VOLUME 72, NUMBER 8 PHYSICAL REVIEW LETTERS 21 FEBRUARY 1994

Reaction m+y .-m+mop near Threshold and Chiral Symmetry Breaking

D. Pocanic, E. Frlez, K. A. Assamagan, J. P. Chen, ' K. J. Keeter, R. M. Marshall, R. C. Minehart,and L. C. Smith

Department of Physics, University of Virginia, Charlottesville, Viryinia PP901

G. E. Dodge, ~ S. S. Hanna, and B. H. King&Department of Physics, Stanford University, Stanford, California 9)805

3. N. KnudsonLos Alamos National Laboratory, Los Alamos, Neio Mexico 875)5

(Received 9 June 1993)

We have measured total cross sections for the reaction m+y —+ m+vr p at incident pion kineticenergies of 190, 200, 220, 240, and 260 MeV. We use this result to deduce a new value of thechiral symmetry breaking parameter, ( = —0.25 + 0.10, in a global constrained fit of the five nirNnear-threshold amplitudes. Consequently, we report new soft pion model values for the 8-wave vrx

scattering lengths.

PACS numbers: 13.75.ax, 11.30.Rd

Quantum chromodynamics (QCD) is universally ac-cepted as the theory of strong interactions, largely be-cause of its considerable success in describing processesinvolving large momentum transfer, i.e., short interactiondistances. At intermediate and low energies, however,as the coupling constant becomes large, QCD becomesnonperturbative and practically intractable by availablecalculational methods. In order to overcome this prob-lem, a broad theoretical efFort is under way to developphenomenological Lagrangian models based solely on thesymmetry properties of the full QCD, as suggested byWeinberg [1]. Among the symmetries of the strong in-

teraction, chiral symmetry is of particular significance atlow energies, since it is violated only slightly in the SU(2)realization. Indeed, chiral symmetry is essential to theunderstanding of the lightest hsdrons, and it provides theframework for all efFective Lagrangian models, e.g. , thechiral perturbation theory (ChPT) [2], and recent QCDformulations of the Nambu —Jona-Lasinio model in SU(2)and SU(3) fiavor space (for a comprehensive recent re-view see [3]). A full understanding of the mechanism ofchiral symmetry breaking is, therefore, imperative.

The mar system at zero momentum provides the mostsensitive means to study chiral symmetry breaking, sincen7r scattering lengths vanish in the chiral limit [4]. Earlymodels of chiral symmetry breaking gave predictions ofao' (air), the I = 0, 2 s-wave scattering lengths, basedmainly on current algebra and PCAC (partial conserva-tion of axial-vector current) [4—6]. Using soft-pion theory,Olsson and Turner [7] parametrized the different pre-dictions in terms of (, a single chiral symmetry break-ing parameter. More recent calculations of urer scatter-ing lengths include the work of Jacob and Scadron [8],Gasser and Leutwyler [9] (ChPT), and Ivanov and Troit-skaya [10] (model of dominance by quark loop anomalies,QLAD).

Aside from the decay K —+ vr x+e v, all of the

information on the arm interaction has been extractedfrom studies of the 7rN —+ vr7rN reactions. After a pe-riod without much new data, the past few years havebrought about a number of measurements of the AN —&

irvrN reactions close to threshold [ll—13]. Consequently,Burkhardt and Lowe [14] incorporated the existing ir7rN

data in a comprehensive soft-pion analysis which pro-duced a consistent global solution for the isospin ampli-tudes, and, hence, a new value for (. However, the avail-able data in the a+nap channel below 300 MeV werescarce and of accuracy too low to constrain the globalfit. Moreover, the analysis was complicated by incon-sistencies in the published cross sections for the n+vr+nchannel.

The present work studies the n+p ~ @+mop channelin the region of incident pion kinetic energy from 190 to260 MeV (the threshold is at 164.8 MeV). Our purposeis twofold: (i) to extract the angle-integrated cross sec-tions needed for a comprehensive soft-pion analysis, and

(ii) to measure exclusive cross sections with sufficientlyhigh accuracy and phase-space coverage to allow a model-independent urer phase shift analysis. In the interest oftimeliness, in this paper we present only the integratedcross sections and their soft-pion analysis, leaving themore complex discussion of exclusive cross sections for alater publication.

