The Photon Content of the (Un)polarized Nucleon and the QED Compton Process

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1 UNIVERSITÄT DORTMUND The Photon Content of the (Un)polarized Nucleon and the QED Compton Process in ep eγp and ep eγx Cristian Pisano 36. Herbstschule für Hochenergiephysik Maria Laach 7-17 September 4 in collaboration with M. Glück, A. Mukherjee, E. Reya

2 The photon content of the nucleon Based on the Equivalent Photon Approximation (EPA), originally applied to a charged fermion. The EPA can be extented to the nucleon N = p, n (non-pointlike particle) to simplify the calculation of complicated cross sections: ( )σ NY ( )σ EPA NY = ( )γ ( )ˆσ γy In ( )σ NY Y = l, N interacts with N via virtual photon Q = t = k : virtuality of the photon The EPA is a good approx. when Q In ( )σ EPA NY ( )ˆσ γy : real photoproduction cross section µ : momentum scale in ( )ˆσ γy x: fraction of the proton s momentum carried by the (collinear) photon ( )γ(x, µ ): universal, scale dependent, equivalent photon distribution of the nucleon ( )γ(x, µ ) = ( )γ el (x) + ( )γ inel (x, µ ) elastic γ k γ k N N N X G E (t) G M (t) ( ) ( ) q (x B, Q ) The reliability of ( )γ(x, µ ) has to be tested

3 In terms of the elastic form factors G E (t), G M (t) (m: nucleon mass, τ = t/4m ): γ el (x) = α tmax ] dt {[ x + m x G M π t min t t (t) ] [1 x + m x G M (t) G } M(t) G E (t) t 1 + τ Glück, C.P., Reya, PL B54, 75 () γ el (x) = α tmax { [ ( ) ] π x dt 1 1 t min t x x 1 + m t G E (t) + τ G M (t) } + G M 1 + τ (t) Kniehl, PL B54, 67 (1991) t min, t max m x /(1 x) ( )γ el (x) can be integrated analitically ( )γ inel obeys the LO evolution equation d d ln µ ( )γ inel(x, µ ) = α π q=u,d,s x y ( ) x [( )q(y, ( )P γq µ ) + ( ) q(y, µ ) ] y e q 1 Glück, Stratmann, Vogelsang, PL B343, 399 (1995) Glück, C.P., Reya, PL B54, 75 () P γq (y) = y, P γq (y) = [1 + (1 y) ]/y ( ) q : LO pol. parton distr. GRSV1 (v.s.) ( ) q dy : LO unpol. parton distr. GRV98 minimal not compelling boundary condition ( )γ inel = at µ =.6 GeV

4 Photon distribution of the proton x γ p (x, µ ) /α µ = M W x γ p (x, µ ) /α 1 elastic µ = M W x µ is in GeV x γ p (x, µ ) vanishes at small x, x γ p (x, µ ) increases: γ p (x, µ ) γ p (x, µ ), for x 1 3 x γ p el (x), x γp inel (x, µ ) as x x γ p el (x), x γp inel (x, µ ) as x γ p el (x)/γp el (x) 1 as x 1 The elastic contribution dominates at moderate values of µ : ( )γ p el (x) ( )γp inel (x, µ ), for µ 1 GeV

5 Photon distribution of the neutron.6.4 x γ n (x, µ ) /α. µ = M W 1 x γ n (x, µ ) /α 15 1 µ = M W elastic x γ n (x, µ ) is sizeable smaller than γ p (x, µ ) γ n inel (x, µ ) is marginal for x., γel n (x) is marginal and non-singular as x At small x, ( )γ n (x, µ ) behaves as ( )γ p (x, µ ): x γ n el (x), x γn inel (x, µ ) as x x γ n el (x).78, x γn inel (x, µ ) as x γel n (x)/γn el (x) 6/7 as x 1

6 Asymmetries A p,n γ (x, µ ) = γp,n (x, µ ) γ p,n (x, µ ) 1.8 A p γ (x, µ ) γ p el (x) / γ p el (x) µ = M W.6 1 µ = M W. elastic x 1.8 A n γ (x, µ ) γ n el (x) / γ n el (x).6 µ = M W 1 µ = 1. M W elastic x

7 The QED Compton process It is one of the most important processes for measuring ( )γ(x, µ ) and testing the EPA It provides information about F 1, (x B, Q ) and g 1, (x B, Q ) in the low-q region Blümlein, Levman, Spiesberger, JP G19, 1695 (1993) e l Exact l' e EPA γ k k ' γ e l l' e p P P x γ X + crossed + crossed p k' γ EPA limit: S m ŝ Q S = (P + l), ŝ = (k + l), ˆt = (l l ) The exact cross section σ is known manifestly covariant Mukherjee, C.P., EPJ C3, 477 (3) helicity formalism Courau, Kessler, PR D46, 117 (199) ( )σ EPA has also been calculated with µ = ŝ Glück, C.P., Reya, Schienbein, EPJ C7, 47 () De Rújula, Vogelsang PL B451, 437 (1999) HERA-H1 cuts: E e, E γ > 4 GeV, E e + E γ > GeV,.6 < θ e, θ γ < π.6, Φ = π Φ e Φ γ < π/4 Lendermann, DESY-THESIS--4 Lendermann et al., EPJ C31, 343 (4)

