002882111 001__ 2882111
002882111 005__ 20241110043013.0
002882111 0248_ $$aoai:cds.cern.ch:2882111$$pcerncds:FULLTEXT$$pcerncds:CERN:FULLTEXT$$pcerncds:CERN
002882111 0247_ $$2DOI$$9APS$$a10.1103/PhysRevD.110.092005$$qpublication
002882111 035__ $$9Inspire$$a2830419
002882111 037__ $$9arXiv$$aarXiv:2409.12696$$chep-ph
002882111 037__ $$aCERN-EP-2023-276
002882111 041__ $$aeng
002882111 088__ $$9CERN-EP-DRAFT-PS212-2023-001
002882111 100__ $$aAdeva, B.$$uSantiago de Compostela U.$$vSantiago de Compostela University, Santiago de Compostela, Spain
002882111 245__ $$aThe $\pi^+\pi^-$ Coulomb interaction study and its use in the data processing
002882111 269__ $$aGeneva$$bCERN$$c22 Dec 2023
002882111 260__ $$c2024-11-01
002882111 300__ $$a11 p
002882111 506__ [email protected]
002882111 506__ $$mcds-edboard-dirac [CERN]
002882111 506__ $$mcds-ph-ep-publications-referee-non-lhc [CERN]
002882111 520__ $$aIn this work the Coulomb effects (Coulomb correlations) were studied using experimental $\pi^+\pi^-$ pair distributions in $Q$, the relative momentum in the pair center of mass system (c.m.s), and its projections $Q_L$ (longitudinal component) and $Q_t$ (transverse component) relative to the pair direction in the laboratory system (l.s.). The major part of the pion pairs is produced by decay of $\rho, \omega$ and $\Delta$ and other short-lived sources (Coulomb pairs). In these pairs the significant Coulomb interaction at small $Q$ occurs. The minor part of the pairs is produced if one or both pions arose from long-lived sources like $\eta, \eta'$ or in different interactions (non-Coulomb pairs). In this case the Coulomb interaction in the final state is practically absent. The $Q$, $Q_L$ and $Q_t$ distributions of Coulomb pairs in the c.m.s. were simulated assuming that they are described by the phase space modified by the known Coulomb correlation function $A_C(Q)$. The same spectra of non-Coulomb pairs were simulated without $A_C(Q)$. In all $Q_t$ intervals, the experimental $Q_L$ spectrum shows a peak around $Q_L = 0$ caused by the Coulomb final state interaction. The full width at half maximum increases with $Q_t$ from 3~MeV/$c$ for $0<Q_t<0.25$~MeV/$c$ to 11~MeV/$c$ for $4.0<Q_t < 5.0$~MeV/$c$. The experimental $Q_L$ distributions were fitted with two free parameters: the fraction of Coulomb pairs and the normalization constant. The precision of the description of these distributions is better than $2\%$ in $Q_t$ intervals 2-3, 3-4 and 4-5 MeV/$c$, and better than $0.5\%$ in the total $Q_t$ interval 0-5 MeV/$c$. It was shown that the number of Coulomb pairs in all $Q_t$ intervals, including the small $Q_t$ (small openning angles $\theta$ in the l.s.) is calculated with the theoretical precision better than 2\%. The comparison of the simulated and experimental number of Coulomb pairs at small $Q_t$ allows to check and to correct the detection efficiency for the pairs with small $\theta$ (0.06 mrad and smaller) in the laboratory system. It was shown that Coulomb pairs can be used as a new physical tool to check and to correct the simulated events quality. The special property of the Coulomb pairs is the possibility to check and to correct the detection efficiency, especially for the pairs with small opening angles.
