On the background in the γp→ω( π 0 γ)p reaction and mixed event simulation
aa r X i v : . [ nu c l - t h ] M a r EPJ manuscript No. (will be inserted by the editor)
On the background in the γp → ω ( π γ ) p reactionand mixed event simulation M. Kaskulov , E. Hern´andez , and E. Oset Institut f¨ur Theoretische Physik, Universit¨at Giessen, D-35392 Giessen, Germany Grupo de F´ısica Nuclear, Departamento de F´ısica Fundamental e IUFFyM, Universidad de Salamanca, E-37008 Salamanca,Spain Departamento de F´ısica Te´orica e IFIC, Centro Mixto Universidad de Valencia-CSIC, Institutos de Investigaci´on de Paterna,Aptd. 22085, E-46071 Valencia, SpainReceived: / Revised version:
Abstract.
In this paper we evaluate sources of background for the γp → ωp , with the ω detected through its π γ decay channel, to compare with the experiment carried out at ELSA. We find background from γp → π π p followed by decay of a π into two γ , recombining one π and one γ , and from the γp → π ηp reactionwith subsequent decay of the η into two photons. This background accounts for the data at π γ invariantmasses beyond 700 MeV, but strength is missing at lower invariant masses which was attributed to photonmisidentification events, which we simulate to get a good reproduction of the experimental background.Once this is done, we perform an event mixing simulation to reproduce the calculated background and wefind that the method provides a good description of the background at low π γ invariant masses but fakesthe background at high invariant masses, making background events at low invariant masses, which aredue to γ misidentification events, responsible for the background at high invariant masses which is due tothe γp → π π p and γp → π ηp reactions. PACS.
The interaction of vector mesons with nuclear matter hasattracted attention for a long time and has been tied tofundamental aspects of QCD. Yet, the theoretical mod-els offer a large variety of results from a large attractionto a large repulsion. Early results on this issue withinthe Nambu Jona Lasinio model produced no shift of themasses [1] while, using qualitative arguments, a universallarge shift of the mass was suggested in [2]. More recentdetailed calculations show no shift of the mass of the ρ meson in matter [3,4,5]. Experimentally the situation hasundergone big steps recently with the NA60 collaborationreporting a null shift of the ρ mass in the medium [6,7]in the dilepton spectra of heavy ion reactions and also anull shift in the γ induced dilepton production at CLASS[8]. On the other hand the KEK team had earlier reportedan attractive mass shift of the ρ in [9,10]. As explainedin detail in [8], the different conclusions can be tracedback to the way the background is subtracted. Thus, thetreatment of the background is an essential part of the in-vestigation of the vector meson properties in nuclei. Thecase of the ω in the medium is more obscure. Theoreti-cally there are about twenty different works with claimsfrom large attraction to large repulsion (see [11,12,13] fordetails). Experimentally there are claims of a large shift of the mass of the ω from the study of the photon induced ω production in nuclei, with the ω detected through its π γ decay channel [14,15]. However, it was shown in [12]that the shift could just be a consequence of a particu-lar choice of background subtraction and that other rea-sonable choices led to different conclusions. For instance,choosing a background in the nuclear case proportional tothe background on the proton in the region below the ω peak, the experimental data could be explained without ashift of the ω mass in the medium.The method to determine the mass shift is very dif-ferent from the one used to determine the width in themedium. This latter one relies upon the production crosssection in different nuclei, which leads to the transparencyratio that allows to determine a large width of the ω inthe medium [12,16]. By contrast the measurement of themass requires the analysis of the shape of the invariantmass distribution, which is barely affected in nuclei be-cause practically all ω decays occur in the nuclear surfaceor outside the nucleus.The discussion on the issue of the ω mass shift wasfollowed by the evaluation of the background with themixed event technique in [17]. There the background fora nuclear target was evaluated and found to be the sameas assumed in [15], and again it was concluded that thedata