!"# $ % &
')(+*-,/.0(21436587:9<;=7:>?*-@+,BAC*D5E(14@!FHG?7I9JGK*L7MAF4NC58(+7POK5E14@+Q2149JQSRTFUQ67:VWFXNY7IVL7I.I5E9JFHAW7:14Z*L@[587:9]\
14.M5E*LF4@+,:^_.:F?@+.I7:@[5E981X5E*-@+>F4@58(+7`1X987a1X,b9J7:VL7MGX14@[5b58Fc58(+7`1X@214V-dK,J7:,e*L@5E(+*-,<58(+7:,J*L,IfhgB5E(67:@
Q+7I,8.:9J*L;=7i5E(+7<3+9JFUQ+j6.I5E*-F?@kF4Nl5E(+7<,J*L@+>?V-7M\m1X@+Qnoj+V-58*D\p36(+F45EF4@`7IG47:@[5E,qAC*-58(cne*L,J,8*-@+>r7:@+7I98>4d
*L@`7ast7vuc.IF?VLV-*L,J*LF?@+,CGK*w1x*-@+*-58*w14Vy\p,]501X587z9E14Q+*L1X5E*-F?@`*-@`5E(67i@+7:j65898*-@+Fr3214*-9]\p3698FKQ+j+.I58*LF?@T3+98FK.:7I,8,If
gp@r{W(+14365E7I9W|U^Kg"AC*LVLV+14VL,JFqQ6*L,8.Ij+,8,_,87MG?7:9814V=@+7IAh36(}dK,J*L.:,_nbFKQ+7IVL,AC(+F?,J7Ynb14@+*DN~7:,J5E1X5E*-F?@+,.:14@
;=7N~F4j+@+QPj+,8*-@+><5E(+*-,)7IG?7I@[5,J*L>?@21v5Ej+9J7B1v5)5E(+7ql 7 s 7 u
.IF?VLV-*LQ+7I9:f
rH $ /ol P
JJ }W +¡2¢C£¤¥¦ +§]¢_
')(+7>?F[1XVtF4N"32149J58*L.IVL73+([dK,8*-.:,m*L,58FeQ67:,8.I98*-;¨7z5E(67q7IVL7Inb7I@}5E149Jd.:F?@+,]5E*D5Ej+7I@}58,CF4N©nb1X5J5E7:9C1X@+Q
5E(67_*-@}587:9814.I58*LF?@+,1XnbF?@6>C58(+7:nªf«')(+*L,¬27IVLQqF4N+3+([dK,8*-.:,«7:@[5E7I987IQ/*-58,nbFKQ+7:9J@B36(214,87_1X55E(677I@+Q
F4N58(+7e@+*L@+7M5E7I7:@[5E(!.I7:@[5Ej+9]dN~F4VLVLFHAC*-@+>P1T@}j+n/;=7:9BF4NWN~j6@+Q214ne7:@[501XV_Q+*-,8.IF®G47:9J*L7:,I^*L@6.:VLj6Q+*L@+>
5E(67iQ+*L,J.:FHG?7I9JdF4N5E(67i7:VL7I.I5898F?@t^¨5E(+7/¬29J,J5q32149]5E*-.:VL7B,J58*LVLV«.:F4@+,8*-Q+7:9J7:Qc7:VL7Inb7I@[50149]dT58FUQ21ad4^;}d
¯6f°¯6f2')(+F?ne,8F?@ª*L@±H²4³[´Pµy±:¶·f
¸
G?7:9T5E(+7@+7M¹K5c´4ºd?7:1498,F4j+9`j+@6Q+7:9J,J501X@+Q+*L@6>»F4N/58(+7321X9J5E*-.:V-7cA_F?98V-Q¼14QUG41X@+.:7IQ½;}d
VL7:143+,e14@+Q;=F?j+@+Q+,I^.:j6VLne*L@21X58*L@+>`*L@5E(+7PQ+7MG?7:V-F?3+ne7:@[5bF4N58(+7O}5014@+Q+1498Q RTFKQ+7:VCF4N32149]\
5E*-.:V-7b3+([dK,8*-.:,If')(+77:V-7:.M5E98FHA_7a14Zk5E(67:F?9]d?^Q+7MG?7:V-F?3=7:Q!;[d!O=f©f¾zVw1X,8(+FHA^©¿BfO61XVw14nª^©1X@+Q
O¨f6À7:*-@};¨7I98>iN~98F?nÁ±H³?Â6±z58Fr±H³?Â?²i3+9JF®GK*-Q+7:,m1/j+@+*D¬27:QªQ+7I,8.:9J*L3658*LF?@rFXN©7IVL7:.M5E9JF?nx1X>?@+7I58*L.z1X@+Q
A_7a14Z*L@[5E7I9E14.M5E*-F?@+,`µÄÃv¶·fÅ')(+7`3+9JF?;+V-7:n F4Nznb14,8,b>?7:@67:9E1v5E*LF4@ *L@5E(+7T>[14j+>47ª58(+7:F?9J*L7I,bAW14,
+ 7I98ne*LF?@6,
VL7I.I5898*L. VL7I.I5898*L.
