Difficulties for the particle interpretation of positron anomalies in high-Z collisions

Volume 169B, number I PHYSICS LETTERS 20 March 1986

DIFFICULTIES FOR T H E PARTICLE I N T E R P R E T A T I O N OF P O S I T R O N ANOMALIES IN H I G H - Z C O L L I S I O N S

Kenneth LANE

Lyman Laboratory of Physics. Harvard Unh'ersity. Cambridge, MA 02138. USA and Department of Physics. Ohio State University. Columbus, OH 43210. USA i

Received 6 January 1986

Production of a new spinless particle, and its subsequent decay to e*e , has been proposed as the origin of narrow positron peaks observed in collisions of a variety of very heavy nuclei. It is shown that none of the conventional mechanisms for producing such particles in these collisions is compatible with experimental observations.

Quite puzzling peaks have been observed in the kinetic energy spectra of positrons emitted in collisions of high-Z nuclei [1,2]. The salient features of the data from the two experiments are these:

(i) The peaks are observed only when the kinetic energy of the projectile nucleus is near the Coulomb barrier (i.e., ~6 MeV/nucleon) and the scattering angle of the projectile is large (presumably to reduce background from conventional sources of continuum positrons).

(ii) The positron kinetic energy at the peak is E k ~-

335 keV, very nearly independent of the total Z = Z 1 + Z 2 of the two nuclei (Z = 180-188).

(iii) All the peaks are very narrow, 70 -80 keV. These widths are consistent with the Doppler broaden- ing expected for emission from a source moving with the center-of-mass (v = c/20), but inconsistent with emission from either the projectile or target nucleus.

(iv) The CM differential cross sections for production of the positron peaks are ~ 10 pb/sr for all sys- tems. This corresponds to "" 10 -5 peak-energy positrons per collision.

Point (i) suggests that the source of the positrons is activated only when the two nuclei are close enough to touch and, thus, that it arises from the high total charge or atomic number of the nuclear system. The second point suggests that the positron source is an

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entity quite independent of the fine details of the col- liding nuclei and is not, e.g., spontaneous e+e- emission from the vacuum for which the peak E k is claim- ed to vary as Z 20 [3]. These conclusions are strength- ened by the indication that the source is moving with the CM velocity. Furthermore, the narrowness of the peaks requires that the nuclear complex hangs together to emit the source for at least ~i/70 keV "" 10 -20 s. This is "-10 times longer than the collision time for Coulomb scattering of the two nuclei.

A natural hypothesis for the origin of these monoenergetic positrons is that a new neutral particle, ¢, of mass 1.69 MeV, is created nearly at rest in the CM of the long-lived nuclear complex and decays to e÷e - some time after the complex has ceased to exist. Indeed, several theoretical groups have made this (or a similar) proposal, with ¢ a spinless particle [4-6] . Their hypothesis is given some support by a very re- cent paper announcing observation of an excess of monoenergetic electrons, with kinetic energy E k, in coincidence with the peak positrons [7]. Note that the conclusion that ¢ lives longer than the complex is necessary to understand why the e + and e - energies are not made dissimilar by the strong EM field of the nuclei.

In this letter we use some of the work of previous authors [4,6] together with new results to show that no convent ional mechanism exists for production of such a new spinless particle ¢ which is compatible

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with published experiments. The conventional mechanisms we might imagine are t~-emission from the atomic electrons [4], the nucleons [4], or the strong EM field surrounding the nuclei [5,6] * ~. Although Sch~ifer et al. [4] argued in favor o f a pseudoscalar emitted from light quarks/nucleons, we shall argue against this possibility below. Then we shall show that production from the strong EM field is ruled out on two counts:

(1) The necessity of a longqived nuclear complex for understanding the sharpness of the positron peaks implies that ~'s produced with momenta k "" m~ generally are more likely than those produced at rest. Thus, the monochromatic lines should not be seen above a broad background extending to several MeV.

(2) The observed rate of ~-production requires a coupling to the EM field which implies r(t~ ~ ~,~,) = 10 -18 - 1 0 -19 s. This is at least five orders of magni- tude shorter than the r(~ -~- e÷e - ) allowed by measurement o f g - 2 for the electron, thereby reducing ~- production from the EM field to an absurdity.