8 QED Compton process at HERA σ (pb) σ (pb) Exact σ = (σ el + σ inel ) versus σ EPA and σ Len The bins are in Q l = ˆt and x l, with x l = Q l P (l l ) In σ, σ EPA, σ Len : F parametriz. ALLM97 (Q ) σ Len : estimated via iterative approx. procedure σlen σ 4%, max 14% in th bin; σ σ Len σ inel inel σ inel Q l (GeV (a) ) %, max 6% in th bin < x l < < x l < Q l (GeV ) (c) σ (pb) σ (pb) σ el = 1.73 nb, while σ inel = 1.1 nb < x l < exact Lendermann EPA Q l (GeV (b) ) < x l < Q l (GeV ) (d) The EPA is a very good approx. for the elastic process: σepa el σ el σ el =.3%, while σepa σ = 14% σ

9 QED Compton process at HERMES The exact σ has been recently calculated Mukherjee, C.P., PR D7, 349 (4) only elastic Ji, PR D55, 7114 (1997) ( )σ and ( )σ EPA are in x γ bins, x γ = l k P l x γ is the fraction of longitudinal momentum of the proton carried by the photon x γ x l x = ŝ as Q S F param. ALLM97, g, g 1 : Badelek et al. 3 5 Exact: EPA: 3 5 Exact: EPA: σ (pb) 15 σ (pb) (a) 5 (b) x γ x γ σ el = 6. pb σ el = pb σ inel = 6.3 pb σ inel =.34 1 pb Kinematical cuts: E e, E γ > 4 GeV, ŝ > 1 GeV,.4 < θ e, θ γ <., ŝ > Q EPA works better than at HERA: (smaller Q ) σ EPA σ σ σ el σ EPA el σ el = 6.%, = 5.7%, σ EPA σ σ σ EPA el σ el σ el = 7.1% = 8.% Experimental data are needed to confirm the validity of the photon content ( )γ p,n (x, µ )

10 Asymmetries Asymmetry: A LL = σ σ σ = 1 (σ ++ σ + ); σ = 1 (σ ++ + σ + ).5.4 Exact: EPA: A LL x γ Asymmetry very small for smaller x γ bins; increases as x γ increases Agreement with the EPA better except in the last bin Expected statistical error is large for high x γ bins. Error: δa LL 1 P e P p Lσbin ; P e = P p =.7, L = 1 fb 1. g p 1 can be measured in the range. x B.7 (Bjorken x) and.7 Q 7. g p 1 and γp (x, µ ) are accessible at COMPASS and erhic as well

11 Virtual Compton Scattering Background VCS: major background contribution, the photon is emitted from the hadronic vertex e l l' e p P γ k' P X γ X Elastic contribution: generalized parton distributions. Approx.: pointlike proton Inelastic contribution: effective parton model d( )σ inel dx B dq dŝ dˆt dϕ = q ( ) q(x B, Q ) d( )ˆσ q dŝ dq dˆt dϕ, ϕ : azimuthal angle of the outgoing e γ system in the e γ c. m. frame d( )ˆσ q : differential cross section of the subprocess e(l) + q(p) e(l ) + γ(k ) + q(p ), with q = u, d, s, ū, d, s. ( ) q(x B, Q ): effective parton distribution, extrapolated down to Q

12 Suppression of VCS Background (HERA) Invariant: Ŝ = (p + k ) = ˆt(x l x B ) x l q(x B, Q ) = Q Q +a Q q(x B, Q + Q ) a = 1/4 and Q =.4 GeV, q(x B, Q ): NLO GRV98. q(x B, Q ) q(x B, Q ) for Q Q Mukherjee, C.P., EPJ C35, 59 (4) QEDCS: VCS: ALLM97 (GRV98) eff (GRV98) eff 1 1 σ inel (pb) s - S Inelastic interference between QEDCS and VCS: negligible. VCS is suppressed when ŝ < Ŝ Similar behaviour also for the polarized VCS cross section at HERMES and erhic Imposing a cut on Ŝ can be very effective in reducing the background contribution from VCS

13 Conclusions The photon content of the nucleon ( )γ N (x, µ ) evaluated in the EPA allows for a simpler and more efficient calculation of photon-induced subprocesses in elastic/deep ep and hadronic (pp,...) reactions Some of these reactions (QED Compton process in ep eγp and ep eγx) will provide informations concernig the structure functions F 1, and g 1, in the low Q region Kinematical cuts have been studied in order to extract ( )γ N (x, µ ) from experiments and check its range of validity and accuracy γ p (x, µ ): measurable at HERA γ p (x, µ ): measurable at HERMES, COMPASS, erhic