattering, dipole size k ⊥ − ∆ ⊥ − ⊥ − ∆ ⊥ k 2 2 does not change. Extra propagator and coupling. In the small- x limit, the dipole S -matrix is related to the the Fourier transform of the gluon Wigner distribution (or directly to the GTMD) in diffractive dijet production (Hatta, Xiao, Yuan, PRL 116, 202301, 2016). ⊥ − ∆ 2 2 N c � � x → 0 xG ( � k ⊥ , � k 2 S ( � k ⊥ , � ⊥ ∆ ⊥ ) ≈ ∆ ⊥ ) , α s 4

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Observables Observables Deeply Virtual Compton Scattering γ ∗ γ Vector meson production

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Observables Exclusive dijets in UPC Hagiwara, Hatta, Pasechnik, Tasevsky, Teryaev, PRD 96, 034009 (2017). Exclusive dijets in UPC are a way to probe the GTMDs. The convolution involving the dipole S -matrix components and the light-cone wave function can be analytically inverted in the back to back limit. Problem 1: at low transverse momentum there is no hard scale. Problem 2: Measuring jets coming from light quarks is very hard at relatively low transverse momentum.

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Observables Exclusive dijets in UPC Hagiwara, Hatta, Pasechnik, Tasevsky, Teryaev, PRD 96, 034009 (2017). Exclusive dijets in UPC are a way to probe the GTMDs. The convolution involving the dipole S -matrix components and the light-cone wave function can be analytically inverted in the back to back limit. Problem 1: at low transverse momentum there is no hard scale. Problem 2: Measuring jets coming from light quarks is very hard at relatively low transverse momentum. What if we use heavy quarks?

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Exclusive heavy quark photoproduction in UPC Ultraperipheral collisions (UPC), photon is real and has comes from the projectile (nucleus) with Weizsäcker–Williams flux: � � ξ jA K 0 ( ξ jA ) K 1 ( ξ jA ) − ξ 2 d ω = 2 Z 2 α dN γ ja K 2 1 ( ξ jA ) − K 2 � � 0 ( ξ jA ) . πω 2 with ξ jA = ω ( R j + R A ) /γ The Z 2 enhancement in the photon flux makes the process much more efficient in probing the Wigner distribution then pp collisions. We study the forward direction, such that the contribution to the longitudinal quark momentum is small.

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Light-cone Feynman rules To calculate the interaction among the photon and the two gluons light-cone Feynman rules. The rule for particles on-shell are as in usual Feynman rules (spinors and polarization vectors). Each intermediate state denotes a factor 1 in k − − � int k − + i ǫ � where in denotes initial states and int intermediary ones. For each internal line include a factor θ ( k + ) / k + . Vertices are changed by a normalization factor, for instance, quark-gluon vertice: − g γ µ t a ij . Each independent momentum must be integrated with a measure � dk + d 2 k ⊥ 2 ( 2 π ) 3 .

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Dipole T matrix As a final step, we need the probability of having two gluons from the target. It will be given by the Wigner distribution (a.k.a. dipole scattering amplitude) squared. Focusing on the first harmonic, we can expand T = 1 − S as: T ( � k ⊥ , � ∆ ⊥ ) = T 0 ( k ⊥ , ∆ ⊥ ) + T ǫ ( k ⊥ , ∆ ⊥ ) cos 2 ( φ k − φ ∆ ) + · · · The elliptic part is the one that will produce correlations, which can be solely responsible for observed final state asymmetries If | � k ⊥ | ≫ | � ∆ ⊥ | , the isotropic component will be the largest and we can neglect terms with order higher than the elliptic one.

