RUN 2 - BEAM MONITORING - Eric Adleberger during the initial phases of the experiment is also

BEAM MONITORING

RUN 2 RUN 2

o. o. o. o. o. o. o. o. o. o. o. o. o. o. o. o. o.

o. o. o. o. o. o. o. o. o. o. o. o. o. o. o. o. c.

600-g: o. o. o. ô.o. o. o. o. ô.3.0 2.0 o. c. ô.1.0 1.0· o. o. ô.o. 9.0 •.o •• o 13.0 20.0 ô.o. o. u.o ô.o. o. 3,Q ô.o. o. o. 5.C ô.o. o. o. o. ô.o. o. o. o. ô.o. o. o. o. ô.o. o. o. o. ô.o. o. o. o. ô.o. o. o. c. o. o. o. o. o. o. o. o. o. c. c. G. c. c. c.

700 ^_o.o. _o.o. o. ô.o. _o.o. o. ô.o. o. o. o. ô.o. o. o. o. ô.o. o. o. o. ^9.01.0 o. o. o. ^12.016.0 o. o. 2.0 ^22.c41.c 25.0 o. 5.c 12.0 52.0 35^{•• o}5.0 .o 21.0 •o.o u.o ô.•• o 11.0 n.c 57.0 ôo ^•• 36.0 11.0 ô.o. 1.0 u.o ô.o. o. o. ô.o. o. c. o. ô.o. o. o. o. ô.c. o. c. o. ^c.c. c. ( . c. ~ _~13

eoo-g: · ô.o. o. o. o. ô.o. ô. ô.o. ^c.c. o. ô.o. ô.o. o. ô.o. ô.o. o. ô.o. ô.o. _o. ô.o. ô.o. _o. ô.o. o. o. ô. ^c.o. o. o. ô. c. c. o. ^9,Q1.0 ^46.01.0 o. o. o. ^)6,QJl,C 6.0 2.0 _o. ^21.04:5.0 21.0 5,0 o. 21.c 21.c ^~.c1.c ~.c ^1.c3.C 1.c 6,0 1.c o. o. c. o. c. ^{( .}c. c. c. c. .1.

900-g: o. o. o. o. o. o. o. o. ~. o. o. ô. c. o. ô.c. o. o. o. ô.o. o. o. o. o. o. I ô.ô.o. o. o. o. o. ô.ô.o. o. o. o. o. ô.o. o. o. o. o. ô. ô.o. o. o. o. o. ô.

I

ô.o. o. o. o. o. o. ô.c. o. o. o. o. o. ô.o. o. o. o. o. o. ô.o. o. o. o. o. o.

1

ô.o. o. o. o. o. ô. c. c. c. o. o. ^c.².o o. o. o. o. o. ô.1.0 c. c. c. o. c. o. ô. ^{( .}c. c. ( . c. c. ^c.

1.0 1.2 1.4 k(BeV)

RUN 3

Experimental Event Distribution TABLE I

2 N(k, m, i) - b N (k, m, i) - b N(k, m, i) - b*N*(k, m, i) 2

X = ( ps ps p )

(Jk . _m1

where

b ps + b P + b* = 1

crkmi is the total r. m. s. uncertainty in the numerator.

In addition, since the detection efficiencies at a given k, m, and i are sharply peaked in the center-of-mass production angle e, it is assumed that the events in the interval k, m, i give information on the cross sections only at one value of e, namely e(k, m, i) (see Table VIII).

A. Phase Space Production

The phase space production cross section is independent of the c. m. production angle 8, and is described by

where

w =

=

q =

=

g (^k m) = pq a ps ' . -W o

total c. m. energy

proton momentum in the c. m. system

pion momentum in the dipion c. m. system.

an unknown constant.

The phase space detection efficiency Eps (k, m, i) has been described in Appendix V. , The event distribution expected from phase space production alone is then given by

where

~m = 20 MeV (the m mass interval)

TTiT

N (k, i) = the number of incoming photons in a 50 MeV

interval about k, for experimental run i NH = 4. 64 x 1023

protons/ cm 2 Cps = is a normalization factor •

B. Rho Production

The cross section for p ⁰production by any model can be described by a function

gp (k, m, i) = dc;;m (k, m, ekmi) •

To properly determine the detection efficiency E (k, m, i), one must

first know the decay distribution of the p ⁰ in its rest frame. This e},..1Jeriment was only sensitive to the decay angles 8 d = 90° ± 9° and cpd= 90° ± 17° (e d is the angle between the decay 11+ and the incoming

photon in the p0 rest frame, and cpd is the Trieman-Yang angle(40)).