demanded a shift of the ω mass in the medium. M. Kaskulov et al.: On the background in the γp → ω ( π γ ) p reaction and mixed event simulation The former discussion indicates that the treatment ofbackground is an essential issue in this problem. In viewof this we decided to face the problem and investigate thedetails on how the mixed event technique works in thepresent case. For this we followed the strategy of evaluat-ing the background for the proton target. We could tracetwo sources of background that account for the experi-mental cross section at π γ invariant masses of the orderof the ω mass and beyond. The rest of the backgroundat lower invariant masses was simulated to account for γ misidentification events, as found in [14]. Once a back-ground consistent with the experiment is obtained theo-retically, we apply the mixed event technique to obtainthe background and compare it with the theoretical one.In this way we can determine the ability of the mixed eventmethod to reproduce the background in this reaction. Theresults that we find are that the method can provide thebackground at low invariant masses, where the cross sec-tions are large, but it actually fakes the background in theregion of invariant masses around and beyond the ω mass.We show that the mixed event generated background inthat region is completely tied to the real events at low π γ invariant masses where the dσ/dM π γ distribution islarger. As a result, we show that the distribution obtainedwith the mixed event method in the region of invariantmasses around and beyond the ω mass is largely insensi-tive to the actual background contributing in that region.But this is precisely the region where the background isneeded to determine changes of the ω signal in the nu-clear medium. As a consequence we clearly show that themixed event technique is unsuited in the present case asan instrument to determine possible shifts of the ω massin the medium.In the meantime, a recent reanalysis of the backgroundof the reaction of [14,15] done in [18] concludes, however,that one cannot claim a shift of the ω mass from thisexperiment. γp → ωp ( ω → π γ ) The reaction that we study is γp → ωp where the ω isdetected through its ω → π γ decay mode. This is thereaction studied in the CBELSA/TAPS experiment. Ac-cording to the study in [14], in the region of the recon-structed invariant mass of the π γ one of the main sourcesof background comes from the γp → π π p reaction fol-lowed by the decay of any of the two π into γγ . Then,background events appear from the combination of oneof these photons and the remaining π . Another source isthe γp → π ηp reaction. We evaluate the cross section forthose two processes in the following subsection. γp → π π p reaction This reaction has been thoroughly studied at Mainz [20,21,22,23] and more recently at ElSA [24,25], GRAAL [26] and Jefferson Lab [27,28,29]. We are interested not only inthe cross section for the reaction but at the same time tohave an event generator that provides events weighed bytheir probability determined by the available phase space.For this purpose the Monte Carlo evaluation of the crosssection integral is the most suited algorithm since it pro-vides the events allowed by phase space properly weightedand the cross section in the end.The γp → π π p cross section is given by σ = M N s − M N Z d p (2 π ) Z d p (2 π ) Z d p (2 π ) × E ( p ) 12 E ( p ) 12 E ( p ) | T | × (2 π ) δ ( p γ + p p − p − p − p ) , (1)which includes the 1/2 symmetry factor to account forthe two identical pions in the final state. The variables p , p , p are the momenta of the final proton and the two π respectively and T stands for the transition matrix forthe γp → π π p process. In the | T | factor a sum over finalspins and a proper average over initial spins is implicit.Since d p/E ( p ) is a Lorentz invariant measure, we pro-ceed to evaluate the last two integrals in Eq. (1) in thereference frame where p γ + p p − p = which guaranteesthat p + p = . The cross section is then written as σ = M N s − M N Z d p (2 π ) E ( p ) θ ( M − m π ) × Z dΩ ˜ p π M | T | , (2)where M is the invariant mass of the two π given by M = ( p γ + p p − p ) = s + M N − p γ + p p ) p . (3)We shall work in the laboratory (lab) frame that allows usto implement easily all the experimental cuts. The variable˜ p in Eq. (2) is the π momentum in the π π rest frame˜ p = λ ( M , m π , m π )2 M , (4)and dΩ is performed in the π π rest