002882111 520__ $$9APS$$aIn this work, the Coulomb effects (Coulomb correlations) in <math display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>-</mo></msup></math> pairs produced in <math display="inline"><mrow><mi mathvariant="normal">p</mi><mo>+</mo><mi>Ni</mi></mrow></math> collisions at <math display="inline"><mrow><mn>24</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi><mo>/</mo><mi>c</mi></mrow></math>, are studied using experimental <math display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>-</mo></msup></math> pair distributions in <math display="inline"><mi>Q</mi></math>, the relative momentum in the pair center-of-mass system (c.m.s.), and its projections <math display="inline"><msub><mi>Q</mi><mi>L</mi></msub></math> (longitudinal component) and <math display="inline"><msub><mi>Q</mi><mi>t</mi></msub></math> (transverse component) relative to the pair direction in the laboratory system (LS). The major part of the pion pairs (“Coulomb pairs”) is produced in the decay of <math display="inline"><mrow><mi>ρ</mi></mrow></math>, <math display="inline"><mrow><mi>ω</mi></mrow></math> and <math display="inline"><mi mathvariant="normal">Δ</mi></math> resonances and other short-lived sources. In these pairs, the significant Coulomb interaction occurs at small <math display="inline"><mi>Q</mi></math>, dominating the <math display="inline"><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>-</mo></msup></math> interaction in the final state. The minor part of the pairs (“non-Coulomb pairs”) is produced if one or both pions arose from long-lived sources like <math display="inline"><mi>η</mi><mo>,</mo><msup><mi>η</mi><mo>′</mo></msup></math> or from different interactions. In this case, the final state interaction is practically absent. The <math display="inline"><mi>Q</mi></math>, <math display="inline"><msub><mi>Q</mi><mi>L</mi></msub></math>, and <math display="inline"><msub><mi>Q</mi><mi>t</mi></msub></math> distributions of the Coulomb pairs in the c.m.s. have been simulated assuming they are described by the phase space modified by the known point-like Coulomb correlation function <math display="inline"><msub><mi>A</mi><mi>C</mi></msub><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></math>, corrected for small effects due to the nonpointlike pair production and the strong two-pion interaction. The same distributions of non-Coulomb pairs have been simulated according to the phase space, but without <math display="inline"><msub><mi>A</mi><mi>C</mi></msub><mo stretchy="false">(</mo><mi>Q</mi><mo stretchy="false">)</mo></math>. In all <math display="inline"><msub><mi>Q</mi><mi>t</mi></msub></math> intervals, the experimental <math display="inline"><msub><mi>Q</mi><mi>L</mi></msub></math> spectrum shows a peak around <math display="inline"><msub><mi>Q</mi><mi>L</mi></msub><mo>=</mo><mn>0</mn></math> caused by the Coulomb final state interaction. The full width at half maximum increases with <math display="inline"><msub><mi>Q</mi><mi>t</mi></msub></math> from <math display="inline"><mrow><mn>3</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><mi>c</mi></mrow></math> for <math display="inline"><mn>0</mn><mo><</mo><msub><mi>Q</mi><mi>t</mi></msub><mo><</mo><mn>0.25</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><mi>c</mi></math> to <math display="inline"><mrow><mn>11</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><mi>c</mi></mrow></math> for <math display="inline"><mn>4.0</mn><mo><</mo><msub><mi>Q</mi><mi>t</mi></msub><mo><</mo><mn>5.0</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo>/</mo><mi>c</mi></math>. The experimental <math display="inline"><msub><mi>Q</mi><mi>L</mi></msub></math> distributions have been fitted with two free parameters: the fraction of Coulomb pairs and the normalization constant. The precision of the description of these distributions is better than 2% in <math display="inline"><msub><mi>Q</mi><mi>t</mi></msub></math> intervals 2–3, 3–4, and <math display="inline"><mrow><mn>4</mn><mi>–</mi><mn>5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo stretchy="false">/</mo><mi>c</mi></mrow></math> and better than 0.5% in the total <math display="inline"><msub><mi>Q</mi><mi>t</mi></msub></math> interval <math display="inline"><mrow><mn>0</mn><mi>–</mi><mn>5</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi><mo stretchy="false">/</mo><mi>c</mi></mrow></math>. It is shown that the number of Coulomb pairs in all <math display="inline"><msub><mi>Q</mi><mi>t</mi></msub></math> intervals, including the small <math display="inline"><msub><mi>Q</mi><mi>t</mi></msub></math> (small opening angles <math display="inline"><mi>θ</mi></math> in the LS) is calculated with theoretical precision better than 2%. The comparison of the simulated and experimental numbers of Coulomb pairs at small <math display="inline"><msub><mi>Q</mi><mi>t</mi></msub></math> allows us to check and correct the detection efficiency for the pairs with small <math display="inline"><mi>θ</mi></math> (0.06 mrad and smaller). It is shown that Coulomb pairs can be used as a new physical tool to check and correct the quality of the simulated events. The special property of the Coulomb pairs is the possibility of checking and correcting the detection efficiency, especially for the pairs with small opening angles.