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion MV model For the dipole T -matrix we use the MV model improved for an inhomogeneous target in the transverse plane by Iancu and Rezaeian, Phys. Rev. D 95, 094003, 2017. With a large gluon occupation number at small x , the color field is treated as a classical one in the presence of sources. The saturation scale Q s grows with A 1 / 3 . 5 25 ∆ ⊥ = 0 . 10 GeV ∆ ⊥ = 0 . 10 GeV 4 20 ∆ ⊥ = 0 . 20 GeV ∆ ⊥ = 0 . 20 GeV T ǫ ( GeV − 4 ) × 10 − 3 ∆ ⊥ = 0 . 25 GeV ∆ ⊥ = 0 . 25 GeV 15 T 0 ( GeV − 4 ) 3 ∆ ⊥ = 0 . 50 GeV ∆ ⊥ = 0 . 50 GeV 10 2 5 Lead 1 Lead 0 0 − 5 − 10 − 1 0 1 2 3 4 0 1 2 3 4 k ⊥ (GeV) k ⊥ (GeV) The larger the ∆ , the more important the elliptic part is.

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Putting it all together Hadron level cross section: d σ Aj d σ Aj d PS = dy 1 dy 2 d 2 � P ⊥ d 2 � ∆ ⊥ q z ( 1 − z ) 1 = ω dN d ω 2 ( 2 π ) 2 N c α em e 2 P 2 ⊥ ( z 2 + ( 1 − z ) 2 ) [ A ( P ⊥ , ∆ ⊥ ) + B ( P ⊥ , ∆ ⊥ ) cos 2 ( φ P − φ ∆ )] 2 � × + m 2 � f [ C ( P ⊥ , ∆ ⊥ ) + D ( P ⊥ , ∆ ⊥ ) cos 2 ( φ P − φ ∆ )] 2 . P 2 ⊥ where 2 � P ⊥ = � k 1 ⊥ − � k 2 ⊥ . The above can be thought as the photon to quark pair wavefunction convoluted with target structure functions.

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Mass-corrected A and B structure functions � ∞ P 2 ⊥ A ( P ⊥ , ∆ ⊥ ) = k ⊥ dk ⊥ � Q ) 2 − 4 P 2 k 2 ⊥ + P 2 ⊥ + m 2 ( k 2 ⊥ + P 2 ⊥ + m 2 ⊥ k 2 0 Q + ⊥   P 2 ⊥ + m 2 Q − k 2 ⊥  T 0 ( k ⊥ , ∆ ⊥ ) , ×  1 + � Q ) 2 − 4 P 2 ( k 2 ⊥ + P 2 ⊥ + m 2 ⊥ k 2 ⊥ � ∞ 1 dk ⊥ k ⊥ ( P 2 ⊥ − k 2 ⊥ − m 2 B ( P ⊥ , ∆ ⊥ ) = Q ) T ǫ ( k ⊥ , ∆ ⊥ ) 2 P 2 0 ⊥   Q ) 2 − 2 k 2  ( k 2 ⊥ + P 2 ⊥ + m 2 ⊥ P 2 ⊥ − ( P 2 ⊥ + k 2 ⊥ + m 2  . × Q ) � Q ) 2 − 4 P 2 ( k 2 ⊥ + P 2 ⊥ + m 2 ⊥ k 2 ⊥

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion New C and D structure functions � ∞ P 2 ⊥ C ( P ⊥ , ∆ ⊥ ) = k ⊥ dk ⊥ T 0 ( k ⊥ , ∆ ⊥ ) , � Q ) 2 − 4 P 2 ( k 2 ⊥ + P 2 ⊥ + m 2 ⊥ k 2 0 ⊥   � ∞ Q ) 2 − 2 P 2 ( k 2 ⊥ + P 2 ⊥ + m 2 ⊥ k 2 dk ⊥  k 2 ⊥ + P 2 ⊥ + m 2 ⊥ D ( P ⊥ , ∆ ⊥ ) = Q −  k ⊥ � Q ) 2 − 4 P 2 ( k 2 ⊥ + P 2 ⊥ + m 2 ⊥ k 2 0 ⊥ × T ǫ ( k ⊥ , ∆ ⊥ ) .