+ 14ne*LVDd 7:3658F?@
.0(2149J>?7
R`14,J,-,·RT7/.10 2j21498Z
.0(2149J>?7
R`14,J,-,·¾73.40
56
º 7 |48[±aºKu:9 j Ã<;X| ,]±<=?>*@!ÉA0CB±HºKu:D
±?f
7 E ± ºUfF>U±4± Q E=± ;X| ,~É4@²G0CB±HºKu:D
5H
º 7»º%=-±a³ . Ã<;X| ±?fD± >IE±?fÄ|G>
ÃUf J E ± ±aºG>Uf°´ , E=± ;X| º6fĺ?²EPº6fD±H|
5K
º 7 ±H²%=°Ã 5 Ã<;X| ±H´XÉ=Ä|MLN>=-±
|6f O E ± ±®´?´4´ ; E=± ;X| É+fD±PExÉ+fÄÉ
¾14j+>?7z;=F?,JF?@+,
VL7I.I5E9J*L.
gp@[5E7:9814.I58*LF?@ OKdKn/;=F?V
.0(21498>47
OU3+*-@ R`14,8,,·¾73.40
VL7I.I5898F?nb14>?@+7M5E*-. Q º ± º
À L± ± ²?º%=ÆÉ[|RL»º%=ĺ4É
À7:14Z S º ± ³U±<=-±a²?²RL»º%=ĺ?º[Ã
O}5E98F4@+> > º ± º
¾981aGU*D5pd ¾ º Ã º
'"14;+VL7)ÃUf-±"TU+2j+@+Q+14nb7I@[5014V+.IF?@+,]5E*-58j+7:@[58,FXN=58(+7mOK5E14@+Q2149JQeRTFKQ+7:V·f©1X9J5E*-.:V-7nx1X,8,87I,
F?9inb14,8,<V-*Lne*-5E,o149875E14Z47I@SN~9JF?n µËÂX¶·f ¾z9E1aGK*-58F?@t^l;=7:VL*-7IG47:Q5EFk;¨7r58(+7P.a149J98*L7I9iF4N
>?981HGK*D5pd?^2*L,C1XVL,8FiV-*L,]5E7:Q¦f
Q+7I,8.:9J*L;+*-@+>58(+7`,]5E9JF?@+>*-@}587:9814.I58*LF?@A1X,*L@[5E9JFUQ6j+.:7IQ *L@ ±H³[´4|c;[d ÈqfV+29J*-5XWI,8.0(t^)Rf¾z7:V-VD\
R`14@6@t^¦Èqf¦7MdK5pA)dKV-7:9:^ZY/f¯6f¨¾z98F?,J,:^¦14@+Q[+_f ÀÊ*-VL./W:7:ZcµÉ4¶·fC')(+7/3+9JFUF4N©F4N9J7:@+F?9Jnx1XVL*\W:14;+*-VL*-5pd
F4N_5E(+7OK5014@6Q21498QRTFKQ+7:VlAW14,B>4*-G?7I@;[d¾<f^]Ë5oÈYFKF4N 5q*L@±H³[´U±`µ_>®¶ f')(67:,87e5E(+7IF?987M5E*-.a14VlQ+7 \
G?7IVLF?36nb7I@}58,).:F?ne3+9J*L,8758(+7N~F?j+@6Q21X5E*-F?@+,FXN«58(+7BOK501X@+Q2149JQªRTFUQ67:V14,C1/@+F4@U\p¿Y;¨7IVL*w1X@>[14j+>47
5E(67:F?9]dr;214,J7:Q`F4@P58(+7,JdKnenb7M5E9Jd>?98F?j63a`bc,·|<0edBf`bg,·Ã<0ihjBkbg, ± 0ill^+AC(+7I9875E(+7`bc,·|G0id
>?9JF?j+3 .IF?989J7:,J3¨F?@6Q+,x5EF5E(+7T,J5E9JF?@+>*L@[5E7I9E14.M5E*LF4@+,bFXNÌKj+14@[5Ej+n .0(+98F4nbFKQ6dK@214ne*L.I,a,m2{CY40
14@+QP5E(67-`bc, Ã"0ihnBobc,]±0il>498F?j+36,m.IF?989J7:,J3¨F?@6QT5EFi58(+77:VL7I.I5898FHAW7:14Zr*L@[587:9E1X.I5E*-F?@+,If
