-·· / - .- NEUTRAL STRANGE PARTICLE PRODUCTION IN l!"-p INTERACTIONS AT 147 By TUNGCHING OU c /!?-f v.- ' A thesis submitted to The Graduate School of Rutgers, The State University of New Jersey in partial fulfillment of the tor the degree of Doctor of Philosophy Graduate Program in Physics /_ .... Written the direction of Professor Terence L. Watts and approved by Hew Brunswick, NP.w May, 1979 FERMiLAB LIBRAR\' ..
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-·· /
-
.-
NEUTRAL STRANGE PARTICLE PRODUCTION
IN l!"-p INTERACTIONS AT 147 G~V/c
By TUNGCHING OU
c /!?-f v.- '
A thesis submitted to
The Graduate School
of
Rutgers, The State University of New Jersey
in partial fulfillment of the requir~ments
tor the degree of
Doctor of Philosophy
Graduate Program in Physics /_....
Written und~r the direction of
Professor Terence L. Watts
and approved by
Hew Brunswick, NP.w J~rsey
May, 1979
FERMiLAB LIBRAR\'
15~
..
,,
Abstract
Neutral.Strange Particle Production
in lr-p Interactions at 147 Gi!V/c
By Tungching Ou
Thesis Director:. Professor Terence L. Watts
The production of K~, /\, /\, and Y in n--p collisions at
147 Gev/c is analyzed. We present neutral single particl'!
distributions, energy dependence of average neutral
multiplicities in - and collisions, neutral-charg'!d n- p pp
correlations in the KNO framewo~ and two-particle . )
inclusive neutral cross sections.
!
I
....
~
\
---·-.. -
------
- '
----
--·\
Acknowledgements
I would like to thank
Terry Watts, for his guidance over the years;
member's of the. bubble chamber group who have lent me
their expertise on almost every phase of the experiment
Rich Plano, Lenny Koller, By Brucker, Pete Stamer, and
Pieter Jacques;
the scanners and PEPR operators at Stevens, Rutgers,
and the rest of the consortium, for the difficult job of
measuring the film;
Ray Badiak and Annamary Mccann, for fixing all kinds of
The neutral-neutral correlations Ca b are given by ' cr(a b)
= O"(a)O"(b) Of.nel
those
85
= <nanb> <na><nb>
Chap.3
= <n 2 (n 2 -1)> <na><na>
, a~b
, a=b
-86 -
-All quoted errors are statistical only. The K~K~, K~ A, and -
K~ A cross sections are slightly larger but consistent with
being equal to the· results from -rr-p 250 Gev/c but with
better statistics [38].
The trend of thE Jeutral-neutral correlations in Table 11
is that the correlations between pairs containing zero or
one strange particle are comparable to the neutral-charged
and charg~d-charged correlations in the last section.
Correlations between two strange particles, with the
possible exception of A /\, seem to be larger than the rest.
---------------
Chapter 4: Conclusions
A's are produced primarily in the fragmentation region
of the target proton; <n A> in pp collisions is larger than
<nA> in 11"-p collisions; neither is changing with energy.
'lfo, K~, and A's are centrally produced like the bulk of
the charged particles. <n 11" o>, <nKo>, and <n A> are the same s
for 'lf-p and pp collisions and are rising logarithmically
with energy. The central region K~/charged ratio, measured
by dO-/dy at y=O, is (4.06±0.71)%. The ratio of the
inclusive cross sections is slightly smaller (2.36±0.18)%.
The semi-inclusive neutral cross sections are consistent
with KNO scaling. Neutral-charged correlations are weaker
than charged-charged correlatfons.
K°K0 and K0 /\ correlations are 1-2 standard deviations s s s
above the un-correlated value 1. The other neutral-neutral
correlations are consistent with no correlation.
87
Appendix 1: Excerpts from rules for Scan-1A
(III) Scanning for Events
Figure 41 shows how the fiducials and frame number appear in each of the 3 views. The dott~d box in view 1 defines the fiducial volume. If the primary vertex of an event lies outside the fiducial volume, no information need be recorded.