frame.The γp → π π p reaction has been studied theoret-ically at E γ < . E γ > . | T | to be a constantover the phase space and fit its value to reproduce theexperimental results for the cross section in the region ofinterest to us. We take the cross section for γp → π π p at the needed photon energies from [24,25].The next step is to write ˜ p in the lab frame. We havein the π π rest frame ˜ p = ˜ p sinθ cosϕsinθ sinϕcosθ (5) . Kaskulov et al.: On the background in the γp → ω ( π γ ) p reaction and mixed event simulation 3 ˜ p = − ˜ p (6)with θ, ϕ angles in the π π rest frame. We then perform aboost of ˜ p to the lab frame where p + p = p γ + p p − p = P p = (cid:20)(cid:18) E M − (cid:19) ˜ p · PP + ˜ p M (cid:21) P + ˜ p , (7)where E is the two pion energy in the lab frame E =( M + P ) . Similarly we boost ˜ p to p in the initial γp lab frame.Assume now that the pion with momentum p is theone that decays into γγ . In the pion rest frame the two γ ’swill go back to back and one γ will have the momentum ˜ p γ = m π sinθ γ cosϕ γ sinθ γ sinϕ γ cosθ γ , (8)with θ γ , ϕ γ angles of the photon in this one π rest frame.Once again we boost this photon momentum to the framewhere the pion has momentum p p γ = "(cid:18) E m π − (cid:19) ˜ p γ · p p + ˜ p γ m π p + ˜ p γ . (9)Since we can have a π γ combination from either of thetwo π or the two γ ’s, we would obtain a combinatorialfactor of four to account for these possibilities.All this said, the cross section for γp → π π p → γγ π p → γπ + X reads σ = 4 M N s − M N Z d p (2 π ) E ( p ) | T | θ ( M − m π ) (10) × Z − dcosθ Z π dϕ ˜ p π M π Z − dcosθ γ Z π dϕ γ recalling from Eq. (3) that in the lab frame M = s + M N − E γ in + M N ) E ( p ) + 2 p γ in · p (11)Next one generates random numbers for p , θ, ϕ, θ γ , ϕ γ with | p | restricted between zero and | p | maxlab = | p | maxCM + v E max CM √ − v (12)with | p | maxCM and E max CM the maximum momentum andenergy allowed for the final proton in the γp center of mass(CM) frame, corresponding to the case when the two π go together | p | maxCM = λ ( s, M N , m π )2 √ s (13)and v is the velocity of the γp CM system measured inthe lab frame v = | p γ in | E γ in + M N (14) For each of these events we evaluate the invariant mass M inv ( π γ ) = ( p γ + p ) (15)and store the events, properly weighted by | T | and phasespace factors, in boxes of M inv ( π γ ) for a suitable parti-tion of M inv ( π γ ). γp → π ηp reaction We also evaluate the background for the γp → π ηp reac-tion. In this case η → γγ and we get one photon from thereplus the π to reconstruct the π γ invariant mass. Thechanges with respect to the former reaction are minimal.Since now there is only one π , we do not have to includethe 1/2 symmetry factor and the combinatorial factor offour before is now a factor of two and the mass of one pionmust be changed to the mass of the η when needed. Thereare data for this reaction in [36,37,38,39]. There are alsorecent detailed models for the reaction [40,41] accountingfairly well for the cross section [36,37] and the asymme-tries [38]. However, once again, for the present problem itsuffices to repeat the procedure done for the γp → π π p reaction in the former section taking a constant | T | andimplementing properly the phase space demanding thatwe reproduce the data of [36,37,39]. As we shall see in the results section, the γp → π π p and γp → π ηp reactions can account for the backgroundobserved in the CBELSA/TAPS experiment [14,15] in theregion of the ω excitation and higher π γ invariant masses.However, it does not account for the large backgroundobserved in the region of π γ invariant masses lower than m ω . Once again we resort to the findings of [14] suggestingthat such events could come from reactions like γp → π π + n with a misidentification of the neutron by a photonand other possible sources of γ misidentification. In thispart we do not make a theory since the events come fromignorance of the occurring reactions and misidentificationof particles which have to do with the detector system.However, we would like to have π γ events correspondingto this region in order to perform later on the mixed eventanalysis.To generate background events in this region we writethe corresponding cross section as σ = Z M maxinv M mininv dM πγ | T ( M πγ ) | (16) × Z − dcosθ Z π dϕ Z d P CM θ (500 MeV / c − | P CM | ) , where | T ( M πγ ) | is a function to be determined from ex-periment. θ, ϕ are the π angles in the π γ rest frame.There the pion momentum is ˜ p π = ˜ p π sinθ cosϕsinθ sinϕcosθ , (17) M. Kaskulov et al.: On the background in the γp → ω ( π γ ) p reaction and mixed event simulation with ˜ p π = M πγ − m π M πγ , ˜ p γ = − ˜ p π . (18)Eq. (16) contains an integral over P CM with a maximumof 500 MeV for | P CM | . This momentum represents the π γ total momentum in the γ in p CM frame. In this framethe momenta are more evenly distributed than in the labframe and then we take an isotropic distribution for P CM with the constraint | P CM | <
