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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

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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.

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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. The spectra shown have been obtained by smearing the kinematic variables according to a simplified model of the detector in which hadron energies are measured with a resolution of 0.55x/E, the electron energy with a resolution of 0.15x/F and the angle of particles with a resolution of 10 mrad up to 175 deg (with respect to the proton beam). The peak at E., : 0 corresponds to the Born contribution (including final state radiation events with photons collinear to the outgoing electron), whereas the peak at E., = yeEe corresponds to the low Q? hard initial state photon bremsstrahlung events. Fig. 2 shows clearly that Born and hard initial state radiation events can be efficiently separated. The efficiency to identify radiative events is almost uniquely determined by the de tector ability to measure the energy of hadrons over a large angular range. If hadrons are detected up to 175°, events containing not directly observed hard initial state radia tion photons of energies larger than M 5 GeV are identified with high efiiciency and the probability of Born event misclassification can be kept below 0.1 Some of hard photons associated with the deep inelastic scattering can be observed also in the main H1 (Zeus) electromagnetic calorimeters. Those photons are predominantly emitted in the direction of the scatterd electron and their deposited energy is added to the energy deposited by the scattered electron. Photons which can be separated spacialy from scattered electron could orginate either from radiation or from ¢r" decays. The method of classifying photons into a ”radiative sample” and a ”hadronic sample” has been developed by G. Levman using the neural network method It has been demonstrated that the method allows for an unambigous assignment of photons into these event classes. OCR Output dN I i·

30

20

100 HI`

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Figure 2: The generated [solid line} and the reconstructed (full circles} spectrum of the energy of radiative photons for 4 >•< 10“4 § me § 8 =•<10"4 and 0.5 f ye § 0.6.

Another class of radiative events that can be rather easily identified at HERA is that of ”Compton events” They can be viewed as resulting from the emission of a quasi real photon from a quark or proton followed by a subsequent Compton scattering ey —> ey. The radiative events corresponding to the Compton contribution contain a photon which balances the transverse momentum of the scattered electron and very weak, if any, hadronic activity in the detector. Events in which the photon is lost in the beam hole (low ace, high ye), can be identified using the method based on a reconstructed missing longitudinal energy , while those with a visible hard photon may be identified on the basis of their acoplanarity [10] as well as on the basis of pe matching.

3 Experimental control of radiative corrections

ln this section we discuss the radiative corrections to the measured differential cross section °i°;;!;`,d; expressed in terms of the electronic variables ye, re. The measured differential cross section contains all the electroweak higher order contributions which must be subtracted in order to obtain the Born cross section expressed in terms of the Lorentz invariants characterizing the exchanged vector boson. The relation between the measured and the Born cross section can be written as follows:

MEA dO.dO.BORN(I Z 1. y : y — : 1 6 , . e. e 10

where 6RC(.re, ye) is the radiative correction which is known to be large {ll] f12]. At HERA the uncertainty in the size of the radiative correction originates from, a priori unknown, shape of the structure functions in the unmeasured kinematical region OCR Output rather than from the technical aspects of the matrix element integration. The uncertainty range is shown in Fig. 3, where the leptonic corrections are drawn at fixed Q2 for several available parametrizations of the structure functions.

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0.0 0.25 0.5 Figure 3: The leptonic radiative correction 6RC(a:c, ye) calculated for several parametriza— tions of the structure functions.

The sensitivity of the radiative correction size to the shape of the input structure functions arises from the processes of hard photon emission. In the presence of hard photons the differential cross section in a ;c,.,Q§ bin depends upon the structure function shape in the whole domain of sc 2 xc and y f ye: dO.MEA 1 yd dUBoRN(x y) ’ ——— dmedye = d d I' 6, €·—·; wvxlw ymy) dm, 11 ( )

The analytical form of the kernel K(x€,yc;x,y) can be found e.g. in [12]. The inte gration region contributing to the cross section at me : 0.001,Qg : 95GeV and at me : 0.009,Qg = 95GeV are indicated by the dashed lines in Fig 4a and Fig. 4b respectively. The shadowed areas correspond to the kinematical domains which have been, or are going to be, explored in the deep inelastic scattering experiments. The HERA band is restricted by the accuracy of the measurement of the scattered electron energy to the ye 2 0.1 region [13] and by the maximal angle at which the electron energy can be measured (172 deg). The solid line on the left side of the (:z:€,y€) point shows the integration region in the case where the photon is collinear with the incoming electron. The curve is described by the following equations:

