DISTO data on Kpp
M. Maggiora, P. Kienle, K. Suzuki, T. Yamazaki, DISTO Collaboration, M. Alexeev, A. Amoroso, F. Balestra, Y. Bedfer, R. Bertini, L. C. Bland, A. Brenschede, F. Brochard, M. P. Bussa, S. Choi, M. L. Colantoni, R. Dressler, M. Dzemidzic, J. Cl. Faivre, L. Ferrero, J. Foryciarz, I. Fröhlich, V. Frolov, R. Garfagnini, A. Grasso, S. Heinz, W. W. Jacobs, W. Kühn, A. Maggiora, D. Panzieri, S. Sosio, H. W. Pfaff, G. Pontecorvo, A. Popov, J. Ritman, P. Salabura, V. Tchalyshev, S. E. Vigdor
DDISTO data on K − p p M. Maggiora ∗ ,a , P. Kienle b,c , K. Suzuki b , T. Yamazaki d,e , M. Alexeev a , A. Amoroso a , F.Balestra a , Y. Bedfer f,1 , R. Bertini a,f , L. C. Bland g,2 , A. Brenschede h,3 , F. Brochard f , M. P.Bussa a , S. Choi f,4 , M. L. Colantoni a , R. Dressler m,5 , M. Dzemidzic g,6 , J. Cl. Faivre f , L. Ferrero a ,J. Foryciarz j,k,7 , I. Fr¨ohlich h,8 , V. Frolov i,9 , R. Garfagnini a , A. Grasso a , S. Heinz a,f,10 , W. W.Jacobs g , W. K¨uhn h , A. Maggiora a , D. Panzieri l , S. Sosio a , H. W. Pfa ff h , G. Pontecorvo , A.Popov i , J. Ritman h,11 , P. Salabura j , V. Tchalyshev i , S. E. Vigdor g,12 a Dipartimento di Fisica Generale “A. Avogadro” and INFN, Torino, Italy b Stefan Meyer Institute for Subatomic Physics, Austrian Academy of Sciences, Vienna, Austria c Excellence Cluster Universe, Technische Universit t M nchen, Garching, Germany d Department of Physics, University of Tokyo, Tokyo, 116-0033 Japan e RIKEN Nishina Center, Wako, Saitama, 351-0198 Japan f Laboratoire National Saturne, CEA Saclay, France g Indiana University Cyclotron Facility, Bloomington, Indiana, U.S.A. h II. Physikalisches Institut, Univ. Gießen, Germany i JINR, Dubna, Russia j M. Smoluchowski Institute of Physics, Jagellonian University, Krak´ow, Poland k H. Niewodniczanski Institute of Nuclear Physics,Krak´ow, Poland l Universit`a del Piemonte Orientale and INFN, Torino, Italy m Forschungszentrum Rossendorf, Germany
Abstract
The data from the DISTO Collaboration on the exclusive pp → pK + Λ production acquired at T p = . GeV have been re-analysed in order to search for a deeply bound K − pp ( ≡ X ) state,to be formed in the binary process pp → K + X . The preliminary spectra of the ∆ M K + missing-mass and of the M p Λ invariant-mass show, for large transverse-momenta of protons and kaons, adistinct broad peak with a mass M X = ± MeV / c and a width Γ X = ± MeV / c . Key words: ¯ K nuclei, kaon condensation, super-strong nuclear force, strange di-baryon PACS: ∗ on behalf of the DISTO collaboration Email address: [email protected] (M. Maggiora) Present address: DAPNIA / SPhN, CEA Saclay, F Present address: BNL, USA Present address: DIAMOS AG, Sulzbach, D Present address: Seoul National University, Seoul, KR Present address: Paul Scherrer Institut, Villigen, CH Present address: IU School of Medicine, Indianapolis, USA Present address: Motorola Polska Software Center, Krak´ow, PL Present address: IKF, Frankfurt, D Present address: Dip. di Fisica Generale and INFN, Torino, I Present address: GSI, Darmstadt, D Present address: FZ, Juelich, D Present address: BNL, USA
Preprint submitted to Nuclear Physics A October 31, 2018 a r X i v : . [ h e p - e x ] D ec he simplest kaonic nuclear bound system K − pp is currently interpreted in the literature intwo di ff erent kinds of scenarios: the strong binding regimes and the weak binding regimes . In theformer case the K − pp has been predicted to be a quasi-stable state with mass M = MeV / c ,binding energy B K =
48 MeV and partial decay width Γ Σ π p =