500 MeV/c. This is a conser-vative estimate that exceeds the phase space of Eq. (16)when | P | = | p π + p γ | the total π γ momentum in the γ in p lab frame is restricted to values smaller than 500 MeV/c.Next we boost the π and the γ momenta from their CMframe to the γ in p CM frame where the π γ system hasmomentum P CM . We have p ′ π = (cid:20)(cid:18) E πγ M πγ − (cid:19) ˜ p π · P CM P CM + ˜ p π M πγ (cid:21) P CM + ˜ p π , (19) E πγ = q P CM + M πγ , (20) p ′ γ = P CM − p π . (21)The next step is the boost to the lab system where the γ in p has momentum p γ in and energy E γp = p γ in + M N ,hence p π = "(cid:18) E γp √ s − (cid:19) p ′ π · p γ in p γ in + p ′ π √ s p γ in + p ′ π , (22)and a similar one for p γ . On these γ and π momentumwe enforce now the cut | p π + p γ | <
500 MeV / c . (23)The function T ( M πγ ) of Eq. (16) is determined empiricallysuch that the sum of the cross section for γp → π π p plus γp → π ηp , plus the new one simulating γ misidenti-fication events, gives the total experimental cross sectionof [14,15]. In the mixed event simulation the idea is to obtain thebackground from the real data by evaluating M π γ se-lecting the π and the γ from two different events. Theinvariant mass distribution is then given by M π γ ( M E ) = ( p π (1) + p γ (2)) . (24)There is abundant literature on the subject [42,43,44,45,46] and it has become a popular instrument to determinebackground and isolate particular reactions that peak ata certain place.In our case where all the integrals of the cross sectionsare performed by Monte Carlo, the mixed event simulation is particularly simple to implement. The Monte Carlo inte-grals are done by generating random events into a volume V containing the whole phase space and then the integralis given by the average value of the integrand, that weshall denote as d | T | , times the volume σ = P Ni =1 d | T i | N V, (25)where one understand that d | T i | is zero if the event gen-erated does not belong to the phase space. Assume nowthat we take pair of events i, j corresponding to a reactionchannel. We have σ = P Ni =1 d | T i | N V P Nj =1 d | T j | N V, (26)or equivalently σ = 1 σ N X i =1 N X j =1 d | T i | V d | T j | VN . (27)We can then generate pairs of events in the phase spacevolume V and the former integral gives the cross sec-tion. Simultaneously with the evaluation of the cross sec-tion we can obtain M π γ for each pairs of events as donein Eq. (24) and store the event, with its correspondingweight, in a box of a certain M π γ value. After the dou-ble sum in Eq. (27) we obtain the normalized dσ/dM π γ distribution.The generalization to four channels as we have in ourcase, γp → π π p , γp → π ηp , the channel from γ misiden-tification and the γp → ωp → π γp channel is straightfor-ward σ tot = 1 σ tot X α X β N X i =1 N X j =1 d | T (1) i,α | V d | T (2) j,β | VN , (28)where σ tot = σ + σ + σ + σ , (29)and α, β run from 1 to 4. In order to obtain dσ/dM π γ from these mixed events we evaluate again M π γ fromEq. (24) and store the events in boxes of M π γ and weobtain at the end the histogram that provides us with thenormalized dσ/dM π γ distribution from mixed events. In Fig. 1 the contributions from the ω -signal and differentsources discussed above are compared with the experimen-tal invariant mass dσ/dM π γ distribution in the reaction γp → π γp from CBELSA/TAPS experiment.The sources of background are γp → π π p with eitherof the two pions decaying into two γ , which was stud-ied in section 2.1. This is the most important source of . Kaskulov et al.: On the background in the γp → ω ( π γ ) p reaction and mixed event simulation 5
500 600 700 800 900 1000 1100M π γ [MeV]10 d σ / M π γ [ c oun t s / M e V ] π π π ηπ γ (misidentified) ω (782) - signal & exp. res. ω (782)-signal & backgroundExp. data (CBELSA/TAPS) E γ = 0.9 − 2.6 GeV, p π γ < 500 MeV
Fig. 1.