QI2 QQ? (ml OCR Output Cc Z $63/C22 (13) ye 'l' zi “ 1 where ye : QZ/aces and z, : (Ee — EW)/Ee is a function of the hard photon energy Ee, (1 2 zi 2 (1 — ye)/(1 — ;reye)). Each point on the curve corresponds to a unique ze(EW) value. The points corresponding to the E, values of Ej : 3j GeV, j = 1,jme are displayed on the figure as stars (the star closest to the full circle corresponds to the energy EW of 3 GeV). The dotted line on the right side of the (a:e,ye) point shows the integration region in the case where the photon is collinear with the outgoing electron, The curve is described by the following equations:

Q2 I ZJQE (M)

x Z ;_”‘€y€Zf (15) 1 — Zf + 2196 where ye : QQ sres and Zf : (Ee + Ee,)/Ee is the function of the hard photon energy EW (1 $ Zf § 1/(1 + szteye — ye)). Again, the points corresponding to the Eq values of Ej : 3j GeV, : 1,jmee are displayed on the figure as stars (the star closest to the full circle corresponds to the energy Ev of 3 GeV). The dominant contribution to the measured cross section at (;z:e,ye) comes from narrow paths around the curves discussed above. These regions, often called the ”s-peak” region and_ ”p-peak” region [14], correspond to the domain where the kernel K(:ce,ye,a;,y) is large. The widths of these paths of z ,/me/Ee and x ,/me/Ee respectively reflect the peaking behaviour of the photon angular distribution. The other factor that determines the magnitude of the contribution to the measured cross section at (me, ye) is the Born differential cross section. This cross section is large in the low Q2 (Q2 ——+ 0) region and can outweigh the small kernel value K(.re, ye, xr, y), which falls rapidly as the hard photon emission angle increases, giving rise to a substantial contribution to the measured cross section at (xe,ye). This contribution often called the ”t—peak” [14] can be also called the ” Compton contribution” [6] because it can be viewed as resulting from the emission of a quasi real photon from a quark or proton followed by a subsequent Compton scattering ey —+ ery. Another substantial contribution to the measured differential cross section at (;z:e,ye) comes from elastic electron scattering (the x : 1 line in Fig. 4) where the cross section is large at small Q2 but dies away rapidly with increasing Q2 Having pointed out the main sources of large radiative corrections, their me and ye dependence can be understood qualitatively. ln the region of large ye and small me the lower kinematical bound of Ze approaches O and the s-peak line is pushed towards the low Q2 region where the differential cross section is significantly larger than at ln addition, the s-peak line crosses the elastic.;r : 1 line at small Q2, where the elastic cross section is still large. A sizeable contribution from the t—peak is also expected in this region because the Q2 : O limit is approached closely by the s-peak line. At low ye and low re the ze (EW) domain shrinks and only soft photons of energies up to 2: yeEe are kinematicaly allowed. This is shown in Fig. 4b, where the distance between the s-peak line and the p—peak line is smaller than the one shown in Fig. 4a. The region of small Q2 is thus not accessed and the correction remains small. The decrease of the hard photon radiative contribution at large x is due to the shrinking y and x integration regions. As we have already shown in Fig. 3, the hard photon radiative correction depends strongly upon the shape of the structure functions. As it is shown in Fig. 4 a substantial OCR Output Q o

