The production of K+K- pairs in proton-proton collisions below the phi meson threshold
Q.J. Ye, M. Hartmann, D. Chiladze, S. Dymov, A. Dzyuba, H. Gao, R. Gebel, V. Hejny, A. Kacharava, B. Lorentz, D. Mchedlishvili, S. Merzliakov, M. Mielke, S. Mikirtytchiants, H. Ohm, M. Papenbrock, A. Polyanskiy, V. Serdyuk, H.J. Stein, H. Stroeher, S. Trusov, Yu. Valdau, C. Wilkin, P. Wuestner
aa r X i v : . [ nu c l - e x ] J u l The production of K + K − pairs in proton-proton collisions below the φ mesonthreshold Q. J. Ye,
1, 2, ∗ M. Hartmann, † D. Chiladze,
2, 3
S. Dymov,
4, 5
A. Dzyuba, H. Gao, R. Gebel, V. Hejny, A. Kacharava, B. Lorentz, D. Mchedlishvili,
2, 3
S. Merzliakov,
2, 5
M. Mielke, S. Mikirtytchiants,
2, 6
H. Ohm, M. Papenbrock, A. Polyanskiy,
V. Serdyuk,
2, 5
H. J. Stein, H. Str¨oher, S. Trusov,
9, 10
Yu. Valdau,
2, 11
C. Wilkin, and P. W¨ustner Department of Physics and Triangle Universities Nuclear Laboratory, Duke University, Durham, NC 27708, USA Institut f¨ur Kernphysik and J¨ulich Centre for Hadron Physics,Forschungszentrum J¨ulich, D-52425 J¨ulich, Germany High Energy Physics Institute, Tbilisi State University, GE-0186 Tbilisi, Georgia Physikalisches Institut, Universit¨at Erlangen-N¨urnberg, D-91058 Erlangen, Germany Laboratory of Nuclear Problems, Joint Institute for Nuclear Research, RU-141980 Dubna, Russia High Energy Physics Department, Petersburg Nuclear Physics Institute, RU-188350 Gatchina, Russia Institut f¨ur Kernphysik, Universit¨at M¨unster, D-48149 M¨unster, Germany Institute for Theoretical and Experimental Physics, RU-117218 Moscow, Russia Institut f¨ur Kern- und Hadronenphysik, Helmholtz-Zentrum Dresden-Rossendorf, D-01314 Dresden, Germany Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, RU-119991 Moscow, Russia Helmholtz-Institut f¨ur Strahlen- und Kernphysik, Universit¨at Bonn, D-53115 Bonn, Germany Physics and Astronomy Department, UCL, London WC1E 6BT, United Kingdom Zentralinstitut f¨ur Elektronik, Forschungszentrum J¨ulich, D-52425 J¨ulich, Germany (Dated: November 11, 2018)The pp → ppK + K − reaction was measured below the φ threshold at a beam energy of 2.568 GeVusing the COSY-ANKE magnetic spectrometer. By assuming that the four-body phase space is dis-torted only by the product of two-body final state interactions, fits to a variety of one-dimensionaldistributions permit the evaluation of differential and total cross sections. The shapes of the dis-tributions in the Kp and Kpp invariant masses are reproduced only if the K − p interaction is evenstronger than that found at higher energy. The cusp effect in the K + K − distribution at the K ¯ K threshold is much more clear and some evidence is also found for coupling between the K − p and¯ K n channels. However, the energy dependence of the total cross section cannot be reproduced byconsidering only a simple product of such pair-wise final state interactions. PACS numbers: 13.75.-n, 25.40.Ep, 13.75.Jz
I. INTRODUCTION
The original motivation for the study of kaon-pair pro-duction in the pp → ppK + K − reaction near thresh-old was the investigation of the structure of the scalarmesons a (980) or f (980) [1]. Such measurements wereinitially performed by the COSY-11 collaboration at sev-eral different excess energies below the φ -meson produc-tion threshold [2–4]. However, their results showed thatscalar meson production cannot in fact be the dominantdriving mechanism in kaon pair production [3] and thatthe data can be explained without the explicit inclusionof the a /f . Furthermore, they showed that the K − p and K − pp invariant mass spectra were strongly distorted,presumably by the K − p final state interaction (FSI) [4].This was most apparent in the ratio of the differentialcross sections in terms of the K − p and K + p invariantmasses.The pp → ppK + K − reaction was also investigated ∗ Electronic address: [email protected] † Electronic address: [email protected] with higher statistics above the threshold for the produc-tion of the φ meson, mainly with the aim of investigatingthe properties of that meson [5–8]. After removing the φ contribution in the spectra, it was clear that the K − p and K − pp distributions in the non- φ data were both stronglyinfluenced by the K − p interaction [6, 8]. It has beensuggested that this is connected with the