The invariant mass dσ/dM π γ distribution in the reaction γp → π γp . The signal and different background contributionsare also shown. background in the region of the ω and beyond. The otherimportant source of background is the γ misidentificationstudied in Section 2.3. This source competes with the for-mer one in the region of the omega and becomes dom-inant at smaller γπ invariant masses. The third sourceconsidered is the one coming from γp → π ηp followedby the η decay into two γ . This source has a smallerstrength than the other two, but was found to be im-portant to understand a peak in the experiment at lower γπ invariant masses than the omega in [13] when protonswere measured in coincidence. The omega signal comesfrom our study in [12]. The fit to the unnormalized datais done by adjusting the strength of the γp → π π p source to the experiment distribution at large invariantmass, since this is the most important source in this in-variant mass region. The source of the γp → π ηp , as wellas the signal are rescaled keeping their ratio, in order tokeep the theoretical proportion between all these differ-ent sources. Finally, the source of misidentified γ is addedin order to complete a good description of the data. Asone can see from the figure, the agreement of the theoret-ical model with the experimental data is very good. Notethat we also have adapted our theoretical set up to theexperimental one by choosing E γ = 0 . − . GeV and p π γ = | p π + p γ | ≤ M eV . We should note that the experimental spectrum shownin Fig. 1 is not acceptance corrected. The reason is thatexperimentally one observes only three out of four photonsin the final state due to the detector inefficiencies, or theoverlap of photon clusters, and the latter depends on theenergy of the photon [18]. Yet, in the unnormalized spec-trum to which we make the fit, the differences are of theorder of 20 % from the lower mass part of the spectrumto the higher mass one, and have irrelevant consequencesfor the argumentations and conclusions that follow. Theconsideration of acceptance would be more important incase one would like to compare our different sources ofbackground with the acceptance uncorrected experimen-tal determinations [18], which is not our concern here.
On the first hand we make the ME simulation that wasdone in [17] taking two independent events and demandingthat | p (1) π + p (2) γ | <
500 MeV / c (30)for the mixed event. We call it method I. This choicehas in principle a conceptual flaw. Indeed, the curve in M. Kaskulov et al.: On the background in the γp → ω ( π γ ) p reaction and mixed event simulation
500 600 700 800 900 1000 1100M π γ [MeV]10 d σ / M π γ [ c oun t s / M e V ] Mixed events Actual background ω (782)-signal & backgroundExp. data (CBELSA/TAPS) Fig. 2.