')(+7N~j+@+Q21Xnb7I@}5E14V?321X9J5E*-.:V-7:,tF4N6OK5E14@+Q21X98QBRTFKQ+7:V[1X987Q+*DGU*-Q+7:Qz*-@[5EFN~7:9Jnb*-F?@+,1X@+Qz;¨F4,8F?@+,If
')(+7N~7I98ne*LF?@6,W149J7,J3+*L@±;?ÃB32149]5E*-.:VL7I,_.IF?@+,]5E*-58j65E*-@+>B58(+7nb1X58587:9l¬27:V-Q+,:flG47:9JdbN~7:9Jnb*-F?@x(21X,
N~7:9Jnb*-F?@+,z.:14@;=7b,Jj+;=Q+*-GK*LQ67:Qc*L@[5EFP5pAWFT>?98F4j+3+,:^5E(6F?,87<5E(21v5B.:14@*-@[5E7:9814.I5GK*w1r5E(67b,]5E98F4@+>
N~F?9J.:74^+14@+Q5E(6F?,8758(21X5).:14@+@+F45:f')(+7¬29J,J5C>?9JF?j+3r*L,_.a14V-VL7IQx5E(+7zÌ}j21X98Z},C14@+Q58(+7z,87I.:F?@+QP5E(67
VL7I365EF4@+,:fWF45E(k>?9JF?j+3+,z.IF?@[5014*-@,8*y¹32149]5E*-.:VL7I,5E(+1X5.a14@k;=7i,87I32149E1v5E7:Qc*L@[58FP|>?7:@+7I9E1X58*LF?@6,
,~N1Xnb*-VL*L7I, 0 ^+7a14.0(`.:F?@+,J*L,]5E*L@6>xF4N5pA_FV-7:3658F?@+,mF?9m5pA_FÌ}j2149JZ},:f')(67o3+9J*Lnb149JdrV-7:3658F?@+,YF4N5E(67
5E(6987:7>?7I@+7:981X5E*-F?@+,m149J7q7IVL7I.I5E9JF?@t^+noj+F?@t^ 14@6Qª5E14j27a1X.0(T(21X,Y1X@`14,J,8FK.:*L1X5E7IQª@67:j65898*L@6F+fl')(+7
Ì}j2149JZK,q149J7ij+3t^Q+FHAC@t^.0(2149JnT^¦,J5E9814@+>?7X^5EF?3t^1X@+Qk;¨F45J5EF?nªfq'©14;6VL7eÃUfD±i.:F?@[5E14*L@+,1rV-*L,J5F4N
5E(67N~7:98ne*LF4@+,14@6QP58(+7:*-9nb14,8,J7:,:flg 5C,J(+F?j+V-Qr;¨7z@+FX5E7:Qr58(21X558(+7qOK501X@+Q2149JQ`RªFUQ+7IVt.:F4@}5E14*L@6,
@+F<7M¹U3+VL14@21X58*LF?@rN~F?958(+7:,J7o|i>?7I@+7:981X5E*-F?@+,)@+F49C58(+7Q+*¨7:9J7:@[5mnx1X,8,87I,CF4N"58(+7zN~7:9Jnb*-F?@+,:f
')(+7;=F?,8F?@6,r14987`*L@[5E7I>?9E14Vm,836*L@h32149]5E*-.:VL7I,bAC(+*-.0(hnb7IQ+*w1v5E7T58(+7*-@}587:9814.I58*LF?@+,b;¨7M5pAW7I7:@
5E(67<N~7I98ne*LF?@6,:fo')(67e;=F?,JF?@k,87:.M5EF?9F4N5E(67eOK5014@6Q21498QRTFKQ+7:V©*L@+.IVLj+Q+7I,5E(+7<3+(6F45EF?@¦^t5E(+7iÀ
14@+Q
S
;¨F4,8F?@+,I^5E(+7eÈY*->?>?,I^14@+Q5E(+7<>?V-j+F?@+,g, ,87I7b'"14;+V-7<ÃUfD± 0Mfo')(+7b36(+F45EF4@cne7:Q6*w1X587:,5E(67
