Detection and measurement of very short flight paths in nuclear emulsions

Nuclear Instruments and Methods 174 (1980) 53-60 © North-Holland Publishing Company

DETECTION AND MEASUREMENT OF VERY SHORT FLIGHT PATHS IN NUCLEAR EMULSIONS Sergio PETRERA and Giorgio ROMANO Istituto di Fisica dell'Universitd, Roma, and Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Italy

Received 10 May 1979 and in revised form 7 January 1980

The application of the nuclear emulsion technique to detect and measure flight paths of unstable particles shorter than a few microns is given. Besides the description of the method of measurement and of the analysis, particular care is paid to the possible sources of biases. It is concluded that the transverse distances of the decay prongs to the primary vertex can be determined with a mean accuracy ~0.05 Ore.

1. Introduction Measurements of very short flight paths of particles or fragments originating in interactions occurring in nuclear emulsion have been proposed and used in the past, for instance in a measurement o f the n o, meson mean life-time [1] or in the detection of cryptofragments [2]. The method has recently gained new interest and was applied in trying to detect "new" heavy particles with short life-times [3,4]. A similar technique has also been used [5] or proposed [6] in bubble-chamber experiments, where the minimum detectable path, however, is two or three orders of magnitude longer than in emulsion. The aim of this work is to show the possibilities and limits of the emulsion technique, and the experimental results obtained so far. The method consists in measuring the plane coordinates of the individual grains of the tracks produced in an interaction, fitting them to straight lines and finding the intersection points. The presence of one or more tracks missing a common vertex is possible evidence of a decay; the flight time can be evaluated from the distance.

2. Method of measurement 2.1. Technique

The plane coordinates x and y of each grain were measured on tracks originating from nuclear interactions. Only grains occurring within the same field o f view, which is not moved during the measurement,

were considered. Depth-coordinates (z) were not measured because they were affected by an uncertainty at least 10 to 20 times higher than that for x and y. What follows mainly refers to measurements on high-energy neutrino interactions [3] found by a wide collaboration in a previous experiment [7]; the emulsions, Ilford K5 disposed with the surface parallel to the incoming particles, were exposed to the neutrino beam at FNAL and processed at CERN. The coordinates were measured on a Koristka R4 microscope with the aid of a pair o f filar micrometric eyepieces; the digitized read-out was directly punched on cards. With objectives 100× and 53× the sensitivity was 1 div = 0.023/am and 0.045/am respectively, the field diameter ~90/am and ~ 1 7 5 tam, respectively. 3 to 4 pairs o f coordinates per minute were recorded; a complete interaction, depending on the number of prongs, was measured in 0 . 5 - 2 h, but equally as much time was usually needed before the measurement in order to carefully inspect the star. In fig. 1 we show a drawing of one of the measured interactions. A hyperfragment, 3/am long, was produced at the primary vertex together with evaporation prongs (black and grey tracks) and six minimum ionization particles; track no. 1 was identified by the external detectors as being due to a /a-meson, the typical signature of a charged-current neutrino interaction. Tracks nos. 3 and 4, nearly superimposed in the emulsion plane, are quite well separated in the vertical one. The six minimum ionization tracks and a grey one (a) were considered for the measurement; about ten grains close to the vertex

54

S. Petrera, G. Romano /Detection and measurement of very short flight paths

EV.62]102 TR. a° ~°

\

\

•

150f

1 -16,2 -5.5 (p,) 2 -I.2 ~7 3 0.0 3.5 4 0.1 153 5 3.3 5.1

I 2• I~

rf )1I, '

a

16. -69.

,'

REI POINTS

~=1.44

100 .-=1.51

\ I

\ ~

5O

tp~m)

\

%--

"

,il ',

a

IS % ~

L

,

40

~._~__ ~-.~-:~_~_~_

,.-,

-6 -4 -2

30

~,,

'(~ ~"

10

,*

~

/

b'

0~~1~/_A!~' ' ' ~ &

0

2

4 6 Ax(div.)

