% the conference proceeding contribution of Torbjorn Sjostrand to 
% Photon' 95, Sheffield, U.K., 8-13 April 1995

% This file is written with LaTeX2e conventions; where the contents within
% \begin{filecontents} and \end{filecontents} are written to files with
% the indicated names. This means that LaTeX2e/dvips will automatically 
% include the eps figures in the final postscript output.

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00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16
neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D
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EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0
0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7D7 BB BB 7D 7D FE FE 7D
7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16
0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE
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DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16
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FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF >} image } if PT 18 eq {
16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EEFF FF BB BB DD DD EE EE
FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq
{ 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6
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BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image }
if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0
E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > }
image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ]{ < 70 70 F7 F7 F7 F7 F7
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} image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16] { < AA AA 55 55 A9 A9
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54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def
gsave Xcurr Ycurr translate PT DP gr } for } for gr } def
/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
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/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
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/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
/Times-Roman /Times-Roman accvec ReEncode
/Times-Italic /Times-Italic accvec ReEncode
/Times-Bold /Times-Bold accvec ReEncode
/Times-BoldItalic /Times-BoldItalic accvec ReEncode
/Helvetica /Helvetica accvec ReEncode
/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
/Helvetica-Bold /Helvetica-Bold accvec ReEncode
/Helvetica-BoldOblique /Helvetica-BoldOblique  accvec ReEncode
/Courier /Courier accvec ReEncode
/Courier-Oblique /Courier-Oblique accvec ReEncode
/Courier-Bold /Courier-Bold accvec ReEncode
/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
/oshow {gsave [] 0 sd true charpath stroke gr} def
/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
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/stwb { /fs exch def /fn exch def /nbas exch def /textf exch def
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fn findfont fs sf textf dup length nbas sub nbas getinterval sw
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/accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal
69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral
74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright
79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus
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 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset
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 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown
 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
/Symbol /Special accspe ReEncode
gsave .25 .25 scale 
%%EndProlog
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\begin{filecontents}{lutp95143.epspm}
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%%BoundingBox: 0 0 397 241
%%Title: /usr/users/torbjorn/text/gaga/lutp95143.epspm
%%Creator: HIGZ Version 1.22/07
%%CreationDate: 95/05/24   09.52
%%EndComments
80 dict begin
/s {stroke} def /l {lineto} def /m {moveto} def /t {translate} def
/sw {stringwidth} def /r {rotate} def /rl {roll}  def /R {repeat} def
/d {rlineto} def /rm {rmoveto} def /gr {grestore} def /f {eofill} def
/c {setrgbcolor} def /lw {setlinewidth} def /sd {setdash} def
/cl {closepath} def /sf {scalefont setfont} def /black {0 setgray} def
/box {m dup 0 exch d exch 0 d 0 exch neg d cl} def
/NC{systemdict begin initclip end}def/C{NC box clip newpath}def
/bl {box s} def /bf {box f} def /Y { 0 exch d} def /X { 0 d} def 
/mp {newpath /y exch def /x exch def} def
/side {[w .77 mul w .23 mul] .385 w mul sd w 0 l currentpoint t -144 r} def
/mr {mp x y w2 0 360 arc} def /m24 {mr s} def /m20 {mr f} def
/mb {mp x y w2 add m w2 neg 0 d 0 w neg d w 0 d 0 w d cl} def
/mt {mp x y w2 add m w2 neg w neg d w 0 d cl} def
/m21 {mb f} def /m25 {mb s} def /m22 {mt f} def /m26{mt s} def
/m23 {mp x y w2 sub m w2 w d w neg 0 d cl f} def
/m27 {mp x y w2 add m w3 neg w2 neg d w3 w2 neg d w3 w2 d cl s} def
/m28 {mp x w2 sub y w2 sub w3 add m w3 0 d 0 w3 neg d w3 0 d 0 w3 d w3 0 d
 0 w3 d w3 neg 0 d 0 w3 d w3 neg 0 d
 0 w3 neg d w3 neg 0 d cl s } def
/m29 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
 4 {side} repeat cl fill gr} def
/m30 {mp gsave x w2 sub y w2 add w3 sub m currentpoint t
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/m31 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d
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 sub m w w d s} def
/m2 {mp x y w2 sub m 0 w d x w2 sub y m w 0 d s} def
/m5 {mp x w2 sub y w2 sub m w w d x w2 sub y w2 add m w w neg d s} def
/DP {/PT exch def gsave 47.2 47.2 scale PT 1 eq { 1616 1 [ 16 0 0 16 neg 0 16
] { < AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55 AA AA 55 55
AA AA 55 55 AA AA 55 55 > } image } if PT 2 eq { 16 16 1 [ 16 0 0 16 neg 0 16
] { < BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE BB BB EE EE
BB BB EE EE BB BB EE EE > } image } if PT 3 eq { 16 16 1 [ 16 0 0 16 neg 0 16
] { < FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE FF FF BB BB FF FF EE EE