7:V-7:.M5E98F4nx14>4@+7I58*L.N~F?9J.:74^258(+7qÀ 14@+Q
S
nb7IQ+*w1v5E7z5E(+7A_7a14ZrN~F?9J.:74^=14@6QT5E(67B>?V-j+F?@+,Cne7:Q+*L1X5E7
5E(67,J5898F?@+>/N~F498.:7Xf¾981aGU*D5pde*L,W@6F45)*L@6.:VLj6Q+7:Q*-@x5E(67OK501X@+Q2149JQPRTFKQ+7:V·^6;+j65*-5_*L,;=7:V-*L7IG47:Qx58F
;=7Wne7:Q+*L1X5E7IQB;[dB,83+*-@U\]Ã)>?9E1aGK*-58F?@tf«')(+73+(6F45EF?@6,©14@6Q/>?VLj6F?@+,"149873+987I,8j+ne7:Q/58F;=7_nb14,J,8VL7I,8,I^
AC(+*-VL758(+7ÀÇ^
S
^+1X@+QªÈY*L>4>?,;=F?,8F?@6,C14987znb14,8,J*-G474f')(+7ne7:.0(214@6*L,8n ;[dAC(+*L.0(r58(+7À 1X@+Q
S
;¨F?,JF?@+,m14.IÌKj6*L987nb14,8,J7:,)AC*LV-Vt;=7zQ+*L,J.:j+,J,87:Q`*L@r5E(+7@+7 ¹K5Y,J7:.M5E*LF4@tf
')(+7YOK501X@+Q2149JQRTFKQ+7IV65E(+7IF?9Jd/(214,,8FN149,]5EFKFUQ<j+3i58FB1XVLVU587:,]5E,5E(21v5l(21aG?7C;¨7I7:@b143+3+V-*L7IQ
5EF*-5Pj6,8*L@6>S321X9J5E*-.:V-7.:F?V-VL*L,J*LF?@6,r1X5P5E(+7k(+*->?(+7I,J5T3¨F?,J,8*-;+VL77I@+7:9J>?*L7I,T9J7a14.0(21X;+VL75EFKQ21ad?^1X,
A_7:VLV14,3+9J7:.I*L,8*-F?@»ne7a14,Jj+987Inb7I@[5E,r1X5xVLFHA_7:97I@+7:9J>?*L7I,:f½')(+7*-@[5E7:9Jnb7IQ+*w1v5E7`(67a1aG}d G?7I.I58F?9
;=F?,8F?@6,:^ À 14@+Q
S
^2A_7:9J7oQ+*-,8.:FHG47:987IQ*L@c±H³?²?|b14@+Q±H³?²4Ée;[dª58(+7i{OU_Oª7M¹U3¨7I98*-nb7I@}58,
Y¿B±c14@+QY¿ÃU^YAC*D5E(Ênx1X,8,87I,P*L@Ê14>?9J7:7Inb7I@}5PAC*D5E(»5E(67c7 ¹U3¨7I.I501v5E*LF4@+,PF4N5E(+7OK5E14@+Q2149JQ
RTFKQ+7:V·fC')(+7B58(+*L9JQTN14ne*LVDdF4NN~7I98ne*LF?@6,m(+14,;=7:7I@.:F?ne3+V-7I5E7IQ`*-@±H³?³XÉx14@6QkÃ4º?º?ºiAC*-58(`5E(67
Q+*-,8.:FHG47:9Jd<FXN¨58(+75EF?3<Ì}j2149JZi14@+Qi58(+7)5014j<@+7Ij65E9J*L@+F;[d/5E(67m{CY1+W^GY ¸;
µÆ´v¶·^U1X@+Q Y ¸ mj+' µÆ²X¶
7M¹U3=7:9J*Lne7:@[5E,m1X5R+27I98ne*LVw1X;tf +©*->?j+9J7ÃUfD±z*LVLV-j+,J589E1X587:,5E(+7,8j6.:.:7I,8,mF4N«5E(+7qOK5E14@+Q21X98QTRTFKQ+7:V*-@
Q+7I,8.:9J*L;+*-@+>BGX149J*LF?j6,N~7I98ne*LF?@b14@+Q;=F?,JF?@x3+9JFUQ6j+.I58*LF?@b3+98FK.:7I,8,87I,)*L@b7 s 7 u .:F?V-VL*-,8*LF4@+,l1X5W«l«f