If a primary vertex lies within the fiducial volume in view 1, record an 'event ID by setting the thumb wheel switches as follows:
experiment U = 41 event-type = 1(IPD) or 3(HM) frame # = 6-digit frame number additional event remeasurement # = 1 at present scan # = 1 at present operator IJ track count 3-digit roll # comment=1 faint or crowded event
=2 problem event =O accepted event
All other switches should be set to O.
If there are 2 or more events in a frame, measure them in the order in which the primary vertices appear as you follow the beam tracks from the bottom of the picture to the top. Set additional event =0 for first event, =1 for second event, =2 for third, etc.
Track-count originating from Dalitz electrons. (0,2,4,6, •• ).
is the
The
the number of charged secondaries primary vertex excluding identified track count will usually be even
An event should be flagged as comment 1 (faint or
-88 -
------------
crowded event) if any of the following is satisfied: -
1. The tracks in the event are faint. 2. There are more than 10 beam tracks entering the
fiducial volume. 3. There are more than 10 incoming secondary tracks
entering the fiducial volume.
An event that is not faint or crowded should be flagged as comment 2 (problem event) if any of the following is
--
satisfied: •
- -.
Appendix 1
1. There is a secondary interaction within 5mm of the primary ver-tex.
2. It is impossible to find the sa::ne number- of tracks originating from the primary vertex in all 3 views. (The track-count in this case should contain the maximum of the track-counts obtained in 3 views.)
Note that for comment 1 and comment 2 events, the track-count should ·be recorded in switches 27-28, but no track points are needed. All other events should be flagged with comment O (accepted event), and the track points measured according to the rules in the next section.
Frame numbers of blank frames should be recorded in the log book.
89
' ' If " ' , I t
I I .. II I I I • -···· ,.,... ...... F"s
t- x
'
~~ Pl .
x f 4 ft Fl F4- fs- Fr
F' >t- x ~ x X ·- -----x-~ x ~ x t- I
I )( ')(
.1.-I -4-
FS' )( x x F''
x x Fl. : >t
x
F7
* x x ')(. t" Tl )(
)(
Fl F5 pr x Fir>< : I >(
l I
I x x I XFS x nX1 I x
Fl. f5 I
f 7 I f I ....... f71
r i x --xJ
I I II " • • I . r .. --••••••
~e.w~ v~iw l view 1
Fig 41. The fiducial volume
I I . I I I I l I . I . I •• I I I I I I
-
-
-
Appendix 1
(IV) Measuring Tracks (IPD)
A point is measured by the measuring switch/foot pedal (denoted by bO), or one of eight buttons on the IPD table (denoted by b1, ••• , b8).
A. Generation 1 Information The first 7 points measured in each view shall be:
1. fiducial 01,labeled f1 in Figure 41,(bO) 2. fiducial #2 (bO) 3. primary vertex (bO) 4. CP on beam track (bO) 5. EP on beam track (bO) 6. 1st point on reference ionization track, near the
downstream end of track (bO) 1. 2nd point on reference ionization track, slightly
before primary vertex (bO)
If an· interacting beam track or a secondary track is used as the reference ionization track, the first point should be farther away from the primary vertex than the second one. The beam track and the reference ionization track should each have exactly 2 points measured.
B. Generation 2 Tracks Each secondary track shall consist of the following
points:
1. ·.uHP (b1) if vertex is obscured from the main body of the track
2. CP (bO) near the middle of the track 3. one or more ECP (b2) if there are small angle
crossing tracks 4. EP (bO) near the point where track leaves the chamber
(But do not measure a track through more than a third of a circle-120 degree turning angle)
or SP (b3) at the point where the track stops
or MUV ( b 5) at the point where -rr decays into p
or DV (b6) at the secondary vertex or decay vertex
Use UHP and ECP's whenever a track is obscured by flares or other small-angle crossing tracks. However, if 2 or more forward tracks are nearly on top of each other throughout the entire length of the chamber, simply measure 2 points (CP and EP/SP/MUV/DV) for each track even though they may not be useful to PEPR.