FF FF BB BB FF FF EE EE > } image } if PT 4 eq { 16 16 1 [ 16 0 0 16 neg 0 16
] { < DF DF BF BF 7F 7F FE FE FD FD FB FB F7 F7 EF EF DF DF BF BF 7F 7F FE FE
FD FD FB FB F7 F7 EF EF > } image } if PT 5 eq { 16 16 1 [ 16 0 0 16 neg 0 16
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EF F7 F7 FB FB FD FD FE FE > } image } if PT 6 eq { 16 16 1 [ 16 0 0 16 neg 0
16 ] { < BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB BB
BB BB BB BB BB BB BB BB BB > } image } if PT 7 eq { 16 16 1 [ 16 0 0 16 neg 0
16 ] { < FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00 00 FF FF FF FF FF FF 00
00 FF FF FF FF FF FF 00 00 > } image } if PT 8 eq { 16 16 1 [ 16 0 0 16 neg 0
16 ] { < EE EE 47 47 83 83 C5 C5 EE EE 5C 5C 38 38 74 74 EE EE 47 47 83 83 C5
C5 EE EE 5C 5C 38 38 74 74 > } image } if PT 9 eq { 16 16 1 [ 16 0 0 16 neg 0
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38 FE FE FE FE 7D 7D 83 83 > } image } if PT 10 eq {16 16 1 [ 16 0 0 16 neg
0 16 ] { < EF EF EF EF EF EF 00 00 FE FE FE FE FE FE00 00 EF EF EF EF EF EF
00 00 FE FE FE FE FE FE 00 00 > } image } if PT 11 eq { 16 16 1 [ 16 0 0 16
neg 0 16 ] { < F7 F7 B6 B6 D5 D5 E3 E3 D5 D5 B6 B6 F7 F7 FF FF 7F 7F 6B 6B 5D
5D 3E 3E 5D 5D 6B 6B 7F 7F FF FF > } image } if PT 12 eq { 16 16 1 [ 16 0 0
16 neg 0 16 ] { < E3 E3 DD DD BE BE BE BE BE BE DD DD E3 E3 FF FF 3E 3E DD DD
EB EB EB EB EB EB DD DD 3E 3E FF FF > } image } if PT 13 eq { 16 16 1 [ 16 0
0 16 neg 0 16 ] { < FE FE 7D 7D BB BB D7 D7 EF EF D7D7 BB BB 7D 7D FE FE 7D
7D BB BB D7 D7 EF EF D7 D7 BB BB 7D 7D > } image } if PT 14 eq { 16 16 1 [ 16
0 0 16 neg 0 16 ] { < 00 00 EE EF EE EF EE EF 0E E0 EE EE EE EE EE EE 00 EE
FE EE FE EE FE EE 00 00 FE EF FE EF FE EF > } image } if PT 15 eq { 16 16 1 [
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DD AA AA DD DD FF FF 77 77 AA AA 77 77 FF FF > } image } if PT 16 eq { 16 16
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16 1 [ 16 0 0 16 neg 0 16 ] { < EE EE DD DD BB BB FFFF EE EE DD DD BB BB FF
FF EE EE DD DD BB BB FF FF EE EE DD DD BB BB FF FF >} image } if PT 18 eq {
16 16 1 [ 16 0 0 16 neg 0 16 ] { < BB BB DD DD EE EEFF FF BB BB DD DD EE EE
FF FF BB BB DD DD EE EE FF FF BB BB DD DD EE EE FF FF > } image } if PT 19 eq
{ 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 1F FC 67 F3 7B EF BD DE BD DE DE BD E6
B3 F8 0F E6 B3 DE BD BD DE BD DE 7B EF 67 F3 1F FC 7F FF > } image } if PT
20 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < DD DD EE EE EE EE EE EE DD DD BB
BB BB BB BB BB DD DD EE EE EE EE EE EE DD DD BB BB BB BB BB BB > } image }
if PT 21 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < 0E 0E EF EF EF EF EF EF E0
E0 FE FE FE FE FE FE 0E 0E EF EF EF EF EF EF E0 E0 FE FE FE FE FE FE > }
image } if PT 22 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ]{ < 70 70 F7 F7 F7 F7 F7
F7 07 07 7F 7F 7F 7F 7F 7F 70 70 F7 F7 F7 F7 F7 F7 07 07 7F 7F 7F 7F 7F 7F >
} image } if PT 23 eq { 16 16 1 [ 16 0 0 16 neg 0 16] { < AA AA 55 55 A9 A9
D1 D1 E1 E1 D1 D1 A9 A9 55 55 AA AA 55 55 A9 A9 D1 D1 E1 E1 D1 D1 A9 A9 55 55
> } image } if PT 24 eq { 16 16 1 [ 16 0 0 16 neg 0 16 ] { < FF FE FF FC EA
A8 D5 54 EA A8 D5 54 E8 28 D4 54 E8 E8 D4 D4 E8 EA 54 D5 A8 EA 54 D5 00 C0 00
80 > } image } if PT 25 eq { 16 16 1 [ 16 0 0 16 neg0 16 ] { < FF FE FF FC
FF F8 FF F0 F0 00 F0 00 F0 20 F0 60 F0 E0 F1 E0 F3 E0 F0 00 E0 00 C0 00 80 00
00 00 > } image } if gr } def /FA { /PT exch def gsave clip 0 0 translate 1 1
54 { 1 sub 47.2 mul /Xcurr exch def 1 1 74 { 1 sub 47.2 mul /Ycurr exch def
gsave Xcurr Ycurr translate PT DP gr } for } for gr } def
/reencdict 24 dict def /ReEncode {reencdict begin /nco&na exch def
/nfnam exch def /basefontname exch def /basefontdict basefontname findfont def
/newfont basefontdict maxlength dict def basefontdict {exch dup /FID ne
{dup /Encoding eq {exch dup length array copy newfont 3 1 roll put} {exch
newfont 3 1 roll put} ifelse} {pop pop} ifelse } forall newfont
/FontName nfnam put nco&na aload pop nco&na length 2 idiv {newfont
/Encoding get 3 1 roll put} repeat nfnam newfont definefont pop end } def
/accvec [ 176 /agrave 181 /Agrave 190 /acircumflex 192 /Acircumflex
201 /adieresis 204 /Adieresis 209 /ccedilla 210 /Ccedilla 211 /eacute
212 /Eacute 213 /egrave 214 /Egrave 215 /ecircumflex 216 /Ecircumflex
217 /edieresis 218 /Edieresis 219 /icircumflex 220 /Icircumflex
221 /idieresis 222 /Idieresis 223 /ntilde 224 /Ntilde 226 /ocircumflex
228 /Ocircumflex 229 /odieresis 230 /Odieresis 231 /ucircumflex 236 /Ucircumflex
237 /udieresis 238 /Udieresis 239 /aring 242 /Aring 243 /ydieresis
244 /Ydieresis 246 /aacute 247 /Aacute 252 /ugrave 253 /Ugrave] def
/Times-Roman /Times-Roman accvec ReEncode
/Times-Italic /Times-Italic accvec ReEncode
/Times-Bold /Times-Bold accvec ReEncode
/Times-BoldItalic /Times-BoldItalic accvec ReEncode
/Helvetica /Helvetica accvec ReEncode
/Helvetica-Oblique /Helvetica-Oblique accvec ReEncode
/Helvetica-Bold /Helvetica-Bold accvec ReEncode
/Helvetica-BoldOblique /Helvetica-BoldOblique  accvec ReEncode
/Courier /Courier accvec ReEncode
/Courier-Oblique /Courier-Oblique accvec ReEncode
/Courier-Bold /Courier-Bold accvec ReEncode
/Courier-BoldOblique /Courier-BoldOblique accvec ReEncode
/oshow {gsave [] 0 sd true charpath stroke gr} def
/stwn { /fs exch def /fn exch def /text exch def fn findfont fs sf
 text sw pop xs add /xs exch def} def
/stwb { /fs exch def /fn exch def /nbas exch def /textf exch def
textf length /tlen exch def nbas tlen gt {/nbas tlendef} if
fn findfont fs sf textf dup length nbas sub nbas getinterval sw
pop neg xs add /xs exch def} def
/accspe [ 65 /plusminus 66 /bar 67 /existential 68 /universal
69 /exclam 70 /numbersign 71 /greater 72 /question 73 /integral
74 /colon 75 /semicolon 76 /less 77 /bracketleft 78 /bracketright
79 /greaterequal 80 /braceleft 81 /braceright 82 /radical
83 /spade 84 /heart 85 /diamond 86 /club 87 /lessequal
88 /multiply 89 /percent 90 /infinity 48 /circlemultiply 49 /circleplus
50 /emptyset 51 /lozenge 52 /bullet 53 /arrowright 54 /arrowup
55 /arrowleft 56 /arrowdown 57 /arrowboth 48 /degree 44 /comma 43 /plus