-6 -4 -2

0

~.~ 4 6 Ay(divl

Fig. 2. Reproducibility of measurements. Distributions of differences between measured coordinates of the same reference grain after correction for drift. Results obtained with a 53× objecffve (1 div = 0.045 #m).

c dl

J

Fig. 1. Drawing of a measured interaction (dimensions of the grains nearly to scale). Arrows show measurements rejected by the fitting procedure. The measurements of three reference grains (o) enabled systematic displacements of the field to be acounted for.

(and not shown) were not measured because it was not possible to assign each one to a single track. The confusion produced by the minimum and black prongs in the neighbourhood of the vertex, as shown in this example, very often prevents detection by eye of flight paths shorter than ( 5 - 2 0 ) / a m . 2.2. Reproducibility

Such measurements are usually reproduced with an accuracy far from the sensitivity because even with

great care (thermal insulation, stabilization of the microscope, etc.) the whole field drifts in a random way at a rate ~0.01/am per minute. In this work the drift was accounted for by measuring the coordinates of three "reference" grains before and after each track. Assuming that the drift was regular in between, all the measured coordinates were corrected so as to reproduce their value at a given time. •In fig. 2 we show the distributions of the differences (Ax, Ay) between subsequent measurements o f two reference grains after having corrected for drift as computed from the third one alone. The distributions are nearly Gaussian with dispersion/a ~ 1.5 div. The reproducibility (a* =/a/x/2) turned out to be about twice the sensitivity (0.5 div) at any magnification. The difference is partly due to the subjectivity involved in setting the centre of a grain, but also to other kinds of noise (use of a binocular, electronics, etc.). The value of the reproducibility is much smaller than both the size of the developed grains of the emulsion (0 A - 0 . 6 /am) and of the wavelength of the light (X ~-- 0.5/am). It should be noted, however, that the centre of the diffraction patterns associated with

S. Petrera, G. Romano / Detection and measurement o f very short flight paths

the grain is measured and reproduced, and not a particular point of the grain itself.

30-

2.3. Optical distortions

20-

The orthoscopy af the system was checked by several measurements of the same grains of a track in different positions within the field (through the centre and displaced to opposite sides). The results showed that deviations from linearity were not in excess of (0.01-0.02)/am. The optical axis was accurately centred before each measurement in order to avoid systematic correlations between plane coordinates and depth. While a sizeable curvature of the field had no serious consequence because z coordinates were not measured, a disturbing effect was the poorer quality of the image close to the edge of the field compared with that in the centre. As a consequence of these results the centre of the interaction was placed on the most convenient side within the field, depending on the topology of the event. On average, about ~ of the field diameter, around the centre, was considered as the fiducial region for the measurements.

3. Intrinsic dispersion of the grains and cut-off criteria

55

N ~

100

~

w

. •

5 I

0

.05

~'r'rrn

.10

.15

.20

d~n)

I ~

.25

Fig. 3. Distribution o f projected distances o f measured grains to the fitted track o f a high energy g-meson. The dashed area represents " a n o m a l o u s " blobs (out o f focus, oblique, etc.), measured b u t n o t used in the fitting procedure. Results obtained with a 100X objective.

focus, etc. were also measured and marked. In fig. 3 we show the distribution of projected distances to the fitted line for both normal and anomalous grains: the last ones are uniformly spread between 0-0.25/am, represent ~10% of the sample and contribute to large extent to the tail. The dispersion is Oo = (0.052 -+ 0.004)/am without anomalous grains; it would increase by ~25% if they were considered as well.

3.2. Cut-off criteria 3.1. Intrinsic dispersion The intrinsic dispersion Oo, defined as rms distance (projected onto the emulsion plane) of the centre of the grains to the track, is expected to be of the order of half the radius of the undeveloped crystal, i.e. ~0.05/am in Ilford K5 emulsions. Experimental results obtained by different authors, mainly based on the computed grain noise from multiple scattering measurements [8], roughly agree with the predictions, but with a wide spread which probably reflects the strong influence of a subjective cut-off. Indeed, the actual distance distribution could be enlarged by several factors, among them an asymmetrical growth of the crystals, the presence of short 6-rays, random displacements and background grains. Oo has been determined by measuring the coordinates of the grains along the track of a high energy /a-meson aligned on a wire. Anomalous grains, like blobs oblique to the track, grains slightly out of