The mixed event background with method I is shown, together with the actual background, the results of the modelfor ω signal plus background and the data. Fig. 1 corresponds to events in which one has imposed | p π + p γ | <
500 MeV/c in the π and γ momenta ofthe same event. This restricts the phase space consider-ably. Now if one imposes Eq. (30) after the mixing, onecan have both events (1) and (2) or one of them thatdo not fulfill separately | p π + p γ | <
500 MeV/c and, asa consequence, these are events which do not contributeto the distribution of Fig. 1. In other words, one canbe using events that do not provide any information toFig. 1 to obtain its corresponding background throughthe mixed event method. Clearly in the extreme case thatmost events in the ME simulation do not pass the individ-ual | p π + p γ | <
500 MeV/c test one would be obtainingthe background of the curve from a physical situation thathas no relationship with the distribution of Fig. 1. Howfar is one in practice from this situation depends of courseon the cut.In Fig. 2 we show the results that we get from themixed event simulation for the background, compared tothe real background of the theoretical model. We can seethat there is a remarkable agreement between the twoin the whole range of invariant masses. We might con-clude from there that the mixed event method is reallygood to reproduce the background. Yet, let us investigatewith more detail how this shape has been produced. Uponrenormalization of the generated mixed event distribution we reproduce the real background, but we know that oneis using for sure information not included in the spectrumof Fig. 1.Another way to proceed is to select two independentevents from Fig. 1, meaning that each one separately ful-fills | p π + p γ | <
500 MeV/c, and then reconstruct theinvariant mass of Eq. (24) for the mixed events, impos-ing also the cut of Eq. (30) to the pair of events of themixing. We call that method II. This would correspond toa ME reconstruction from experimental events that havebeen filtered with the | p π + p γ | <
500 MeV/c condition,which imposes a certain correlation, which might be unde-sired, in the events chosen for the mixing. The results canbe seen in Fig. 3. Now we normalize the background atlow invariant masses where it is maximum. Then we ob-serve that in the rest of the invariant mass region there isa clear disagreement of this new mixed events backgroundwith the real one. Hence, the result has been a very poorreproduction of the real background by the mixed eventmethod II.Going back to method I, and in order to understandwhat is really happening, we have conducted another test.Let us realize that the mass distribution of Fig. 1 is expo-nential and there are three orders of magnitude differencebetween the strength of dσ/dM π γ at low and large invari-ant masses. From pure statistics it looks quite logical that . Kaskulov et al.: On the background in the γp → ω ( π γ ) p reaction and mixed event simulation 7
500 600 700 800 900 1000 1100M π γ [MeV]10 d σ / M π γ [ c oun t s / M e V ] Mixed events: Method IMixed events: Method II ω (782)-signal & real backgroundExp. data (CBELSA/TAPS) Fig. 3.
The effect of the momentum cut on the mixed events before and after the mixing (method II). if we take two independent events to reconstruct the mixedevent π γ invariant mass, these two events belong to theregion of the spectrum that has larger cross section, evenif the mass that we obtain corresponds to the large invari-ant mass where dσ/dM π γ is small. In other words, it isperfectly acceptable that the background that one obtainsin the large invariant mass region is largely determined byevents far away from this region, sitting at much lowerindividual π γ invariant masses. If this were the case onewould be attributing the background in the high invariantmass region to different reactions than those responsiblefor it and hence one would be distorting the physics ofthe process. Certainly in such a case there would be aninteresting side effect: the distribution obtained with themixed event method at large invariant masses would belargely insensitive to the actual background contributingin that region. In this case the ME method would thusrender a background in this region that has nothing to dowith the actual one.In order to illustrate more dramatically the problem,we change arbitrarily the background of our model at large M π γ by imposing | T | → | T | f ( M π γ ) (31) where f ( M π γ ) is a distortion factor. We consider twosharp cuts with(1) f ( M π γ ) = (cid:26) M π γ <
850 MeV0 for M π γ >
850 MeV (32)and (2) f ( M π γ ) = (cid:26) M π γ <
750 MeV0 for M π γ >
750 MeV (33)The distortion factor in Eq. (32) cuts off the backgroundat higher invariant masses beyond the ω -signal and (33)removes both the signal and the background.In Fig. 4 we show the results for the background fromthe ME method, with method I and the real data, com-pared with those obtained with the distorted spectra ofEqs. (32) and (33). Note that the sharp cut off becomes inthe figure a smoother fall down because we implement thefolding of the π γ invariant mass with the experimentalresolution of [15] of 50 M eV . What we see in Fig. 4 is thatthe ME method output barely changes with the actualbackground from Eqs. (32,33), or in other words, that theME method is unable to produce the actual background.It produces a background largely tied to the events atlow invariant mass and is unsuited to produce a realisticbackground in the region of large M π γ masses. M. Kaskulov et al.: On the background in the γp → ω ( π γ ) p reaction and mixed event simulation
500 600 700 800 900 1000 1100M π γ [MeV]10 d σ / M π γ [ c oun t s / M e V ] Mixed events of real spectrum: Method IDistorted spectrum (1)Mixed events of distorted spectrum (1)Distorted spectrum (2)Mixed events of distorted spectrum (2) ω (782)-signal & real backgroundExp. data (CBELSA/TAPS) Fig. 4.