production ofthe Λ(1405) excited hyperon [9], which might be treatedas a ¯ KN quasi-bound state with a width that overlapsthe ¯ KN threshold [10]. This idea was put on a quanti-tative footing by assuming that the Λ(1405) was formedthrough the decay N ⋆ → K + Λ(1405) [11]. The strengthand details of the ¯ KN interaction are clearly importantelements in the interpretation of possible kaon nuclearsystems, such as the deeply bound K − pp states [12].In addition to the K − p FSI, and one between the twoprotons, the data also showed an enhancement at low K + K − invariant masses with some possible structure atthe K ¯ K threshold [6–8]. Though the effects are small,they might be influenced by the a (980) or f (980) scalarmesons. However, the investigation of this region washampered by the need to separate the non- φ from the φ contribution and the fact that the data were spread overa very wide range of K + K − invariant masses. Measure-ments below the φ threshold can provide useful informa-tion on these interesting FSI effects without suffering thedistortion of the φ meson. However, the limited statisticsin the low-energy COSY-11 data [2–4] are insufficient fordetailed studies.Previous measurements of the pp → ppK + K − reac-tion were carried out at the COSY-ANKE magnetic spec-trometer at ε = 51, 67, and 108 MeV [6, 8], where the φ threshold is at ε = 32 . ε = √ s − m p + m K ) c , where √ s is the totalcenter-of-mass energy and m p and m K are the particlemasses in the final state. Because of the limited accep-tance of this spectrometer, an ansatz has to be maderegarding the distribution of events over the four-bodyphase space in order to convert count rates into cross sec-tions. This was done assuming that the distortions werethe products of those present in the two-particle subsys-tems. All the ANKE non- φ data seemed to be consistentwith an effective scattering length of a K − p = (0+1 . i ) fmwith no obvious influence of an energy dependence associ-ated with an effective range term. The dominance of theimaginary part is not unexpected because of the strongcouplings to the Σ π and Λ π channels but, due to thepresence of two other final-state particles, this parame-ter is not necessarily an intrinsic feature of the isolated K − p system.The ANKE measurements at three excess energiesalso showed some enhancement at low K + K − invari-ant masses but with at least a break of slope at the K ¯ K threshold. A combined analysis of all the resultsin this region [7, 8] shows that the data can be under-stood in terms of a final state interaction involving both K + K − elastic scattering plus a contribution from the K + K − ⇋ K ¯ K charge exchange. Although suggestive,the data are not sufficient to draw firm conclusions.In this paper we present much more precise pp → ppK + K − differential cross section data at a beam en-ergy of T p = 2 .
568 GeV ( ε = 23 . φ -meson threshold, we could studythe effects of the final state interactions in the K − p and K + K − systems in greater details.The paper is organized as follows. We first describe theexperimental setup and data analysis in Sec II. Giventhat the procedures involved are similar to those em-ployed at higher energies [6, 8], this can be quite brief.The fitting of the phenomenological parametrization tothe raw pp → ppK + K − data in order to make accep-tance corrections is also described here. The resultingdifferential cross sections and total cross section for the pp → ppK + K − reaction are presented in Sec III, followedby our conclusions in Sec IV. II. EXPERIMENT AND DATA ANALYSIS
The measurement of the pp → ppK + K − reaction wasperformed at an internal target station of the Cooler Syn- chrotron (COSY) of the Forschungszentrum J¨ulich [13].The ANKE spectrometer [14, 15], which consists ofthree dipole magnets, registers positively and negativelycharged ejectiles in the side detection systems, with thefast positively charged particles being detected in the for-ward detector. Particle identification relies on time-of-flight measurements [6, 15–17] from START and STOPcounters, and momentum information obtained from themultiwire proportional chambers. ] p) [GeV/c - K + Missing mass (K ) C oun t s / ( M e V / c FIG. 1: The pK + K − missing-mass distribution in the pp → pK + K − X reaction at T p = 2 .
