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Initial revision

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1378 4222 310 4 v 1471 4299 a Fm(@)5 b(X)1720 4242 y
Fn(=)23 b(\(1)18 b(+)g(tan)2103 4207 y Fh(2)2154 4242
y Fm(\036)2203 4207 y Fl(\003)2203 4262 y Fk(q)r(\031)2281
4242 y Fn(\))2323 4177 y Fm(@)5 b(\036)2421 4147 y Fl(\003)2421
4198 y Fk(q)r(\031)p 2323 4222 176 4 v 2349 4299 a Fm(@)g(X)2509
4242 y(;)1070 b Fn(\(15\))150 4412 y(giv)n(es,)1413 4635
y Fm(@)5 b(\036)1511 4605 y Fl(\003)1511 4655 y Fk(q)r(\031)p
1413 4680 V 1439 4756 a Fm(@)g(X)1681 4699 y Fn(=)1839
4635 y Fm(p)1881 4605 y Fl(\003)1915 4580 y Ff(0)1881
4655 y Fk(x)1951 4584 y(@)t(p)2024 4559 y Ff(\003)2055
4543 y(0)2024 4601 y Fd(y)p 1951 4616 131 4 v 1967 4663
a Fk(@)t(X)2110 4635 y Fj(\000)18 b Fm(p)2235 4605 y
Fl(\003)2269 4580 y Ff(0)2235 4655 y Fk(y)2305 4593 y(@)t(p)2378
4567 y Ff(\003)2409 4551 y(0)2378 4609 y Fd(x)p 2305
4616 V 2322 4663 a Fk(@)t(X)p 1839 4680 607 4 v 1887
4756 a Fn(\()p Fm(p)1961 4732 y Fl(\003)1995 4715 y Ff(0)1961
4777 y Fk(x)2022 4756 y Fn(\))2054 4732 y Fh(2)2110 4756
y Fn(+)g(\()p Fm(p)2267 4732 y Fl(\003)2301 4715 y Ff(0)2267
4777 y Fk(y)2328 4756 y Fn(\))2360 4732 y Fh(2)2474 4699
y Fm(;)1105 b Fn(\(16\))150 4937 y(where)27 b Fm(X)34
b Fn(is)26 b(either)h(cos)13 b Fm(\022)976 4949 y Fk(q)r(\031)1081
4937 y Fn(or)26 b Fm(\036)1231 4949 y Fk(q)r(\031)1309
4937 y Fn(.)37 b(So,)28 b(the)g(deriv)-5 b(ativ)n(e)24
b(of)k Fm(\036)2175 4907 y Fl(\003)2175 4957 y Fk(q)r(\031)2280
4937 y Fn(with)f(resp)r(ect)h(to)f(some)f(lab)g(v)-5
b(ariable)25 b(can)i(b)r(e)150 5055 y(done)e(using)g(the)h(ab)r(o)n(v)n
(e)e(form)n(ula,)f(with)j(the)g(expressions)d(for)i(the)h
Fm(p)2330 5025 y Fl(\003)2364 5000 y Ff(0)2330 5076 y
Fk(n)2416 5055 y Fn(deriv)n(ed)e(ab)r(o)n(v)n(e)g(and)i(assuming)d
(that)j(the)150 5155 y Fm(R)213 5167 y Fk(nn)329 5155
y Fn(and)j Fm(\014)539 5167 y Fk(n)614 5155 y Fn(do)g(not)h(dep)r(end)g
(on)g(the)g(pion)e(angles)g(\(whic)n(h)g(they)i(should)f(not)g(b)r
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(initial)f(quan)n(tities\).)42 b(The)30 b(expression)d(for)j(the)g