The mixed event background with Method I for different input invariant mass distributions.
In order to test the former suggestion that the back-ground at large invariant masses in the ME method is tiedto events at low invariant masses, we construct the cor-relation matrix C ( M πγ ( ini ) , M πγ ( f in )) where M πγ ( ini )refers to any of the two events used in the mixed eventsimulation and M πγ ( f in ) refers to the ME final invariantmass determined through Eq. (24).In Fig. 5 we plot the correlation function. We havetaken M πγ ( f in ) = 800 M eV . Then keeping this variablefixed we plot on the y-axis in an arbitrary scale the num-ber of events (summing the two events used in the mix-ing) that would have a certain M πγ ( ini ). As we can see,the initial events used in the mixing accumulate in the re-gion where M πγ ( ini ) is about 400-500 MeV. This certainlyis distorting the physics of the problem, since the back-ground associated to the region M πγ ( f in ) = 800 M eV isgenerated after mixing by events around 400 MeV, wherethe origin of the background is quite different from thereal one around M πγ ( f in ) = 800 M eV . In summary, what we have seen is that due to the pecu-liar shape of the background in the present process and thefast drop as a function of M πγ , the mixed event methodis unsuited to provide an even qualitative reproduction of the real background of the process. Even if a first runseemed encouraging because it gave a good reproductionof the background, further insight into the method re-vealed its flaws since we could prove that different meth-ods to do the cuts gave rise to very different mixed eventsbackground. Further we could prove that the results pro-vided by the mixed event method were practically insensi-tive to the value of the real background beyond 750 MeV,to the point that we could take any arbitrary backgroundas input in that region and the mixed event method wouldalways provide the same background, with no resemblanceto the one that it was supposed to reproduce. The study ofthe correlations of events gave us an explanation for thisfinding, since we saw that even at large invariant masses,the events of the mixing that generated the final M πγ were collected for the region of M πγ ( ini ) around 400-500MeV. In that region the origin of the background is verydifferent from the one for the real events at large invari-ant masses, such that the mixing event method not onlyproduces an unrealistic numerical background, but gets itfrom physical processes quite different from those respon-sible for the real background at large invariant masses,thus grossly distorting the physics of the process. Acknowledgments
We would like to thank V. Metag, M. Nanova, S. Friedrichand M. Kotulla for discussions on the issue and on the ex- . Kaskulov et al.: On the background in the γp → ω ( π γ ) p reaction and mixed event simulation 9 π γ [MeV]00.51 C [ M π γ ( i n i ) , M π γ (f i n )] Fig. 5.
The correlation function C ( M πγ ( ini ) , M πγ ( fin )) (see the details in the text) perimental data. Useful information on mixed events wasprovided by C. Djalali and R. Nasseripour. This work wassupported by DFG through the SFB/TR16, by DGI andFEDER funds, under contracts FIS2006-03438, FPA2007-65748, The Generalitat Valenciana in the Prometeo Pro-gram and the Spanish Consolider-Ingenio 2010 ProgrammeCPAN (CSD2007-00042), by Junta de Castilla y Le´onunder contract SA 016A07 and GR12, and it is part ofthe EU integrated infrastructure initiative Hadron PhysicsProject under contract number RII3-CT-2004-506078. References
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