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, ∆) = (2π)−4

• d4z eiz·k

×

• p(P + 1

2∆)|¯ q(−1 2z)Γq(1 2z)|p(P − 1 2∆)

• k − 1

2∆

k + 1

2∆

P − 1

2∆

P + 1

2∆

H(k, P, ∆) H(x, k, ξ, ∆) H(x, ξ, ∆2) n

k=0 Ank(∆2) (2ξ)k

H(x, k, ξ, b) H(x, ξ, b) W(x, k, b) f(x, b) f(x, k) f(x) Fn(b) Fn(∆2) f(k, P) f(x, z)

• d2b
• d2b
• d2k
• d2k
• dk−
• dk−
• d2k
• dx xn−1

∆ = 0 ξ = 0 ξ = 0 ξ = 0 FT FT FT GTMD GPD TMD form factor GFFs PDF parton correlation function parton correlation function distribution impact parameter

• dx xn−1

Wigner distribution

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Distributions

Quark Wigner distribution

W (x, k⊥, b⊥) = 1 2

• d2

b⊥ (2π)2 ei

∆⊥· b⊥

dz− 2π eiz−xP+ d2 z⊥ (2π)2 e−i

z⊥· k⊥

×

• p(P + ∆⊥

2 )|¯ q(−z 2)Γq(z 2)|p(P − ∆⊥ 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⊥: Lz ==

• dx d2

k⊥ d2 b⊥( b⊥ × k⊥)W (x, k⊥, 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

S( k, ∆⊥) = d2 r⊥ d2 b⊥ (2π)4 ei

∆⊥· b⊥+i k⊥· r⊥

1 Nc TrU

• b⊥ +

r⊥ 2

• U†
• b⊥ −

r⊥ 2

• The dipole S-matrix provides

information on correlations in impact parameter space During scattering, dipole size does not change. Extra propagator and coupling.

− ⊥ − ∆ ⊥

k k

2 ⊥ − ∆ ⊥ 2

k1 k2

In the small-x limit, the dipole S-matrix is related to the the Fourier transform

• f the gluon Wigner distribution (or directly to the GTMD) in diffractive dijet

production (Hatta, Xiao, Yuan, PRL 116, 202301, 2016). xG( k⊥, ∆⊥)

x→0

≈ 2Nc αs

• k2

⊥ − ∆2 ⊥

4

• S(

k⊥, ∆⊥) ,

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: dNγ dω = 2Z 2α πω

• ξjAK0(ξjA)K1(ξjA) − ξ2

ja

2

• K 2

1 (ξjA) − K 2 0 (ξjA)

• .

with ξjA = ω(Rj + RA)/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− + iǫ

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: −gγµta

ij.

Each independent momentum must be integrated with a measure dk+d2k⊥ 2(2π)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⊥, ∆⊥) = T0(k⊥, ∆⊥) + Tǫ(k⊥, ∆⊥) cos 2(φk − 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 Qs grows with A1/3.

−1 1 2 3 4 5 1 2 3 4 Lead T0(GeV−4) k⊥ (GeV) ∆⊥ = 0.10 GeV ∆⊥ = 0.20 GeV ∆⊥ = 0.25 GeV ∆⊥ = 0.50 GeV −10 −5 5 10 15 20 25 1 2 3 4 Lead Tǫ(GeV−4) × 10−3 k⊥ (GeV) ∆⊥ = 0.10 GeV ∆⊥ = 0.20 GeV ∆⊥ = 0.25 GeV ∆⊥ = 0.50 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: dσAj dPS = dσAj dy1 dy2 d2 P⊥ d2 ∆⊥ = ω dN dω 2(2π)2Ncαeme2

q z(1 − z) 1

P2

⊥

×

• (z2 + (1 − z)2) [A(P⊥, ∆⊥) + B(P⊥, ∆⊥) cos 2(φP − φ∆)]2

+ m2

f

P2

⊥

[C(P⊥, ∆⊥) + D(P⊥, ∆⊥) cos 2(φP − φ∆)]2

• .

where 2 P⊥ = k1⊥ − k2⊥. 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

A(P⊥, ∆⊥) = ∞ k⊥dk⊥ P2

⊥

k2

⊥ + P2 ⊥ + m2 Q +

• (k2

⊥ + P2 ⊥ + m2 Q)2 − 4P2 ⊥k2 ⊥

×  1 + P2

⊥ + m2 Q − k2 ⊥

• (k2

⊥ + P2 ⊥ + m2 Q)2 − 4P2 ⊥k2 ⊥

  T0(k⊥, ∆⊥), B(P⊥, ∆⊥) = 1 2P2

⊥

∞ dk⊥ k⊥ (P2

⊥ − k2 ⊥ − m2 Q)Tǫ(k⊥, ∆⊥)

×   (k2

⊥ + P2 ⊥ + m2 Q)2 − 2k2 ⊥P2 ⊥

• (k2

⊥ + P2 ⊥ + m2 Q)2 − 4P2 ⊥k2 ⊥

− (P2

⊥ + k2 ⊥ + m2 Q)

  .