When measuring in working conditions, a track is usually not aligned on a wire (the axes are fixed) and somewhat dipped. In this case it is very difficult to reject by eye in an objective way anomalous or spurious grains lying within ~0.5/am of the track. On the other hand, keeping them in the sample produces not only an increase of the dispersion but also a bias in the slope, especially if they belong to one end of the track. Therefore, the procedure adopted in this work was to reject before measurement all the grains close to the vertex that could not be unequivocally assigned to a single prong and the blobs oblique to the track, and to measure all the remaining ones in the above mentioned conditions. This procedure is still likely to retain spurious grains, thus a cut-off criterion was applied in the analysis stage. As a loose criterion is not effective and a severe cut-off leads to a ficticious underestimate of errors, after some trial a suitable procedure proved to

56

S. Petrera, G. Romano /Detection and measurement of very short flight paths

be that of dropping the measurements of points falling at a distance larger than 2•5o. The correctness of this choice is justified by the overall results (section 6). • .

..

.

.'.

.

";-..':"" ....'

.-.'i

<.:.~!~".(. 4. Fit of single tracks

. :

.05

•

..-'

"

4.1. M e t h o d and experimental dispersion L

°oo

Each track (n measured points) was independently fitted to a straight line

20 +

30 +

40 °

0°

600

0°

800

900

laq

(1)

y = a + bx

assuming that both measured coordinates (xi,Yi) have an equal error, but keeping o, the rms distance of the centre of the grains to the fitted line, as a parameter• We found that

'"i

| • .

ot 5

2B

:!i~,.._ .;:+i :" .• ::!~v~ :

•°5i

A + (A 2 + 4B2) 1/2 b-

100

10

••

•

. i. ~~. • • ~ •

15

20

25

30

35

n

Fig. 4. Plots of the experimental dispersion of the grains around the fitted lines as a function of plane angle (a), and number of measured points (b).

where A = ( Z x ) 2 - ( Z y ) 2 + n ( X y 2 _ X x 2)

B = nY~xy - E x E y

Depending on the magnification, the mean value of the dispersion was respectively

1

a =.-(~y - b~x), n

o2_

1 n-2

(2)

E(y - a - bx) 2 1 +b 2 '

o~ = o2(1 + b 2) n / A /

oa2 = o2(I + b 2 ) ( Z x 2

-

no2)/A l

"Cab= --a2(1 + b 2) Z x / A

I

)

obj. 53×

(o) = 0.065 tam,

obj. 100×


practically coincident with the combination of the intrinsic dispersion Oo (section 3.1) and the reproducibility of the measurements (section 2.2). 4.2. lnfluence o f track length

where

A = n ~ x 2 -- (]~X) 2 -- n2o 2 • O~ and Oa2 are the variances of b and a respectively, tab the covariance between a and b; o is not correlated with a or b (roa = rob = 0). In fig. 4 we show a plot of o as a function of plane angle (a = tan-Xb) and of the number of measured points (n) for a sample of events measured with a 53× objective. No correlation is seen neither between o and a (fig. 4a) nor between o and n (fig. 4b), but o spreads on a wider interval towards small values of n, as expected from statistical considerations• No correlation was even detected between o and any other parameter, such as dip angle or measured length•

The resolving power of the method is determined by the statistical uncertainty across a track at the vertex (ol), which by turn mainly depends on o, n and d~, the distance of the first measured grain to the star centre• If the vertex is taken as the origin

a~--

2 Oa 1 + b:

(3)

and assuming the grains are at an equal distance e 0.2

4a2{(n 2

3n--l)

__~ - -

n +3~n--1)

-2d. __ + ( - ~ ) 2 ] } ~ n 2 _ 1), e

where the approximation holds for ale < < n.