002882111 520__ $$9arXiv$$aIn this work the Coulomb effects (Coulomb correlations) in $\pi^+\pi^-$ pairs produced in p + Ni collisions at 24 GeV/$c$, are studied using experimental $\pi^+\pi^-$ pair distributions in $Q$, the relative momentum in the pair center of mass system (c.m.s), and its projections $Q_L$ (longitudinal component) and $Q_t$ (transverse component) relative to the pair direction in the laboratory system (l.s.). The $Q$, $Q_L$, and $Q_t$ distributions of the {\sl Coulomb pairs} in the c.m.s. have been simulated assuming they are described by the phase space modified by the known point-like Coulomb correlation function $A_C(Q)$, corrected for small effects due to the nonpoint-like pair production and the strong two-pion interaction. The same distributions of {\sl non-Coulomb pairs} have been simulated according to the phase space, but without $A_C(Q)$. It is shown that the number of {\sl Coulomb pairs} in all $Q_t$ intervals, including the small $Q_t$ (small opening angles $\theta$ in the l.s.) is calculated with the theoretical precision better than 2%. The comparison of the simulated and experimental numbers of {\sl Coulomb pairs} at small $Q_t$ allows us to check and correct the detection efficiency for the pairs with small $\theta$ (0.06 mrad and smaller). It is shown that {\sl Coulomb pairs} can be used as a new physical tool to check and correct the quality of the simulated events. The special property of the {\sl Coulomb pairs} is the possibility of checking and correcting the detection efficiency, especially for the pairs with small opening angles.
002882111 540__ $$3Preprint$$aCC-BY-4.0
002882111 542__ $$3Preprint$$dCERN$$g2023
002882111 562__ $$cPublic comments
002882111 595__ $$aCERN EDS
002882111 6531_ $$9CERN$$aQCD
002882111 6531_ $$9CERN$$adetector
002882111 6531_ $$9CERN$$aparticle correlations and fluctuations
002882111 65017 $$2SzGeCERN$$aParticle Physics - Experiment
002882111 690C_ $$aCERN
002882111 690C_ $$aARTICLE
002882111 693__ $$aCERN PS$$ePS212
002882111 700__ $$aAfanasyev, L.$$uDubna, JINR$$vJINR Dubna, Dubna, Russia
002882111 700__ $$aAnania, A.$$uINFN, Messina$$vMessina University, Messina, Italy
002882111 700__ $$aAogaki, S.$$uBucharest, IFIN-HH$$vIFIN-HH, National Institute for Physics and Nuclear Engineeringhttps://ror.org/00d3pnh21, Bucharest, Romania
002882111 700__ $$aBenelli, A.$$uPrague, Tech. U.$$vCzech Technical University in Prague, Prague, Czech Republic
002882111 700__ $$aBrekhovskikh, V.$$uSerpukhov, IHEP$$vIHEP Protvino, Protvino, Russia
002882111 700__ $$aCechak, T.$$uPrague, Tech. U.$$vCzech Technical University in Prague, Prague, Czech Republic
002882111 700__ $$aChiba, M.$$uTokyo Metropolitan U.$$vTokyo Metropolitan University, Tokyo, Japan
002882111 700__ $$aChliapnikov, P.$$uSerpukhov, IHEP$$vIHEP Protvino, Protvino, Russia
002882111 700__ $$aDrijard, D.$$uPrague, Tech. U.$$uCERN$$vCERNhttps://ror.org/01ggx4157, Geneva, Switzerland$$vCzech Technical University in Prague, Prague, Czech Republic
002882111 700__ $$aDudarev, A.$$uDubna, JINR$$vJINR Dubna, Dubna, Russia