91
Appendix 1
C. Generation 3 Tracks Measure all generation 3 tracks except the Jl in a lr
,U -e and tracks originating from a secondary vertex. This class includes decays, vee•s, gamma pairs, and Dalitz electrons. The order in which generation 3 tracks are measured is important. A track originating from a decay vertex should be measured immediately after the secondary track from which it ~ecayed. Vee's, gamma pairs, and Dalitz electrons should be measured in that order, after all secondary tracks. Generation 3 tracks are measured like generation 2 tracks with the following points added:
1. vertex of vee (b3) immediately before the 2 tracks of the vee
2. vertex of the gamma-pair (b5) immediately before the 2 tracks of the gamma pair
3. primary vertex (b6) immediately before Dalitz electrons
4. decay vertex (b7) immediately before track originating from decay vertex
Ignore vee 's, gamma pairs, and visible in all 3 views. If a secondary in all 3 views, IPD the track as if secondary interaction.
decays that are not vertex is not visible it did not undergo a
If there are 2 events in the same frame and a vee (or gamma pair) may be associated with either event, measure the vee (or gamma pair) once for each event.
The tracks of a vee should be matched in 3 views. For example, if the positive track is measured before the negative track in view 1, then do the positive track first in view 2 and 3.
If there are 2 or more vee's in the same event, measure the vee' s in the same order in all 3 views. The same 5oes for gamma pairs and Dalitz electrons.
The following table summarizes the button functions.
button
bO b1 b2 b3 b5 b6 b7 b9
function
fiducials,CP,EP UHP ECP SP ;vertex of vee MUV ;vertex of gamma pair DV ;vertex of Dalitz electron
;decay vertex terminate view
-92
-
----------....
Appendix 1
D. Error Messages If more than 99 points are measured in any view, ONLINE
types "no more points". These events should be killed and re-entered as comment 3. After ( b9) is pushed, the online program will check that the number of generation 2 tracks you have measured is equal to the track count in switches 27-28 and also that the total number of tracks measured is the same as in previ9us views ("view incomplete").
A 110 command will type out "pts: nn/01. tkv:aa/cc. tks: bb/dd." nn is the number of points measured this view. cc = 1 + the total number of tracks required this view. dd = 1 + the number of secondary tracks required this view. aa,bb are the corresponding measured quantities this view.
E. Fiducial Measurement At the beginning of the day, or at the beginning of a
new roll, or when you change roll to a new table, pick a frame without an interaction and measure the 7 labelled fiducials in all 3 views (see Fig. 41). Set up the event ID as for an event but with track-count =0 and event-type =2.· measure the points in the order f1, f2, f3, f4, f5, f6, f7, then (b9).
Do not use a frame that has any event in it. If, however, the first frame on a roll or at the beginning of the day has an event in it, measure that frame but set a frame number that 1~ one less in the switches.
93
Appendix 2: The SimplP.X Approximation
When fitting to experimental data, very often the measured values are Gaussianly distributed. The techniques for making linear fits in these cases are well known. We want to introduce a linear fitting technique that is applicable when the probability for obtaining an experimental result is uniformly distributed in some interval and zero outside. This situation occurs when attempting to recoQstruct straight line trajectories of charged particles traversing a set of multi-wire ~~oportional chambers.
Suppose we measure N quantities for which we experimental values xi with errors ()·. We "theoretical" expressions for these quantities
M ti(a 1 , ••• ,aM) = [ Ci,ua,u
}l =1
obtain the also have
which are linear homogeneous functions of M parameters a )J •
The parameters are to be adjusted to give a best fit to the data.