So if the p0 decay distribution is not changing with energy, the efficiencies E P (k, m, i) and Eps (k, m, i) may differ only by a multi- plicative constant. Furthermore, since the decay distribution does

(12 13) not show an enhancement at ed = 11/ 2 and cpd= 11/ 2 ' , the

efficiencies E (k, m, i) and E (k, m, i) were assumed identical. If

P ps

future experiments find that this is not true, then the p ⁰ cross sections found below must be multiplied by the appropriate constant.

where

The event distribution expected from p 0

production alone is

N (k, m, i) = C H(k, i) E (k, m, i) g (k,. m, i)

p p p p

H(k, i) has been described above for phase space C is a normalization constant. ·

For any of the theoretical models, the cross section is factored into

g (k, m, i) = P (m)

~~

(k, m, ekm.)

p p UH l

where

P (m)

m p

r(m)

ak _m1.

=

the resonant factor

mm r(m)

=

^A ₂ _{2 2}^p ₂ ₂

(m - m ) + m r(m)

. p p

resonant mass of the ⁰

=

3 m

=

¹^o(q/qo) ^.^_e._m

=

central width of the p 0 resonance

=

momentum of the ^TT⁺^{in the}

= the value of q for m = m

0 rest frame

= the c. m. production angle at which the efficiency E (k, m, i) is peaked

= normalization constant such that

JP

^(m)dm⁼^{1 •}

The form for r(m) is given by Jackson(41) using first order perturbation theory. Throughout the fitting procedure, r and m

0 p

will be variable and their values for any particular p ⁰ model will be determined by minimizing the

x

² defined at the beginning of this section.

gives

where

The following models for p ⁰ production will be tried.

1. The unmodified one pion exchange (OPE) model(lS, 19)

g 2

r

2 ... 2

( dcr ) = ( TT NN )( ~) _!__ ( 3 p )( " + m ) 2 _1 _ do 0 PE 4rr m m 2 2k2 t + m 2 m 2 B

TT p Lab

gTTNN is the TT-N coupling constant

r

is the width for the process p ... 1T +

y

P1TY

t is the invariant momentum transfer p is the momentum of the P0 '· in the lab

m (m ) is the proton (pion) mass p TT

m is the dipion mass

e

is the angle of the proton in the lab.

2. The OPE model with a form factor dependence on the pion propagator <24) gives

2 2 ( da ) = ( da ) ( x )

do FF do OPE t + x²

In this case the value of x is to be determined by minimizing

x

²• 3. The Amati-Fubini-Staghellin/22, 24) model for diffr.action production gives

where

p(E) is the momentum. (energy) of the p ⁰

e

is the p 0 production angle

( da) do TTil

gwrry and g prrw are the wrry and pnw vertex coupling constants (

~

)rrN is the differential cross section for the reaction

rr+p-+n+p .

The diffraction model, however, is of dubious applicability in this energy region for several reasons. First, the reaction rr + p ~ rr + p is not dominated by diffraction at the low energies considered here.

Second, the formula above is an approximation valid only for '

e

^~^O.

Third, the phase space available for p ⁰ production is changing

significantly over the energy interval 850 < k < 1500 MeV and the above formula is a higher energy approximation. Nevertheless, the . diffraction model will be tried as a matter of interest. The form of the n-p cross section is

The energy variation of (

~~

) is small in the relevant energy region and was thus considered constant. The momentum transfer

dependence, t

0, is then a variable to be determined by the usual

x

minimization.

Since the formula for (

~~

) diff is a higher energy. approximation, two methods for simulating the p0 threshold effects were tried. First, (

~~

) diff was simply multiplied by the density of final states. Second, (do/ ctn) diff was multiplied by the phenomenological threshold factor

f(k) =

V

^{k -}

~(m)

^{- • 013}

Mev-

1 (k-.~(m))

which was the form of f(k) given by the phenomenological model below. This second method gave a slightly better

x

²fit than the first, so in the discussion below, the "diffraction model" refers to the second method for representing the threshold effects.