 45 /angle 42 /angleleft 47 /divide 61 /notequal 40 /equivalence 41 /second
 97 /approxequal 98 /congruent 99 /perpendicular 100 /partialdiff 101 /florin
 102 /intersection 103 /union 104 /propersuperset 105 /reflexsuperset
 106 /notsubset 107 /propersubset 108 /reflexsubset 109 /element 110 /notelement
 111 /gradient 112 /logicaland 113 /logicalor 114 /arrowdblboth
 115 /arrowdblleft 116 /arrowdblup 117 /arrowdblright 118 /arrowdbldown
 119 /ampersand 120 /omega1 121 /similar 122 /aleph ] def
/Symbol /Special accspe ReEncode
gsave .25 .25 scale 
%%EndProlog
 gsave 0 0 t black [] 0 sd 1 lw 1304 794 227 113 bl 1588 964 0 0 C 1304 794 227
 113 C 227 1066 m -953 Y 13 X 767 Y 13 X -79 Y 13 X -49 Y 13 X -37 Y 13 X -28 Y
 13 X -25 Y 13 X -20 Y 13 X -19 Y 13 X -16 Y 13 X -15 Y 13 X -13 Y 13 X -13 Y 13
 X -10 Y 13 X -11 Y 14 X -12 Y 13 X -9 Y 13 X -7 Y 13 X -8 Y 13 X -8 Y 13 X -8 Y
 13 X -6 Y 13 X -7 Y 13 X -6 Y 13 X -10 Y 13 X -1 Y 13 X -6 Y 13 X -4 Y 13 X -5
 Y 13 X -7 Y 13 X -5 Y 13 X -1 Y 13 X -4 Y 13 X -8 Y 26 X -6 Y 13 X -4 Y 13 X -1
 Y 14 X -3 Y 13 X -6 Y 13 X -4 Y 26 X -8 Y 13 X -1 Y 13 X 1 Y 13 X -2 Y 13 X -6
 Y 13 X 1 Y 13 X -6 Y 13 X 1 Y 13 X -4 Y 13 X 1 Y 13 X -4 Y 26 X -3 Y 13 X -6 Y
 13 X -1 Y 13 X -2 Y 13 X 2 Y 13 X -3 Y 14 X 1 Y 13 X -4 Y 13 X 3 Y 13 X -2 Y 13
 X -2 Y 13 X 1 Y 13 X -5 Y 13 X 3 Y 13 X -7 Y 13 X -1 Y 13 X 1 Y 13 X 4 Y 13 X
 -7 Y 13 X 2 Y 39 X -3 Y 13 X -1 Y 13 X 1 Y 13 X 2 Y 13 X -4 Y 26 X -1 Y 14 X 2
 Y 26 X -2 Y 26 X -4 Y 13 X 3 Y 13 X 1 Y 13 X 1 Y 13 X 1 Y 13 X -2 Y 13 X 1 Y 13
 X 3 Y 13 X 2 Y 13 X 2 Y 13 X 4 Y 13 X 8 Y 13 X 29 Y 13 X 677 Y s NC 227 113 m
 794 Y s 261 113 m -34 X s 98 123 m 3 2 d 5 4 d -31 Y s 133 129 m -4 -1 d -3 -5
 d -2 -7 d -5 Y 2 -7 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5
 1 d -3 X cl s 138 147 m 22 X s 172 157 m 3 1 d 3 4 d -26 Y s 194 156 m 1 Y 1 2
 d 1 2 d 3 1 d 5 X 2 -1 d 1 -2 d 1 -2 d -2 Y -1 -3 d -2 -3 d -12 -13 d 17 X s
 244 137 m -17 X s 244 151 m -17 X s 244 161 m -17 X s 244 169 m -17 X s 244 175
 m -17 X s 244 181 m -17 X s 244 185 m -17 X s 244 189 m -17 X s 261 193 m -34 X
 s 98 203 m 3 1 d 5 5 d -32 Y s 133 209 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3
 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 138 227 m
 22 X s 172 236 m 3 2 d 3 3 d -25 Y s 196 236 m 3 2 d 3 3 d -25 Y s 244 217 m
 -17 X s 244 231 m -17 X s 244 241 m -17 X s 244 248 m -17 X s 244 255 m -17 X s
 244 260 m -17 X s 244 265 m -17 X s 244 269 m -17 X s 261 272 m -34 X s 98 282
 m 3 2 d 5 4 d -32 Y s 133 288 m -4 -1 d -3 -5 d -2 -8 d -4 Y 2 -8 d 3 -4 d 4 -2
 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 5 d -5 1 d -3 X cl s 138 306 m 22 X s 172
 316 m 3 1 d 3 4 d -26 Y s 200 321 m -4 -2 d -2 -3 d -1 -6 d -4 Y 1 -6 d 2 -4 d
 4 -1 d 2 X 4 1 d 2 4 d 2 6 d 4 Y -2 6 d -2 3 d -4 2 d -2 X cl s 244 296 m -17 X
 s 244 310 m -17 X s 244 320 m -17 X s 244 328 m -17 X s 244 334 m -17 X s 244
 339 m -17 X s 244 344 m -17 X s 244 348 m -17 X s 261 352 m -34 X s 114 361 m 3
 2 d 5 5 d -32 Y s 149 368 m -5 -2 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3
 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 2 d -3 X cl s 162 386 m 22 X s 208 392
 m -1 -4 d -2 -2 d -4 -2 d -1 X -4 2 d -2 2 d -1 4 d 1 Y 1 3 d 2 3 d 4 1 d 1 X 4
 -1 d 2 -3 d 1 -4 d -6 Y -1 -7 d -2 -3 d -4 -1 d -2 X -4 1 d -1 2 d s 244 376 m
 -17 X s 244 390 m -17 X s 244 399 m -17 X s 244 407 m -17 X s 244 413 m -17 X s
 244 419 m -17 X s 244 423 m -17 X s 244 427 m -17 X s 261 431 m -34 X s 114 441
 m 3 1 d 5 5 d -32 Y s 149 447 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2
 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 162 465 m 22 X s 199
 479 m -4 -1 d -1 -2 d -3 Y 1 -2 d 3 -1 d 4 -1 d 4 -2 d 2 -2 d 2 -2 d -4 Y -2 -3
 d -1 -1 d -3 -1 d -5 X -4 1 d -1 1 d -1 3 d 4 Y 1 2 d 2 2 d 4 2 d 5 1 d 2 1 d 1
 2 d 3 Y -1 2 d -3 1 d -5 X cl s 244 455 m -17 X s 244 469 m -17 X s 244 479 m
 -17 X s 244 487 m -17 X s 244 493 m -17 X s 244 498 m -17 X s 244 503 m -17 X s
 244 507 m -17 X s 261 510 m -34 X s 114 520 m 3 2 d 5 4 d -31 Y s 149 526 m -5
 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d
 -3 5 d -5 1 d -3 X cl s 162 544 m 22 X s 210 559 m -12 -26 d s 193 559 m 17 X s
 244 534 m -17 X s 244 548 m -17 X s 244 558 m -17 X s 244 566 m -17 X s 244 572
 m -17 X s 244 578 m -17 X s 244 582 m -17 X s 244 586 m -17 X s 261 590 m -34 X
 s 114 600 m 3 1 d 5 5 d -32 Y s 149 606 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3
 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 162 624 m
 22 X s 208 635 m -1 2 d -3 1 d -3 X -3 -1 d -3 -4 d -1 -6 d -6 Y 1 -5 d 3 -2 d
 3 -1 d 1 X 4 1 d 2 2 d 2 4 d 1 Y -2 4 d -2 2 d -4 2 d -1 X -3 -2 d -3 -2 d -1
 -4 d s 244 614 m -17 X s 244 628 m -17 X s 244 638 m -17 X s 244 645 m -17 X s
 244 652 m -17 X s 244 657 m -17 X s 244 662 m -17 X s 244 666 m -17 X s 261 669
 m -34 X s 114 679 m 3 2 d 5 4 d -32 Y s 149 685 m -5 -1 d -3 -5 d -1 -8 d -4 Y
 1 -8 d 3 -4 d 5 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d -3 5 d -5 1 d -3 X cl s
 162 703 m 22 X s 207 718 m -12 X -1 -11 d 1 1 d 4 1 d 3 X 4 -1 d 2 -2 d 2 -4 d
 -2 Y -2 -4 d -2 -3 d -4 -1 d -3 X -4 1 d -1 2 d -1 2 d s 244 693 m -17 X s 244
 707 m -17 X s 244 717 m -17 X s 244 725 m -17 X s 244 731 m -17 X s 244 736 m
 -17 X s 244 741 m -17 X s 244 745 m -17 X s 261 749 m -34 X s 114 758 m 3 2 d 5
 5 d -32 Y s 149 765 m -5 -2 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3 X 5 1
 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 2 d -3 X cl s 162 783 m 22 X s 205 797 m -12
 -17 d 18 X s 205 797 m -25 Y s 244 773 m -17 X s 244 787 m -17 X s 244 796 m
 -17 X s 244 804 m -17 X s 244 810 m -17 X s 244 816 m -17 X s 244 820 m -17 X s
 244 824 m -17 X s 261 828 m -34 X s 114 838 m 3 1 d 5 5 d -32 Y s 149 844 m -5
 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -4 d 5 -2 d 3 X 5 2 d 3 4 d 1 8 d 4 Y -1 8 d
 -3 4 d -5 2 d -3 X cl s 162 862 m 22 X s 195 876 m 13 X -7 -9 d 4 X 2 -1 d 1 -2
 d 2 -3 d -3 Y -2 -3 d -2 -3 d -4 -1 d -3 X -4 1 d -1 1 d -1 3 d s 244 852 m -17
 X s 244 866 m -17 X s 244 876 m -17 X s 244 884 m -17 X s 244 890 m -17 X s 244
