Photon induced processes from semi-central to ultraperipheral - PowerPoint PPT Presentation

Photon induced processes from semi-central to ultraperipheral collisions: Introduction Wolfgang Schäfer 1 1 Institute of Nuclear Physics, PAN, Kraków COST workshop on Interplay of hard and soft QCD probes for collectivity in heavy-ion collisions Lund University, Sweden, 25. February - 1. March 2019

Outline Peripheral/ultraperipheral collisions Weizsäcker-Williams fluxes of equivalent photons electromagnetic dissociation of heavy nuclei “Soft to hard” in the diffractive photoproduction of vector mesons diffractive dissociation color dipole approach J /ψ photoproduction on the proton Diffractive processes on the nuclear target & multiple scattering expansion Coherent exclusive & incoherent diffraction with breakup of nucleus production in ultraperipheral HI collisions From ultraperipheral to semicentral collisions dileptons from γγ production vs thermal dileptons from plasma phase diffractive J /ψ in semi-central collisions A. Łuszczak and W. S., Phys. Rev. C 97 (2018) no.2, 024903 [arXiv:1712.04502 [hep-ph]]. A. Łuszczak and W. S., arXiv:1901.07989 [hep-ph]. M. Kłusek-Gawenda, R. Rapp, W. S. and A. Szczurek, Phys. Lett. B 790 (2019) 339 [arXiv:1809.07049 [nucl-th]].

Centrality RA b e.g. from optical limit of Glauber: d σ in = 2 π b (1 − e − σ in NN T AA ( b ) ) AA db σ in AA ∼ 7 barn for Pb at LHC. fraction of inelastic hadronic events contained in the centrality class C , � b max db d σ in 1 AA f C = . σ in db AA b min experimentally, centrality is determined by binning in multiplicity and/or transverse energy. Probability of no inelastic interaction: P surv ( b ) = exp[ − σ in NN T AA ( b )] ∼ θ ( b − 2 R A )

Fermi-Weizsäcker-Williams equivalent photons Heavy nuclei Au , Pb have Z ∼ 80 v ∼ 0 equivalent photons v ∼ c ion at rest: source of a Coulomb field, the highly boosted ion: sharp burst of field strength, with | E | 2 ∼ | B | 2 and E · B ∼ 0. (See e.g. J.D Jackson textbook). acts like a flux of “equivalent photons” (photons are collinear partons). E ( ω, b ) = − i Z √ 4 πα em � ω b � � E ( ω, b ) � b ω b � ; N ( ω, b ) = 1 1 � 2 γ K 1 2 π b 2 γ ω π � d ω d 2 b N ( ω, b ) σ ( γ B ; ω ) σ ( AB ) =

Finite size of particle → charge form factor 1e-01 with formfactor pointlike 1e-02 1e-03 bN ( ω, b ) [ fm − 1 ] 1e-04 ω = 1 GeV , γ = 100 1e-05 1e-06 2 4 6 8 10 12 14 16 18 20 b [fm] � � d 2 q q q 2 + ω 2 /γ 2 F em ( q 2 + ω 2 /γ 2 ) E ( ω, b ) = Z 4 πα em (2 π ) 2 exp[ − i bq ] 1 F em ( Q 2 ) = exp[ − R 2 ch Q 2 / 6] , Q 2 ≪ . R 2 ch Seen from a large distance, the ion indeed acts like a pointlike charge. When we come closer, the finite-size charge distribution important. Sometimes its effect is simulated by a sharp lower cutoff in b .

Ultraperipheral collisions some examples of ultraperipheral processes: A A A A A γ γ γ γ γ V V γ A * A * A A A A A photoabsorption on a nucleus diffractive photoproduction with and without breakup/excitation of a nucleus γγ -fusion. electromagnetic excitation/dissociation of nuclei. Excitation of Giant Dipole Resonances. the intact nuclei in the final state are not measured. Each of the photon exchanges is associated with a large rapidity gap. very small p T of the photoproduced system.