4. Finally, the event distribution can be fit with a purely phenomenological cross section

da 2 3 do = f(k)[l + a.

2(1- cose) + a.

3(1- cose) + a.

4(1- cose)

J

where a.

2, a.

3, and a.

4 are parameters to be optimized. Several forms for f(k) were tried. The form which gave the best fit was

where k.r(m) is the threshold energy for producing a dipion with mass m.

The presence of the a.

4 term in

~~

improves the

x

negligibly and changes the parameters b, b , m, and

r

by only

ps o

a small fraction of their errors. This is evidence that a higher order polynomial in cos e would not significantly improve the

cm final fit.

C. N* Production

Since N* production produced so few events in this experi-

ment, we could not reasonably expect to determine any of the parameters for N* production better than has been done already. For the initial fits, the energy and angular dependence of the N* cross section was taken from Tables IV and V of Michael Hauser:'sthesis, and the absolute value of the cross section was treated as variable. The expected

contribution from the N* should have been

=

^{10. 2%.}

Since most fits gave b* ~ 8% :I: 2%, the event distribution for N*

production was then considered constant at b* == 10. 2% in all future fits.

The event distribution expected from N* production was determined as follows. Since both the energy and angular dependence of the cross section and the shape of the N* mass distribution are known, we have

where

N*(k, m, i) == [H(k, i)/4rr] g*(k, m, i)

~ (k,m,i) == cr*(k)

J

E*(k,m,i,m*) P*(m*) dm*

1080

a*

(k) is the total cross section for N* production

m* m r(m*) p * (m*) == A 2 2 o 2 2 2

(m* - m ) + m

r

(m*)

0 0

== 1238 MeV

r(m*) ⁼ ro(q/qo)3 p(m*) p(mo)

r

0 = 123 MeV

q(q ) is the momentum of the decay pion in the N* c. m.

system for an N* mass of m'* (m )

2 2 (m* + m ) - m

p(m*)

=

^p ^TT

m*2

A is a normalization constant such that

J

P(m*) dm* = 1 1080

E* (k, m, i, m*) is discussed below

m2 is the upper limit on the N* mass which can be produced by photon energy k .

The efficiency E* (k, m, i, m*) is the efficiency for detecting an N* event produced with isobar mass m*, dipion mass m, and photon energy k, for experimental run i. The N* detection efficiency program (see Appendix V. D) only determined the efficiency

E(k, i, m*), where

E(k, i, m*) =

J

E*(k, m, i, m*) dm.

Thus, E* (k, m, i, m*) is simply a decomposition of E (k, i, m*) into its dipion mass spectrum. The factor g*(k, m, i) then represents the number of N* events expected in the interval k, m, i per target proton and per incident photon.

The final event distribution N* (k, m, i) obtained with b*

=

10. 2%

is shown in Table II.

o. -o.

o. 2.)7 0.69 o. o. o. o. o. o. o. o. o. c. o. o. o. -o.

o. o. o.•1 o. 21 o. o. o. o. o. o. o. o. o. o. o. o. -o.

600 ^_ô.o. o. o. o. o. o. ô.o. o. o. o. o. o. ^1.11 c. ^{.... 61}1.11 c. o. ^0.690.59 o. 3.07 2 •• o ô.^0.46z. 2. 1.02 85 7• ô.c. o. 50 2. 72 3.3" ô.o. o. 0.21 1. 5e ô.o. o. o. 0.5. ô.o. o. o. 0.06 ô.o. o. o. c. ô.c. c. c. c. ô.c. c. c. c. ô.o. o. o. o. ô.o. o. o. o. ô.o. c. cc. . ^-o.-o. --o. -o. c.

100- g: ô._o. ô._o. _c.ô. ô._o. ô._c. _c.^1.2•₀₁ ^4.CC_1.H ^{1. 72}_{3. 52} ^C_1.21^.2⁶ ^{c .c5}_c.2c ^c._c. ^c._c. ô._o. ô._o. ^c._c. ^-o._-_c.

o. o. o. o. o. o. o. 0.21 1.15 2.31 1.12 C. l l c.02 o. o. c. -o. s

o. o. o. c. o. o. c. o. 0.25 1.01 1.~. I. IC c. 14 o. o. 0. -o. _::I.

o. o. o. c. o. o. o. o. o. ^{(j . 4 ]} l.H 1.5< C.61 o.ce o.co c. -c. _::I.