 895 m -17 X s 244 900 m -17 X s 244 904 m -17 X s 261 907 m -34 X s 114 917 m 3
 2 d 5 4 d -31 Y s 149 923 m -5 -1 d -3 -5 d -1 -7 d -5 Y 1 -7 d 3 -5 d 5 -1 d 3
 X 5 1 d 3 5 d 1 7 d 5 Y -1 7 d -3 5 d -5 1 d -3 X cl s 162 941 m 22 X s 194 950
 m 1 Y 1 2 d 1 2 d 3 1 d 5 X 2 -1 d 1 -2 d 1 -2 d -2 Y -1 -3 d -2 -3 d -12 -13 d
 17 X s 227 113 m 1304 X s 227 147 m -34 Y s 253 130 m -17 Y s 279 130 m -17 Y s
 305 130 m -17 Y s 331 130 m -17 Y s 357 147 m -34 Y s 383 130 m -17 Y s 409 130
 m -17 Y s 436 130 m -17 Y s 462 130 m -17 Y s 488 147 m -34 Y s 514 130 m -17 Y
 s 540 130 m -17 Y s 566 130 m -17 Y s 592 130 m -17 Y s 618 147 m -34 Y s 644
 130 m -17 Y s 670 130 m -17 Y s 696 130 m -17 Y s 723 130 m -17 Y s 749 147 m
 -34 Y s 775 130 m -17 Y s 801 130 m -17 Y s 827 130 m -17 Y s 853 130 m -17 Y s
 879 147 m -34 Y s 905 130 m -17 Y s 931 130 m -17 Y s 957 130 m -17 Y s 983 130
 m -17 Y s 1010 147 m -34 Y s 1036 130 m -17 Y s 1062 130 m -17 Y s 1088 130 m
 -17 Y s 1114 130 m -17 Y s 1140 147 m -34 Y s 1166 130 m -17 Y s 1192 130 m -17
 Y s 1218 130 m -17 Y s 1244 130 m -17 Y s 1270 147 m -34 Y s 1296 130 m -17 Y s
 1323 130 m -17 Y s 1349 130 m -17 Y s 1375 130 m -17 Y s 1401 147 m -34 Y s
 1427 130 m -17 Y s 1453 130 m -17 Y s 1479 130 m -17 Y s 1505 130 m -17 Y s
 1531 147 m -34 Y s 225 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3
 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 321 85 m 3 1 d 5 5 d -32
 Y s 356 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d
 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 386 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y
 1 -8 d 3 -5 d 5 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s
 448 83 m 2 Y 2 3 d 1 1 d 3 2 d 7 X 3 -2 d 1 -1 d 2 -3 d -3 Y -2 -3 d -3 -5 d
 -15 -15 d 21 X s 486 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X
 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 516 91 m -4 -2 d -3 -4 d
 -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 4 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2
 d -4 X cl s 580 91 m 17 X -9 -12 d 4 X 4 -2 d 1 -1 d 2 -5 d -3 Y -2 -4 d -3 -4
 d -5 -1 d -4 X -5 1 d -1 2 d -2 3 d s 617 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1
 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 647
 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 4 5 d 1 8 d 4
 Y -1 8 d -4 4 d -4 2 d -3 X cl s 723 91 m -15 -21 d 22 X s 723 91 m -32 Y s 747
 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4
 Y -1 8 d -3 4 d -5 2 d -3 X cl s 777 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3
 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 856 91 m
 -15 X -1 -14 d 1 2 d 5 1 d 4 X 5 -1 d 3 -3 d 1 -5 d -3 Y -1 -4 d -3 -4 d -5 -1
 d -4 X -5 1 d -1 2 d -2 3 d s 878 91 m -5 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5
 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 908 91 m -5
 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d
 -3 4 d -4 2 d -3 X cl s 988 86 m -1 3 d -5 2 d -3 X -4 -2 d -3 -4 d -2 -8 d -7
 Y 2 -6 d 3 -4 d 4 -1 d 2 X 4 1 d 3 4 d 2 4 d 2 Y -2 4 d -3 3 d -4 2 d -2 X -4
 -2 d -3 -3 d -2 -4 d s 1008 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5
 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1038 91 m -4 -2 d
 -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4
 d -5 2 d -3 X cl s 1120 91 m -15 -32 d s 1099 91 m 21 X s 1138 91 m -4 -2 d -3
 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d
 -5 2 d -3 X cl s 1169 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3
 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1237 91 m -4 -2 d -2 -3
 d -3 Y 2 -3 d 3 -1 d 6 -2 d 4 -1 d 3 -3 d 2 -3 d -5 Y -2 -3 d -1 -2 d -5 -1 d
 -6 X -4 1 d -2 2 d -1 3 d 5 Y 1 3 d 3 3 d 5 1 d 6 2 d 3 1 d 1 3 d 3 Y -1 3 d -5
 2 d -6 X cl s 1269 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4
 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1299 91 m -4 -2 d -3 -4 d -2
 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d
 -3 X cl s 1380 80 m -2 -4 d -3 -3 d -4 -2 d -2 X -4 2 d -3 3 d -2 4 d 2 Y 2 4 d
 3 3 d 4 2 d 2 X 4 -2 d 3 -3 d 2 -6 d -7 Y -2 -8 d -3 -5 d -4 -1 d -3 X -5 1 d
 -1 4 d s 1399 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d 3 -5 d 4 -1 d 3 X 5 1 d
 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1430 91 m -5 -2 d -3 -4 d -1 -8
 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X
 cl s 1480 85 m 3 1 d 4 5 d -32 Y s 1515 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8
 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1545
 91 m -5 -2 d -3 -4 d -1 -8 d -4 Y 1 -8 d 3 -5 d 5 -1 d 3 X 4 1 d 3 5 d 2 8 d 4
 Y -2 8 d -3 4 d -4 2 d -3 X cl s 1575 91 m -4 -2 d -3 -4 d -2 -8 d -4 Y 2 -8 d
 3 -5 d 4 -1 d 3 X 5 1 d 3 5 d 1 8 d 4 Y -1 8 d -3 4 d -5 2 d -3 X cl s 1304 794
 227 113 C [12 12] 0 sd 227 1066 m -976 Y 13 X 760 Y 13 X -85 Y 13 X -54 Y 13 X
 -41 Y 13 X -32 Y 13 X -28 Y 13 X -25 Y 13 X -19 Y 13 X -18 Y 13 X -20 Y 13 X
 -16 Y 13 X -15 Y 13 X -12 Y 13 X -14 Y 14 X -13 Y 13 X -8 Y 13 X -14 Y 13 X -8
 Y 13 X -8 Y 13 X -8 Y 13 X -8 Y 13 X -14 Y 13 X -10 Y 13 X -4 Y 13 X -10 Y 13 X
 -4 Y 13 X -9 Y 13 X -8 Y 13 X -6 Y 13 X -5 Y 13 X -13 Y 13 X -5 Y 13 X -6 Y 26
 X -9 Y 13 X -4 Y 13 X -10 Y 14 X -2 Y 13 X -9 Y 13 X -7 Y 13 X -5 Y 13 X -7 Y
 13 X -4 Y 13 X -2 Y 13 X -8 Y 13 X -19 Y 13 X 11 Y 13 X -17 Y 13 X 11 Y 13 X
 -26 Y 13 X -14 Y 13 X 19 Y 13 X -6 Y 26 X -17 Y 13 X -13 Y 13 X 9 Y 13 X -8 Y
 13 X -11 Y 14 X -13 Y 13 X 22 Y 13 X -14 Y 13 X -13 Y 13 X -2 Y 13 X -1 Y 13 X
 -19 Y 13 X 22 Y 13 X -39 Y 13 X 12 Y 13 X 8 Y 13 X -35 Y 13 X 8 Y 13 X -1 Y 13
 X -7 Y 26 X 17 Y 13 X -17 Y 26 X 13 Y 13 X -13 Y 261 X 976 Y s
 [12 15 4 15] 0 sd 227 1066 m -976 Y 13 X 722 Y 13 X -97 Y 13 X -63 Y 13 X -48 Y
 13 X -40 Y 13 X -32 Y 13 X -33 Y 13 X -25 Y 13 X -25 Y 13 X -19 Y 13 X -19 Y 13
 X -24 Y 13 X -15 Y 13 X -17 Y 14 X -14 Y 13 X -18 Y 13 X -11 Y 13 X -14 Y 13 X
 -17 Y 13 X -17 Y 13 X -1 Y 13 X -16 Y 13 X -13 Y 13 X -22 Y 13 X -1 Y 13 X -40
 Y 13 X 16 Y 13 X -47 Y 13 X 28 Y 13 X -21 Y 13 X -40 Y 13 X 18 Y 13 X 12 Y 13 X
 -16 Y 13 X -27 Y 13 X 21 Y 13 X -25 Y 822 X 976 Y s
gr gr showpage
end
%%EOF
\end{filecontents}