(deriv)-5 b(ativ)n(e)27 b(of)j Fm(\036)2845 5224 y Fl(\003)2845
5275 y Fk(q)r(\031)2953 5254 y Fn(in)n(v)n(olv)n(es)c(deriv)-5
b(ativ)n(es)27 b(of)150 5354 y(the)i(comp)r(onen)n(ts)d(of)j(the)f
(rotated,)g(cen)n(ter)g(of)g(mass)e(pion)h(momen)n(tum.)37
b(These)28 b(deriv)-5 b(ativ)n(es)25 b(are)i(cum)n(b)r(ersome)1561
5656 y(6)p eop
%%Page: 7 7
7 6 bop 150 390 a Fn(and)28 b(will)e(not)i(all)e(b)r(e)j(giv)n(en)d
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b(the)j(deriv)-5 b(ativ)n(e)25 b(of)j(the)h(y-comp)r(onen)n(t)150
490 y(of)f(the)g(b)r(o)r(osted,)f(rotated)g(pion)f(momen)n(tum)f(with)i
(resp)r(ect)h(to)f(lab)g Fm(\036)2394 502 y Fk(q)r(\031)2472
490 y Fn(,)1204 683 y Fm(@)5 b(p)1295 653 y Fl(\003)1329
628 y Ff(0)1295 704 y Fk(y)p 1192 728 176 4 v 1192 804
a Fm(@)g(\036)1290 816 y Fk(q)r(\031)1401 747 y Fn(=)23
b Fm(R)1552 759 y Fk(y)r(x)1661 691 y Fm(@)5 b(p)1752
661 y Fl(\003)1752 712 y Fk(x)p 1639 728 V 1639 804 a
Fm(@)g(\036)1737 816 y Fk(q)r(\031)1843 747 y Fn(+)18
b Fm(R)1989 759 y Fk(y)r(y)2098 683 y Fm(@)5 b(p)2189
653 y Fl(\003)2189 704 y Fk(y)p 2075 728 V 2075 804 a
Fm(@)g(\036)2173 816 y Fk(q)r(\031)2279 747 y Fn(+)18
b Fm(R)2425 759 y Fk(y)r(z)2533 691 y Fm(@)5 b(p)2624
661 y Fl(\003)2624 712 y Fk(z)p 2509 728 V 2509 804 a
Fm(@)g(\036)2607 816 y Fk(q)r(\031)2695 747 y Fm(:)884
b Fn(\(17\))150 977 y(The)28 b(partial)c(deriv)-5 b(ativ)n(es)25
b(of)i(the)h(unrotated,)g(b)r(o)r(osted)f(comp)r(onen)n(ts)f(are)h(giv)
n(en)f(b)n(y)-7 b(,)637 1142 y Fm(@)5 b(p)728 1112 y
Fl(\003)728 1163 y Fk(x)p 615 1179 V 615 1255 a Fm(@)g(\036)713
1267 y Fk(q)r(\031)884 1198 y Fn(=)82 b Fj(\000)p Fm(p)14
b Fn(sin)e Fm(\022)1306 1210 y Fk(q)r(\031)1398 1198
y Fn(sin)h Fm(\036)1563 1210 y Fk(q)r(\031)1659 1198
y Fn(+)18 b Fm(p)1794 1142 y(\015)23 b Fj(\000)18 b Fn(1)p
1794 1179 191 4 v 1845 1255 a Fm(\014)1896 1231 y Fh(2)1994
1198 y Fm(\014)2041 1210 y Fk(x)2097 1198 y Fn(sin)13
b Fm(\022)2252 1210 y Fk(q)r(\031)2329 1198 y Fn(\()p
Fm(\014)2408 1210 y Fk(y)2462 1198 y Fn(cos)g Fm(\036)2636
1210 y Fk(q)r(\031)2733 1198 y Fj(\000)18 b Fm(\014)2863
1210 y Fk(x)2918 1198 y Fn(sin)13 b Fm(\036)3083 1210