568 GeV. The hatched his-togram shows the cuts imposed for the selection of the non-detected proton. The solid line, which is a second-order poly-nomial fit, was used to estimate the background contributionunder the proton peak.
In close-to-threshold production experiments, the to-tal cross section changes very rapidly with small changesin the excess energy. The proton beam energy, T p =2 .
568 GeV, was therefore determined very preciselythrough a careful monitoring of the Schottky spectra [18].The resulting value of the excess energy with respect tothe ppK + K − production threshold, ε = 23 . φ threshold. However it shouldbe noted that this is an average value, since the beamenergy decreases by up to 4.6 MeV through the course ofa machine cycle due to the interaction with the target.This effect was also investigated in the simulation.The experiment relied on a triple-coincidence, involv-ing the observation of a K + K − pair in the side detec-tors and a fast proton in the forward detector. The pp → ppK + K − reaction was then identified by requir-ing that the missing mass of the K + K − p system be con-sistent with that of a proton. In the analysis, a ± σ ( σ = 2 MeV/ c ) cut was applied on the missing-massdistribution of the selected K + K − p events, as shown inFig. 1. The fraction of misidentified events inside thecut window around the proton mass was estimated tobe about 5%, which was subtracted from the peak usingweighted data from the side bands, as parameterized bythe solid line. Any ambiguity in this procedure, which isless than 3%, is one source of systematic uncertainty. ) kkk θ cos( -1 -0.5 0 0.5 C oun t s (a) ) c.m.kk θ cos( -1 -0.5 0 0.5 1 (b) ) ppp θ cos( -1 -0.5 0 0.5 (c) ) ppp ψ cos( -1 -0.5 0 0.5 1 (d) [GeV/c] p P (e) ] [GeV/c p - K + K M (f) FIG. 2: Differential distributions of experimental (points) andsimulated (histograms) yields for kaon pair production in the pp → ppK + K − reaction at ε = 23 . K + in the K + K − reference frame, (b) the polarangle of the kaon pairs in the overall c.m. frame, (c) the polarangle of the emitted proton in the pp reference frame relativeto the beam direction, (d) the polar angle of the proton in the pp reference frame relative to the direction of the kaon pair,(e) the proton momentum in the pp reference frame, and (f)the K + K − p invariant mass. After identifying clean pp → ppK + K − events inANKE, acceptance corrections must be performed in or-der to evaluate differential cross sections. The simpleansatz used on data taken above the φ meson produc-tion threshold tried to take into account the influence offinal state interactions in the various two-particle sub-systems [6, 8]. This ansatz, which is also the basis forthe current simulation, assumes that the overall enhance-ment factor F is the product of enhancements in the pp , K + K − , and K − p systems: F = F pp ( q pp ) × F Kp ( q Kp ) × F Kp ( q Kp ) × F KK ( q KK ) , (1) where q pp , q Kp , q Kp , and q KK are the magnitudesof the relative momenta in the pp , the two K − p , andthe K + K − system, respectively. It is believed that the K + p interaction might be weakly repulsive and, if so, itsneglect would be interpreted as extra attraction in the K − p system. The FSI enhancement in the K − p casewas calculated in the scattering length approximation, F Kp ( q ) ≈ / | − iqa | and the best fit to the higherenergy data [6, 8] was found with a purely imaginaryeffective scattering length, a K − p ≈ . i fm. The proton-proton enhancement factor was derived from the Jostfunction [6, 8]. The enhancement factor in the K + K − system takes into account elastic K + K − scattering plusthe charge-exchange K + K − ⇋ K ¯ K [7].The seven degrees of freedom required to describe theunpolarized ppK + K − final state were chosen to be fourangles, the K + K − and K + K − p invariant masses, andthe relative momentum of the protons in the pp sys-tem [6, 8]. Distributions in these seven variables weregenerated inside the ANKE acceptance and comparedwith the experimental data, some of which are shownin Fig. 2. The best fit to the data was achieved with a K − p = (2 . ± . i fm, which is significantly largerin magnitude than the starting value of a K − p = 1 . i fm.The uncertainty in the real part is large and strongly cor-related with the imaginary part. To allow easy compari-son with the analysis of the higher energy data [6, 8], theeffective scattering length was taken to be purely imagi-nary.The ¯ KK scattering lengths for isospin-one and zerowere taken as in our previous work [7] and the ratio ofthe I = 1 and I = 0 production amplitudes of s -wave K ¯ K pairs was parameterized as Ce iφ c . The best fit wasobtained with C = 0 . ± .