61 MeV [1, 2]. The strongbinding arises from the migration of the K − between the two protons in a molecule-like structured K − pp , causing a ”super-strong nuclear force” [3, 4]. Such a picture originates from the ansatzthat the Λ (1405) resonance is an I = KN quasi-bound state embedded in the Σ π continuum.Recent Faddeev calculations [5, 6, 7] lead as well to a deeply bound K − pp state. A di ff erentapproach based on chiral dynamics [8, 9, 10] places the K − p pole close to the ¯ KN threshold, at1420 ÷ MeV / c , leading to a weak ¯ KN interaction and to a shallow K − pp bound state [11].Whereas the dispute on the location of the K − p state, at 1405 or at 1420, remains unresolved,the importance to distinguish between the strong binding and the weak binding regimes by anexperimental investigation of the K − pp formation in pp reactions is supported by its implicationon kaon condensation [15, 16] and on the existence of dense kaonic nuclear states [1, 2, 12, 13,14].The formation of a strongly bound K − pp system with a short p - p distance in a pp → K + + K − pp reaction has been predicted [1, 2] as the consequence of a significantly large stickingprobability between Λ (1405) and p , due to the short range and large momentum transfer of the pp reaction [3, 4]. We report herewith the search for a possible candidate of such an exotic K − pp deeply bound state in the existing experimental data acquired by the DISTO spectrometer for the pp → pK + Λ reaction.
1. Data sample
The DISTO spectrometer, described in details elsewhere [17], was aimed to investigate hy-peron and meson productions in pp collisions, making use of the transversely polarised protonbeam of SATURNE (Saclay, France) and of an unpolarised liquid hydrogen target. The maingoal of the hyperon program was determining di ff erent spin observables (polarisation, analysingpower, depolarisation transfer) [18, 19] in exclusive hyperon production like pp → pK + Λ and pp → pK + Σ , selecting the di ff erent exclusive contributions by a complete kinematic recon-struction of the final state, for three di ff erent kinetic energies of the beam: T p = .
85, 2 . Reaction T p , thr ( GeV ) Charged particle trigger (cid:126) pp → pK + (cid:126) Λ pK + ( p π − ) (cid:126) pp → pK + (cid:126) Σ , (cid:126) Σ → (cid:126) Λ γ pK + ( p π − ) (cid:126) pp → pK + Σ ∗ pK + ( p π − ) from Λ π or Σ π pK + π + ( π − ) from Σ − π + pK + π − ( p ) or ( π + ) from Σ + π − (cid:126) pp → pK + Λ ∗ (1405) pK + π + ( π − ) from Σ − π + pK + ( p π − ) from Σ π pK + π − ( p ) or ( π + ) from Σ + π − Table 1: Exclusive hyperon production channels that can be accessed at T p = . GeV . The particles selected for eachsingle final state by the charged particle trigger, a trigger with charged particle multiplicity four, can be found in the rightcolumn, the () evidencing those particles emerging from a displaced secondary vertex . igure 1: All the spectra reported herewith refer only to those events that survived the kinematically constrained refitdescribed in the text. On the left, the ∆ M pK missing mass spectrum post-refit ( ∆ M pK is left free in the refitting procedure).On the right, the acceptance corrected Dalitz plot, M ( Λ p ) vs M ( K Λ ) , of pp → pK + Λ at T p = . GeV . . GeV . The trigger was set in order to acquire events with at least four emerging chargedparticles. The data sample chosen to probe the existence of a possible bound K − pp system isconstituted by those events acquired at the higher T p (in such a case those exclusive channelreported in Tab. 1 can be accessed) for the pK + Λ final state, in which a complete reconstructionof the final state is performed, and no particle goes undetected.A first event selection is performed asking for: a π + -veto (no track in the final state positivelyidentified as a π + ); the positive track emerging from the displaced secondary vertex to be clearlyidentified as a proton (the proton of the weak-decay Λ → p π − ); its polar angle in the Λ rest frameto be bounded to its kinematic limit ( | θ CM Λ p | < . rad ); a primary vertex reconstructed withinthe target region ( | z V R | < . cm ); a minimum Λ decay length of 4 cm . The events in which a Λ has been produced are identified through the invariant-mass of the two tracks emerging fromthe displaced secondary vertex ( M p π − ∼ M Λ ), and then fed to a refit constrained by the followingkinematic requirements: the reconstructed invariant mass M p π − is constrained to the Λ mass( M p π − = M Λ ); the momentum conservation at the secondary vertex is enforced by constrainingthe reconstructed