y Fk(q)r(\031)3161 1198 y Fn(\))19 b(+)1031 1316 y Fi(\022)1102
1376 y Fm(p)1144 1346 y Fl(\003)1144 1397 y Fk(x)1205
1376 y Fn(+)f Fm(\015)5 b(\014)1383 1388 y Fk(x)1424
1376 y Fm(E)p 1102 1414 388 4 v 1275 1490 a(p)1518 1433
y Fj(\000)18 b Fm(\015)5 b(\014)1696 1445 y Fk(x)1760
1376 y Fm(p)p 1748 1414 67 4 v 1748 1490 a(E)1824 1316
y Fi(\023)1951 1376 y Fm(@)g(p)p 1909 1414 176 4 v 1909
1490 a(@)g(\036)2007 1502 y Fk(q)r(\031)2113 1433 y Fm(;)1466
b Fn(\(18\))638 1604 y Fm(@)5 b(p)729 1574 y Fl(\003)729
1625 y Fk(y)p 615 1649 V 615 1725 a Fm(@)g(\036)713 1737
y Fk(q)r(\031)884 1668 y Fn(=)82 b Fm(p)14 b Fn(sin)f
Fm(\022)1242 1680 y Fk(q)r(\031)1333 1668 y Fn(cos)g
Fm(\036)1507 1680 y Fk(q)r(\031)1604 1668 y Fn(+)18 b
Fm(p)1739 1612 y(\015)k Fj(\000)c Fn(1)p 1739 1649 191
4 v 1789 1725 a Fm(\014)1840 1701 y Fh(2)1939 1668 y
Fm(\014)1986 1680 y Fk(y)2040 1668 y Fn(sin)12 b Fm(\022)2194
1680 y Fk(q)r(\031)2272 1668 y Fn(\()p Fm(\014)2351 1680
y Fk(y)2405 1668 y Fn(cos)h Fm(\036)2579 1680 y Fk(q)r(\031)2675
1668 y Fj(\000)18 b Fm(\014)2805 1680 y Fk(x)2861 1668
y Fn(sin)13 b Fm(\036)3026 1680 y Fk(q)r(\031)3104 1668
y Fn(\))19 b(+)1031 1787 y Fi(\022)1102 1840 y Fm(p)1144
1810 y Fl(\003)1144 1860 y Fk(y)1203 1840 y Fn(+)f Fm(\015)5
b(\014)1381 1852 y Fk(y)1420 1840 y Fm(E)p 1102 1885
384 4 v 1273 1961 a(p)1515 1904 y Fj(\000)18 b Fm(\015)5
b(\014)1693 1916 y Fk(y)1754 1848 y Fm(p)p 1742 1885
67 4 v 1742 1961 a(E)1818 1787 y Fi(\023)1946 1848 y
Fm(@)g(p)p 1903 1885 176 4 v 1903 1961 a(@)g(\036)2001
1973 y Fk(q)r(\031)2107 1904 y Fm(;)1472 b Fn(\(19\))639
2076 y Fm(@)5 b(p)730 2046 y Fl(\003)730 2096 y Fk(z)p
615 2113 V 615 2189 a Fm(@)g(\036)713 2201 y Fk(q)r(\031)884
2132 y Fn(=)82 b Fm(p)1083 2076 y(\015)23 b Fj(\000)18
b Fn(1)p 1083 2113 191 4 v 1134 2189 a Fm(\014)1185 2165
y Fh(2)1284 2132 y Fm(\014)1331 2144 y Fk(z)1383 2132
y Fn(sin)12 b Fm(\022)1537 2144 y Fk(q)r(\031)1615 2132
y Fn(\()p Fm(\014)1694 2144 y Fk(y)1748 2132 y Fn(cos)h
Fm(\036)1922 2144 y Fk(q)r(\031)2019 2132 y Fj(\000)18
b Fm(\014)2149 2144 y Fk(x)2204 2132 y Fn(sin)13 b Fm(\036)2369
2144 y Fk(q)r(\031)2447 2132 y Fn(\))19 b(+)1031 2249
