We discuss the puzzling experimental results on baryon-antibaryon production
in e+e- annihilation close to the threshold, in particular the fact that
sigma(e+e- --> nbar n) >~ sigma(e+e- --> pbar p). We discuss an interpretation
in terms of a two-step process, via an intermediate coherent isovector state
serving as an intermediary between e+e- and the baryon-antibaryon system. We
provide evidence that the isovector channel dominates both e+e- --> pions and
from Nbar N annihilation at rest, and show that the observed ratio of
sigma(e+e- --> nbar n)/sigma(e+e- --> pbarp p) can be understood quantitatively
in this picture.Comment: 13 pages, 4 figure

Amado R D

Anderson S (CLEO Collaboration)

Bisello D (DM2 Collaboration)

Eidelman S

John Ellis

Karliner M

L3 Collaboration

Marek Karliner

Schechter J

Skyrme T H

New Journal of Physics

English

arXiv

Crossref

On electron-positron annihilation into nucleon-antinucleon pairs

We discuss the puzzling experimental results on baryon-antibaryon production in e+e- annihilation close to the threshold, in particular the fact that sigma(e+e- --> nbar n) >~ sigma(e+e- --> pbar p). We discuss an interpretation in terms of a two-step process, via an intermediate coherent isovector state serving as an intermediary between e+e- and the baryon-antibaryon system. We provide evidence that the isovector channel dominates both e+e- --> pions and from Nbar N annihilation at rest, and show that the observed ratio of sigma(e+e- --> nbar n)/sigma(e+e- --> pbarp p) can be understood quantitatively in this picture.We discuss the puzzling experimental results on baryon-antibaryon production in e+e- annihilation close to the threshold, in particular the fact that sigma(e+e- --> nbar n) >~ sigma(e+e- --> pbar p). We discuss an interpretation in terms of a two-step process, via an intermediate coherent isovector state serving as an intermediary between e+e- and the baryon-antibaryon system. We provide evidence that the isovector channel dominates both e+e- --> pions and from Nbar N annihilation at rest, and show that the observed ratio of sigma(e+e- --> nbar n)/sigma(e+e- --> pbarp p) can be understood quantitatively in this picture

Ellis, John R.