800-~: ô._o. ô._o. ^c._c_•_. ^c._o. ô._o. ^c._c. ô._o. ô._o. ^0.06_o. ^c.t2_c.c. _c.^1.41_5' ^C.96_C.96 ^0.11 ô.c2 ^c^.oo ^-o.

0 · ' ' o.o• 0 .co -o. .l.

o. o. o. o. o. o. o. c. o. o. o. o. c. o. o. o. o. o. o. o. c. o. c.co c. C.69 c.u o.,. ^0.3] c.o.u ct c .co -o. c.co -o.

o. o. o. o. o. o. c. c. o. o. o. o. c. o.o. o.o• c.co -o.

900-g: -o. -o. -o. -o. -o. -o. -o. -o. -o. -o. ô._o. -o. -o. -o. -o. -o. ô._o. -c. -o. --o. -o. ô._c.c. -o. -o. -o. -o. -o. ô._o. -o. --o. -o. -o. ô._o.o. -o. -o. -o. -o-o. ô._o.. -o--o. -o. -o. ô.o. _o.. -o. -o. -o. -o. -o. ô._o. -o. -o. -o. -o. -o. ô._o. -c. -o. -o. -o. -c. ^c._c. -c. --c. -c. -o. ^c._c.c. -c. -c. --c. -c. ^c._c.c. -o. -o. -o-o. -o. ô._o.. -o. -o. -o. --o. ^0.01_o.ooo. -o. -o. -c. -c, -o. ^{c .co}c .co -c. ^-o.o. o. o. o. o.

RUN 1

2.11 o. o. o. o. o. o. o. o. o. o. o. o. o. o. o. -o.

2 •• , 3. l4 o. o. o. o. o. o. o. o. o. o. o. o. o. o. -o.

o. •·2' ^1.99 ô. ô. ô. ô. ô. ô. ô. ô. ô. ô. o. o. o. -o.

600 ô.o. o. o. o. ô.o. o. o. o. ^{•• 2.}o.Jo. o. o. ~ ^3.22a.c. 3.c. 01 22 ^0.102 .za •·2• l .06 o ... ô.o.o.

··"

l .'l't 6.19 ô.o. o.oq 1.35 ^'·⁵⁰ ô.o. o. o.c1 ^1.11 ô.o. o. o. ^0.10 ô.o. o. o. ô. ô.o. o. o. ^c. ô.o. o. c. ^c. ô.o. o. c. ^c. ô.o. o. o. ô. ô.o. o. o. ô. o. o. o. c. ^c. -o. -o. -o. -^-o.o.

700 - ô.o. _o. ô.o. _o. ô.o. _o. c. _o.^c. ô.o. _o. o. _o.^{o. 22} _c.'1.05 · 59 ^{4. 64}⁶_1.12^.14

•·37

1. 28 _{5. 22} 0.2. ô.ao_3.₇₀ c. ô.11t_c.ec c. ô._c.10 c. ^c._c. o. ô._o. o. ô._o. c. ^c._c. -o. ^-_-o.ô. _s

o. o. o. c. o. o. o. c.01 2.35 •• 01 2.n c.11 c.1• o. o. c. -c. ::I.

o. o. o. c. o. o. c. o. o.37 2.13 1.1. 2.•0 c • ., o.c1 o. c. -o. ::I.

800 - o . ô.o. o. o. ô.o. o. o. o. ô.o. o. o. o. ^c.c. o. o. o. o. ô.o. o. o. ô.o. o. o. o. ô.o. c. o. o. ô.o. o. o. o. ô.o. o. o. o. ^0.9lo. o. o. o. ^2ol9c.c. o. o. 11 o.u c. ^2.35'c.11 .29 c.29 ^1.•1c.10 1.34 1.0. Ô.H0 .t5 o.B 0.12 o.t4 ^0.01o.c1 o.C6 0.11 ColC ô.c c.co -o. c .co -o. c .co -o. .co ^--c. ô. .l.