(4)

S. Petrera, G. Romano / Detection and measurement of very short flight paths

where K is the distortion vector, A a the plane angle between track and K, 6o the undistorted dip angle and s the original emulsion thickness. In fig. 6 we show the situation schematically: the bias (P) introduced by distortion could easily simulate a short path decay. With the same hypotheses used in the previous section

2,O g

1.0

•

•

•

57

15

K L2 In P =-fi -~- sin(Ao0 tan26o - -- 2

1

I

I

I

I

I

1

I

I

1

2

3

4

5

6

7

8 d,/~

J

i

6 dl ~ - n-le -

;

n Fig. 5. Statistical error as a function of the distance (dl) between first measured grain and origin, and of the number of measured points (n). a± is the uncertainty across the track at the vertex, e the mean distance between grains. Experimental results, independent of the magnification, in the following ranges of measured points: (A) n = 8-10; (e) n = 1518; (e) n = 25-30.

Quite large values o f d l / e may be found, even if the distribution o f gaps between grains [9] is such that (dl} = e, because very often the grains closest to the vertex are not measured (section 3.2). In fig. 5 we show oa]o as a function o f d l / e for different values o f n [computed from eq. (4)] and some experimental results in the quoted ranges o f n [computed from eq. (3)], independently of the magnification. The quick increase o f o± with d l for small values o f n shows that it is usually more convenient to measure many grains rather than trying to find the one closest to the vertex. In any case it seems difficult to overcome the limit ojJo = ( 0 . 4 - 0 . 5 ) with minimum ionization tracks (e ~ 5/~m) measured up to a length L ~ 100/am (see section 5).

1

(5)

'

where L = e(n - 1) is the measured projected length. The extra spread added by fitting a distorted track to a straight line is

o' ~ CL 2/~/180 , usually a small contribution even in the extreme cases computed below. In fig. 7 we show P as a function o f d~/e for minimum ionization tracks and for different values o f the undistorted dip angle in the average conditions found in this work. As a comparison, the dependence o f o± on d l / e is also shown. It is readily seen that F, for I~ol ~<20°, is smaller than a± up to high values o f dl/e, unless n increases too much; much larger values o f P could be found on longer tracks or with larger dip angles, and strongly depend on d l . Measurements performed on several tracks in different conditions nicely agree with these predictions.

5. Biases introduced by track distortion and multiple

scattering 5.1. Track distortion A straight track in the undeveloped emulsion appears with a parabolic shape when projected onto the plane o f the processed emulsion as a consequence o f a "C-shaped" distortion [ 10]. It is found that

y = A + Bx + 6"3c~; C - IKI sin(Aa) tan28o --

32

r, ~ o

¢'

.

Fig. 6. Effect of a "C-shaped" distortion described by vector K. (a) undistorted track; (b) real shape; (c) fit of the distorted track to a straight line. r is the systematic error thus introduced, dl the distance of the first grain to the vertex (V), e the mean distance between grains. All quantities in the emulsion plane.

S. Petrera, G. Romano /Detection and measurement of very short flight paths

58

*K sin c=~=30 /~m s=6OO/an

61°~

=T

I

%--5/xm

.15

d,/~

6

4

2

-

.10 -

-

.05

0

-

0

2

4

6

d,/~

Fig. 7. I" as a function of dl/e (quantities defined in fig. 6) for different values of the undistorted dip angle 8 o. Calculations performed for minimum ionization tracks measured with n = 8 and 15 grains (observed on average with 100X and 53× objectives respectively) and with the mean values of the thickness (s) and distortion vector (K) found in these plates. As a comparison, typical values of o± are also shown.

are reported, we show that multiple scattering is n o t expected to seriously bias the measurements if particles with pfl > 500 MeV c -1 are considered and measurements up to L ~ 100/am are performed; tracks of particles with a lower p/3 could be used if measured over a shorter length. A cut-off for the ionization (g/go < 2 for protons) allows to use light-grey tracks too. In order to detect a curvature due to distortion or multiple scattering, a check on the correlation b e t w e e n displacement and length was i n t r o d u c e d in the c o m p u t e r procedure. As the choice of the total magnification restricted the useful length of track to ~ 1 0 0 / s m or less, only few steep or grey tracks showed a sizeable effect. In these cases the standard procedure was to reduce the n u m b e r o f grains, rejecting the last ones, until the effect disappeared within the errors involved.