First consider the case where the probability distribution for the experimental results xi are Gaussian. This will lead to the familiar linear least square fit. The likelihood function is
L(a) = k exp( -~x 2 )
where k is a normalization constant and
2 N 2 2 X = L (xi-ti) /a-i •
i:1
Define a "data vector" X and a "measurement matrix" M with components as follows /
94 -------- .
------
* -Then the condition that L( a) is maximum at a=a may be written as the matrix equation
-with solution.
-
Appgndix 2
* -1 a :M X.
The errors in the fitted parameters are
..6all = oc1 )1/2 ,- }l }J
We may also write
2 M * * X (a) = [. (a }l -a }l )M }l ~(ap-ap)
}l ,p= 1
and verify the following
* [ M a}l = <ap> = Jd a a}lL(a) (13)
[ M * * = ] d a (a }l -a }l ) ( ap-ap) L (a) ( 14)
i.e. if we think of the likelihood L as a probability density in M-dimensional parameter space, then the best fit for the parameters a are just the first moments of L, the elements of the errof matrix are just the second moments of L.
Now consider the case where the probability distribution for the experimental results is uniform in some finite region. The normaliz~d likelihood is
N L(a) = k n [6(ti-xi+o-i) - e(ti-xi-o-i) ]
i=1
Since ti (a) is linear in a }l ,
ti(a) - xi + o-i = 0
is the equation of a hyper-plane in M-dimensional parameter space. The step function e(ti-xi+o-i) corresponds to the inequality ti-xi+cri L 0 which constrains L to be zero on one side of the hyper-plane. Thus L is a constant and non-zero inside a "feasible region" V. The boundaries of the feasible region are hyper-planes. On a boundary hyper-plane, one of the 2N inequalities is satisfied as an equality. A vertex of the feasible region is the point at which M hyper-planes intersect. At a vertex, M of the 2N inequalities are satisfied as equalities.
Since L is constant, the usual technique of obtaining the maximum by setting the first derivative equal to zero is not applicable. However it still makes sense to calculate
95
Appendix 2
moments of L. If we think of the feasible region as a Mdimensional solid object with unit mass and uniform density, i.e. L is a ~ass density, then equations 13 and 14 say the best fit for a is just the center of gravity of ·the solid and the error fatrix is just the moment of inertia tensor.
For- an irregularly shaped object, one might think of resorting to numerical integration to calculate its volume (or mass), center of gravity, and moment of inertia. But that is not necessary. In fact, these calculations are quite trivial if we use the superposition principle which says that we can divide up the object into many pieces and treat each piece as if all its mass is concentrated at its center of gravity. We'll illustrate this with an example M=2, N=3.
Suppose the inequalities, which are just half planes bounded by straight lines, are as shown in Fig. 42a. The feasible region, which is the intersection of all the half planes, is shaded. Note that not every line contributes to the boundary. There are 6 lines but the feasible region has only 5 sides. It is intuitively obvious that thP. feasible region will always be a convex polygon with its center of gravity located inside the polygon. Choose any point in the interior of the feasible region, connect it to all the vertices dividing the polygon into 5 triangles as shown in Fig. 42b. For the j-th triangle with vertices at
-a 1 , a 2 , a 3 ,
the center of gravity is at
1 - - -gj = 3Ca1+a2+a3)
and its area is
For the whole
G =
a 1x a 1y 1 a2x a2y 1 a3x a3Y 1
polygon, the center of gravity is
~ m ·g · I ~ m • L J J L J j:1 j:1
and the moment of inertia tensor is
Ixy = t mj(gjx-Gx)(gjy-Gy) • j:1
To reconstruct trajectories from hits in a set of multiwire proportional chambers, 4 numbers are needed to
-96 -
-----------------
97
(~)
(b)
Fig 42. A feasible region in 2-dimensions
Appendix 2
parametrize a straight line so M=4; let's say there are N=16 planes. The generalization to 4 dimensions is no problem. A vertex is the intersection of 2 lines in 2 dimensions, 3 planes in 3 dimensions, and 4 hyper-planes in 4 dimensions. Finding a vertex requires solving 4 simultaneous linear equations or inverting a 4x4 matrix. A triangle in 2 dimensions becomes a tetrahedron in 3 dimensions and a 4-simplex in 4 dimensions. Such an object has 5 vertices and 5 boundary hyper-plan~s formed by taking the vertices 4 at a time. Once the vertex coordinates of a 4-simplex are known, the center of gravity can be calculated by taking an average, and the volume calculated from a 5x5 determinant. For- N= 16, there are 32 inequalities. The feasible region will have a large number of vertices. This is not a difficulty in principle. In practice, a little care will save a lot of computer time. E.g. to find the vertices of the feasible region, it is not necessary to calculate all possible intersections of 32 hyper-planes taken 4 at a time. Suppose we have inverted a matrix A and found that it corresponds to a vertex of the feasible region. To find the coordinates of a neighboring vertex which shares 3 hyperplanes in common, it is not necessary to invert a mat9ix B from scratch. Si~ce A and B differ in only one row, B- can be found fro~ A- after one Gaussian elimination step.