\documentclass[12pt]{article}
\usepackage{epsfig}
\newcommand{\mrm}[1]{\mathrm{#1}}
 
%define page size
\setlength{\textheight}{24cm}
\setlength{\topmargin}{-5mm}
\setlength{\headheight}{0mm}
\setlength{\headsep}{0mm}
\setlength{\footskip}{12mm}
\setlength{\textwidth}{6in}
\setlength{\oddsidemargin}{0mm}
\setlength{\evensidemargin}{0mm}
 
%some frequent physics symbols
\newcommand{\alphas}{\alpha_{\mrm{s}}}
\newcommand{\alphaem}{\alpha_{\mrm{em}}}
\newcommand{\ssintw}{\sin^2 \! \theta_W}
\newcommand{\scostw}{\cos^2 \! \theta_W}
\newcommand{\pT}{p_{\perp}}
\newcommand{\pTmin}{p_{\perp\mrm{min}}}
\newcommand{\br}[1]{\overline{#1}}
\newcommand{\pom}{\mrm{I}\!\mrm{P}}
\newcommand{\reg}{\mrm{I}\!\mrm{R}}
 \newcommand{\Jpsi}{\mrm{J}/\psi}
\newcommand{\ee}{\e^+\e^-}
\newcommand{\ep}{\e\p}
\newcommand{\pp}{\p\p}
\newcommand{\pbarp}{\pbar\p}
\newcommand{\qqbar}{\q\qbar}
\newcommand{\gammaZ}{\gamma^* / \Z^0}
 