Schiifer et al. considered ~-production from either the atomic electrons or the nucleons for the five ~- particle types S, V, T, A, P. They showed that the maximum allowable discrepancy between experimental and theoretical values o f (g - 2)e implies a @- production cross section from the electronic shell which is "" 105 times smaller than observed [1,2] ,2

Next, Schafer et al. examined the case of ~-production from nucleons by making an analogy to nuclear bremsstrahlung. From the observed production rate, they deduced a squared coupling strength of to nucleons, ap/n > l0 -2 o~ ~ 10 -4 . Combining this with the requirements that ~ decay within the active region of the detector and that the nucleon-electron Yukawa interaction mediated by ~ be compatible with atomic energy level measurements,.they con- cluded that @ must be a pseudoscalar* a. Then, consis-

,1 Since the nuclei barely touch, it is extremely unlikely that fluctuations in the gluon field can be responsible for O- production.

~2 Sch~fer et al. took the discrepancy in (g - 2) e to be 3 X 10-1 t, which is actually the old error on the measurement. The actual discrepancy is (2.5 • 1.5) X 10 -1°, which in- creases their estimates of the ~ge coupling by x / ~ and de- creases the shortest lifetimes r(¢ --+ e+e -) by 1/10. I thank T. Kinoshita for an up-to-date discussion of this.

• 3 Such a large ooupling of a pseudoscalar ~ to light quarks may be observable in D* -~ De and B* ~ B¢ if the 0-life- time is not too short.

tency with (g - 2)e and axion search experiments [8] require that 6 × 10 -14 s < r(~b(0-) -+ e+e - ) < 10 -11 s.

In this bremsstrahlung scenario, there is no reason for ¢'s to be produced always nearly at rest in the CM. For a C-momentum of only 1/2 MeV, the ~ will move at most ~0 .3c (10 -11 s) = 0.1 cm before decaying to positrons whose energy spread will be 400 keV, much greater than the width of the observed peaks. A nuclear origin for producing ¢'s at rest thus seems ruled out unless we invoke discrete energies. We shall have more to say on this possibility shortly.

Let us turn to the remaining conventional source of ~-production, the strong EM field-surrounding the nuclei. We shall treat this field as a classical external source. The ~-production rate from the field is then an exactly soluble quantum-field theoretic exercise. As we stated at the outset, the narrowness o f the peaks make it necessary to assume that the nuclear complex resonates for a time T>~ 10 -20 s. Though we have no idea how reasonable this assumption may be for the several nuclei involved, we shall incorporate it via a simple model into our description of C-production.

We consider that ~ is a scalar particle coupled to the strong electric field of the nuclear complex,

"~s =fs (~E2 ~- - ~ f s ~ F u v F u r . (1)

We ignore the magnetic term B 2 ~ u2E 2, where u is a small nuclear velocity.fs is a coupling constant with dimension (mass) - l . Chodos and Wijewardhana (CW, hereafter), ref. [6], considered emission of a pseudoscalar ~) from the EM field of a resonating nuclear complex, with the interaction

.l~p = fpcpE" B -- ~:p~FuvF ~v . (2)

Our numerical results are similar to theirs, but our conclusions are much more negative.

We need to calculate ~, the probable number of ¢'s emitted per collision. Experimentally,/3 -~ 10 -5 [ 1,2]. From this, we can estimate the coupling fs. Actually, this will be an underestimate offs because our calculation offl from the interaction J2 s does not include the probability per collision o f forming the bound nuclear complex nor the probability of ¢ decay to e+e- . In the neglect of these, fl is given by

=f d3k 2, (3) (2rr)326o k

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where w k = (k 2 + m2)l/2 and

/ ( k , / c o ) = f d4x e-v~ .XfsE2(x ' t) . (4)

Our model for the nuclear complex is that o f two spheres of radius R0, charges Z l e and Z2e , oscillating harmonically along the z-axis with frequency co 0 = O(1 MeV). The positions of the nuclear centers at time t are +r(t), where

r(t) = ~ £ [R 1 + R0 + (R 1 - g 0 ) sin w 0 t] . (5)

The radius R 0 -~ 7 fm -~ 1/30 (MeV) -1 , and we shall assume R 1 = 3R 0 (although this is not too important so long as R 1 < (l MeV)- I ) . The oscillation goes on for a time T, with cooT>> 1, so that $'s are emitted with sharp energies. The electric field, ignoring small relativistic effects, is

E(x, t) = E l + E 2

_ Z2e x + r ( t ) Z l e x - r ( t ) + - - _

X/Tff i x - r ( t ) l 3 ~ Ix+r(t)l 3 " (6)