Karliner, Marek

CERN Document Server

hep-ph/0108259CERN-TH/2001-234TAUP{2678-01On Electron-Positron Annihilation intoNucleon-Antinucleon PairsJohn Ellisa and Marek Karlinerba) Theory Division, CERN, Geneva, Switzerlandb) School of Physics and Astronomy,Raymond and Beverly Sackler Faculty of Exact SciencesTel Aviv University, Tel Aviv, IsraelAbstractWe discuss the puzzling experimental results on baryon-antibaryonproduction in e+e− annihilation close to the threshold, in particularthe fact that σ(e+e− ! n¯n) > σ(e+e− ! p¯p). We discuss an inter-pretation in terms of a two-step process, via an intermediate coher-ent isovector state serving as an intermediary between e+e− and thebaryon-antibaryon system. We provide evidence that the isovectorchannel dominates both e+e− ! pions and from N¯N annihilation atrest, and show that the observed ratio of σ(e+e− ! n¯n)/σ(e+e− !p¯p) can be understood quantitatively in this picture.CERN{TH/2001-234TAUP{2678-01August 2001John.Ellis@cern.chmarek@proton.tau.ac.ilExperimental data from the FENICE collaboration [1] indicate that(e+e− ! nn) is relatively large close to threshold. Their data may be com-pared with earlier data on e+e− ! pp [2, 3] and also with data on the time-reversed reaction pp ! e+e−, for which more precise data are available [4].As seen in Fig. 1, the combined data indicate that (e+e− ! nn)=(e+e− !pp) > 1 when ECM  2 GeV. Averaging over the available data on both thedirect and time-reversed reactions, which are very consistent, and ignoringany possible variation with energy, we nd:(e+e− ! pp)(e+e− ! nn) = 0:66+0.16−0.11 (1)The fact that this ratio is less than unity requires conrmation, but even equalcross sections for e+e− ! pp and e+e− ! nn would be quite surprising.We recall that the ratio of the cross sections for the corresponding t-channel processes ep(n) ! ep(n) should be innite at zero momentum trans-fer, where the form factor simply measures the total proton and neutroncharges, corresponding to a coherent sum over the electromagnetic chargesof their constituent quarks. It is also believed that the ratio (1) should belarge at high momentum transfers. In a naive perturbative description ofe+e− annihilation into baryons, the virtual time-like photon rst makes a‘primary’ qq pair, which is then dressed by two additional quark-antiquarkpairs that pop out of the vacuum. This dressing is thought to be a perturba-tive QCD process at high momentum transfers, which does not distinguishbetween the u and d quarks, since gluon couplings are flavor-blind. Thus, inthis conventional perturbative picture, the only dierence between the pro-duction rates of proton and neutron is through the dierent electric chargesof the primary qq pairs. The total perturbative cross section is obtained bysuperposing the amplitudes with dierent primary qq pairs and squaring theresult:(e+e− ! NN) /∣∣∣∣∣∣∑q2NQqaNq (s)∣∣∣∣∣∣2; (2)where aNq (s) denotes the amplitude at E2CM = s for making the baryonN with a given primary flavor q, which is determined by the baryon wavefunctions.Since the wave functions of the baryon octet have a mixed symmetry,the amplitudes aNq (s) tend to be highly asymmetric in specic models. For2Figure 1: Comparison of the cross sections for e+e− ! nn and pp in thethreshold region ECM  2 GeV. In the case of e+e− ! pp, the direct-channeldata are combined with the data for the time-reversed reaction pp ! e+e−(marked by ). The dash-dotted and dotted lines denote the average and 1-error bars, respectively, for the pp and nn data sets.3example, in the Chernyak-Zhitnitsky proton wave function [5], the u quarkdominates, i.e., apu = O(1), apd  1 and similarly and = O(1), anu  1. In sucha limiting case we have(e+e− ! pp)(e+e− ! nn) −!Q2uQ2d= 4: (3)While this is an extreme case, on general grounds we expect that the ucontribution dominates in the proton and the d in the neutron, so that(e+e− ! pp)=(e+e− ! nn)  1 at large momentum transfers.We nd it puzzling that the experimental ratio (1) is apparently belowunity when E2CM = s  4 GeV2, whereas the ratio should be much larger thanunity at both larger (timelike) and smaller (spacelike) momentum transfers.Clearly, the mechanism at work here is qualitatively dierent from thoseresponsible for the above intuition.The lack of a conventional theoretical explanation is part of the moti-vation for the proposed new asymmetrical e−e+ high-statistics