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion

New C and D structure functions

C(P⊥, ∆⊥) = ∞ k⊥dk⊥ P2

⊥

• (k2

⊥ + P2 ⊥ + m2 Q)2 − 4P2 ⊥k2 ⊥

T0(k⊥, ∆⊥), D(P⊥, ∆⊥) = ∞ dk⊥ k⊥  k2

⊥ + P2 ⊥ + m2 Q −

(k2

⊥ + P2 ⊥ + m2 Q)2 − 2P2 ⊥k2 ⊥

• (k2

⊥ + P2 ⊥ + m2 Q)2 − 4P2 ⊥k2 ⊥

  × Tǫ(k⊥, ∆⊥).

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion

Nuclear structure functions from MV model

−0.12 −0.09 −0.06 −0.03 2 4 6 8 10 ∆⊥ = 0.2 GeV APb (GeV−2) P⊥ (GeV) mQ = 0 mc mb −0.04 −0.02 0.02 0.04 2 4 6 8 10 ∆⊥ = 0.2 GeV CPb (GeV−2) P⊥ (GeV) mc mb −4 −2 2 4 2 4 6 8 10 ∆⊥ = 0.2 GeV BPb (GeV−2) × 10−3 P⊥ (GeV) mQ = 0 mc mb 1 2 3 4 2 4 6 8 10 ∆⊥ = 0.2 GeV DPb (GeV−2) × 10−3 P⊥ (GeV) mc mb

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Angle-integrated results

Angle-integrated results

We focus on lead as the target. To present our results, we integrate in azimuthal angle. We calculate the hadron cross section integrated in angle with exact kinematics. However, in the limit k1,2⊥ → P⊥, azimuthal integration produces terms proportional to 2A2 + B2 or 2C 2 + D2. Since B and D are small compared to A and C this is a measure of the isotropic component. We numerically investigated this approximation and found that it has negligible impact on the final result for our choice of small ∆⊥.

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Angle-integrated results

Angle-integrated results

10−2 10−1 100 101 102 103 104 105 106 2 4 6 8 10 y1,2 = 1 ∆⊥ = 0.2 GeV √sNN = 2.76 TeV b¯ b dσ

dPS (nb·GeV−4)

P⊥ (GeV) full A, B, C A, B A 10−6 10−5 10−4 10−3 10−2 10−1 100 101 102 103 0.1 0.2 0.3 0.4 0.5 P⊥ = 10 GeV y1,2 = 1 5.02 TeV

• 2.76 TeV
• dσ

dPS (nb·GeV−4)

∆⊥ (GeV) b¯ b c¯ c c¯ c b¯ b

The A structure function is the dominant one, but where P⊥ 4 GeV and P⊥ 7 GeV, C has a non negligible contribution, and can be measured with an appropriate choice of kinematical cuts. By fixing P⊥ we see the dips present in the cross section, as expected in the small-x region. The dips (minima) are not affected by changing the c.m. energy; they are a feature of the nucleus structure.

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Cosine-weighted angular average

Cosine-weighted angular average

As seen above, the angular-integrated cross sections discussed above are not very convenient for getting any physics information about the elliptic part. Therefore, instead we would like use the cosine-weighted angle average determined as follows: dσpA dPS cos 2(φP − φ∆)

• =

2π dφP⊥ 2π dφ∆⊥ cos 2(φP − φ∆) dσpA dy1dy2 d2 P⊥ d2 ∆⊥ Roughly speaking, the more positive this observable is, the more P⊥ and ∆⊥ are parallel (or antiparallel); the negative case correlates with perpendicular vectors. If we integrate the cross section averaged by cos 2δφ, only crossed terms (AB and CD) appear in the limit k1,2⊥ → P⊥, allowing us to obtain information on the elliptic component.

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Cosine-weighted angular average

Cosine-weighted angular average results

−0.06 −0.03 0.03 0.06 0.09 2 4 6 8 10 √sNN = 2.76 TeV ∆⊥ = 0.2 GeV y1,2 = 1 b¯ b cos 2δφ

dσ dPS / dσ dPS

P⊥ (GeV) full AB CD −1 −0.5 0.5 1 0.1 0.2 0.3 0.4 0.5 y1,2 = 1 P⊥ = 10 GeV √sNN = 2.76 TeV b¯ b cos 2δφ

dσ dPS / dσ dPS

∆⊥ (GeV) full AB CD

The azimuthal angle distribution is easy to measure and is not affected by

• fragmentation. Also, the ratio is less affected by experimental
• uncertainties. It is not possible to disentangle the AB and CD

contribution, so the measurement is of both B and D simultaneously. In the right, we see the rise of the elliptic contribution with ∆⊥, which

• ccurs due to the rapidly falling of T0.