To save programming effort, the reconstruction program PWGP does not use the simplex technique. Instead, uniform probability distributions corresponding to hits from wire plane~ are replaced by Gaussians with the same average and variance and tracks are obtained from a linear least squares fit. We have not implemented the simplex algorithm and compared with PWGP's results. Our guess is the differences are small for clean events in which adjacent wires do not fire simultaneously.
In a multi-track enviroment when several adjacent wires do fire simultaneously, the simplex technique will probably be superior. For a bunch of adjacent hits,· using a single Gaussian whose mean is at the center of the bunch is a bad approximation if the distribution is very wide. Alternatively, setting up a narrow Gaussian for each wire in a bunch and using only one of them in the fit is a procedure that creates infor::nation where there is none and can only lead to spurious tracks. In the simplex technique, single wir-e hits and multiple-adjacent-wire hits ar~ treated in exactly the same way. Each hit corresponds to 2 hyperplanes in 4-diroensional parameter space. A hyperplane constrains the traje_ctory iff it is a boundary of the feasible region. The reconstruction of a track will not.be biased by the fact there are other tracks present.
In summary, we have outlined a linear fitting technique
98
-
---...
----
---
App".:lndix 2
that is applicable whenever the experimental results are uniformly distributed. The solution is computationally straightforward and can be easily implemented in a computer program.
99
Notes and References 100
[ 1] Experiment 11154 by PHSC. The Proportional Hybrid Spectrometer Consortium is a collaboration of 50 physicists from the following institutions.
Brown University CERN Fermilab Illinois Institute of Technology University or Illinois Indiana University Johns Hopkins University Massachusetts Institute of Technology Oak Ridge National Laboratory Rutgers University Stevens Institute of Technology University of Tennessee' Yale University
[2] A.E.Snyder, thesis, The Reaction -rr-p--7 11"-TI"+TI"-p at 147 Gev/c, #C00-1195-349, University of Illinois, (1975).
[3] J.Lach and S.Pruss, Instrumentation of the hadron beams in the neutrino area, Fermilab report TM-298 (1971).
[4] P.F.Jacques et al., On-line display aids for the automated measuring of bubble chamber film at Fermilab energies, Rev. Sci. Instrum. 48 963 (1977).
[5] We used the Gaussian form for programming convenience. Actually, the probability is more like a sum of two step functions than a Gaussian, i.e. the probability density is uniform and non-zero inside a finite interval and zero everywhere else. For an alternative to using the Gaussian approximation, see Appendix -2.
[ 6] W. Bugg, PHS Consortium internal news note 1130, August
-------------
1974. -
[7] The minimum ~it probability of 10-4 is small enough to include as fits some badly measured events but not too small to bring in garbage. In the final sample of neutrals, the effective minimum probability cut-off is actually higher because the r-eally bad fits will not pass physicist inspection.
