Measurement of Diffractive Scattering of Photons with Large Momentum Transfer at HERA
aa r X i v : . [ h e p - e x ] J u l Measurement of Diffractive Scattering of Photons withLarge Momentum Transfer at HERA
Tom´aˇs Hreus (On behalf of the H1 Collaboration)Universit´e Libre de Bruxelles - I.I.H.E.Boulevard du Triomphe, CP230, 1050 Bruxelles, BelgiumThe first measurement of diffractive scattering of quasi-real photons with large momen-tum transfer γp → γY , where Y is the proton dissociative system, is made using theH1 detector at HERA. Single differential cross sections are measured as a function of W , the incident photon-proton centre of mass energy, and t , the square of the four-momentum transferred at the proton vertex. The W dependence is well described bya perturbative QCD model using a leading logarithmic approximation of the BFKLevolution, whereas the measured | t | dependence is harder than predicted. e e γ (*) p Y } γ x IP , t ( k ) ( k ′ ) ( p γ )( q )( p ) ( p Y )∆ η Figure 1: Schematic illustration of the ep → eγY process.The study at the ep collider HERA of exclu-sive diffractive processes in the presence ofa hard scale provides insight into the partondynamics of the diffractive exchange. Thefour-momentum squared transferred at theproton vertex, t , provides a relevant scaleto investigate the application of perturba-tive Quantum Chromodynamics (pQCD)for | t | ≫ Λ [2]. The diffractive photon-proton scattering, γp → γY at large | t | gives an experimentally clean and almostfully perturbatively calculable process tostudy the parton dynamics. Its cross sectionmeasurement [3] is performed at HERA bystudying the reaction e + p → e + γY in thephotoproduction regime (initial photon vir-tualities Q < .
01 GeV ) and at 4 < | t | <
36 GeV , with a large rapidity gap between thefinal state photon and the proton dissociative system Y (as illustrated in Fig. 1) and the γp centre of mass energy in the range 175 < W <
247 GeV.Diffractive photon scattering can be modelled in the proton rest frame by the fluc-tuation of the incoming photon into a q ¯ q pair, which is then involved in a hard inter-action with the proton via the exchange of a colour singlet state. In the leading log-arithmic approximation (LLA), the colour singlet exchange is modelled by the effectiveexchange of a gluon ladder (Fig. 2), described at sufficiently low values of Bjorken x bythe BFKL [4] approach. In the LLA BFKL model the gluon ladder couples to a singleparton within the proton. Due to the quasi-real nature of the incoming photon, the trans-verse momentum of the final state photon, P γT , is entirely transferred by the gluon ladderto the parton in the proton. The separation in rapidity between the parton scattered bythe gluon ladder and the final state photon is given by ∆ η ≃ log(ˆ s/ ( P γT ) ), where ˆ s isthe invariant mass of the system formed by the incoming photon and the struck parton. DIS 2009 (*) p Y } γ Figure 2: Illustration of the γ ( ∗ ) p → γY pro-cess in a LLA BFKL approach.In addition to the usual DIS kinematicvariables, the longitudinal momentum frac-tion of the diffractive exchange with respectto the proton, x IP and the elasticity of the γp interaction, y IP , are defined as (Follow-ing the notation in Fig. 1) x IP = q · ( p − p Y ) q · p , y IP = p · ( q − p γ ) p · q . The data, corresponding to an integratedluminosity of 46 . − , were collected withthe H1 detector during the 1999 − E e = 27 . E p = 920 GeV. The detailed descrip-tion of the H1 detector can be found in [5]. The quantity W is calculated from the measuredenergy of the scattered positron, E e ′ , using the relation W ≃ ys ≃ s (1 − E e ′ /E e ) with therelative resolution 4%, where s = ( k + p ) is the ep centre of mass energy squared. Thescattered positron is detected in a small calorimeter 33 m downstream the main detector.The photon candidate is detected as a cluster in the electromagnetic section of the calorime-ter, with no associated track and is furthermore required to have an energy E γ > P γT > | t | is reconstructed as | t | ≃ ( P γT ) , with the resolution of 11%. The hadronic final state Y is reconstructed us-ing a combination of tracking and calorimetric information. The event inelasticity of the γp interaction is reconstructed as y IP ≃ P Y ( E − P z ) / [2( E e − E e ′ )], where the summationis performed on all detected hadronic final state particles in the event. Diffractive eventsare selected by requiring y IP < .