The integral(4) over E 2 diverges at the nuclear centers and must be cut off. The sensible cut-off is at Ixl ~ R 0, so we replace Ix -'Z'r(t)1-4 in E 2 by (Ix -+ r(t)l 2 +R02)-2. Short distances still dominate the integral, and it is not t o o bad an approximation to drop the E 1 • E 2 term. Now the integral may be done exactly and, in the limit T--* 0% we obtain

; (k , k O) ~- fs f e - i k ' x [E2(x,t) + e2(x , t)] Ro

= (2n3aZ1Z2fs /Ro)e-kRo

X ~ Jn(~_)[e i~+ + ( - l ) n e - i ~ + ] 6 ( k 0 - m o 0 ) . " =- ~" (7)

Here, k = Ikl, ~± = kz(R 1 +- R0)/2 and "In is the usual Bessel function with "In (~) "" (~/2) n/n ! if I ~1 "¢ 1 and n ~> 0 (the only terms that contribute to 3). The short-distance singularity o f E 2 is reflected in the factor I /R O. This singularity is absent for the E . B cQu- piing o f CW. We expect the contributions o f E 1 -E 2 in our model to be O ( I / R I ) times a similar sum over

: , , ( ~ _ ) 8 ( k o - n ~ o ) . The expression (7) for ' / (k) has important features

which transcend the particular model we have adopted

for the bound nuclear complex. Since the complex and its EM field oscillate with characteristic frequency w0, /"(k) necessarily is a sum of ~-functions in the limit T--* oo. This also happens in ref. [6]. Clearly, any model for the classical EM field arising from two nuclei bound in a potential well would lead to a similar result. Next, because the EM field originates and is most intense in region of size R0, the uncertainty principle by itself implies no particular cut-off to O- momenta until they exceed kma x "" 1/R O. This is

kRo manifested in our model by the factor e - . On the other hand, it is difficult for the EM field to produce ¢'s with k much less than this natural momentum scale. That is why the individual terms in eq. (7) vanish rapidly for k(R 1 +_R0) ,~ 1. For us, the terms of or- der 2n - 1 and 2n go to zero as k 2"n ; for CW, they ap- pear to go even faster. We believe that these depend- encies on k and k 0 are very general. Indeed, we expect similar effects if ~ were to be produced instead from the nuclear matter distribution o f a long-lived complex.

It is easy to see now that E 2, and E • B for that matter, cannot account for the experimental observations [1,2,7]. The natural way to obtain sharp positron peaks is to produce ~ nearly at rest in the CM. This can happen if, fortuitously, 6o 0 -~ m J N , where N is a small positive integer. For definiteness, we take w 0 = (k 2 + m2) 1/2 with k I = 50 keV. But then, production o f ~ with to k --- 2600 = (k 2 + m2) 1/2, k 2 =

x/~rno ~ 2.9 MeV is ~ (k2/k 1) 5 [(R 1 -RO) / (R i + R0)]2 X exp [ - 2 ( k 2 - k l ) R 0 ] ~ 10 7 times more probable! This problem also exists in the model of ref. [6]. However, it is much less serious because only the even harmonics (w k = 2nw0) occur. In view of the remarks made above, we also expect the positron peaks to be obliterated (or, at least, smeared out) in models o f C- production from an oscillating nuclear matter distribution.

The only loophole we can imagine here is that ~'s with momentum k ~ m~ live long enough to escape the active region of the detector and so their decay positrons are missed. We cannot exclude this possibility on the basis oflifetime limits from ref. [8] because we have made no assumption of ~'s coupling to nucleons. A more careful study of axion search experiments might close this loophole, but that does not seem necessary in view of the next problem we raise.

Let us estimate fs for U - U scattering from the n = 1

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term in ] (k ) . Remember that this is really an underestimate since it does not include the jo int probabil i ty of forming the nuclear resonance and decaying ¢ to e+e - . In squaring]n=l(k) to get/3, we put 2zr5(0) = T and take T = 10-20 s "" 15 MeV -1 . For k = 50 keV, we get

7r3(txZ1Z2)2f~s kS(R 2 - R2) 2

/~1 = 160 g02 T

= 2.5 X 1 0 - 4 f 2 MeV 2 . (8)

Hence,fs -~ 0.2 MeV -1 if/31 = 10 -5 . If we assumed 600 ~m$/2 and k = 50 keV, we would obtain f s -~ 1.6 MeV -1 . And, if we increase k to 100 keV and T t o 10 -19 s, we decrease our estimates o f f s by 1 / ~ . CW could find no reasonable value Offp for ¢ produced nearly at rest. This led them to consider the possibility that m~ ~- 2me, with k = 1.35 MeV. Then, taking T = 100 MeV-1 , they found fp ~- 0.3 MeV-1 , comparable to our estimates.