collider atSLAC for the regime 1:4 <ps < 2:5 GeV [6]. This machine will yieldhigh-precision data on baryon production in e−e+ annihilation at thresh-old, providing a check on the FENICE data and an accurate benchmark fortesting possible theoretical explanations.The rst thing one must realize is that even though q2 > 4m2N  2QCD,the process is highly nonperturbative. This is because the ‘extra’ kineticenergy available to the quarks is very small.Our approach [7] to this puzzle is based on thinking about the time-reversed processes: NN ! e+e−. These may be viewed as two-step pro-cesses, with a coherent meson state serving as an intermediate state. One pos-sible motivation for this picture might be provided by the Skyrme model [8,9], according to which baryons appear as solitons in a purely bosonic chiralLagrangian. This model is formally justied as a low-energy approximationto large-Nc QCD [10, 11], and is known to provide a good description ofmany low-energy properties of baryons: see [12, 13] for reviews. Skyrmion-anti-Skyrmion annihilation provides [14]-[17] a fairly accurate descriptionof low-energy baryon-antibaryon annihilation. Just after the Skyrmion andanti-Skyrmion touch, they ‘unravel’ each other, and a coherent classical pionwave emerges as a burst that takes away energy and baryon number as quicklyas causality permits. A specic parametrization of the initial pion congu-4ration is [16]:F (r; t = 0) = hrr2 + a2e−r/a ; (4)where F is the prole of the chiral eld, U = exp[ i   r^ F (r; t) ], a is a rangeparameter, h is chosen so that the total energy is that of the NN pair, andthe form of F guarantees that the pion conguration has zero net baryonnumber. This crude model has been shown [16] to reproduce satisfactorilythe inclusive single-pion spectrum in pp annihilation at rest and the branchingratios for multi-pion nal states.The details of this specic conguration are unimportant for our pur-poses: what is important is that the data are not inconsistent with such amodel. Indeed, although the Skyrme model provides some motivation for ourapproach, it is not even essential for our purpose. What is important is that asingle intermediate state should dominate the two-step NN ! e+e− process.This could, for example, equally well be a single intermediate JPC = 1−−resonant meson state.To be more precise, since NN annihilation is a strong-interaction process,one must consider separately the I = 1 and I = 0 channels. Accuratelystated, our key assumption is that both of these channels are dominated bysingle states. These might be some excited  and ! mesons, for example,just as well as coherent pion congurations (4) with I = 1 and I = 0.With this picture in mind, we write the I = 1; 0 NN ! e+e− annihilationamplitudes as A1; eiαA0, where the overall phase is irrelevant, A1 and A0 arerelatively real, and  is the relative phase between the I = 1 and I = 0amplitudes. We then havef  (e+e− ! pp)(e+e− ! nn) =∣∣∣∣∣A1 + eiαA0A1 − eiαA0∣∣∣∣∣2: (5)It is apparent from (5) that (e+e− ! nn)=(e+e− ! pp)  1 if eitherA1  A0 or vice versa.Remarkably, there is evidence from both e+e− and NN annihilations thatI = I final states dominate by large factors.The clearest evidence comes from e+e− ! n, where it is found by mea-suring nal states with even and odd numbers of pions respectively that(e+e− ! (2m))(e+e− ! (2m + 1))  9 for ECM  2 GeV; (6)5Figure 2: Cross sections for e+e− ! multi-pion final states, for ECM 2 GeV [19]. We note the dominance of I = 1 final states with even numbersof pions by about an order of magnitude over I = 0 states with an odd numberof pions.6as seen in Fig. 2.y At these energies, we expect most nal states createdby e+e− ! ss to contain K K pairs, so that (6) corresponds to the non-ssinitial states we expect to dominate in NN annihilation. The value (6) issimilar to that found at lower energies, where Γ( ! e+e−)  9  Γ(! !e+e−), in agreement with naive quark models. The fact that the ratio (I =1)=(I = 0) continues to be large at higher energies is consistent with ideasof generalized vector meson dominance. The data from NN annihilations areless clear. Theoretically, there are various calculations and other suggestionsthat the cross sections for NN annihilations into I = 1 and I = 0 maybe similar. Experimentally, several initial states contribute, including 1S0,3S/D1 and various P waves, but we are interested only in the JPC = 