05, ensuring a large pseudorapidity gap, ∆ η , between thephoton and the proton dissociative system Y , since y IP ≃ e − ∆ η .After applying all selection criteria, described in a more detail in [3, 6], 240 events remainin the data sample. The
HERWIG | t | photonscattering using the LLA BFKL model [7, 8, 9]. At leading logarithmic accuracy there aretwo independent free parameters in the BFKL calculation: the value of the strong coupling α s and the scale, c , which defines the leading logarithms in the expansion of the BFKLamplitude, ln( W / ( c | t | )). In exclusive production of vector mesons, the scale parameter c is related to the vector meson mass. In the case of diffractive photon scattering, theunknown scale results in the absence of a normalisation prediction of the cross section. Inthe calculations considered here, the running of α s as a function of the scale is ignoredand will henceforth be referred to as α BF KLs . The choice of α BF KLs = 0 .
17 is used for thesimulation for this measurement.
DIS 2009 n the asymptotic approximation of the calculations [9], the W dependence of the crosssection follows a power-law, σ ( W ) ∼ W ω , where the exponent is given by the choiceof α BF KLs by ω = (3 α BF KLs /π ) 4 ln 2. For the t dependence of the cross section, anapproximate power-law behaviour is predicted of the form d σ/ d | t | ∼ | t | − n , where n dependson the parton density functions of the proton and on the value of α BF KLs . In order to describethe data, the t dependence of the diffractive photon scattering simulation was weighted bya factor | t | . . This weighted HERWIG prediction is used only to correct the data forresolution and acceptance effects.Possible sources of background were estimated using MC simulations and two of thesesources were identified as non-negligible. The background from inclusive diffractive pho-toproduction events ( ep → eXY , where the two hadronic final states are separated by arapidity gap) is simulated using the PHOJET
MC event generator. This background con-tributes when a single electromagnetic particle fakes the photon candidate and the processis estimated to amount to 3% of the measured cross section. The background from elec-tron pair production ( ep → ee + e − X ) is modelled using the GRAPE event generator. Thisprocess contributes to the selection if two of the leptons fake signals from the photon can-didate and the scattered electron, whereas the remaining lepton escapes detection. Thisbackground contributes 4% of the measured cross section.
The ep → eγY differential cross sections are defined using the formula:d σ ep → eγY d W d t = N data − N bgr L A ∆ W ∆ t , where N data is the number of observed events corrected for trigger efficiency, N bgr theexpected contribution from background events, L the integrated luminosity, A the signalacceptance and ∆ W and ∆ t the bin widths in W and t , respectively. The γp → γY differential cross section is then extracted from the ep cross section using:d σ ep → eγY d W d t = Γ( W ) d σ γp → γY d t ( W ) , where the photon flux, Γ( W ), is integrated over the range Q < .
01 GeV according tothe modified Weizs¨acker-Williams approximation [10]. The γp cross section is obtainedby modelling σ γp → γY as a power-law in W , whose parameters are iteratively adjusted toreproduce the measured W dependence of the ep cross section. The differential γp crosssection in | t | is then extracted from the ep cross section by correcting for the effect of thephoton flux over the visible W range. The γp cross section as a function of W is obtainedby first integrating the above equation over the | t | range, and then correcting for the effectof the photon flux in each bin in W .The systematic error on the measurement stems from experimental uncertainties andfrom model dependences. They are calculated using the weighted HERWIG simulation ofthe signal process. The uncertainty on the PHOJET MC normalisation and the size of thevariation of the model dependence on x IP , | t | and M Y , are estimated from the measureddistributions in the data: the variation corresponds to the a range where the model stilldescribes the data. Each source of systematic error is varied in the weighted HERWIG DIS 2009 [GeV]
180 190 200 210 220 230 240 [ nb ] Y γ → p γ σ H1 Data =0.26
BFKLs α =2.73 δ fit: δ W =0.14
BFKLs α LLA BFKL =0.37
BFKLs α LLA BFKL at large |t| γ H1 Diffractive Scattering of IP y W [GeV]
180 190 200 210 220 230 240 [ nb ] Y γ → p γ σ ] |t| [GeV ] / d t [ pb / G e V Y γ → p γ σ d H1 Data fit: n=2.60 -n |t| =0.14 BFKLs α LLA BFKL =0.26
BFKLs α LLA BFKL =0.37
BFKLs α LLA BFKL < 0.05 IP yW = 219 GeV at large |t| γ H1 Diffractive Scattering of ] |t| [GeV ] / d t [ pb / G e V Y γ → p γ σ d a) b)Figure 3: The γp cross section of diffractive scattering of photons as a function of a) W ,b) | t | . The solid line represents a fit to the cross section. Additional curves show the LLABFKL predictions corresponding to different α BF KLs .Monte Carlo within its uncertainty. The largest systematic error on the cross sectionscomes from the uncertainty on the x IP and M Y dependences. The total systematic erroron the W and | t | dependence of the cross section varies from 10% to 17% and from 8% to14%, respectively. An additional global uncertainty of 4% arises from the γp cross sectionextraction procedure. The total systematic errors are comparable to or smaller than thestatistical errors. The cross sections are measured in the domain 175 < W <
247 GeV, 4 < | t | <
36 GeV , y IP < .
05 and Q < .