g 5_*L,:^K(+FHA_7IG?7I9:^+AC*-Q+7:VDd<;¨7IVL*L7MG?7IQb5E(+1X5_58(+7zO}5014@+Q+1498QPRªFUQ+7IV¨*-,_@6F451q.:F?ne3+V-7I5E7C5E(67:F?9]dx1X@+Q
*L,©F?@+V-dB1V-F®A\ 7:@+7I98>4d/143+3+9JFa¹6*-nx1v5E*LF4@oF4N=1neF?987W.:F?ne3+987I(+7:@6,8*-G475E(+7IF?9JdBAC(+*L.0(<,J(+F?j+V-Q<14VL,JF
*L@6.:F?9J3¨F?981X5E7z>49E1aGK*-5pd?f')(67B,]501X58j+,CF4N"58(+7BOK501X@+Q2149JQRTFKQ+7IV*L,)Q+*-,8.:j6,8,87IQ*L@PneF?987zQ67I501X*LVt*-@
√ s (GeV)
Cross section (pb)
e + e − →e + e – qq − e + e − →qq − (γ) e + e − →µ + µ − (γ) e + e − →νν _ (γ)
e + e − →W + W − e + e − →ZZ e + e − →γγ e + e − → W + W − γ
L3 preliminary
10 -1 1 10 10 2 10 3 10 4
80 100 120 140 160 180 200
+©*->?j+987bÃUfD±<T<O}5014@+Q+1498QRTFUQ67:V_1X5B«l T5E(+7b.:j+9]G?7:,o,8(+FHA 5E(+7xOK5E14@+Q2149JQ!RTFKQ+7IV
3+9J7:Q+*-.I5E*-F?@+,iN~F?9/58(+7T.I98F?,J,]\ ,87:.M5E*-F?@+,eF4NYGX149J*LF?j6,e3698FKQ+j+.I58*LF?@3+9JFU.I7:,J,87:,b7M¹U3=7:.I587:Q
5EF!;=7F?;6,87:9]G?7IQ *-@h7as¦7®u .IF?VLV-*L,J*LF?@+,e1X5.:7:@[587:9]\ F4Nw\pnb14,J,r7:@+7I98>?*-7:,k, 0b9E1X@+>?*L@6>
N~98F4n²?³e¾7.58FxÃXº?²e¾7.<^+AC(+*LV-75E(+7qQ+F458,m9J7:3+9J7:,J7:@[558(+7q14.I58j214Vne7a14,Jj+987Inb7I@}58,
3=7:9JN~F498ne7:QrAC*-58(P58(+7q|eQ+7M5E7I.I5EF49Y1v5m«l½µË³X¶·f
Jp ¥¦ +¡2¢ }W «¡¥¦ +§ ¢W
')(+*-,m58(+7:,J*L,.IF?@+.I7:@[5E981X5E7I,F?@ª5E(+7B7:VL7I.I5898FHAW7:14ZP,87I.I5EF49F4N"5E(+7/OK5014@6Q21498QRTFKQ+7:V_µÆÃv¶ ^ AC(+F?,J7
14>?9814@+>?*[email protected]@ª;=7AC98*-5J5E7I@`14,m1i,8j6nF4N«N~F?j+9)5E7I98ne, T
6! #"%$
'&)(
"+*
u-,
!.!.!/0$
21
!*#*#/3$
'&54+6(78( = ,·ÃUf-±0
')(+7R+27:9Jnb*-F?@i14>?9814@+>?*L14@/Q+7I,8.I98*L;=7:,58(+7)Q6dK@214ne*L.I,F4N 5E(67N~7:98ne*LF4@+,:^?*·fÄ7Xf-^X5E(+7I*L9Z}*L@67I5E*-.7:@K\
7:9J>4do14@+Q/*-@}587:9814.I58*LF?@+,«AC*-58(o5E(+7_>[14j+>47W;=F?,8F?@6,:f')(+7:9_14@+>X\ RT*LV-VL,«14>?9E1X@+>?*[email protected]?@[5014*-@+,©5E(67