%roman names for particles in math mode
\renewcommand{\a}{\mathrm{a}}
\renewcommand{\b}{\mathrm{b}}
\renewcommand{\c}{\mathrm{c}}
\renewcommand{\d}{\mathrm{d}}
\newcommand{\e}{\mathrm{e}}
\newcommand{\f}{\mathrm{f}}
\newcommand{\g}{\mathrm{g}}
\newcommand{\hrm}{\mathrm{h}}
\newcommand{\lrm}{\mathrm{l}}
\newcommand{\n}{\mathrm{n}}
\newcommand{\p}{\mathrm{p}}
\newcommand{\q}{\mathrm{q}}
\newcommand{\s}{\mathrm{s}}
\renewcommand{\t}{\mathrm{t}}
\renewcommand{\u}{\mathrm{u}}
\newcommand{\A}{\mathrm{A}}
\newcommand{\B}{\mathrm{B}}
\newcommand{\D}{\mathrm{D}}
\newcommand{\F}{\mathrm{F}}
\renewcommand{\H}{\mathrm{H}}
\newcommand{\J}{\mathrm{J}}
\newcommand{\K}{\mathrm{K}}
\renewcommand{\L}{\mathrm{L}}
\newcommand{\Q}{\mathrm{Q}}
\newcommand{\R}{\mathrm{R}}
\newcommand{\W}{\mathrm{W}}
\newcommand{\Z}{\mathrm{Z}}
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\begin{document}
 
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\begin{flushright}
LU TP 95--14\\
May, 1995
\end{flushright}

\vspace*{1cm}
 
\begin{center}
\mathversion{bold}
{\LARGE\bf $\gamma$p and $\gamma\gamma$ QCD Physics 
at High Energies}\mathversion{normal}\footnote{to appear in 
the proceedings of Photon '95, Sheffield, UK, April 8--13, 1995} 
\\[10mm]
{\large Torbj\"orn Sj\"ostrand} \\[2mm]
{\em Department of Theoretical Physics,} \\[1mm]
{\em University of Lund, S\"olvegatan 14A,} \\[1mm]
{\em S-223 62 LUND, Sweden}\\[15mm]
\end{center}

\begin{center}
ABSTRACT \\[2mm]
\begin{minipage}{\abstwidth}%
{\small 
The challenge of $\gamma\p$ and $\gamma\gamma$ studies is a
complexity in excess of that encountered elsewhere in particle
physics. In order to construct a complete and consistent model of 
all main phenomena, several aspects have to be mastered. Here is 
presented a status report on progress towards such a model.
Topics covered include the nature of the photon, total and
partial cross sections, parton distributions and event shapes
(comparing $\p\p$, $\gamma\p$ and $\gamma\gamma$). Remaining problems 
are enumerated, with emphasis on eikonalization aspects of the 
anomalous part of the cross section.}
\end{minipage}
\end{center}

\subsubsection*{1.~~Introduction}

In this talk I review a model for $\gamma\p$ and $\gamma\gamma$ 
events being developed in collaboration with Gerhard Schuler.
By necessity, most topics will be covered very briefly.
It is therefore important to note that several papers have
already appeared on various aspects \cite{gammap,haha,paris,ftwoga}.
The emphasis is on QCD physics in collisions between (almost) real
photons, while aspects such as photon flux factors or experimental
acceptances are left aside. 

The study of $\gamma\p$ and $\gamma\gamma$ physics has a long history, 
and so it would not be possible to give a complete survey of related
previous studies. Further references may be found in other 
presentations at this meeting and at other recent workshops 
\cite{workshop}.  