03 and φ c = − ◦ ± ◦ , whichare consistent with our earlier evaluation [7, 8] based onthe above φ threshold data. The resulting descriptionsof the experimental data in Fig. 2 are very good and cer-tainly sufficient for evaluating the acceptance corrections.The luminosity needed in the analysis was determinedwith an overall systematic uncertainty of 9% by measur-ing pp elastic scattering in the forward detector [6]. Thiswas checked by simultaneous studies of the beam currentand Schottky spectra [18], which could fix the absoluteluminosity with a systematic uncertainty of 6%. Withinthese uncertainties the two methods agreed but, in orderto be coherent with our previous work, the luminosityextracted from the pp elastic scattering data was used inthe final analysis. III. RESULTS
The differential cross section for the pp → ppK + K − reaction at an excess energy ε = 23 . K + K − invariant mass. Alsoshown are simulations based on a four-body phase spaceand this distorted by the final state interactions in the K + K − , pp , and K − p systems within the product ansatz ] [GeV/c - K + K M ) ] b / ( G e V / c µ [ - K + K / d M σ d K K FIG. 3: (Color online) The pp → ppK + K − differential crosssection at ε = 23 . K + K − invariantmass. The dotted curve shows the four-body phase spacesimulation whereas the inclusion of the final state interactionsthrough Eq. (1) gives the dashed curve for a K − p = 1 . i fmand the red solid curve a K − p = 2 . i fm. The dot-dashedcurve was obtained by considering only the pp and K − p finalstate interactions with a K − p = 2 . i fm. of Eq. (1). This was done separately with effective scat-tering lengths of a K − p = 1 . i fm and a K − p = 2 . i fm.The most striking features in the data are the strengthnear the K + K − threshold and the dip at M K + K − ≈ .
995 GeV/ c , which corresponds precisely to the K ¯ K production threshold [7]. This is compelling evidence fora cusp effect coming from the K ¯ K ⇋ K + K − transi-tions. To investigate this phenomenon in greater detail,the K + K − invariant mass distribution was divided by asimulation where only the final state interactions in the pp and K − p , with a K − p = 2 . i fm, were considered.The best fit to the data shown in Fig. 4 is achieved witha contribution from the isospin-zero channel that is aboutthree times stronger than the isospin-one. This finding isconsistent with our earlier result [7]. The deviations ap-parent in Figs. 3 and 4 at high K + K − invariant massesmight be connected with the approximations made in ourcoupled-channel model [7].Previous analyses of the pp → ppK + K − reaction atdifferent excess energies [4, 6, 8, 19] have all shown astrong preference for low values of the K − p and K − pp invariant masses, M K − p and M K − pp . To study this fur-ther, we have evaluated differential cross sections as func-tions of these invariant masses and also the ratios: R Kp = dσ/dM K − p dσ/dM K + p ,R Kpp = dσ/dM K − pp dσ/dM K + pp · (2) ] [GeV/c - K + K M E nh a n ce m e n t F ac t o r FIG. 4: Ratio of the measured pp → ppK + K − differentialcross section at ε = 23 . K + K − invariant mass to a simulation that includes only K − p and pp final state interactions (shown by the dot-dashed curvein Fig. 3). In addition to the current data (solid circles),weighted averages of previous measurements (open squaresand circles) are also presented. The solid curve representsthe best fit in a model that includes elastic K + K − FSI and K ¯ K ⇋ K + K − charge-exchange [7]. The best fits neglect-ing charge exchange and including only this effect are shownby the dashed and dot-dashed curves, respectively. The corresponding experimental data and simulationsare shown in Figs. 5 and 6. Both R Kp and R Kpp displaythe very strong preferences for lower invariant massesseen in the earlier data. The low mass enhancementsin Figs. 5c and 6c clearly indicate once again that the pp → ppK + K − reaction cannot be dominated by theundistorted production of a single scalar resonance a or f . Within a four-body phase space simulation bothratios should be constant and equal to one and such asimulation also fails to describe the M Kp and M Kpp dis-tributions. Whereas the inclusion of a K − p FSI with aneffective scattering length a K − p = 1 . i fm improves thesituation, it overestimates the data in the high invariantmass regions for both R