Absorption corrected flux of photons A A γ γ V V A * A A � A 1 ( ω ) σ ( γ A 2 → VA 2 ; 2 ω √ s ) + (1 ↔ 2) d ω N eff σ ( A 1 A 2 → A 1 A 2 V ; s ) = � N eff ( ω ) = d 2 b P surv ( b ) N ( ω, b ) survival probability: � � P surv ( b ) = S 2 el ( b ) = exp − σ NN T A 1 A 2 ( b ) ∼ θ ( | b | − ( R 1 + R 2 ))

Electromagnetic excitation of heavy ions 3 10 (mb) 2 A 1 A 1 A ∗ 1 ( E ∗ 1 = E 1 ) 10 A 1 Pb 208 γ σ E 1 E 10 E 2 2 3 4 5 10 10 10 10 10 E (MeV) 2 ( E ∗ = E ) A 2 A ∗ A 2 A ∗ 2 ( E ∗ 2 = E 2 ) � ∞ ¯ n A 2 ( b ) ≡ dE N A 1 ( E , b ) σ tot ( γ A 2 ; E ) . E min � � E max σ tot ( A 1 A 2 → A 1 A ∗ d 2 b P surv ( b ) exp[ − ¯ 2 ; E max ) ≈ n A 2 ( b )] dE N A 1 ( E , b ) σ tot ( γ A 2 ; E ) . E min Huge peak in the photoabsorption cross section – Giant Dipole Resonance.

Electromagnetic excitation of heavy ions 800 250 30 γ γ γ ( ,n) ( ,2n) ( ,3n) 1972 2003 1970 700 1978 2003 γ γ 1985 ( ,2n)+( ,2n+p) 25 200 1964, 1985 Livermore 600 (mb) 1970, (mb) (mb) 1991 Saclay 1993 20 γ γ ( ,n)+( ,n+p) 500 Pb 150 Pb Pb 1964, Livermore 206 205 207 1970, Saclay 2n 3n n 400 15 → → → Pb Pb 100 Pb 300 208 208 208 10 γ σ γ γ σ σ 200 50 5 100 5 10 15 20 25 30 15 20 25 30 35 20 25 30 35 40 45 E (MeV) E (MeV) E (MeV) γ γ γ Giant dipole resonance decays through emission of few neutrons. experimental data on excitation functions for the reactions γ 208 Pb → k neutrons + Pb allow us to calculate the fractions f ( E , k ) of a final state with k = 1 , 2 , 3 neutrons. we can calculate “topological cross sections” with given numbers of neutrons in the forward region of either ion. Monte Carlo Code “Gemini” for evaporation of neutrons based on Hauser-Feshbach Theory. � d 2 b P surv ( b ) P exc A 1 ( b , m ) P exc σ ( A 1 A 2 → ( m N , X )( k N , Y )) = A 2 ( b , k ) .

Electromagnetic excitation of heavy ions 3 3 10 10 total total 2 2 10 10 1n 1n (b) (b) EMD EMD σ 2n σ 2n 10 10 1 1 2 3 2 3 10 10 10 10 10 10 s (GeV) s (GeV) NN NN electromagnetic dissociation cross section for 208 Pb . Data from SPS and LHC (ALICE). calculations from M. Kłusek-Gawenda, M. Ciemala, W. S. and A. Szczurek, Phys. Rev. C 89 (2014) 054907. cross section at LHC ∼ 200 barn! these processes play an important role as “triggers” for ultraperipheral processes.

Inelastic diffraction: kinematics & t-channel exchanges Ԃ To bridge a gap (say ✁ y ✂ 3) : ✄ (0) ✂ 1 (Pomeron, C= +1; Odderon(??), C = -1). Ԃ Exchange of secondary Reggeons: � (0)=0.5 for ☎ , ✆ ,f2,a1; � (0)=0 for pions dies out exponentially with the gap size (no exchange of color or charge over a large gap!) . Ԃ Pomeron/Odderon: multigluon exchanges ; Reggeons: q q - exchange Ԃ Photons (J=1, C=-1) also qualify!

Total photoproduction cross sections V γ * p p From soft to hard diffraction in the photoproduction of vector mesons. Pomeron intercept depends on the meson...