\subsubsection*{2.~~The model}

To first approximation, the photon is a point-like particle. However,
quantum mechanically, it may fluctuate into a (charged) 
fermion--antifermion pair. The fluctuations 
$\gamma \leftrightarrow \q\qbar$ can interact strongly and therefore 
turn out to be responsible for the major part of the $\gamma\p$ and 
$\gamma\gamma$ total cross section. The spectrum of fluctuations 
may be split into a low-virtuality and a high-virtuality
part. The former part can be approximated by a sum over low-mass 
vector-meson states, customarily restricted to the lowest-lying vector 
multiplet. Phenomenologically, this Vector Meson Dominance (VMD) ansatz 
turns out to be very successful in describing a host of data. The 
high-virtuality part, on the other hand, should be in a perturbatively 
calculable domain. 

In total, the photon wave function can then be written as
\begin{equation}
|\gamma\rangle = c_{\mrm{bare}} |\gamma_{\mrm{bare}}\rangle +
\sum_{V = \rho^0, \omega, \phi, \Jpsi} c_V |V\rangle +
\sum_{\q = \u, \d, \s, \c, \b} c_{\q} |\q\qbar\rangle +
\sum_{\ell = \e, \mu, \tau} c_{\ell} |\ell^+\ell^-\rangle ~.
\label{gammawavefunction}
\end{equation} 
In general, the coefficients $c_i$ depend on the scale $\mu$ used to 
probe the photon. Introducing a cut-off parameter $k_0$ to separate 
the low- and high-virtuality parts of the $\q\qbar$ fluctuations, one
obtains $c_{\q}^2 \approx (\alphaem/2\pi) 2e_{\q}^2 \ln(\mu^2/k_0^2)$.
The $c_V$ coefficients are $\mu$-independent and phenomenologically 
determined. The $c_{\mrm{bare}}$ is always close to unity. Usually the 
probing scale $\mu$ is taken to be the transverse momentum of a 
$2 \to 2$ parton-level process. Our fitted value $k_0 \approx 0.6$ GeV 
(see below) then sets the minimum transverse momentum of a perturbative 
branching $\gamma \to \q\qbar$.

The subdivision of the above photon wave function corresponds to the 
existence of three main event classes in $\gamma\p$ events:
\begin{Enumerate}
\item The VMD processes, where the photon turns into a vector meson
before the interaction, and therefore all processes
allowed in hadronic physics may occur. This includes elastic and 
diffractive scattering as well as low-$\pT$ and high-$\pT$ 
non-diffractive events.
\item The direct processes, where a bare photon interacts with a 
parton from the proton.
\item The anomalous processes, where the photon perturbatively branches
into a $\q\qbar$ pair, and one of these (or a daughter parton thereof)
interacts with a parton from the proton. 
\end{Enumerate}
All three processes are of $O(\alphaem)$. However, in the direct 
contribution the photon structure function is of $O(1)$ and the 
hard scattering matrix elements of $O(\alphaem)$, while the opposite 
holds for the VMD and the anomalous processes. 

Also the parton distributions of the photon can be split according 
to the pattern of eq.~(\ref{gammawavefunction}). Four different
parametrizations along these lines are presented in ref. \cite{ftwoga}.

A generalization of the above picture to $\gamma\gamma$ events is 
obtained by noting that each of the two incoming photons is
described by a wave function of the type given in 
eq.~(\ref{gammawavefunction}). In total, there are therefore 
three times three event classes. By symmetry, the `off-diagonal' 
combinations appear pairwise, so the number of distinct classes 
is only six: VMD$\times$VMD, VMD$\times$direct, VMD$\times$anomalous,
direct$\times$direct, direct$\times$anomalous and
anomalous$\times$anomalous.
The first three classes above are pretty much the same as the three 
classes allowed in $\gamma\p$ events, since the interactions of a VMD
photon and those of a proton are about the same.

\begin{figure}[t]
\begin{center}
\mbox{\epsfig{file=lutp95141.epspm}} 
\end{center}
\begin{picture}(0,0)(0,0)
\put(345,25){$E_{\mrm{cm}}$ [GeV]}
\put(45,270){$\sigma_{\mrm{tot}}^{\gamma\gamma}$ [nb]}
\end{picture}\\[-8mm]
\captive%
{The total $\gamma\gamma$ cross section. Full curve: the 
parametrization of eq.~(\protect\ref{sigtotgaga}). 
Dashed curve: result from sum of integrations of the six components. 
Data points: open triangles PLUTO 1984, filled triangles PLUTO 1986,
open squares TPC/2$\gamma$ 1985, spades TPC/2$\gamma$ 1991, circles MD-1 
1991, filled square CELLO 1991.
\label{lutp95141}}
\end{figure}

Empirically, both the $\p\p$ and $\gamma\p$ total cross sections are
well described by a pomeron plus reggeon ansatz. If the same approach 
is extended to $\gamma\gamma$, one obtains a prediction  
\begin{equation}
\sigma_{\mrm{tot}}^{\gamma\gamma}(s) \approx 211 \, s^{0.0808} + 
215 \, s^{-0.4525} ~~[\mrm{nb}] ~.
\label{sigtotgaga}
\end{equation}
The VMD component of the $\gamma\p$ cross section, about 80\% of the 
total, is also given by a pomeron plus reggeon parametrization. The
remaining part can be fitted to a sum of direct and anomalous cross 
sections, by picking a lower cut-off $k_0 \approx 0.6$~GeV for 
$\gamma \leftrightarrow \q\qbar$ fluctuations plus a cut-off 
$\pTmin^{\mrm{anom}} = 0.7 + 0.17 \log^2(1+E_{\mrm{cm}}/20)$~[GeV]
for QCD processes in the anomalous sector. Here SaS set 1D is used 
for the parton distributions of the photon, and CTEQ set 2L for 
those of the proton. With parameters determined in 
$\gamma\p$ physics, the cross section for each of the six 
$\gamma\gamma$ components can be obtained. In Fig.~\ref{lutp95141} 
the sum is compared with the parametrization (\ref{sigtotgaga}). 
The good agreement, also with the data, indicates that the model 
with six components is internally consistent.   
 