y Fi(\022)1102 2310 y Fm(p)1144 2280 y Fl(\003)1144 2331
y Fk(z)1201 2310 y Fn(+)f Fm(\015)5 b(\014)1379 2322
y Fk(x)1420 2310 y Fm(E)p 1102 2347 384 4 v 1274 2423
a(p)1515 2366 y Fj(\000)18 b Fm(\015)5 b(\014)1693 2378
y Fk(z)1753 2310 y Fm(p)p 1741 2347 67 4 v 1741 2423
a(E)1817 2249 y Fi(\023)1944 2310 y Fm(@)g(p)p 1902 2347
176 4 v 1902 2423 a(@)g(\036)2000 2435 y Fk(q)r(\031)2106
2366 y Fm(:)1473 b Fn(\(20\))275 2596 y(Although)19 b(the)j(algebra)17
b(in)n(v)n(olv)n(ed)h(in)i(the)h(cen)n(ter)f(of)h(mass)e(to)h(lab)g
(transformation)d(is)j(tedious,)h(it)f(is)g(straigh)n(t-)150
2695 y(forw)n(ard.)35 b(The)28 b(ab)r(o)n(v)n(e)e(form)n(ulation)d(w)n
(as)j(c)n(hec)n(k)n(ed)h(to)g(mak)n(e)e(sure)i(that)h(it)f(reduced)g
(to)g(the)h(simpler)c(\\collinear)150 2795 y(b)r(o)r(ost")j(case.)36
b(An)28 b(alternativ)n(e,)c(more)i(elegan)n(t)g(form)n(ulation)e(can)j
(b)r(e)h(found)g(in)f(Ref.)37 b([6)o(].)150 3070 y Fo(References)192
3251 y Fn([1])k(H.)28 b(Meier-Ha)5 b(jduk)25 b Fa(et)30
b(al.)p Fn(,)f(Nucl.)e(Ph)n(ys.)f Fc(A395)p Fn(,)h(332)g(\(1983\).)192
3418 y([2])41 b(E.)27 b(Jans)g Fa(et)i(al.)p Fn(,)g(Nucl.)e(Ph)n(ys.)g
Fc(A475)p Fn(,)g(687)f(\(1987\).)192 3584 y([3])41 b(P)-7
b(.)34 b(Brauel)f Fa(et)j(al.)p Fn(,)i(\\Electropro)r(duction)31
b(Of)k(Pi+)e(N,)i(Pi-)e(P)h(And)i(K+)e(Lam)n(b)r(da,)321
3683 y(K+)d(Sigma0)e(Final)h(States)i(Ab)r(o)n(v)n(e)f(The)h(Resonance)
f(Region,")e(Zeit.)j(Ph)n(ys.)f Fc(C3)p Fn(,)321 3783
y(101)26 b(\(1979\).)192 3949 y([4])41 b(D.)29 b(Drec)n(hsel,)f(O.)g
(Hanstein,)h(S.S.)g(Kamalo)n(v)c(and)j(L.)h(Tiator,)f(\\A)g(Unitary)g
(isobar)321 4049 y(mo)r(del)22 b(for)h(pion)g(photopro)r(duction)f(and)
h(electropro)r(duction)e(on)i(the)h(proton)f(up)h(to)321
4148 y(1-GeV,")i(Nucl.)h(Ph)n(ys.)g Fc(A645)p Fn(,)g(145)f(\(1999\))h
(n)n(ucl-th/9807001.)192 4314 y([5])41 b(G.)28 b(v)n(on)e(Gehlen,)h
(Nucl.)g(Ph)n(ys.)g Fc(B20)p Fn(,)g(102)f(\(1970\).)192
4480 y([6])41 b(X.)28 b(Li,)e(L.)i(E.)f(W)-7 b(righ)n(t,)27
b(and)g(C.)h(Benhold,)e(Ph)n(ys.)h(Rev.)g Fc(C45)p Fn(,)g(2011)f
(\(1992\).)1561 5656 y(7)p eop
%%Trailer
end
userdict /end-hook known{end-hook}if
%%EOF