1−−3S/D1 initial states. It is in principle possible to distinguish dierent initialstates by comparing annihilations in gas and liquid, as has been done in theanalysis of OZI-violating nal states, but we are unaware of a comparableanalysis of multi-pion nal states. Because the initial state is a mixture withdierent G = 1, it is not possible to separate I = 1 from I = 0 simply bycounting pions, as was the case in e+e− annihilation.The most convincing experimental information known to us comes froman analysis of NN ! KK. By comparing the rates for pp ! K+K− andpp ! K0K0, it has been possible to extract [18]∣∣∣∣∣A(3S=D1 ! KK)I=1A(3S=D1 ! KK)I=0∣∣∣∣∣2 5 to 10; (7)which is comparable to the corresponding ratio (6) in e+e− annihilation. Thefact that I = 1 dominates over I = 0 in the ratio (7) is consistent with thehypothesis that most of the KK nal states are created by uu and dd pairsin the initial NN state, with a ss pair popping out of the vacuum. The ratio(7) would be small if primary ss pairs dominated.We now use the experimental information on the dominance by the I = 1channel in both e+e− (6) and 3S/D1 annihilation (7) in a quantitative analysisof the e+e− ! NN production f ratio (5). Dening   A0=A1, we canrewrite (5) asf =∣∣∣∣∣1 + eiα1− eiα∣∣∣∣∣2: (8)yThe five-pion final state is predominantly ωpipi. The cross section in Fig. 2 correspondsto the final state ωpi+pi−; for the total ωpipi one should multiply it by 1.5 [19].7It is clear that the zero-momentum-transfer limit (e+e− ! pp)  (e+e− !nn) is obtained in the limit  ! 1;  ! 0, and that the high-momentum-transfer limit (e+e− ! pp)  4 (e+e− ! nn) is obtained in the limit  !1=3;  ! 0. In order to estimate  = A1=A0, our assumption of dominancein each isospin channel by a single state (either a coherent multi-pion state(4) or a generalized vector meson V ) tells us that =√√√√(e+e− ! (I = 0))(e+e− ! (I = 1)) √√√√( NN ! (I = 0))( NN ! (I = 1)) : (9)Inserting the experimental indications (6,7) into (9), we estimate that110<  13: (10)The top end of this range seems to us quite conservative, whereas the lowerend surely requires more justication from NN annihilation data. In thefollowing numerical analysis, we keep  general, but focus extra attention onthe limits  = 1=3 and 1=10.It is apparent from (8) that f  1 is possible for any value of , for arestricted range of the relative phase   =2. However, the allowed rangeof  is extended if  is small. It is easy to see that f lies in a narrow rangef around unity if  falls within the following range: ’ f4: (11)It is apparent that f  1 for all values of  if  is small, as suggested (10) bythe available data on e+e− and NN annihilation.The quantitative behaviour of f as a function of 0 <  < 1=2 and − < <  is shown in Fig. 3. Displayed explicitly is the region of the (; ) planewhere f falls within the experimental range (1). We see that this rangefavours jj > =2, whatever the value of . Fig. 4 displays projections ofFig. 3 for the two limiting values  = 1=3 and 1=10. The allowed range (1)of f and the corresponding ranges of  are also shown.We conclude that the a priori puzzling large experimental value of theratio (e+e− ! nn)=(e+e− ! pp) can be understood qualitatively. This isrelatively easy if the I = 1 amplitude dominates over the I = 0 amplitude,as suggested by the available data on e+e− and NN annihilation and our800.10.20.30.40.5ε–pi–2–1012piα02468 Figure 3: Three-dimensional plot of the cross-section ratio f  (e+e− !pp)=(e+e− ! nn) as a function of  and , indicating the region where ffalls within the range (1).9Figure 4: Two-dimensional plot of the cross-section ratio f  (e+e− !pp)=(e+e− ! nn) as a function of  for  = 1=3 (dot-dash curve) and = 1=10 (continuos curve), indicating the ranges where f falls within (1).10assumption of dominance by a single coherent state in each isospin channel.The specic range (1) can be understood quantitatively if the I = 1 andI = 0 amplitude have a large relative phase . We are not in a position tojudge the plausibility of such a large value of , from either an experimentalor a theoretical point of view. It would be interesting to make tests of thispossibility.We comment nally on the surprisingly large value of the ratio (γγ !)