6.

Determination

of

the vertex and search for decays

6.1. Computing procedure

5.2. Multiple scattering The effect o f multiple scattering on low m o m e n t u m particles is very similar b u t i n d e p e n d e n t of dip. P, as previously be c o m p u t e d [11] as a f u n c t i o n of length, and p/3:

the tracks of to distortion, defined, m a y Lo, the real

Two lines on a plane define their intersection point (xo,Yo) with errors (Oxo, ayo). For a pair of tracks symmetrically displayed around the x-axis, taking Xo =Yo = 0; bl = - b 2 = t a n ( a / 2 ) , Oa ~ o/x/2, we find 17

o

P ~ KsLao/2/pfl,

Oxo ~ 2 t a n ( a / 2 ) '

where Ks, slightly d e p e n d e n t on L and fl, has a m e a n value in emulsion of ~ 0 . 0 1 7 5 (MeV/c)/am - v 2 . In table 1, where the results of such calculations

therefore, with a typical opening angle et ~ 6 °, Oxo 20Oy o would result. This shows h o w the m e a s u r e m e n t

Oyo "~-2

Table 1 Influence of multiple scattering. Computed values of I" as a function of p¢~ for different track lengths (L). g/go is the grain density relative to minimum ionization tracks; a track is usually considered as "grey" ifg/go ~ 1.4. The dashed line suggests possible boundaries of the useful region.

Pfl (MeV

100 150 200 300 500 700 1000

g/go

r (~tm) for L =

c- l ) (n-mesons)

(protons)

1.55 1.25 1.14 1.05 1.00 1.00 1.02

6.5 4.5 3.6 2.66 1.88 1.53 1.27

25 ~0.022 0.015 0.011 0.007 0.004 0.003 0.002

50 t I I

0.062 0.041 0.031 0.021 0.012 ' 0.009 0.006

75 0.114 0.076 0.057 ', 0.038 0.023 0.016 0.011

100 (~m) 0.175 0.117 0.088 0.058 [ _0.0_35_ 0.025 ~, 0.018

S. Petrera, G. Romano / Detection and measurement of very short flight paths o f a single grey track at a large angle could reduce the longitudinal uncertainty of the vertex of a high energy interaction by an order o f magnitude. A vertex where more than two tracks are emitted is determined using the function 1

N

2

to be a minimum as a function o f Xo and Yo (Ap is the projected distance o f a fitted track to the vertex, 6Ap is the c o m p u t e d error). If indeed all the tracks belong to a c o m m o n vertex it is in the average A z ~ 1. The rms uncertainty and the standard error on the vertex are respectively defined as the zone within which A 2 increases by 1 or 1/(N-2) units with respect to its minimum value.

6.2. Search for decays The function A was computed for each event keeping o [see eq. (2)] as a constant; the values o f A , ranging from -q3.5 to ~ 2 , were consistent with having observed no double vertex. However, the efficiency o f this method strongly depends on the number of tracks and thus a sample of events with different multiplicities could lead to ambiguous results. On the other hand, as the evidence of a short path decay is obtained if at least one decay prong does not converge to the primary vertex (see fig. 8), it is convenient to compute the distance o f each track o f an event to the "residual" vertex defined by the others. The procedure sketched above was applied to the sample but grey tracks were always included in the primary vertex. In fig. 9 we show distributions o f transverse errors

1

/

f~

59

Table 2 Mean values of 01, Ap a n d Ap/SAp for minimum ionization tracks at different magnifications, a±, defined in section 4, is the computed error across a track at the point of nearest approach to the vertex defined by the others; Ap is the projected distance of a track to the vertex, 6Ap its error. Objective

53 X

100 X

Nos. of events Nos. of minimum tracks (a±) (tam) (urn) Idem, with cut-off a

13 84 0.039 0,058 0,053 1.16 -+ 0.09

15 91 0.052 0.068 0.061 1.10 -+ 0.08

rms

Ap/6Ap

a At 0.15 tam for 53 X obj.; at 0.20 tam for 100 ×.