Our measurements were performed at the Low EnergyPion beamline of the Los Alamos Meson Physics Facil-ity. Pion beams with momentum spread b p/p = +(0.15—0.2)% were focused on a specially constructed thin-walledliquid hydrogen target. Beam charge was monitored bymeans of a sealed ion chamber and a current integra-tor. Almost all protons were removed from the beam bymeans of a thin degrader at the beam focal point in themiddle of the beamline. For each beam energy a resid-ual proton contamination of (0.2—0.7)% was measured byvarying the central momentum of the beamline bending

1156 0031-9007/94/72(8)/1156(4) $06.001994 The American Physical Society

VOLUME 72, NUMBER 8 PHYSICAL REVIEW LETTERS 21 FEBRUARY 1994

magnets downstream of the degrader. Pion content ofthe beam was determined by activation of ~ C in plasticscintillator disk detectors [15]. Long-term reproducibilityof this method was about + 2% or better, while the x+activation cross sections carry uncertainties of (0.9—

4)%%uo

[15].The p rays from neutral pion decays were detect-

ed in the LAMPF no spectrometer [16]. Protons andcharged pions were detected in a specially constructed14-telescope array of plastic scintillator detectors. Eachtelescope included at least one thin (3 mm) and one thick(25 mm) AE counter, and a full absorption counter ca-pable of stopping the pions allowed by the kinematicsof our reaction. Six telescopes positioned at 8l,b & 40'subtended a larger solid angle than the remaining eight.In order to maintain uniform angular resolution, we ar-ranged the thin and thick AE counters on each of thesix telescopes into a 4 x 2 hodoscope. In all, 56 distinctangular bins were covered simultaneously.

The efficiency of the no spectrometer was determinedin a series of measurements using the pion charge ex-change reaction at T'b = 30 MeV on a CHz target, andstudying the spectrometer response to penetrating cos-mic muons. Individual efficiencies were measured for ev-

ery detector in the spectrometer, and the entire no spec-trometer assembly was simulated with the Monte Carlocode GEANT3 [17]. The overall uncertainty in the effi-

ciency, +4%, is dominated by the shower tracking effi-

ciency uncertainty (3%). We determined the thickness ofour liquid hydrogen target to 3% accuracy by compar-ing the charge exchange yield at 30 MeV with the yieldfrom a known CHq target. We determined the efBciencyof the charged particle detectors by detecting elasticallyscattered sr+ and protons in a separate, prescaled triggerthroughout the experiment. This trigger also served asan on-line monitor of the liquid hydrogen target thick-ness.

We detected and recorded xoz+ and 7rop coincidentevents, as well as the triple coincidences, 7rox+p. De-tector acceptances, particle kinematics, and backgroundsources for the three categories of events were very dif-ferent. Thus, the three sets of data had to be analyzedseparately, and can be regarded as three essentially in-dependent measurements. In this way, the experimenthas a built-in consistency check. Acceptances were cal-culated using a suitably modified version of the PIANG

code [18], and checked independently using GEANT3 [17],with excellent agreement. Measurements were made atT = 160 MeV, below the threshold of 7ro production,to ascertain that the signal vanished for all three eventtypes.

Figure 1 shows the missing mass spectra at 260 MeVfor (a) m.op and (b) z o7r+ coincident events, after subtrac-tion of accidental and empty-target backgrounds. Bothsets of data agree well with the Monte Carlo predicteddistributions (shown as histograms), which incorporate

120 —

( )

80

7v'p events260 MeV

200

150

100

260 MeV

40 50

M

C:

LIJ

0

0

0 50

100

~ 2oo — (b)EZ.'