=(γγ ! pp) observed by the CLEO Collaboration [20] (see also [21]-[23]for related experimental work). CLEO nd that (γγ ! pp)  (γγ ! )close to threshold, which seems analogous to FENICE result for the nn=ppratio. For a given quark flavor, the perturbative amplitude for baryon-antibaryon production in the photon-photon reaction scales like the quarkcharge squared, compared with the linear dependence of the amplitudes onthe quark charge in the e+e− case discussed earlier. Thus one might naivelyexpect the ratio ()=(pp) to be even smaller than the correspondingperturbative prediction for (nn)=(pp) in e+e−. It would be interesting toapproach this puzzle from a point of view similar to that adopted in thispaper. However, the situation in γγ collisions is more complicated, becauseof the wider range of possible spin and isospin states. Also, the informa-tion available on the isospin and spin decomposition is sparse compared withthat in e+e− annihilation, which we used above. Data for γγ ! nn close tothreshold might cast light on the (γγ ! )=(γγ ! pp) puzzle, but arenot yet available.We have proposed in this paper a simple model that is able to accommo-date the suprisingly large observed value of the ratio (e+e− ! nn)=(e+e− !pp). Our suggestion is based on a simple two-step approach, in which a singleintermediate state with I = 1 dominates over I = 0. This dominant inter-mediate state could be motivated by a Skyrmion-anti-Skyrmion picture, orcould be some excited  resonance. Our model could be tested by furthermeasurements of the ratios of dierent isospin amplitudes in e+e− and NNannihilation, and suggests a relatively large phase dierence between I = 1and I = 0 amplitudes. We look forward to more experimental data bearingon these issues, for example from a new low-energy e+e− collider [6].11AcknowledgmentsRef. [7] is based on joint work with Stan Brodsky, whom we thank forhis continuing interest. We thank Claude Amsler, Rinaldo Baldini, JaumeCarbonell, Vladimir Ivantchenko, Rolf Landua and Jean-Marc Richard fordiscussions of the experimental data, and in particular Simon Eidelman forhis generous help in obtaining and discussing many of the relevant crosssections.The research of one of us (M.K.) was supported in part by a grant from theUnited States-Israel Binational Science Foundation (BSF), Jerusalem, Israel,and by the Basic Research Foundation administered by the Israel Academyof Sciences and Humanities.References[1] A. Antonelli et al., Nucl. Phys. B 517, 3 (1998).[2] A. Antonelli et al., Phys. Lett. B 334, 431 (1994).[3] D. Bisello et al. [DM2 Collaboration], Z. Phys. C 48, 23 (1990).[4] G. Bardin et al., Nucl. Phys. B 411, 3 (1994).[5] V. L. Chernyak and A. R. Zhitnitsky, Phys. Rept. 112, 173 (1984).[6] Letter of intent for a new asymmetrical e−e+ collider for the regime1:4 <ps < 2:5 GeV,http://www.slac.stanford.edu/grp/rd/epac/LOI/ .See alsohttp://www-project.slac.stanford.edu/pep-n/Default.htm .[7] M. Karliner, “A possible resolution of the e+e− ! NN puzzle”, hep-ph/0108106, invited talk at e+e− Physics at Intermediate Energies,SLAC, 30 Apr { 2 May 2001.[8] T. H. Skyrme, Proc. Roy. Soc. Lond. A 260 (1961) 127.[9] T. H. Skyrme, Nucl. Phys. 31 (1962) 556.12[10] E. Witten, Nucl. Phys. B 160, 57 (1979).[11] G. S. Adkins, C. R. Nappi and E. Witten, Nucl. Phys. B 228, 552(1983).[12] I. Zahed and G. E. Brown, Phys. Rept. 142, 1 (1986).[13] J. Schechter and H. Weigel, hep-ph/9907554.[14] J. J. Verbaarschot, T. S. Walhout, J. Wambach and H. W. Wyld, Nucl.Phys. A 461, 603 (1987).[15] H. M. Sommermann, R. Seki, S. Larson and S. E. Koonin, Phys. Rev.D 45, 4303 (1992).[16] Y. Lu and R. D. Amado, Phys. Rev. C 52, 2158 (1995) [nucl-th/9505021], M. A. Halasz and R. D. Amado, Phys. Rev. D 63, 054020(2001) [hep-ph/0009260] and references therein.[17] R. D. Amado, private communication.[18] C. B. Dover, T. Gutsche, M. Maruyama and A. Faessler, Prog. Part.Nucl. Phys. 29, 87 (1992).[19] S. Eidelman, private communication.[20] S. Anderson et al. [CLEO Collaboration], Phys. Rev. D 56, 2485 (1997)[hep-ex/9701013].[21] M. Artuso et al. [CLEO Collaboration], Phys. Rev. D 50, 5484 (1994).[22] L3 Collaboration, Note 2566,  Formation in Two-Photon Collisionsat LEP, June 2000, submitted to ICHEP-2000 in Osaka.[23] H. Hamasaki et al. [VENUS Collaboration], Phys. Lett. B 407, 185(1997).13

On Electron-Positron Annihilation into Nucleon-Antinucleon Pairs

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On Electron-Positron Annihilation into Nucleon-Antinucleon Pairs

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