Λ momentum along the vertex joiner direction ( (cid:126) p Λ (cid:107) −−−−→ V R V D ); the four-bodymissing mass is constrained either to 0 ( ∆ M b = ∆ M b = M π selects reactions 3 and 4 in the same table). A further ”soft” constraintrequiring the reaction vertex to be along the beam line is achieved including in the event refitting χ a term esplicitly accounting for the distance between the reaction vertex and the beam line. Atight requirement on the event refitting χ is the most e ff ective cut to reach background rejectionand hyperon separation much better than those achieved in earlier stages of these data analyses[18].We can finally resolve the directly produced Λ ’s from those coming from the decays of heav-ier hyperons by the mean of the ∆ M pK missing-mass spectrum shown in Fig. 1.a: the lower masspeak correspond to the exclusive pK + Λ final state; the second peak to reaction 2 of Tab. 1, whilethe bump at higher mass values may contain contributions arising from reactions 3 and 4. Thedata sample corresponding to the exclusive reaction channel: pp → pK + Λ (1)3hat can be extracted from the DISTO data acquired at a beam kinetic energy T p = . GeV ,is composed of ∼ K events, which fullfill all the requirements described above, and inparticular the tight χ cut in the refit procedure. In these kinematic conditions a candidate of the K − pp bound state ( ≡ X ) could be formed in the two-body process: pp → K + X , X → p + Λ (2)and contribute to the low mass peak of Fig. 1.a through the X → p Λ decay, other processes likefree Λ (1405) emission being excluded. The whole pK + Λ sample could then include besides theordinary three-body process (1), acting in the present analysis as a ”background”, also the exoticprocess of the two-body reaction (2).A sample of events simulated for the pK + Λ final state according to an uniform phase-spacedistribution, folded with the DISTO acceptance, and then fed to the complete reconstruction andanalysis chain, fulfilling hence the cuts and the refitting procedure described above, leads to thedistributions reported herewith and marked SIM ; such distributions have to be compared withthe uncorrected experimental data
UNC . In order to minimise the e ff ects of possible uncertain-ties arising from the evaluation of an e ffi ciency matrix we adopt herewith the deviation spectra technique, an e ffi ciency-compensated presentation of the experimental data in which the ratio: DEV = UNCS I M (3)is evaluated bin by bin. A
DEV spectrum is di ff erent from its corresponding intensity distribu-tion, the latter being a ff ected by phase-space limitation and hence bell-shaped. The DEV spec-trum is free, at first order, both from uncertainties in the e ffi ciency-matrix evaluation and fromphase-space constraints. A DEV distribution deviates from its generally flat nature, indicatinga structure, when a physically meaningful deviation from the uniform phase-space distributionoccurs; that should make the comparison with theoretical predictions easier. In those particu-lar cases in which the physical distribution is expected to be flat (as for example in the case ofthe Dalitz distribution), and only in those cases, the
SIM spectra reflect just the e ff ects of theacceptance and of the e ffi ciencies, and the DEV spectra are equivalent to their correspondinge ffi ciency-corrected intensity distributions COR .Fig. 1.b show the acceptance-corrected Dalitz plot of the considered pK + Λ sample in theplane defined by the two invariant-masses M Λ p and M K + Λ . The Dalitz distribution of the ordinarythree-body process (1) should be di ff erent from that corresponding to an uniform phase-spacedistribution, but is expected to be continuous without any local bump structure [20]. The Dalitzplot alone cannot resolve the ”ordinary” process (1) from the ”exotic” one (2), and yet the plotin Fig. 1.b reveals some structure hard to be explained by the latter process only. The angularcorrelations of the three particles in the final state are hence needed to discriminate among thesetwo processes.