002882111 700__ $$aDumitriu, D.$$uBucharest, IFIN-HH$$vIFIN-HH, National Institute for Physics and Nuclear Engineeringhttps://ror.org/00d3pnh21, Bucharest, Romania
002882111 700__ $$aFedericova, P.$$uPrague, Tech. U.$$vCzech Technical University in Prague, Prague, Czech Republic
002882111 700__ $$aGorin, A.$$uSerpukhov, IHEP$$vIHEP Protvino, Protvino, Russia
002882111 700__ $$aGritsay, K.$$uDubna, JINR$$vJINR Dubna, Dubna, Russia
002882111 700__ $$aGuaraldo, C.$$uFrascati$$vINFN, Laboratori Nazionali di Frascati, Frascati, Italy
002882111 700__ $$aGugiu, M.$$uBucharest, IFIN-HH$$vIFIN-HH, National Institute for Physics and Nuclear Engineeringhttps://ror.org/00d3pnh21, Bucharest, Romania
002882111 700__ $$aHansroul, M.$$uCERN$$vCERNhttps://ror.org/01ggx4157, Geneva, Switzerland
002882111 700__ $$aHons, Z.$$uRez, Nucl. Phys. Inst.$$vNuclear Physics Institute ASCR, Rez, Czech Republic
002882111 700__ $$aHorikawa, S.$$uU. Zurich (main)$$vZurich University, Zurich, Switzerland
002882111 700__ $$aIwashita, Y.$$uKyoto U.$$vKyoto University, Kyoto, Japan
002882111 700__ $$aKluson, J.$$uPrague, Tech. U.$$vCzech Technical University in Prague, Prague, Czech Republic
002882111 700__ $$aKobayashi, M.$$uKEK, Tsukuba$$vKEK, Tsukuba, Japan
002882111 700__ $$aKruglova, L.$$uDubna, JINR$$vJINR Dubna, Dubna, Russia
002882111 700__ $$aKulikov, A.$$uDubna, JINR$$vJINR Dubna, Dubna, Russia
002882111 700__ $$aKulish, E.$$uDubna, JINR$$vJINR Dubna, Dubna, Russia
002882111 700__ $$aLamberto, A.$$uINFN, Messina$$vMessina University, Messina, Italy
002882111 700__ $$aLanaro, A.$$uWisconsin U., Madison$$vUniversity of Wisconsin, Madison, Wisconsin, USA
002882111 700__ $$aLednicky, R.$$uPrague, Inst. Phys.$$vInstitute of Physics ASCR, Prague, Czech Republic
002882111 700__ $$aMarinas, C.$$uSantiago de Compostela U.$$vSantiago de Compostela University, Santiago de Compostela, Spain
002882111 700__ $$aMartincik, J.$$uPrague, Tech. U.$$vCzech Technical University in Prague, Prague, Czech Republic
002882111 700__ $$aNemenov, L.$$uDubna, JINR$$vJINR Dubna, Dubna, Russia
002882111 700__ $$aNikitin, M.$$uDubna, JINR$$vJINR Dubna, Dubna, Russia
002882111 700__ $$aOkada, K.$$uKyoto Sangyo U.$$vKyoto Sangyo University, Kyoto, Japan
002882111 700__ $$aOlchevskii, V.$$uDubna, JINR$$vJINR Dubna, Dubna, Russia
002882111 700__ $$aPentia, M.$$uBucharest, IFIN-HH$$vIFIN-HH, National Institute for Physics and Nuclear Engineeringhttps://ror.org/00d3pnh21, Bucharest, Romania
002882111 700__ $$aPenzo, A.$$uINFN, Trieste$$vINFN, Sezione di Trieste, Trieste, Italy
002882111 700__ $$aPlo, M.$$uSantiago de Compostela U.$$vSantiago de Compostela University, Santiago de Compostela, Spain
002882111 700__ $$aPrusa, P.$$uPrague, Tech. U.$$vCzech Technical University in Prague, Prague, Czech Republic
002882111 700__ $$aRappazzo, G.$$uINFN, Messina$$vMessina University, Messina, Italy
002882111 700__ $$aRomero Vidal, A.$$uSantiago de Compostela U.$$vSantiago de Compostela University, Santiago de Compostela, Spain