900 - o . -o. -o-o. -o. -o. ô.. -o. -o. -o. -o. -o. ô.o. -o. -o. -o. -o. -o. ô.o. --o. -o. -c. -o. ^c.c. o. -o. -o. -o. -o. -o. ô.o. -o. -o. -o. -o. -o. ô.o. -o. -o. -o. --o. ô.o. o. -o. -o. -o. -o. -o. ô.o. -o. -o. -o. -o. -o. ô.o. -o. -o. -o. -o. -o. ô.c. -o. -o. -o. -o. -o. ô.c. -c. --c. --o. ^c.c. c. o. --c. -c. -c. -c. ^c.c. c. -o. -o. -o. -o. -o. ^0.2Co. -o. -o. -o. --o. ô.o.o. o. ôe -o. -o. -o. -c. -o. c.co -o. ^c.cc ^-o. c. o. ô.o. o.

RUN 2

0.37 o. o. o. o. o. o. o. o. o. o. . o. o. o. o. o. -o.

o.n 0.26 o. o. o. o. o. o. o. o. o. o. . o. o. o. o. -o.

o. 3,15 o.69 o. o. o. o. o. o. o. o. o. o. o. o. o. -o.

600 - ⁰o. o. o. o. • o. o. o. o. o. ^3.971.56 o. o. o. o ..50 2.47 o. o. • ., o. 0.21 ..59 ....,1 1.01 o. o. o. 1• 3. 2. 79 79 o. o. o. 0.'7 1.•I o. o. o. o. 0.51 o. o. o. o. 0.03 o. o. o. o. o. o. o. o. o. o. o. o. o. c. c. c. o. o. c. c. o. o. o. o. o. o. o. o. o. o. o. o. o. o. o. -o. --o. -o. -o. o.

700 - ô.o. o. _o. ô.o. o. _o. ô.o. o. _o. ô.c. o. _o. ô.o. o. _o. o. o. ^1.56 o. ^3.H1.19 ^l.863.21 2.ZJ ô.•92.c1 3.07 ^0.04o. 22 1.51 ô.c.c1 c:. ]~ ô.c. c .o. ^c.c. c. ô.o. o. ô.o. o. ^c.c. c. -c. -c. -c. s

o. o. o.u 2ol7 2.35 1.0 c. 30 ^c.01 o. o. c. -c. ^::I.

o. o. o. o. o. o. o. o. o.o 2 .a 7 .z.31 c. 76 c.11 o .c 1 o. c. -o. ^::I.

800 ^_ â. ô. ô. ô. â. ô. ô. ô. â. ^1.21 ^{2. zc} ^l.6l ^c.⁵⁴ ô.^c~ ⁰^.co ^c. -c.

o. o. a. c. o. o. o. o. o. c .o• ^c^.t~ 1.,. 1.35 ^0.^2~ 0.01 c.co -c. .l.

o. o. o. o. o. o. o. o. o. o. 0.11 C.93 C,90 0. ,. o.c. c.co -c.

o. o. o. c. o. o. o. o. o. o. o. c.1• c.11 o. 52 o.et c .co -o.

o. o. o. o. o. o. o. o. o. o. c. c. c.12 0 .41 O.tl. c .cc -c.

900 - o . -o. -o. -o. -o. -o. ô. -o. --o. -o. -o. ô.o. o. -o. -o. -o. -o. -o. o. ô. -o. -o. -o. -c. -o. ô.c. I -o. -o. -o. -o. ^-o.ô.o. -o. -o. -o. -o. ^-o.ô.o. --o-c. -o. ^-o.ô.o. o. . -o. -^-o.-o. -o. o. ô.o. I -o-o. -o. -o. ^-o.ô.o. . -o. -^-o.-c. -o. ô.o. o. -c. -c. -c. -o. ^-o.ô.o. ^' -c. -c. -c. -o. ^-a.^c.c.

I

-c. -c-c. -c. ^-c.^c.c. . -o. -o. -o. -^-o^0.2)o.u o. ^. -o. -o. -o-o. ^-o.^o.uo.oJ . -o. -c. -c. -c. ^-o.^c.coc .co -^-c.o. o. o. o. c. ^o.

1.0 1.2 1.4 k(BeV)

Dalam dokumen Eric Adleberger during the initial phases of the experiment is also appreciated (Halaman 37-48)