2. Angular correlations
Fig. 2 shows the
UNC , SIM and
DEV distributions of the momentum p CM versus the polarangle cos ( θ CM ) for the proton and the kaon emerging from the primary reaction vertex, respec-tively. Both the UNC and the
SIM p distributions are strongly peaked in the backward direction,reflecting the corresponding larger acceptance of the DISTO spectrometer for those events show-ing a Λ → p π − decay in the forward direction. An indication of the e ff ectiveness of the deviation4 igure 2: Uncorrected ( UNC ), simulated (
SIM ) and deviation (
DEV ) distributions, for (a) p and (b) K + , of the momentum p CM versus the polar angle cos ( θ CM ) in the pp center of mass frame. Dotted lines define the proton-angle and the kaon-angle cuts, respectively | cos ( θ CM , p ) | < . − . < cos ( θ CM , K + ) < . spectra technique comes from considering the DEV distributions for p and Λ (here not shown):both are remarkably symmetric and peaked at cos ( θ CM ) ±
1, as expected considering the sym-metric p - p scattering in the CM frame.The dominant contribution from protons at extremely backward angles ( cos θ CM , p ∼ − . q T < . GeV / c ) eventsfrom the ”ordinary” process (1), since the maximum proton momentum in (1) is 0 . GeV / c .The p angular distribution with respect to the incident beam has been fitted to a theoreticalmodel [20], predicting a p - p collision length for this dominant component of about 0 . f m (corresponding to an intermediate boson mass of m B ∼ . GeV / c ). On the other hand theevents characterised by a large proton polar angle can be large- q T ”ordinary” process events, butalso events from the ”exotic” process (2) involving the decay of X with a transverse-momentum ∼ . GeV / c . A cut on the proton-emission polar angle, asking for | cos ( θ CM , p ) | < .
6, can thusenhance the contribution from the process (2) by rejecting those events with a small proton polarangle, dominated by the process (1).The
DEV kaon distribution of Fig. 2.b shows a clear mono-energetic component for p CM , K + ∼ . GeV / c , a possible signature from a two-body process (2). It should be stressed that: such acomponent is evident even before enhancing the contribution from reaction (2) by applying theproton-angle cut described above; this structure is already present in the UNC distribution, andcannot be a fake introduced by the deviation spectra technique, since the
SIM distribution issmooth in the corresponding region.To probe the e ff ectiveness of the proton-emission angle cut we can consider in Fig. 3 the DEV spectra, for large-angle (left) and small-angle (right) protons, of the invariant mass M p Λ and of the missing mass ∆ M K + (bottom frames), and their correlation with the kaon polar anglein the CM frame cos ( θ CM , K + ) (top frames) . The vertical structure in the p CM , K + spectra ofFig. 2.b shows up at the corresponding ∆ M K + values, and is clearly enhanced by asking for largeproton-emission polar angles, for which both the DEV spectra of M p Λ and ∆ M K + show a structurearound the abscissa x ∼ .
15, that would correspond to a mass for a K − pp candidate of M X (cid:39) . GeV / c . On the other hand the DEV unidimensional spectra for small proton-emission polarangle (right frames of Fig. 3) do not show such a structure; their linear shapes with constantgradients are well accounted for by the ”ordinary” process (1) assuming a collision length (cid:126) / m B c The uni-dimensional
DEV M p Λ and ∆ M K + distributions have been obtained performing the ratio of the correspond-ing uni-dimensional UNC and
SIM distributions. igure 3: DEV spectra, for large (left four frames) and small (right four frames) proton-emission polar angle in the CMframe, of the invariant mass M p Λ and of the missing mass ∆ M K + (bottom frames), and of their correlation with the kaonpolar angle in the CM frame cos ( θ CM , K + ) (top frames). with m B ∼ . GeV / c [20]. The ”ordinary” process (1) could contribute to the large proton-angle events as well, but with a shorter collision length, and leading to a flat distribution withoutgradient [20], in great contrast with the observed DEV distributions, far from a flat shape aloneand showing the large structure on a flat background.The mono-energetic band in the kaon distribution is clearly enhanced for large K + -emissionpolar angles, as can be seen in the DEV of spectrum of Fig. 2.b, a spectrum obtained performingno cut on the proton polar angle; the cos ( θ CM , K + ) < − . UNC and
SIM spectra. A further cut on the K + CM polar angle, − . < cos ( θ CM , K + ) < .