002882111 700__ $$aRyazantsev, A.$$uSerpukhov, IHEP$$vIHEP Protvino, Protvino, Russia
002882111 700__ $$aRykalin, V.$$uSerpukhov, IHEP$$vIHEP Protvino, Protvino, Russia
002882111 700__ $$aSaborido, J.$$uSantiago de Compostela U.$$vSantiago de Compostela University, Santiago de Compostela, Spain
002882111 700__ $$aSchacher, J.$$uU. Bern, AEC$$vAlbert Einstein Center for Fundamental Physics, Laboratory of High Energy Physics, Bern, Switzerland
002882111 700__ $$aSidorov, A.$$uSerpukhov, IHEP$$vIHEP Protvino, Protvino, Russia
002882111 700__ $$aSmolik, J.$$uPrague, Tech. U.$$vCzech Technical University in Prague, Prague, Czech Republic
002882111 700__ $$aTakeutchi, F.$$uKyoto Sangyo U.$$vKyoto Sangyo University, Kyoto, Japan
002882111 700__ $$aTrojek, T.$$uPrague, Tech. U.$$vCzech Technical University in Prague, Prague, Czech Republic
002882111 700__ $$aTrusov, S.$$uSINP, Moscow$$vSkobeltsyn Institute for Nuclear Physics of Moscow State University, Moscow, Russia
002882111 700__ $$aUrban, T.$$uPrague, Tech. U.$$vCzech Technical University in Prague, Prague, Czech Republic
002882111 700__ $$aVrba, T.$$uPrague, Tech. U.$$vCzech Technical University in Prague, Prague, Czech Republic
002882111 700__ $$aYazkov, V.$$uSINP, Moscow$$vSkobeltsyn Institute for Nuclear Physics of Moscow State University, Moscow, Russia
002882111 700__ $$aYoshimura, Y.$$uKEK, Tsukuba$$vKEK, Tsukuba, Japan
002882111 700__ $$aZrelov, P.$$uDubna, JINR$$vJINR Dubna, Dubna, Russia
002882111 710__ $$5PH
002882111 710__ $$aDIRAC Collaboration
002882111 773__ $$c092005$$mpublication$$n9$$pPhys. Rev. D$$v110$$y2024
002882111 859__ [email protected]
002882111 8564_ $$82497748$$s1414091$$uhttp://cds.cern.ch/record/2882111/files/DIRAC-Coulomb-correct.pdf$$zCorrected version with referee suggestions.
002882111 8564_ $$82495601$$s1472419$$uhttp://cds.cern.ch/record/2882111/files/CERN-EP-DRAFT-PS212-2023-001 - draft.pdf$$yDraft (restricted)$$zStamped by WebSubmit: 04/12/2023
002882111 8564_ $$82562896$$s31250$$uhttp://cds.cern.ch/record/2882111/files/qlSum8910_0_025_new.png$$y00002 The experimental $Q_L$ distributions (black points with errors) of the {\sl Coulomb}, {\sl non-Coulomb} and {\sl atomic $\pi^+\pi^-$ pairs} (sum of three data samples) for the $Q_t$ intervals 0.0\,--\,0.25~MeV/$c$, 0.0\,--\,1.0~MeV/$c$, 2.0\,--\,3.0~MeV/$c$ and 4.0\,--\,5.0~MeV/$c$. The green histogram is the corresponding combination of the {\sl Coulomb} and {\sl non-Coulomb pairs} simulated according to Eq. \ref{dN-dQ}. The fraction of the {\sl Coulomb pairs} and the normalization parameter were obtained by fitting in the total $Q_L$ interval except for the region -2~MeV/$c<Q_L<$ 2 MeV/$c$ populated by the {\sl atomic pairs}. One may see that the histograms well reproduce the increasing widths of the Coulomb peaks with increasing $Q_t$. The fitting histograms that describe the {\sl Coulomb} (blue) and {\sl non-Coulomb} (red) experimental pairs are presented as separate histograms. The excess pairs above the fitting histogram in the interval -2~MeV/$c<Q_L<$ 2~MeV/$c$ is due to the {\sl atomic pairs}.