Vector Meson Dominance γ ∗ ( Q 2 ) V V p p Extrapolate from the VM-pole to spacelike region: � 3Γ( V 0 → e + e − ) M 2 A ( γ ∗ ( Q 2 ) p → Vp ; W , t ) = V A ( Vp → Vp ; W , t ) Q 2 + M 2 M V α em V

Vector Meson Dominance Extrapolate from the VM-pole to spacelike region: � 3Γ( V 0 → e + e − ) M 2 A ( γ ∗ ( Q 2 ) p → Vp ; W , t ) = V A ( Vp → Vp ; W , t ) Q 2 + M 2 M V α em V hadronic structure of the photon parameters of A ( Vp → Vp ; W , t ) can be taken from π N elastic scattering ℑ mA ( Vp → Vp ; W , t = 0) = s · σ tot ( Vp ) σ tot ( ω p ) = 1 σ tot ( ρ 0 p ) 2( σ tot ( π + p ) + σ tot ( π − p )) = σ tot ( K + p ) + σ tot ( K − n ) − σ tot ( π + p ) σ tot ( φ p ) = works well for photoproduction of ρ, ω , cannot be correct in the deeply spacelike region Q 2 ≫ M 2 V connection to QCD degrees of freedom at large Q 2 ? heavy flavours ?

Color dipole/ k ⊥ -factorization approach γ ∗ ( Q 2 ) γ ∗ ( Q 2 ) V V r r Color dipole representation of forward amplitude: � 1 � A ( γ ∗ ( Q 2 ) p → Vp ; W , t = 0) = d 2 r ψ V ( z , r ) ψ γ ∗ ( z , r , Q 2 ) σ ( x , r ) dz 0 � � 1 − e i κ r � d 2 κ ∂ G ( x , κ 2 ) σ ( x , r ) = 4 π , x = M 2 V / W 2 3 α S κ 4 ∂ log( κ 2 ) impact parameters and helicities of high-energy q and ¯ q are conserved during the interaction. scattering matrix is “diagonal” in the color dipole representation. Color dipoles as “Good-Walker states”.

When do small dipoles dominate ? the photon shrinks with Q 2 - photon wavefunction at large r : � ψ γ ∗ ( z , r , Q 2 ) ∝ exp[ − ε r ] , ε = m 2 f + z (1 − z ) Q 2 the integrand receives its main contribution from 6 r ∼ r S ≈ � Q 2 + M 2 V Kopeliovich, Nikolaev, Zakharov ’93 a large quark mass (bottom, charm) can be a hard scale even at Q 2 → 0. for small dipoles we can approximate σ ( x , r ) = π 2 3 r 2 α S ( q 2 ) xg ( x , q 2 ) , q 2 ≈ 10 r 2 for ε ≫ 1 we then obtain the asymptotics 1 1 xg ( x , Q 2 + M 2 A ( γ ∗ p → Vp ) ∝ r 2 S σ ( x , r S ) ∝ × V ) Q 2 + M 2 Q 2 + M 2 V V probes the gluon distribution, which drives the energy dependence. From DGLAP fits: xg ( x , µ 2 ) = (1 / x ) λ ( µ 2 ) with λ ( µ 2 ) ∼ 0 . 1 ÷ 0 . 4 for µ 2 = 1 ÷ 10 2 GeV 2 .

Input to a calculation of J /ψ photoproduction Overlap of light-cone wave functions √ 4 πα em N c � e Q m 2 Ψ ∗ V ( z , r )Ψ γ ( z , r ) = Q K 0 ( m Q r ) ψ ( z , r ) 4 π 2 z (1 − z ) � − [ z 2 + (1 − z ) 2 ] m Q K 1 ( m Q r ) ∂ψ ( z , r ) . ∂ r “boosted Gaussian” wave functions as in Nemchik et al. (’94) � M 2 Q R 2 � 8 z (1 − z ) − 2 z (1 − z ) r 2 ψ ( z , r ) ∝ z (1 − z ) exp − R 2 parameters m Q , R & normalization as in Kowalski et al. (2006) for J /ψ and Cox et al. (2008) for Υ. diffractive slope on a free nucleon: B = B 0 + 4 α ′ log( W / W 0 ) with W 0 = 90 GeV , and α ′ = 0 . 164 GeV − 2 . We take B 0 = 4 . 88 GeV − 2 for J /ψ and B 0 = 3 . 68 GeV − 2 for Υ.