(oi), o f projected distances (Ap) and o f distances in units o f standard deviations (Ap/6Ap) o f the minim u m ionization tracks for the sub-samples measured with a different magnification. Not a single Ap was larger than 3 standard deviations, suggesting that there is no evidence for a short path decay in this sample o f events. There are few cases where Ap is much larger than the average, but for tracks with anomalous conditions (few grains, first grain very far, bad topology, etc.); in fact their errors were large too. In table 2 we summarize the results and show that a possible underestimate o f the overall errors, if present, is surely small. The average dispersion o f the projected distance o f the tracks to the vertex - the resolution power o f the present t e c h n i q u e - i s 6Ap ~ (0.05 to 0 . 0 6 ) / l m , only slightly dependent on the magnification. If evidence for short path decays was found in a sample o f interactions, the distribution o f Ap would

O

~5

Fig. 8. Sketch of the possible configuration of a short path decay. Four particles are produced in 0 (the primary vertex) together with a Fifth one decaying in A, after a projected path Lp, into one charged prong (track 1) and neutrals. The shaded area represents one standard error around the vertex, as determined by tracks 2 to 5.

S. Petrera, G. Romano / Detection and measurement o f very short flight paths

60

l',l+

I

<4, >

I'

20

0

.05

]

]O

.2

.3

.4

1

2

3

N ~ 2

4o~

20-

20

10-

10-

t

.~

.10 g

.1

1

t

2

t

3 3~1~,

Ip.m]

Fig. 9. Distributions of transverse errors (o±), projected distances (A~,) and distances in units of standard deviations (Ap/SAp) of the minimum ionization tracks for the subsamples of events measured with different magnifications.

allow to estimate the m e a n life-time r. In fact, to a first a p p r o x i m a t i o n ,

(Lp sin ~) = ( A p ) ~ Cr i n d e p e n d e n t o f the m o m e n t u m . It can be seen that w i t h this m e t h o d m e a n lifetimes as short as few times l O - t 6 s can be measured *

References

[1] H. Shwe, F.M. Smith and W.H. Barkas, Phys. Rev. 125 (1962) 1024; ibid. B136 (1964) 1839; CERN-65-4 (1965) p. IX-45.

* A recent search based on Monte-Carlo simulation led to similar results, see ref. [12].

[2] S.J. Bosgra and W. Hoogland, Phys. Lett. 9 (1964) 345; S.J. Bosgra and A.G. Tenner, Nucl. Instr. and Meth. 29 (1964) 322. [3] G. Baroni, S.Di Liberto, P. Ginobbi, S. Petrera and G. Romano, Nuovo Cim. Lett. 24 (1979) 45. [4] G. Diambrini-Palazzi, Proc. XIX ICHEP, Tokyo 1978 p. 297. [5] L. Pape, Proc. Topical Conf. on Neutrino Physics at Accelerators, Oxford 1978, p. 167; A. Blondel, ibid. p. 217. [6] D. Crennel, C.M. Fisher and R.L. Sekulin, Nucl. Instr. and Meth. 158 (1979) 111. [7] E.H.S. Burhop et al., Phys. Lett. 65B (1976) 299; A.L. Read et al., Phys. Rev. D19 (1979) 1287. [8] W,H. Barkas, Nuclear Research Emulsions, Vol. I (Academic Press, New York, 1963) p. 306. [9] C. O'Ceallaigh, Nuovo Cim. Suppl. 12 (1954) 412. [10] M,G.E. Cosyns and G. Vanderhaeghe, Universit6 Libre de BruxeUes, Bull. du Centre de Physique Nucl~aire n. 15 (1950); A.J. Apostolakis and J.V. Major, Brit. J. Appl. Phys. 8 (1957) 9. [11] J.D. Jackson, Classical Electrodynamics (John Wiley and Sons, New York, 1972). [12] G. Ingelman et al., Nucl. Instr. and Meth. 165 (1979) 1.