002882111 8564_ $$82562897$$s13392$$uhttp://cds.cern.ch/record/2882111/files/all_new.png$$y00006 The simulated $Q_L$ distributions of $\pi^+\pi^-$ {\sl Coulomb pairs} at the production point for $Q_t$ intervals: ~~0~--~0.25~MeV/$c$, ~~0~--~1~MeV/$c$, ~~2~--~3~MeV/$c$, ~~4~--~5~MeV/$c$. All distributions are normalized to unity. It can be seen that the distribution width significantly increases with $Q_t$.
002882111 8564_ $$82562898$$s11714$$uhttp://cds.cern.ch/record/2882111/files/Data_MC_new.png$$y00007 The simulated $Q_L$ distribution of the {\sl Coulomb} and {\sl non-Coulomb pairs} in each data sample was divided by the same experimental spectrum. The ratios for the three data samples as a function of $Q_L$ were averaged and presented in this Figure. In the intervals of the positive and negative $Q_L$ (excluding region $\pm$ 2MeV/$c$), the points were fitted independently by a constant. It is seen that in the left and right intervals, the average ratios are unity, demonstrating that formula (\ref{dN-dQ}) describes the $Q_L$ distribution well.
002882111 8564_ $$82562899$$s4022743$$uhttp://cds.cern.ch/record/2882111/files/fig-setup.png$$y00001 General view of the DIRAC setup (1 -- target station; 2 -- first shielding; 3 -- micro drift chambers (MDC); 4 -- scintillating fiber detector (SFD); 5 -- ionization hodoscope (IH); 6 -- second shielding; 7 -- vacuum tube; 8 -- spectrometer magnet; 9 -- vacuum chamber; 10 -- drift chambers (DC); 11 -- vertical hodoscope (VH); 12 -- horizontal hodoscope (HH); 13 -- aerogel Cherenkov (ChA); 14 -- heavy gas Cherenkov (ChF); 15 -- nitrogen Cherenkov (ChN); 16 -- preshower (PSh); 17 -- muon detector (Mu).
002882111 8564_ $$82562900$$s27582$$uhttp://cds.cern.ch/record/2882111/files/qlSum8910_0_1_new.png$$y00003 The experimental $Q_L$ distributions (black points with errors) of the {\sl Coulomb}, {\sl non-Coulomb} and {\sl atomic $\pi^+\pi^-$ pairs} (sum of three data samples) for the $Q_t$ intervals 0.0\,--\,0.25~MeV/$c$, 0.0\,--\,1.0~MeV/$c$, 2.0\,--\,3.0~MeV/$c$ and 4.0\,--\,5.0~MeV/$c$. The green histogram is the corresponding combination of the {\sl Coulomb} and {\sl non-Coulomb pairs} simulated according to Eq. \ref{dN-dQ}. The fraction of the {\sl Coulomb pairs} and the normalization parameter were obtained by fitting in the total $Q_L$ interval except for the region -2~MeV/$c<Q_L<$ 2 MeV/$c$ populated by the {\sl atomic pairs}. One may see that the histograms well reproduce the increasing widths of the Coulomb peaks with increasing $Q_t$. The fitting histograms that describe the {\sl Coulomb} (blue) and {\sl non-Coulomb} (red) experimental pairs are presented as separate histograms. The excess pairs above the fitting histogram in the interval -2~MeV/$c<Q_L<$ 2~MeV/$c$ is due to the {\sl atomic pairs}.