01 GeV . The γp → γY cross section as a function of W is shownin Fig. 3a. A power-law dependence of the form σ ∼ W δ is fitted to the measured crosssection, the fit yields δ = 2 . ± .
02 (stat . ) +0 . − . (syst . ) with χ / n.d.f. = 2 . /
2. The steeprise of the cross section with W is usually interpreted as an indication of the presence of ahard sub-process in the diffractive interaction and of the applicability of perturbative QCD.The present δ value, measured at an average | t | value of 6 . , is compatible with thatmeasured by H1 in diffractive J/ψ photoproduction of δ = 1 . ± . . ) ± . . )[11] at an average | t | of 6 . . The Pomeron intercepts associated with these δ valuescorrespond to the strongest energy dependences measured in diffractive processes.The γp cross section differential in | t | , at W = 219 GeV, is shown in Fig. 3b, togetherwith a fit of the form d σ/ d t ∼ | t | − n , where the fitted n = 2 . ± .
19 (stat . ) +0 . − . (syst . )with χ / n.d.f. = 1 . /
1. The | t | dependence is harder than that measured by H1 in thediffractive photoproduction of J/ψ mesons at large | t | [11]. The measured cross sections arecompared to predictions of the LLA BFKL model, using the HERWIG
Monte Carlo with no | t | weighting. The predictions are normalised to the integrated measured cross section, as thenormalisation is not predicted by the LLA BFKL calculation. The W dependence of the cross DIS 2009 ection is well described by the LLA BFKL prediction. Using δ = 4 ω = 4 (3 α F itS /π ) 4 ln 2,the measured W dependence leads to α F itS = 0 . ± .
10 (stat . ) +0 . − . (syst . ). Predictions areshown in Figure 3 also for the values α BF KLs = 0 .
14 and 0 .
37, corresponding to one standarddeviation of α F itS .As shown in Figure 3b, the LLA BFKL calculation for α BF KLs = 0 . , .
26 and 0 .
37, allof which give a reasonable description of the W dependence, predict steeper | t | distributionsthan is measured in the data. The same effect cannot be established for the exclusive ρ measurement [12], where the measured t range is limited to | t | < , although anunderestimate of the cross section was observed at the largest values of | t | . The presentsituation is in contrast with the analysis of J/ψ production [11, 13], where the | t | dependencewas found to be well described by the LLA BFKL prediction over a similar range in t . References [1] Slides: http://indico.cern.ch/contributionDisplay.py?contribId=172&sessionId=18&confId=53294 [2] J. R. Forshaw and P. J. Sutton, Eur. Phys. J. C (1998) 285 [arXiv:hep-ph/9703225].[3] F. D. Aaron et al. [H1 Collaboration], Phys. Lett. B (2009) 219 [arXiv:0810.3096 [hep-ex]].[4] E. A. Kuraev, L. N. Lipatov and V. S. Fadin, Sov. Phys. JETP (1977) 199 [Zh. Eksp. Teor. Fiz. (1977) 377].[5] I. Abt et al. [H1 Collaboration], Nucl. Instrum. Meth. A (1999) 107 [arXiv:hep-ph/9808455].[8] N. G. Evanson and J. R. Forshaw, Phys. Rev. D (1999) 034016 [arXiv:hep-ph/9902481].[9] B. E. Cox and J. R. Forshaw, J. Phys. G (2000) 702 [arXiv:hep-ph/9912486].[10] S. Frixione, M. L. Mangano, P. Nason and G. Ridolfi, Phys. Lett. B (1993) 339[arXiv:hep-ph/9310350].[11] A. Aktas et al. [H1 Collaboration], Phys. Lett. B (2003) 205 [arXiv:hep-ex/0306013].[12] A. Aktas et al. [H1 Collaboration], Phys. Lett. B (2006) 422 [arXiv:hep-ex/0603038].[13] S. Chekanov et al. [ZEUS Collaboration], Eur. Phys. J. C (2003) 389 [arXiv:hep-ex/0205081].(2003) 389 [arXiv:hep-ex/0205081].