\subsubsection*{3.~~Event properties}

The subdivision of the total $\gamma\p$ and $\gamma\gamma$ cross 
sections above, with the related choices of cut-off parameters and
so on, specifies the event composition at the hard-scattering level. For
studies of the complete event structure, it is necessary to add models 
for initial- and final-state QCD radiation (parton showers), for beam
remnants, and for fragmentation and secondary decays. A Monte Carlo 
generation of complete hadronic final states is obtained
with {\sc Pythia}/{\sc Jetset} \cite{Pythia}. Thus any experimental 
quantity can be studied. In particular, we can compare the properties 
of $\p\p$ (which is similar to $\pbar\p$ for the quantities studied 
here), $\gamma\p$ and $\gamma\gamma$ events.

\begin{figure}[t]
\begin{center}
\mbox{\epsfig{file=lutp95142.epspm}} 
\end{center}
\begin{picture}(0,0)(0,0)
\put(345,25){$y$}
\put(45,270){$\d E_{\perp} / \d y$ [GeV]}
\end{picture}\\[-8mm]
\captive%
{Transverse energy flow as a function of rapidity, $\d E_{\perp}/ \d y$,
at 200 GeV c.m. energy. Dashed-dotted histogram is $\p\p$, dashed one
$\gamma\p$ (with the original photon moving in the $+z$ direction) and
full one $\gamma\gamma$.
\label{lutp95142}}
\end{figure}

\begin{figure}[t]
\begin{center}
\mbox{\epsfig{file=lutp95143.epspm}} 
\end{center}
\begin{picture}(0,0)(0,0)
\put(345,25){$\pT$ [GeV]}
\put(45,270){$(1/2\sigma_{\mathrm{tot}}) \, \d \sigma_{\mathrm{jet}} /% 
\d \pT$ [GeV$^{-1}$]}
\end{picture}\\[-8mm]
\captive%
{Parton-level jet $\pT$ distribution at 2 TeV c.m. energy. Dashed-dotted 
histogram is $\p\p$, dashed one $\gamma\p$ and full one $\gamma\gamma$.
The factor $1/2$ compensates for there being 2 jets per event.
\label{lutp95143}}
\end{figure}

In general, event properties show an hierarchy, with $\gamma\gamma$ 
events having the most activity and $\p\p$ ones the least. It is mainly 
related with the large activity expected for interactions involving 
the anomalous photon component, because of the larger 
$\pTmin^{\mrm{anom}}$. The transverse energy flow distribution in
Fig.~\ref{lutp95142} also illustrates how $\gamma\p$ interpolates between 
$\p\p$ and $\gamma\gamma$: the $\gamma\p$ events look like the 
$\gamma\gamma$ ones around the photon direction, while they look 
more like $\p\p$ ones in the opposite direction, with an intermediate 
behaviour in the central region. 

The spectacular differences in the jet rate at large $\pT$
are highlighted in Fig.~\ref{lutp95143}. They mainly come about because 
the direct component involves the full energy of the incoming photon.
Differences are not as visible in minimum-bias events, but the
inclusive $\pT$ spectrum of charged particles shows the same hierarchy.

Distributions show the same pattern at all energies, with most
activity for the $\gamma\gamma$ events. Therefore differences can be
detected at any convenient energy.

\subsubsection*{4.~~Problems and Outlook}

The perturbatively calculated jet cross-section above some fixed $\pTmin$
scale is steeply increasing with the c.m. energy, and ultimately exceeds
the total cross section. In $\p\p$ physics the most likely solution to 
this problem is to allow multiple parton-parton interactions in an
event \cite{TSMZ}. Since hadrons consist of many partons, such an approach
is fairly natural, although there are several elements of arbitrariness 
involved in constructing explicit models. If the photon is considered as 
a hadron, the same ``eikonalization'' approach can also be applied for 
$\gamma\p$ and $\gamma\gamma$ events.

We argue, however, that only the VMD part of the photon can be treated in 
straight analogy with hadrons, and that the anomalous and direct parts 
have to be considered separately. In fact, each fixed-$k_{\perp}$ component
of $\gamma \leftrightarrow \q\qbar$ fluctuations can be considered as a 
separate ``hadron species'', with a density of states 
$\d k_{\perp}^2 / k_{\perp}^2$. The parton distribution inside such a
state is perturbatively calculable, and leads to a decreasing jet rate
with increasing $k_{\perp}$. The fall-off is rather slow, however,
and becomes gradually slower as the c.m. energy is increased. The total
$\gamma\p$ cross section therefore comes out as increasing faster than
data. Standard eikonalization (with smaller photon size for increasing
$k_{\perp}$, according to the uncertainty relation) dampens the growth, 
but not enough. It therefore seems clear that further aspects have to be 
taken into account, such as momentum conservation, coherence effects or 
stricter geometrical cut-offs. This is thus one area where further studies 
are necessary.

Also many other aspects need to be studied. The transition between the
VMD, anomalous and direct classes should obey certain consistency
criteria. The transition from a real $\gamma$ to a virtual $\gamma^*$
is still not well understood. The profile of beam jets and the
structure of uderlying events is not well described at HERA. Jet
production in diffractive systems currently attract much attention.
Further issues could be mentioned, but the conclusion must be that
much work remains before we can claim to have a complete overview
of the physics involved in $\gamma\p$ and $\gamma\gamma$ events, 
let alone understand all the details. 
 
\vspace{\baselineskip}\noindent
\textbf{Acknowledgements:} The organizers should be congratulated to an
interesting, well-run and sunny (!) meeting. This talk was made possible
by an enjoyable collaboration with Gerhard Schuler.

\begin{thebibliographyss}{99}
 
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G.A. Schuler and T. Sj\"ostrand, Phys. Lett. {\bf B300} (1993) 169,
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\bibitem{haha}
G.A. Schuler and T. Sj\"ostrand, Phys. Rev. {\bf D49} (1994) 2257

\bibitem{paris}
G.A. Schuler and T. Sj\"ostrand, in Proc. Workshop on Two-Photon Physics 
from DA$\Phi$NE to LEP200 and Beyond, Paris, France, 1994,
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p. 163;\\
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Symposium on Multiparticle Dynamics, Vietri sul Mare, Italy,
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\bibitem{Pythia}
T. Sj\"ostrand, Comput. Phys. Commun. {\bf 82} (1994) 74

\bibitem{TSMZ}
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\end{thebibliographyss}

\end{document}