Now we use these values of f to determine the rate of ¢ decay to two photons. The coupling of a scalar (pseudoscalar) ¢ to F 2 (F/~) gives

P(q~s ~ 77) = (f2/16rr) m3 ,

P(~bp ~ 77) = (f2/64zr) m3. (9)

F o r / s = 0.2 MeV -1 (fp = 0.3 MeV-1) , the 27-life- time o f ¢ is 10 -19 s (10-18s) . However, the upper bound on the coupling of ¢ to e+e - from (g - 2) e requires the r (¢ ~ e+e - ) >~ 10 -13 s [4]. This does not even admit the possibility that BR(¢ -+ e+e - ) ~ 10 -5 and that one ¢ is produced at rest per collision. Rather, if BR(~b ~ e+e - ) ~< [1 + r ( ¢ ~ e + e - ) / r ( ¢ ~ 73,)] -1 is incorporated into eq. (8) and the new expression equat- ed to 10 -5 , we obtain a negative value o f f 2 !

Finally, there is one way of producing O's at a single energy 600 , without the higher harmonics. We must assume that, for all the nuclei studied, a bound supernucleus X forms that has only two of its energy levels separated almost exactly by me. Further, q~ must couple to light quarks/nucleons and be emit ted, presumably in an s-wave, in the de-excitation o f the upper level X 2. The rate for X 2 ~ X 1 + ¢ must not be swamp- ed by X 2 ~ X 1 + 7, because such monochromatic photons have been searched for and not seen [ 1 ]. Now, this decay must occur before the system X falls apart and, to our knowledge, no one expects a longer time for this than 10 -19 s. Thus, I ' (X 2 ~ X 1 + q~) ~ / / 1 0 -19

s -~ 7 keV. Even if we allow for coherent ~b-emission from X, we crudely estimate that such a large rate requires a 0-nucleon coupling already ruled out by axion search experiments [8]. A careful calculation of F(X 2 -* X 1 + ¢) needs a reasonable model of the supernucleus and might use some of the techniques applied to axion emission in nuclear de-excitation.

To conclude, there appears to be no known mechanism within the environs of a quasi-bound nuclear complex for producing a still-longer-lived spinless ele- mentary particle ¢ whose decay to e+e- can account for the narrow peaks observed in high-Z collisions. Although we have not considered other spin assign- ments for ¢, we expect that the problems we have en- contered will recur, especially the difficulty of producing ¢ nearly at rest in the collision CM. If the data persist and if it is determined that e + and e - are emitted in coincidence with sharp invariant mass, we wilt be faced with a pret ty problem indeed. It may be that some new fundamental production mechanism exists. In our view, it is more likely that some quite intricate nuclear phenomena and some very lucky coincidences will need a lot of explanation. In any case, there can, and surely will, be particle physics experiments to search for the new particle.

We have enjoyed many profitable discussions with S. Coleman, E. Eichten, S.L. Glashow, L. Hall, R. Kass and R. Schwitters. We are especially grateful to the High-Energy Theory Group and the Physics Depart- ment at Harvard for their hospitality and support during the fall of 1985. This research was supported in part by the National Science Foundat ion under Grant No. PHY82-15249, and by Ohio State Univer- sity and the US Department of Energy under Con- tract No. EY-76-C-02-1545.

References

[ 1 ] J. Schweppe et al., Phys. Rev. Lett. 51 (1983) 2261 ; T. Cowan et al., Phys. Rev. Lett. 54 (1985) 1761.

[2] M. Clemente et al., Phys. Lett. 137B (1984) 41. [3] J. Reinhardt et al., Z. Phys. A303 (1981) 173. [4] A. Sch~ifer et al., J. Phys. 11 (1985) L69. [5] A. Balantekin et al., Phys. Rev. Lett. 55 (1985) 461. [6] A. Chodos and L. Wijewardhana, Yale prepfint (1985),

submitted to Phys. Rev. Lett. [7] T. Cowan et al., Yale pteprint (1985), submitted to Phys.

Rev. Lett. [8] F. Calaprice et al., Phys. Rev. D20 (1979) 2708;

T. Donnelly et al., Phys. Rev. D18 (1978) 1607, and references therein.

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Difficulties for the particle interpretation of positron anomalies in high-Z collisions

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