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Hard QED Radiation at HERA

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Hard QED Radiation at HERA L P N H E 93-07 2 Jr Qbklgq CERN LIBRHRIES, GENE?/F1 IIIIIIIIlll|IlI| @Qiil||IIIlIIIIIII a Hard QED radiation at HERA M.W. KRASNY Laboratoire de Physique Nuciéaire Eneries et de Hautes g LPNHE - Paris N2P3 - Universités Paris Vi et VH CNRS — i4, place75252 Jussieu aris-Tour 33 - Rez-de-Chaussée PCedex 05 s F OCR Output Ta. ;ss ( 1 )44 27 6313 - FAX. as (1 )44 27 45 ss- Téigx; 202 sz OCR OutputM.C. ESCHER "Anneoux concentriques/’ fc) by SPADEM l983 OCR Output OCR OutputHard QED radiation at HERA l\/[.W. Krasny L.P.N.H.E IN2P3-CNRS, Universities Paris VI et VII 4, pl. Jussieu, T33 PtdC 75252 Paris Cedex 05, France and High Energy Physics Lab., Institute of Nuclear Physics,Pl-BOO55 Cracow, Poland Abstract: The deep inelastic electron—proton collisions at HERA are fre quently associated with emissions of hard photons. A large fraction of these events can be identified either by the direct detection of radiative photons, or, indirectly, by a mismatch between the event kinematics determined from the scattered electron energy and its angle and that determined from the hadronic flow associated with a deep inelastic scattering. This unique feature of HERA experiments provides an experimental check on the size of radiative correc tions. The emission of photons collinear with the incident electrons leads to a reduction of the effective beam energy. This effect can be used to measure the longitudinal structure function. Invited Talk presented at the Durham Workshop "HERA the new frontier for QCD, Durham, UK, March l993" OCR Output 1 Introduction At HERA the cross section for radiative scattering : ep —> e + 7 + X is large [1] and, especially at small x, can be of the same order of magnitude as the nonradiative cross section. In the majority of previous deep inelastic experiments, the above process could not be , distinguished from the nonradiative scattering: ep —> e + X As a consequence, the corresponding radiative corrections had to be calculated and applied to the measured cross sections prior to extraction of the structure functions. At HERA the corrections get larger and more uncertain, as they depend significantly upon the assumed shape of the structure functions in the kinematical domain that has so far been unexplored. On the other hand, the HERA experiments provide unique possibilities to control experimentally the size of the hard photon radiative corrections. Owing to almost 4vr coverage of the hadronic measurement, a large fraction of events containing unobserved hard initial state radiation photons can be identified on the basis of the measured hadronic energy flow. If these events are eliminated, the remaining correction becomes small and, to a large extent, independent of the assumed shape of the structure functions in the unmeasured region. An important class of radiative events are those in which the hard photon is emitted nearly collinearly to the incident electron and is subsequently measured in the luminosity calorimeter. These events can be interpreted as originating from the scattering at the reduced center—0f—mass energy. They provide means to study the longitudinal structure function. 2 Identification of hard QED radiation events At HERA, a significant fraction of radiative scattering events associated with the emission of hard photons can be identified. The initial state radiation photons can be detected in the H1 and Zeus luminosity monitors [2], [3] providing the E, measurement in the angular range: vr — 0.0005 $ 0 § rr, where 0 is the polar angle with respect to the proton beam direction. A sizeable fraction of the initial state hard radiation photons are produced within this angular range The Ev resolution is deteriorated significantly by the 3 XO thick absorber which shields the 7 counters from the soft synchrotron radiation photons. ln the case of H1, the 3 XO long absorber consist of a 2 XO long passive filter and a l XO long water Cherenkov active filter. The later is used to improve the energy resolution of early photon showers. From a detailed simulation of the H1 detector, one finds that at E, : 25 GeV, a resolution better than 5% can be achieved and that nonlinearities can be kept below 5% for 7.5 GeV f E, § 25GeV. The dominant hard photon background in the luminosity counter comes from the radiative elastic scattering process ep —> ep + 7. The cross section for this process is OCR Output many orders of magnitude larger than that for deep inelastic scattering. At the nominal luminosity, about 5% of bunch crossings will give rise to a 3 GeV of energy in the gamma calorimeter and about 1% of the bunch crossings will give rise to 8 GeV. Random coincidences between the nonradiative deep inelastic scattering and the ra diative elastic scattering process occuring in the same bunch crossing may mimic a hard initial state radiation process associated with a deep inelastic collision. The rate of such a coincidence is proportional to the instantaneous luminosity. At the nominal HERA luminosity this rate is larger, than that for a deep inelastic collision associated with the emission of a hard photon from the projectile electron ( Fig. 1). During the 1992 runs with limited instantenous luminosity the rate of the artificial coincidence was always below 0.2 of the deep inelastic collision rate. L dN(E,)/dE., 1.500 · 105 1.000- 1U" 0.500 - lO° •·••••••••••1•·•!.