150

1 00 1 50 200 250

7I'7T' events

260 MeV

v)

~ —500L

~ 200E

150

100

I I I[

(b)

—0.5 0cos(e«)

Hl-J ilk

I I I I I I

0.5 1

260 MeV

50 50

W w w w w0

850 900 950 1000 1050

m3 (MeV/c )

0

200 250I I I ~ I

300 350 400m (M eV/c 2)

FIG. 1. Measured spectra of the invariant mass of the un-detected particle for (s) x p snd (b) n n+ coincidences at260 MeV, after subtraction of accidental and target-emptybackgrounds (full circles). Histograms shown are the resultof a Monte Carlo calculation which incorporates the e8ects ofdetector acceptances and resolutions, charged particle detec-tion thresholds, and target size. Results at lower energies aresimilar.

FIG. 2. (s) Distribution of cos(g ), the dipion polar angle,measured at 260 MeV (full circles), snd the results of s MonteCarlo simulation (histogrsm). (b) Dipion invariant mass dis-tribution measured at 260 MeV (full circles) snd simulated(histogram). The Monte Carlo simulation is based on pures-wave dynamics (phsse-spsce probability distributions), sndincorporates the actual detector acceptances and resolutionsand the target size.

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VOLUME 72, NUMBER 8 PHYSICAL REVIEW LETTERS 21 FEBRUARY 1994

the effects of instrumental resolution and acceptance, de-tection thresholds for charged particles, and target size.The FWHM of both distributions is about 30 MeV/e .Similar agreement is observed at the four lower energiesin our measurement.

In Fig. 2(a) we compare the distribution of cos(e ),the dipion polar angle, measured at 260 MeV, with arealistic Monte Carlo simulation based on pure s-wavekinematics (phase space), and on our instrumental res-olution and acceptance. In the same way, the dipioninvariant mass distribution measured at 260 MeV is pre-sented in Fig. 2(b). We observe no significant depar-ture from the phase-space distributions for either quan-tity; this remains true at lower energies, as well. Hence,the evaluation of angle-integrated cross sections from therecorded yields is straightforward.

Table I lists the total cross sections for pro productiondeduced from the recorded eon+, irsp, and triple coinci-dences. Cross sections given in the last column of Table Irepresent appropriately weighted averages of the threemeasurements (where available), and are our adoptedvalues. Cross section uncertainties quoted in Table I areonly statistical. In addition, an overall systematic uncer-tainty of approximately 9FO applies to all data points, andhas to be added in quadrature to the statistical uncer-tainty. This uncertainty is due to six approximately equalcontributions, associated with the target thickness, inci-dent 7r+ normalization, mrs absorption, pro and chargedparticle detection efficiencies, and detector acceptances.

The measured total cross sections are plotted againstbeam energy in Fig. 3(a), which includes all availabledata in the energy region studied [11,19,20].

Following the method of Olsson and Turner [7], wehave extrapolated the moduli of the reaction matrix ele-ments a(vrmN) to zero kinetic energy in the s n N barycen-tric system, T' = 0, for all five charge channels, addingour data to the existing database, and imposing the con-

TABLE I. Total cross sections of the reactionn+p ~ m+~op deduced from measurements of (n n+), (vr p),and triple coincidences, respectively, as a function of incidentpion energy. The incident energy ranges indicated in the firstcolumn correspond to the beam momentum spread. Missingentries in the table correspond to measurements with accep-tances too small to allow a statistically significant determina-tion of the cross section after background subtraction. Thelast column lists the appropriately weighted average values.The quoted cross section uncertainties are statistical. Thereis an additional overall systematic uncertainty of 9% whichapplies to all data points.

g10

I

175 200

z, Kernel et ol

225 250 275 300(Mev)

7T 7t' P

CL

g 1.5O

1

05

0 25

straints at T*=O:

a(vr+~+n)/2 = —~2a(it+7r p) = a(~ non) + a(or+a n).