-1 D Y 2 3 4 LOG10(02 (cm) X VSOZ

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-1 ¤ 1 2 s 4 LOG10(Q2(GEV)) X VS Q2 Figure 4: The topology of fhe (LQ?) domains contributing to the radiative differential cross section. See text for further explanations. traction of the integration domain has not been explored so far. ln this domain the input structure functions have to be extrapolated from the large x, low Q2 domain to the unmeasured region. VVhile the extrapolation in the Q2 variable at a Fixed x is well under control in perturbative QCD, the extrapolation towards lower x values at fixed Q2 is to a large extent uncertain. The latter extrapolation has to be made in order to specify the structure functions along the s—peal< curve, which yields the dominant contribution to the OCR Output radiative cross section. The above observation explains the large differences in the size of the radiative corrections observed in Fig. 3. The radiative corrections discussed in this chapter can be drasticaly reduced if hard photon radiative events are unarnbigously identified by applying the methods outlined in the chapter 2. The remaining radiative corrections become less sensitive to the assumed functional form ofthe structure functions as the integration region discussed above shrinks to a region in the closest vicinity of the (:06,yE) point. This is illustrated in Fig. 5 in which the ”inclusive radiative corrections” are compared to those obtained by applying detector cuts described below. This plot results from the detailed simulation of the H1 detector. The open circles correspond to the ”inclusive radiative corrections” (equivalent to those applied in the fixed target deep inelastic scattering experiments). The open squares correspond to a reduction of the radiative correction size owing to the calorimetric measurement of the event kinematics. In such a measurement, the energy of nonresolved final state radiative photons is added to that ofthe scattered electron. The open triangles correspond to the size of the radiative corrections if one demands that at least one charged particle is reconstructed in the central drift chamber and the missing longitudinal energy is smaller than 11.7 GeV. The tracker requirement (equivalent to demanding a reconstructed vertex) rejects most of the Compton events of low invariant hadronic mass, whereas the missing longitudinal energy cut rejects events with hard initial state radiation photons.

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10 OCR Output 4 Determination of the longitudinal structure func tion from radiative events

In order to separate FL(1:,Q2) from F2(a;,Q2) in the cross section for ep —> eX, it is necessary to measure the variation of the cross section with the center-of-mass energy by reducing either the electron or the proton beam energy [15]. Emission of photons in a direction close to that of the incident electrons can be interpreted as a reduction of the effective electron beam energy. This effective beam energy can be determined from the energy of hard photons observed with the help of the luminosity monitors of H1 or ZEUS. The differential cross section for the process ep -2 e·yX, integrated over the photon emission angle inside a cone 0., 2 rr — Ha reads dav 2 1+ (1 — Q2/MS)? = CY P(Z) 2 2 1F2(w»Q )· (1 ·¤)FL(w»Q )1» (16) where 2 E262 1 + z z P = ———-1 if- —- —— (Z) H 17 ( ) , 1 — z mE 1 —— z and 2 1 2 2 S E: (-11) Zz w(=vz—Q/) (18) 1+(1—y)2 x2z2+(xz—Q2/S)? is the polarization of the virtual photon exchanged in the process. In the derivation of eqs. (16, 17) from the exact cross section for ep ——> e»yX, all infrared and collinear finite terms have been neglected. Also terms of order @(221;) are neglected and eq. (17) is valid for not too small angle cutoffs, i.e. for Ha > me/EC. Since we are interested in low Q2, we have restricted ourselves to pure photon exchange. The structure functions are related to cross sections JT and UL for the scattering of transversely and longitudinally polarized photons: F2 : (Q2/4rr2o¢)(0L -1- agp), FL = (Q2/47'1'2Q)O’L. In the following, we are interested in the ratio R : UL/UT. Using these definitions, the cross section is proportional to (1 -|— cR) and the determination of FL, resp. R amounts to determine the slope of the cross section as a function of 6.

lt is seen from equation 18 that at fixed w and Q2, e is a function of z and thus varies with the energy of the bremsstrahlung photons which are measured in the luminosity calorimeter.

A Monte Carlo study has been performed in (81 to study the statistical and systematic accuracy for a possible R measurement which can be reached in a realistic experiment. As an example of results obtained in [8] we show in Fig. 6 the results of our simulation in the bin 15GeV2 § Q2 f 30 Gel/2 and 0.6 · 10"3 f r Q 1.2 · 10`3. The figure contains the simulated values for a measurement of JT-!—c0L as a function of 6. The error bars represent the statistical accuracy. We also show in this figure the result of a linear fit which resulted in R = 0.36 :1; 0.06. The error on (UT + mL) resulting from the finite bin size is typically of the order of 10 % (maximally 20 %). It was found that it is insensitive to variations in the input parton distribution functions. Since the variation of the cross section is dominated by the 1/Q4 behaviour of the photon propagator, a reliable estimate can be obtained without good knowledge of the structure functions. Moreover, the correction depends only slightly on e so that the cross section in each bin receives a correction but the fitted value of R is changed only very little.