Kp and R Kpp . With the largereffective scattering length a K − p = 2 . i fm, these ra-tios, as well as the individual differential cross sections,can be well reproduced. Within the product ansatz ofEq. (1) the K − p final state interaction effectively be-comes stronger at lower excess energies. This illustratesthe limitations of this simple ansatz to the complex four-body dynamics.Although the K − p elastic final state interaction de-scribes well the vast bulk of the data shown in Figs. 5 and6, it is interesting to note that there seems to be a smallbut significant deviation between the K − p data and sim-ulation in Fig. 5b at low invariant masses. Since the ¯ K n threshold is at 1.437 GeV/ c , this suggests that the data ) ] b / ( G e V / c µ [ K p / d M σ d (a) (b) ] [GeV/c Kp M K p R -1 (c) FIG. 5: (Color online) Differential cross sections for the pp → ppK + K − reaction as functions of the invariant masses of K + p (upper panel) and K − p (middle panel), and their ratio R Kp (lower panel). The red solid and dashed black histogramsrepresent estimations based on Eq. (1) that take into account K − p , pp and K + K − final state interactions with a K − p =2 . i fm and a K − p = 1 . i fm, respectively. The four-bodyphase-space simulations are shown by the dotted histograms. in this region might also be influenced by K − p ⇋ ¯ K n channel coupling.Due to the low statistics, the COSY-11 data at 10 and28 MeV [4, 19] cannot distinguish between predictionsbased on effective scattering lengths of a K − p = 1 . i fmand a K − p = 2 . i fm. This illustrated for the R Kp ratioin Fig. 7 but this lack of sensitivity is equally true for R Kpp .The pp → ppK + K − differential cross section, shownin Fig. 3 as a function of the K + K − invariant mass, was )] b / ( G e V / c µ [ K pp / d M σ d (a) (b) ] [GeV/c Kpp
M2.37 2.38 2.39 K pp R (c) FIG. 6: (Color online) Differential cross sections for the pp → ppK + K − reaction with respect to the invariant massesof K + pp (upper panel) and K − pp (middle panel), and theirratio R Kpp (lower panel). The conventions for the theoreticalestimates are as in Fig. 5. used to determine the value of the total cross section, σ =6 . ± . ± .
67 nb, where the first error is statistical andthe second systematic. The systematic effects consideredhere arise from the background subtraction, acceptancecorrection, tracking efficiency correction, and luminositydetermination.The total cross section result is plotted in Fig. 8 alongwith previous measurements from DISTO [5], COSY-11 [2–4, 19], and ANKE [6, 8]. The new point seemshigh compared to the COSY-11 result at ε = 28 MeV,though one has to take into account the limited statis-tics of these data. This value had already been increasedby 50% compared to that originally published [4]. Thiswas achieved through a re-analysis of the data that in- ] [GeV/c Kp M K p R -1 (a) ] [GeV/c Kp M K p R -1 (b) FIG. 7: (Color online) The ratio R Kp for the pp → ppK + K − reaction measured by COSY-11 at (a) ε = 10 MeV and (b)28 MeV [19]. The dotted histograms represent the four-bodyphase-space simulations, whereas the red solid and dashedones represent the theoretical calculations taking into account K − p , pp and K + K − final state interactions with a K − p =2 . i fm and 1 . i fm, respectively. cluded a modified pp and a K − p final state interactionwith a K − p = 1 . i fm [19]. For the lower excess energyof ε = 10 MeV, where the acceptance of the COSY-11apparatus is higher, the re-analysis increased the crosssection by only 20%. Both cross sections would be re-duced slightly if a K − p were increased to 2 . i fm butthe changes would be less than the statistical errors [20].The COSY-11 acceptance is very sensitive to the formassumed for the pp FSI but much less so for that of the K − p [20].It is clear from Fig. 8 that the four-body phase spacecannot reproduce the energy dependence of the totalcross section. With the inclusion of the pp , K + K − ,and K − p FSI, with an effective scattering length of a K − p = 1 . i fm, the data above the φ threshold canbe described well but those at lower energy are signifi-cantly underestimated. An increase in the value of a K − p might help in this region but the coincidence of strong ef-fects in different two- or even three-body channels must [MeV] ∈ [ nb ] t o t σ FIG. 8: Total cross section for the pp → ppK + K − reactionas a function of excess energy ε . The present result (closedcircle) is shown together with earlier experimental data takenfrom DISTO (triangle), ANKE (circles), COSY-11 (squares).The dotted line shows the four-body phase space simulation,whereas the solid line represent the simulations with a K − p =1 . i fm. The predictions of a one-boson exchange model arerepresented by the dashed line [21]. also bring the factorization assumption of Eq. (1) intoquestion. The dashed line, which represents a calcula-tion within a one-boson exchange model [21], also un-derestimates the near-threshold data. This model in-cludes energy-dependent input derived from fits to the K ± p → K ± p total cross sections, though it does notinclude the pp final state interaction. IV. DISCUSSION AND CONCLUSIONS
The production of K + K − pairs has been measuredin the pp → ppK + K − reaction channel at an excessenergy of ε = 23 . c width into account, this is well below the central φ -mesonthreshold at 32.1 MeV. The reaction was identified inANKE through a triple coincidence of a K + K − pair anda forward-going proton, with an additional cut on the K + K − p missing-mass spectrum. The high statistics andlow excess energy allow us to produce a detailed K + K − invariant mass distribution below the φ threshold.The distortion of both the K − p and K − pp spec-tra, which are even stronger than in our higher energydata, can be explained quantitatively within the productansatz of Eq. (1) with an effective K − p scattering length a K − p ≈ . i fm. This is to be compared with the 1 . i fmobtained from the analysis of data measured above the φ production threshold. A full treatment of the dynamicsof the four-body ppK + K − channel is currently imprac-tical. As a consequence, an energy dependence of a K − p is possible because this is merely an effective parameterwithin a very simplistic description of the four-body finalstate interaction. The strong K − p final state interactionmay be connected with the Λ(1405) in the productionprocess and it has been suggested [11] that the produc-tion of non- φ kaon pairs proceeds mainly through the as-sociated production pp → K + p Λ(1405). This would alsolead to deviations from the simple product ansatz for thefinal state interactions, not least because an attractionbetween the Λ(1405) and the proton would involve threefinal particles.Our results show a very strong preference for low K − pp masses and this effect seems to be even more marked thanin the higher energy data [6, 8]. Although this mightbe connected with the ideas of a K − pp deeply boundstate [12, 22–24], it must be stressed that our data weremeasured far above threshold. They should not thereforebe taken as necessarily implying that the K − will bindwith two protons.There is strong evidence for a cusp effect arising fromthe K ¯ K ⇋ K + K − transitions. Our analysis within acoupled-channel description suggests that, with the val-ues of the K ¯ K scattering lengths used, the productionof isospin-zero K ¯ K pairs dominates. Though this is con-sistent with results extracted from data taken above the φ threshold [7, 8], there is clearly room for some refine- ment in the model. On the other hand, the structureof the K − p invariant mass spectrum of Fig. 5 in the1437 MeV/ c region suggests that there might be impor-tant coupling also between the K − p and ¯ K n systems.It is evident that the interactions in the four-body ppK + K − final state are extremely complex. Neverthe-less, the energy dependence of the total cross section canbe well described above the φ threshold by introducingthe effects of the pp , K + K − and K − p final state interac-tion with an effective scattering length of a K − p = 1 . i fm.This would, however, have to be increased to have anyhope of fitting the lower energy data. Further theoreticalwork is required to clarify the reaction mechanisms. Acknowledgments
We would like to thank the COSY machine crew forproviding the good conditions that were necessary for thiswork. We are also grateful for the continued assistanceof other members of the ANKE Collaboration. Discus-sions with P. Moskal and M. Silarski were very helpful.This work was supported in part by the US Departmentof Energy under Contract No. DE-FG02-03ER41231 andCOSY FFE. [1] W. Oelert,
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