4, can hencebe defined in order to enhance the possible two-body signature in the considered pK + Λ sample.The final DEV spectra will thus be obtained asking both for large proton- and large K + -emissionpolar angles (i.e. large transverse momenta).In the present preliminary analysis we have shown how a large structure can be observed inthe DEV spectra of both the M p Λ invariant-mass and the ∆ M K + missing-mass (Fig. 3); such astructure is enhanced selecting separately either large proton-emission or large kaon-emission po-lar angles in the CM frame, and such enhancement is maximum under the combined e ff ect of bothcuts. The large broad peak that appears in the left top frame of Fig. 4, showing the DEV spectraof the ∆ M K + missing-mass for large transverse-momenta protons and kaons ( | cos ( θ CM , p ) | < . − . < cos ( θ CM , K + ) < . DEV spectra for large transverse-momentakaons and small transverse-momenta protons ( | cos ( θ CM , p ) | > . − . < cos ( θ CM , K + ) < . DEV spectrum of Fig. 4leads to: M X = (2 . ± . GeV / c Γ X = (0 . ± . GeV / c (4)The huge di ff erence between the reduced χ ’s obtained considering a Gaussian plus a linearbackground ( χ / nd f = . / = .
4) and the linear background only ( χ / nd f = / ∼ σ .6 igure 4: Left frames: DEV spectra of the ∆ M K + missing-mass for (top) large- q T protons and kaons ( | cos ( θ CM , p ) | < . − . < cos ( θ CM , K + ) < .
4) and for (bottom) large- q T kaons and small- q T protons ( | cos ( θ CM , p ) | > . − . < cos ( θ CM , K + ) < . Σ π threshold. Right frame: pre-dicted [4] cross sections of the pp → K + + K − pp reac-tion at T p = GeV as a function of E Λ (1405) p for di ff erentrms distances R ( Λ (1405) p ) in the case of: A) the originalAkaishi-Yamazaki interaction ( B K = MeV ) [1]; B) a17% enhancement ( B K = MeV ) and C) a 25% enhance-ment ( B K = MeV ).
3. Concluding remarks
The observed structure in the top left frame of Fig. 4 could be interpreted as a possiblecandidate for a deeply bound K − pp state, following the predictions in [3, 4], that it is producedin p - p reactions with high probability at large momentum transfer. The mass M X from (4) isclose to the mass M Λ p ∼ . GeV / c of the K − pp candidate reported in the stopped- K − experiment by FINUDA [21], and would correspond to a binding energy B K = (105 ± MeV for X ≡ K − pp . The observed B K is larger than that originally predicted by Akaishi and Yamazaki,and is compared in the right frame of Fig. 4 with the spectral profiles calculated for the original(A) [1] and for two di ff erently enhanced hypotheses (B, C) [4] of the ¯ KN strength. Accordingto [3, 4] a large formation of K − pp is expected in p - p reactions, its production rate estimated to7e as much as the Λ (1405) production rate ( ∼
20% of the total Λ production rate). Such a largeformation probability indicates the production of a compact system within less than 1 . f m ,much shorter hence than the average N - N distance in ordinary nuclei ( ∼ . f m ). If assuminga two-body mechanism pp → K + X , no candidate other than K − pp for a X with such a largeformation is predicted to date.The ∆ M K + missing-mass spectrum is compared in Fig. 4 with the most relevant particle-emission thresholds: M K − pp = . GeV / c , M Λ (1405) p = . GeV / c , and M Σ + π − p = . GeV / c . The present observation is limited to the non-pionic p Λ decay mode and hence, as theobserved peak is close to the Σ π emission threshold, its spectral shape is expected to be una ff ectedby this threshold, since the pionic decay mode is suppressed to large extent. A K − pp candidateshowing a Γ ∼ . GeV in the p Λ decay mode is thus compatible with a predominance of the Γ p Λ partial width (as predicted by [22, 23]) and points toward a Γ p Σ + π + partial width much smallerthat the original prediction ( ∼ MeV , [24]).The large observed binding energy suggest additional e ff ects to be considered [4, 25], andrequires theoretical studies of the decay shape [24] and branch [22, 23] of K − pp . It points towarda strong binding regime, and does not seem compatible with a shallow ¯ K binding [8, 9, 10, 11]. Acknowledgements.
We are beholden to Professor Y. Akaishi for his helpful interactions withthe authors. This research was partly supported by the DFG cluster of excellence ”Origin andStructure of the Universe” of Technische Universit¨at M¨unchen and by Grant-in-Aid for ScienticResearch of MonbuKagakusho of Japan. One of us (T.Y.) acknowledges the support by an Awardof the Alexander von Humboldt Foundation, Germany.
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