[8] Pull variables are defined ~s (m-f)/(( .Am) 2-( .Af) 2 ) 1/2 wh~re m is the measured value, f is the fitted value, Am and .A f are the corresponding errors. Pull distributions should be Gaussians centered at zero with unit standard deviaton.
---
-
[9)
Notes and References
The variables used by SQUAW are tan(d), k, and ¢where the dip angle d is 1f I 2 minus the polar angle, k=cos ( d) /p, and f6 is the azimuthal angle in a coordinate system with z along the camera axes.
[10] KTRACE program, W.Bugg and D.Petersen.
[11) T.M.Knasel, The Total Pair Production Cross-section in Hydrogen and Helium, DESY 70/2, 70/3 (1970).
[ 12) We used 1. 030x1. 392 Jl bl event for 2-~ rong events and 1.03ox1 .552 Jl b/event for greater-than-2-prong events. The factor 1.030, determined from beam count, accounts for the roll that was not used in this analysis but was used in D.Fong et al., Cross Sections and Charged Particle Multiplicities for n--p and K-p Interactions at 147 Gev/c, Nuc.Phys. B102 386 (1976).
[13] Estimates of systematic errors are based on the following:
Contaminatio~ due to mis-classified ambiguous fits --10% for /\ , 2~ for K;. If cross sections are calculated from the 1 O roll sample alone without resorting to 2nd-scan-only weights and re-measurement weights, the results are o-(K~)= 3.6719 ± 0.3305 mb, o-( /\)= 1.7481 ± 0.2280 mb, 0-(A)= 0.33721 ± 0.12460 mb, ()(}')= 134.93 ± 8.46 mb. Comparing to Table 8, the non-uniform weighting schemes will contribute 5-6% unCfil'tainty to the Ks, /\, Y cross sections and 13'.k to the /\ cross section.
Jo- ( )') will over-estimate the 1f 0 cross section by -5%
Clue to production of I) 0, [
0, and other sources of
)'• s.
[14] The charged particle data come from the same batch of film but were previously analyzed. See Ref. [12].
[15] T.Ferbel Gev/c rr (1963).
and H.Taft, Inelastic Interactions of Mesons in Hydrogen, Nuovo Cimento 28
11. 4 1214
r 16] F. Barreiro et al. , Inclusive neutral-strange-particle production in TI""-p interactions at 15 Gev/c, Phys.Rev. Dll 669 (1978).
(17) P.Bosetti et al., Inclusive Strange Particle Production in 'TI"+p interactions at 16 Gev/c, Nuc.Phys. B~ 21 (1975).
101
Notes and References 102
[18] J.Bartke et al., Hyperon and Kaon Production by 16 Gev/c Negative Pions on Protons, Nuovo Cimento 24 876 ( 1962).
[19] P.H.St~ntebeck et al., Inllusive production of K~, A 0 , and /\ in 18. 5-Gev /c TI" p interactions, Phys. Rev. D.2. 608 ( 1974).
J. T. Powers et al. , Compilation of Data for lr ±p Inclusive Reactions at 8 and 18.5 Gev/c, Phys.Rev. D.§. 1947 (1973).
[20] O.Balea et al., Neutral Strange Particle Production in lr-p, n--n, and "Yr-C Interactions at 40 Gev/c, Nuc.Phys. Bl.9. 57 (1974).
[21] H.Blumenfeld et al., Inclusive Neutral Kaon and Lambda Production in 69 Gev /c pp Interactions, Phys. Let. .!!5.B 528 (1973).
H. Blumenfeld et al., Photon Production in 69 Gev /c pp Interactions, Phys.Let. i5_B 525 (1973).
V.V.Ammosov et al., Average Charged Particle Multiplicity and Topological Cross Sections in 50 Gev/c and 69 Gev/c pp Interactions, Phys.Let. 42B 519 (1972).
[22] E.L.Berger et al., Production of K~, /\, and 't in 100 Gev/c ll"-p Interactions, CERN/D.Ph.II/PHYS 74-27 (1974).