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Proton target

Proton target

What would change if the target were a proton? Smaller cross section. The dependence on ∆⊥ does not show oscillations for the ranges studied.

10−3 10−2 10−1 100 101 102 103 104 2 4 6 8 10 √spN = 5.02 TeV ∆⊥ = 0.2 GeV y1,2 = 1 b¯ b dσ

dPS (nb·GeV−4)

P⊥ (GeV) full A, B, C A, B A 10−2 10−1 0.1 0.2 0.3 0.4 0.5 P⊥ = 10 GeV y1,2 = 1 13 TeV (c¯ c) 13 TeV (b¯ b) 5.02 TeV (c¯ c) 5.02 TeV (b¯ b) dσ

dPS (nb·GeV−4)

∆⊥ (GeV)

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Proton target

Proton target – cosine-weighted average

The dependence on P⊥ is pretty much the same as in the nuclear case. Again no oscillations. The cosine-weighted average increases steadily with ∆⊥.

−0.02 −0.01 0.01 0.02 2 4 6 8 10 y1,2 = 1 ∆⊥ = 0.2 GeV √spN = 5.02 TeV b¯ b cos 2δφ

dσ dPS / dσ dPS

P⊥ (GeV) full AB CD 0.02 0.04 0.06 0.08 0.1 0.1 0.2 0.3 0.4 0.5 √spN = 5.02 TeV P⊥ = 10 GeV y1,2 = 1 b¯ b cos 2δφ

dσ dPS / dσ dPS

∆⊥ (GeV) full AB CD

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

Conclusion

We derived the analytic expressions at leading order for the calculation of the exclusive heavy quark photoproduction. These are of definite importance to understand the angular correlations between the transverse momenta k⊥ and ∆⊥ in the GTMD, and can be related to elliptic flow in hadron and/or nuclei collisions.

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

Conclusion

We derived the analytic expressions at leading order for the calculation of the exclusive heavy quark photoproduction. These are of definite importance to understand the angular correlations between the transverse momenta k⊥ and ∆⊥ in the GTMD, and can be related to elliptic flow in hadron and/or nuclei collisions. Predictions for bottom and charm pair production cross sections in a fully differential form, both for proton and nucleus target.

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

Conclusion

We derived the analytic expressions at leading order for the calculation of the exclusive heavy quark photoproduction. These are of definite importance to understand the angular correlations between the transverse momenta k⊥ and ∆⊥ in the GTMD, and can be related to elliptic flow in hadron and/or nuclei collisions. Predictions for bottom and charm pair production cross sections in a fully differential form, both for proton and nucleus target. We defined the cosine-weighted angular average of the differential cross section in order to access the elliptic part of the hadron structure.

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

Conclusion

We derived the analytic expressions at leading order for the calculation of the exclusive heavy quark photoproduction. These are of definite importance to understand the angular correlations between the transverse momenta k⊥ and ∆⊥ in the GTMD, and can be related to elliptic flow in hadron and/or nuclei collisions. Predictions for bottom and charm pair production cross sections in a fully differential form, both for proton and nucleus target. We defined the cosine-weighted angular average of the differential cross section in order to access the elliptic part of the hadron structure. The study of heavy-quark di-jets is relevant in comparison to its light quark equivalent, since it is less affected by fragmentation effects and has a cleaner QCD background.

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

Conclusion

We derived the analytic expressions at leading order for the calculation of the exclusive heavy quark photoproduction. These are of definite importance to understand the angular correlations between the transverse momenta k⊥ and ∆⊥ in the GTMD, and can be related to elliptic flow in hadron and/or nuclei collisions. Predictions for bottom and charm pair production cross sections in a fully differential form, both for proton and nucleus target. We defined the cosine-weighted angular average of the differential cross section in order to access the elliptic part of the hadron structure. The study of heavy-quark di-jets is relevant in comparison to its light quark equivalent, since it is less affected by fragmentation effects and has a cleaner QCD background. Also, it has much smaller theoretical uncertainties w.r.t. higher order terms, as light quark jets suffer from potentially huge corrections.

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

Future work

To have some precision predictions for comparison with experimental measurements it is necessary to include fragmentation functions (FF) for the q¯ q pair. In the case of the charm quark, FFs for D mesons also should be included to know which range of transverse momentum should be looked. As for light quarks, it is interesting to include FFs for charged pions, which have a high impact in the cross section. Also it is important to study a range of models for the dipole cross section, including some x dependence.

Introduction Exclusive heavy quark photoproduction in UPC Cross section results Conclusion Thanks

Thanks

To organizers of this workshop. To collaborators. To funding agencies Fapesc, CNPq, Capes, INCT-FNA, COST.