·*g;|·g¢.A1nl¤IlA·Il-O I 5.000 10.000 15.000 20.000 25.000 30.000 E7 [GeV] Figure 1: Photon spectra observed in the luminosity gamma arm in random coincidence with a deep inelastic scattering event ofpjmd $ 2GeV at the design luminosity: the radia tive elastic scattering - solid line; the radiative inelastic scattering — full circles. When the HERA design luminosity is reached, it will be impossible to identify the radiative deep inelastic scattering events on an event-by—event basis. However, the size of the radiative elastic scattering background can be monitored by using low ye events where the photon energy is kinematically limited to ye >1= Ee. The ye can be expressed in terms of the scattered electron energy Ee, the angle He and the energy of the incident electron Ee, in the following way: Ee · He 2 ye = 1 — ESIHQ (1) OCR Output An effective event-by-event tag could be made at reduced luminosity using the electron arm of the luminosity system. In its limited energy range an electron associated with the elastic radiative photon should be detected. The random coincidence probability is significantly diminished by requiring that no signal in the energy window centered at E6 = EO — E., be observed. In addition, the difference in the angular distributions of photons from the two above processes can be exploited if the electron beam divergence is kept below z 0.05 mrad, and the transverse position of the photon shower center of gravity is determined with a precision better than x 5 mm. Radiative events with hard photons emitted by the incoming electron can also be identified by means of measuring the hadronic energy flow associated with the scattered electron. In these events, the scattered quark energy and its angle are smaller than those expected from the electron measurement of 1:,, and [6] leading to a significant difference in the electronic and hadronic measurement of x and Q2 The emission of photons in a direction close to the incident electron can be interpreted as a reduction in the effective electron beam energy. The effective electron energy ECU (or the missing energy Em, : E., — EEN) can be calculated from the scattered electron energy Ec, the angle GC and from the hadronic momenta ph and the angles 0;,, in the following way: Emis I EO ’ (2) 1 _ Z/z where: yr = yin = ;E(Eh — pt c¤S9t)/Ea 2 I) (3) T + S11]E The yy; and yi are the Jaquet - Blondel [7] and the ”true” y respectively. The ”true” y describes the interaction of the virtual photon with the hadronic system. Note, that the Emi, can be equivalently expressed in terms of ye and yy}; as: Emis Z E0(ye _ yJB) For the nonradiative (Born) events one expects Em, : 0, whereas for the radiative events with hard unobserved photons emitted collinearly with the incoming electron, Emi, is equivalent to the sum of energy of these photons — E,. For the finite pt initial state photon emission the condition Em, : E, is approximately fulfilled, as the emission angle is small ( of the order of Once the effective electron energy is known, each deep inelastic scattering event can be characterized by the initial state radiation independent variables: (E0 " E0(ye _ yJB))Ee COS2 He/2 I 1 t 1 · 7 EP(Eo " bef]/e _ Z/JB) ' Ee SH12 Ge/2) Q? = 4-E€(EO · EO(y€ - yJB)) COSZ 98/Z (6) OCR Output where Ep denotes the energy of the proton beam. The latter variables must be used to describe the interaction of the virtual photon with the hadronic system as they enter as arguments in the structure functions. If one defines z as: Ee — E 7 (7) one can write simple relations between the above variables and the corresponding variables determined from the electron energy and angle: y+ z — 1 e Q? Z ZQ; mz =scey gqjji z yi I *7 (8) where, 2 2 Qe = 4EeEe cos (Ge/2), me = yes Using both sets of variables, the initial state radiative events can be tagged as those where a significant difference between the reconstructed cve, ye, Q2 and t_he corresponding :1:,, yt, are observed. In Fig. 2 the generated and reconstructed spectrum of radiative photons are shown for a (ave, ye) bin.
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