11 OCR Output I` d d 2 z Q · an ] input 0.3 2 [nb/GeV 1 . ju 0.36 Iii 0.06 7 - 103

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5 .103 Ef 15 GeV2 § Q2 < 30 GeV2 0.6- 10—3 < it < 1.2- 10-3 PT 2 GCV 4 - 103 0.0 0.25 0.50 0.75 1.0

Figure 6: Simulated measurement of (d20/da: dQ2)/l` and a linear jit to the Monte Carlo points for 0.6 ·10`3 § x § 1.2 ·10`3, 15 Gel/2 § Q2 f 30 Gel/2, and pT 2 3GeV. Only statistical errors for ffclt : 200 pb"1 are shown.

As we have discussed in chapter 2, a severe problem that might disturb the R measure ment is the background from quasi-elastic ep ——> epey events. There is a high probability for accidental coincidences of quasi-elastic ep —-> epcy events with deep-inelastic events. At photon energies above 5 Gel/2 , however, it should be possible to use the event kine matics as measured in the main detector to verify the photon energy or at least to test the hypothesis of the event being a radiative deep-inelastic event. From studies of this reconstruction technique (for details see [16]) one finds that only for energies E., 2 5 GeV one can expect the background from misinterpreted Born events to be smaller than l0 %. Further details have been presented in Summarizing, the above method yields in the kinematic range 15 Gel/2 f Q2 § 120 Gel"? and 0.6 - l0‘3 f r f 2 · 10‘2 a statistical accuracy of R ranging from 0.05 to 0.25. Systematic shifts due to finite bin size, pT cut, E, resolution, quasi-elastic back ground and EA, miscalibration were found to be of the order of 0.2 in R. Compared to the potential R measurement by reducing the beam energies, the proposed method should be considered as complementary. At the expense of larger uncertainties in the e measure ment, our method is insensitive to the precision of the luminosity measurement. It has in addition the advantage that the measurement can be performed in parallel to the planned physics program at HERA.

5 Conclusions

At HERA a sizeable fraction of hard radiative processes can be unanibigously identified. This alows one to reduce significantly the uncertainty in the radiative corrections size and

12 OCR Output their sensitivity t0 the input structure functions. It has t0 be stressed that this is a novel feature 0f experimenting at HERA with respect t0 the previous DIS experiments. On the other hand the identified radiative events provide an access to a new kinematicai domain, allowing to measure the longitudinal structure function already at the nominal HERA energy setting.

Acknowledgements

I am indebted to my colleagues from the Hl radiative correction group for valuable dis cussions and to Jorg Gayler for critical reading of the manuscript.

References

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[4] A. Akhundov, D. Bardin, L. Kalinovskaja, DESY 90-130, OCT 1990.

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I6} A. Kwiatkowski, H. Spiesberger, H.-J. Miihring, DESY 90-145, Nov 1990. J. Kripfganz, H.J. Moering, H. Spiesberger, Z. Phys C49,(1991) 501.

[7] A. Blondel, F. Jacquet, DESY 79/48, p. 391. [8] M. W. Krasny, W. Placzek, H. Spiesberger, Z.Phys. C53,(1992) 687.

[9} G. Levman, Proceedings of the HERA workshop, Oct. 1991, p. 876.

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{11] D. Yu. Bardin, C. Burdik, P. Ch. Christova, T. Riemann, Z. Phys. C 42 (1989) 679.

[12] M. B6hm, H. Spiesberger, Nucl. Phys. B 294 (1987) 1081.

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[Ml L.W. Mo, Y.S. Tsai, Rev.Mod.Phys 41 (1969) 205.

[15l A. M. Cooper-Sarkar et al., Proceedings of the HERA workshop, Oct. 1991, p. 155.

[161 M. W. Krasny, W. Placzek, Proceedings of the HERA workshop, Oct. 1991, p. 862.

13 OCR Output