002882111 8564_ $$82562901$$s1668453$$uhttp://cds.cern.ch/record/2882111/files/2409.12696.pdf$$yFulltext
002882111 8564_ $$82562902$$s30273$$uhttp://cds.cern.ch/record/2882111/files/qlSum8910_2_3_new.png$$y00004 The experimental $Q_L$ distributions (black points with errors) of the {\sl Coulomb}, {\sl non-Coulomb} and {\sl atomic $\pi^+\pi^-$ pairs} (sum of three data samples) for the $Q_t$ intervals 0.0\,--\,0.25~MeV/$c$, 0.0\,--\,1.0~MeV/$c$, 2.0\,--\,3.0~MeV/$c$ and 4.0\,--\,5.0~MeV/$c$. The green histogram is the corresponding combination of the {\sl Coulomb} and {\sl non-Coulomb pairs} simulated according to Eq. \ref{dN-dQ}. The fraction of the {\sl Coulomb pairs} and the normalization parameter were obtained by fitting in the total $Q_L$ interval except for the region -2~MeV/$c<Q_L<$ 2 MeV/$c$ populated by the {\sl atomic pairs}. One may see that the histograms well reproduce the increasing widths of the Coulomb peaks with increasing $Q_t$. The fitting histograms that describe the {\sl Coulomb} (blue) and {\sl non-Coulomb} (red) experimental pairs are presented as separate histograms. The excess pairs above the fitting histogram in the interval -2~MeV/$c<Q_L<$ 2~MeV/$c$ is due to the {\sl atomic pairs}.
002882111 8564_ $$82562903$$s198843$$uhttp://cds.cern.ch/record/2882111/files/2010-data-1.png$$y00008 The experimental numbers of {\sl Coulomb pairs} $NC_\mathrm{exp}(\Delta Q_t)$ for different $Q_t$ intervals (gray). The calculated numbers of {\sl Coulomb pairs} $NC_\mathrm{calc}(\Delta Q_t)$ for the same $Q_t$ intervals (brown).
002882111 8564_ $$82562904$$s31309$$uhttp://cds.cern.ch/record/2882111/files/qlSum8910_4_5_new.png$$y00005 The experimental $Q_L$ distributions (black points with errors) of the {\sl Coulomb}, {\sl non-Coulomb} and {\sl atomic $\pi^+\pi^-$ pairs} (sum of three data samples) for the $Q_t$ intervals 0.0\,--\,0.25~MeV/$c$, 0.0\,--\,1.0~MeV/$c$, 2.0\,--\,3.0~MeV/$c$ and 4.0\,--\,5.0~MeV/$c$. The green histogram is the corresponding combination of the {\sl Coulomb} and {\sl non-Coulomb pairs} simulated according to Eq. \ref{dN-dQ}. The fraction of the {\sl Coulomb pairs} and the normalization parameter were obtained by fitting in the total $Q_L$ interval except for the region -2~MeV/$c<Q_L<$ 2 MeV/$c$ populated by the {\sl atomic pairs}. One may see that the histograms well reproduce the increasing widths of the Coulomb peaks with increasing $Q_t$. The fitting histograms that describe the {\sl Coulomb} (blue) and {\sl non-Coulomb} (red) experimental pairs are presented as separate histograms. The excess pairs above the fitting histogram in the interval -2~MeV/$c<Q_L<$ 2~MeV/$c$ is due to the {\sl atomic pairs}.
002882111 8564_ $$82562905$$s276501$$uhttp://cds.cern.ch/record/2882111/files/atom-product.png$$y00000 The atomic, Coulomb, non-Coulomb, and accidental pair production processes. The wave lines denote the Coulomb interaction.
002882111 9031_ $$aApproval requested for number CERN-EP-2023-276$$bCERN-EP-2023-276$$cEPPHAPP$$d2023-11-27 13:41:33$$e2023-12-04 13:41:[email protected]$$swaiting
002882111 9031_ $$aDocument approved$$bCERN-EP-2023-276$$cEPPHAPP$$d2023-12-04 17:27:[email protected]$$sapproved
002882111 916__ $$sn$$w202351
002882111 980__ $$aPS212_Papers
002882111 980__ $$aARTICLE