E.L.Berger et al., Multiplicity Cross Sections for 100 Gev/c TI"-p Interactions,.CERN/D.Ph.II/PHYS 74-9 (1974).
[23] J.W.Chapman et al., Production of in pp Collisions at 102 Gev/c, (1973).
0 0 . -·· -o 't, /\ . , Ks, and /\
Phys.Let. 47B 465
C.Bromberg et al., Cross Sections and Charged-Particle Multiplicities at 102 and 405 Gev /c, Phys. Rev. Let. .31 1563 (1973).
[24] D.Ljung et al., ,,.-P interactions at 205 Gev/c: Multiplicities of charged and neutral particles; production of neutral particles, Phys.Rev. D15. 3163 (1977).
[25] K.Jaeger et al., Characteristics of v0 and 't production in pp interactions at 205 Gev /c, Phys. Rev. Dll 2405 · (1975).
--
-
-
---' ---
-
-"I"
-
Notes and References 103
[ 26] D. Bogert et al. , Inclusive product ion of neutral strange particles in 250 Gev I c l'!" -p interactions, Phys.Rev. Dl.§. 2098 (1977).
J.Albright, private comm.
[ 27] A. Sheng et al., pp interactions at 300 Gev /c: Y and neutral-strange-particle production, Phys.Rev. D.11 1733 (1975).
A.Firestone et Measurement of the total and 2080 (1974).
al., pp interactions at 300 Gev/c: the charged-particle multiplicity and
elastic cross sections, Phys. Rev. DlQ
[28] v.g.Kenney_ et al., Inclusive Production of TI"'o, .K~, A , and /\ 0 in 36 O Gev /c TI" -p Interactions, pre-pr in"'.
A.Firestone et al., -rr-p interactions at 360 Gev/c: Measurement of the total and elastic cross sections a~d the charged-particle multiplicity distribution, Phys.Rev. D~ 2902 (1976).
[29] P.Stix and T.Ferbel, Charged-particle multiplicities in high-energy collisions, Phys.Rev. Dl.5. 358 (1977).
[30] A = 0.859 ± 0.011 B = 0.0448 ± 0.0028 x2 = 47 for 13 degrees of freedom.
[31] M.Antinucci et al., Mulcitplicities of Charged Particles up to !SR Energies, Nuovo Cimento Letters Q 121 (1973).
[32] Z.Koba, H.B.Nielsen, and P.Olesen, Multiplicity Distributions in High Collisions, Nuc.Phys. B40 317 (1972).
Scaling of Energy Hadron
[33] F.T.Dao and J.Whitmore, Particle Correlations in Phys.Let. i.Q.B 252 (1973).
Study High
of Neutral-Charged Energy Collisions,
[ 34] D. Cohen, Some Remarks Concerning K~ and /\ Production in High Energy Proton-Proton Collisions, Phys.Let. 47B 457 (1973).
[ 35] P. Slattery, Evidence for the Onset of Semi-inclusive Scaling in Proton-Proton Collisions in the 50-300 Gev/c Momentum Range, Phys.Rev.Let. £9. 1624 (1972).
[36]
[3?]
[38]
Notes
Using ~~dz zq ~2(z)
~~dz zq !D3(z)
and eq. 9, we get
A:4B3/r (~)
C=6D3.
= =
and References 104
Ar Cg23) I 4Bq+ 3
er<~> I 6Dq+3
In several experiments, no value or error of the semiinclusive neutral cross section was given for some high multiplicity channels presumably because no events was observed. These points have omitted from the fits. In addition, the 18-prgng point in lr-p 360 Gev/c has been omitted from the Tr fit.
Due to a different definition of inclusive two-particle cross sP.ctions, the K°K0 cross section quoted in ref. [ 26] ( O. 62±0. 2 mb) shBuid be multi plied by two before comparing with Table 11.
-----------------...
-
Tungching Ou
1965 graduated from Brent School, Baguio City, Philippines