In our analysis we have used m = 137.5 MeV, f = 90.1MeV, M = 938.9 MeV, and gg/g~ = 1.29, as in Ref. [14],and exact relativistic phase-space factors to extract thematrix element moduli. Like Burkhardt and Lowe [14],we have used linear energy dependence of the amplitudesabove threshold. Figure 3(b) shows the constrained fitof the ~+mop amplitudes (the other four channels dis-

play similar agreement). The minimum y2 of the globalfit is 96 for 93 degrees of freedom [21], resulting in thenew value of the chiral symmetry breaking parameter

( = —0.25 6 0.10. Our value of ( difFers from that ob-tained in Ref. [14] (—0.60 6 0.10). The discrepancy isdue primarily to slightly difFerent amplitude constraintsabove threshold used in the two analyses, and to a lesserextent to difFerences in the data bases considered. Withinthe soft-pion model the new value of (' fixes the eric s wave-scattering lengths at

I i i i i i ~~J50 75 100T*{Mev)

FIG. 3. (a) Total cross sections for the reaction vr+p~ vr+m p as measured in this work (full circles), and pre-viously published [11,19,20]. Full curve: new global fit ofmN ~ nmN isospin amplitudes. (b) Absolute values of them+n p matrix element corresponding to the total cross sec-tions shown in (a) as a function of T', the total c.m. kineticenergy. Solid and broken lines: global linear fit and the asso-ciated uncertainties, respectively.

glab

(MeV)259.5 + 0.7239.5 + 0.7219.5 + 0.6199.5 + 0.6189.5 + 0.5

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mom+

~ (~b)26.1 + 3.715.5 + 3.77.0 + 2.22.6 + 1.31.5 + 2.1

~'p~ (~b)

24.8 + 5.514.9+4.5

~'~+I~ (vb)

27.0 + 5.411.1 + 6.46.2 + 3.42.9 + 2.9

0+3

Averageo (p,b)

26.0 6 2.714.6 + 2.66.8 + 1.82.7 +'l.21.0 6 1.7

coo(7rm. ) = (0.1776 0.006) m

ao(i'm) = —(0.041+ 0.003) ni

These values are to be taken with reservations becausethey do not reflect any uncertainties inherent in the anal-

VOLUME 72, NUMBER 8 PHYSICAL REVIEW LETTERS 21 FEBRUARY 1994

ysis method. The Olsson-Turner model has well knownlimitations and is not based on /CD. ChPT providesa more rigorous framework; however, published directChPT calculations of the nN -+ zz N amplitudes havebeen limited to the tree level, and agree poorly with data[»].

In conclusion, our total cross sections are close to thosemeasured in the vr zop channel [11], which, from sym-metry arguments, is to be expected near threshold. Anew global soft-pion fit including our data gives valuesof the zz scattering lengths close to the predictions ofWeinberg [4] and ChPT [9]. It will be more interesting,however, to extract ao' (zz) f'rom the now available ex-clusive data using the approach of Bolokhov et al. [23],which is free of dynamical model assumptions, as wellas to compare the new data with more realistic ChPTcalculations, once they become available.

We thank the stafF of LAMPF groups MP-7 and MP-8for strong technical support, without which our measure-ments would not have been possible. We are particularlyindebted to Bob Garcia who was responsible for the liq-uid hydrogen target design and construction. We grate-fully acknowledge the help of T. Averett, L. Suddarth,M. Lesko, and A. Wall of U. Va. in detector assemblyand data taking. Our thanks are due to Julian Noblefor many useful discussions and for his support of theexperiment from the very beginning. We also thank J.Beringer, A. Bolokhov, and J. Gasser for a number ofuseful discussions. This work was supported by the U.S.National Science Foundation and Department of Energy.

Present address: Massachusetts Institute of Technology,Laboratory for Nuclear Science, Cambridge, MA 02139.

t Present address: Saskatchewan Accelerator Laboratory,University of Saskatchewan, Saskstoon, Saskatchewan,Canada S7N OWO.Present address: Department of Physics and Astronomy,Vrije Universiteit, de Boelellaan 1081, 1081 HV Amster-dam, The Netherlands.

~ Present address: Institut de Physique Nucleaire, Uni-versite Catholique de Louvain, Chemin du Cyclotron 2,B-1348 Louvain-la-Neuve, Belgium.

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