# QCD Rescattering and High Energy Two-Body Photodisintegration of the Deuteron Page: 3 of 4

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where e and ed are the electric charges of a and d quarks.

The factor f(2/s) accounts for the difference between the

hard propagators in our process and those occurring in

wide angle pn scattering. Within the Feynman mech-

anism, the interacting quark carries the whole momen-

tum of the nucleon (x1 -> 1), thus f(2/s) 1. Within

the minimal Fock state approximation, the evaluation of

the exact form of f(2/s) requires calculating the sum of

~ 106 Feynman diagrams in which five hard-gluon ex-

changes are distributed between six quark lines. Here

we use a qualitative evaluation of f(l2/s). The condi-

tions a, ~ , 0 < xi < 1 according to Eq.(2) require

ki ~ "1(15 1x ~ s'. Thus the dominant contribu-

tion in Eq. (4) is given by diagrams in which the struck

quark exchanges a hard-gluon with other quarks prior to

the interaction with the photon (initial state short range

qq-correlations). For these diagrams, the interchange of

quarks between nucleons in both 1dpn and pn ampli-

tudes is characterized by the same virtuality in the prop-

agator of gluon exchange between nucleons, estimated at

,m 90 to be ~ (pt/3)2. All other propagators that

define the short range part of the nucleon wave functions

are the same. The other QIM diagrams with final state

qq correlations only (which are suppressed in ydpn am-

plitude) enter in the pn amplitude with larger virtuality

for exchanged gluon between nucleons ~ pt and will be

numerically small compared to the diagrams with initial

state correlations. Thus no additional combinatorial fac-

tors enter in the hard scattering mechanism. Since the

additional factor entering from the electromagnetic ver-

tices is ~ 1, f(l2/s) is a function of the order of unity

at 90g. In the further analysis presented here we will use

the approximation: f(P2/s) 1.

The amplitude (4) depends on only small relative mo-

menta of the target nucleons, therefore we should use a

standard non-relativistic (NR) wave function; according

to [14]: t(a,pl) (27) 2dR(pzpL) /mN. We com-

pute the differential cross section averaging IT12 over the

spins of initial photon and deuteron and summing over

the spins of the final nucleons. One obtainsdo,- d-pn

dta 73

- 9s3 X1 1 - 2

167r (s - d Ma)2J mNf(-)A (s, i ) d (pz =, p_) .2pi (5)

Agn M represents a sum of all leading-quark interchange

diagrams with rather general structure of spectator

quark-gluons system. Thus AQM absorbs nonperturba-

tive (noncalculable) part of our calculation. To proceed

we observe that the quark interchange topologies shown

to be the dominant contribution for fixed ,em 900

high momentum transfer (non strange) baryon-baryon

and meson-baryon scattering [18]. Thus in the region

of ,em 90 we replace AQIN by the experimental data

- Axp. In this replacement we neglect the contribution

of a channel (backward) rescattering, since it is a nu-merically small contribution to the pn amplitude, and is

additionally suppressed due to the presence of the elec-

tromagnetic vertex of y - neutron scattering. We also

observe that the integrand in Eq. (5) is dominated by

small values of pl PAL, PBL. Thus we evaluate AQnM

at tN (PB - Pd/)2 by pulling this term out of the

integral and expressing it through the differential cross

section of pn -> pn scattering- d-do,,d-Pn 4a 4 1 tN doupnp(s, tN)

dt 9 s' - ( s ) dt

J2 2

X pd (pz = 0, pL N (2)(6)

Eq. (6) shows that the dLd depends on the soft com-

ponent of the deuteron wave function, the measured high

momentum transfer pn -> pn cross section, the scaling

factor C(4) f2(tN/s) ~ 1 at ,m ~ 90 (and slowly

varying as a function of 0,m) and the additional factor

coming from the y - q interaction. Note that, Eq. (6) is

qualitatively different from the Glauber approximation.

The latter is applicable only when intermediate nucleons

are near on-mass shell. On the contrary Eq. (6) is derived

when the mass2 of the intermediate state is (~ s m h).

Our approach is close to that of Ref. [19] in which a nu-

clear amplitude is expressed as a product of a reduced

nuclear amplitude and nucleon form-factors. Here the

nuclear amplitude is expressed in terms of the pn hard

scattering amplitude, and this allows us to calculate the

absolute value of the cross section. Note that the pn

cross section scales as s--". This causes Eq.(6) to yield

the same asymptotic s-11 energy dependence (at fixed

t/s) as provided by the quark counting rules.

In the numerical calculations we take C(t) -1. Our

calculations are implemented using the Paris potential

model of XYR [20] (but any realistic wave function would

give the same result) and the experimental data from

[21,22] for doL . The pn -> pn data are not mea-

sured at the tN needed to evaluate Eq. (6), so an ex-

trapolation is necessary. We determine an upper and

lower limit for dPdt P at tN using the existing pn data

at ma such that -tgN < -tN < --tax. Then

Eq.(6) is computed using both the data at t74n and at

ax, so that the calculation will produce a band. Fig-

ure 2 shows that calculations are in agreement with the

measured differential cross sections. Moreover the agree-

ment improves for larger ,em which confirms our expec-

tation that C(tN/s) 1 at ,em 90g. The agreement

with the data verifies our underlying hypothesis that the

size of the photoproduction reaction is determined by

the physics of high-momentum transfer contained in the

hard scattering NN amplitude. The short-distance as-

pects of the deuteron wave function are not important.

This hypothesis, if confirmed by additional studies, may

suggest the existence of new type of quark-hadron "du-

ality", where the sum of the "infinite" number of quark

interactions could be replaced by the hard amplitude of3

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Frankfurt, Leonid L.; Miller, Gerald A.; Sargsian, Misak M. & Strikman, Mark I. QCD Rescattering and High Energy Two-Body Photodisintegration of the Deuteron, article, January 1, 2000; Newport News, Virginia. (digital.library.unt.edu/ark:/67531/metadc741859/m1/3/: accessed December 18, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.