Z}*L@+7M5E*-.M\p7I@+7:9J>4dª14@+QT,87IV-Nw\p*-@[5E7:9814.I58*LF?@r587:98ne,mF4N5E(67B>[1Xj+>?7¬27:V-Q+,:f)')(+7oÈY*->?>?,m14@+Q;9j+Zv1HAW1
X A
')(+7.IF?@+,J5898j+.M5E*-F?@hF4Nz5E(67cOK5014@6Q21498QÅRªFUQ+7IV7IVL7:.M5E9JF®A_7a1XZS5E(67:F?9]d»,J5E149J58,xAC*-58(h14@h*-@}5898FX\
Q+j+.M5E*-F?@ÊF4Ni1!>[14j6>?7M\ .:FHGX1498*L14@[5rQ+7:9J*-GX1X58*-G?7
H
5EF7I@+,8j+9J7c58(+7k>[14j+>47c*-@[G41X98*w1X@+.:7FXNo5E(67
14>?9814@+>?*L14@ T H
H $
±
Ã
H
8
$
! H 8
"$# ,·ÃUfÃ"0
AC(+7I987% 14@+Q
1X9875E(+7q([dU3=7:9J.0(2149J>?7/14@6QT5E(67B.IF?989J7:,83=F?@+Q6*L@+>b>[14j+>?7z¬27IVLQTF4N©58(+7 bc, ± 0il
>?9JF?j+3t^
" Q67:@+F4587:,o58(+7x>47:@+7I9E1X58F?98,BF4N `bc, Ã<0 h>?9JF?j+3,~.:F?neneF?@+V-d`987I3+987I,87:@[587:Q;}d"14j+VL*
nb1X5E9J*L.:7I, 0 ^K58(+7G?7I.I58F?9]\ ;¨F?,JF?@5E9J*L3+V-7I5
! *L,_58(+74`bc, Ã<0 hb>?14j+>?7¬+7:VLQ¦^614@6Q
14@+Q
149J75E(67
bc,]± 0 l!14@+Q `bc, Ã<0 hr.:F?j63+VL*-@+>?,:^6987:,J3¨7I.I58*-G?7IV-d4f
')(+7Wj6@+Q+7:9JV-dK*L@6>m,]dKnbne7I589Jd*L,,J3¨F4@}5E14@+7IF?j+,8VDdq;+98F?ZX7:@B;}d*-@[5E98FKQ+j+.I*L@+>m1C.:F?ne3+V-7M¹qÈm*L>?>?,
Q+F?j6;+VL7M5 ,,J7:7i5E(+7i@67M¹K5,87I.I5E*-F?@ 0 ^14@+Q5E(67i3+([dU,J*L.:14V>[14j6>?7i;¨F4,8F?@+,1X987/F?;U5014*-@+7:Q58(+98F?j6>?(
ne*D¹U*L@+>oF4N©58(+7@+7:j6589E14V
14@6Q&! DC>[14j+>47¬+7:VLQ6, T
'
,8*L@)(+*,! D $
.IF?,-(+*
#
. .:F?,-(+*,! D @,8*-@)(+*
#
,·ÃUf°|<0
AC(+7I987
'
9J7:3+9J7:,87I@[5E,o58(+7b36(+F45EF4@t^«58(+7<.a149J98*-7:9F4NW58(+7e7:VL7I.I5898F?nb14>?@+7M5E*-./N~F?98.I74^"14@+Qk5E(+7/.
;=F?,8F?@r.:14989J*L7I,W5E(+7@+7:j6589E14V=AW7:14Zx.Ij+989J7:@[5 +58(+7A_7a14Zbnb*y¹U*L@+>o14@+>?V-7*L,_Q+7I¬+@+7:Qª14,.IF?,-(0
21
$3
f©')(+7_.0(2149J>?7:Q/A_7a14Z*-@}587:9814.I58*LF?@+,"149J7Wne7:Q+*L1X5E7IQo;[d5E(+74!Çsb14@+Q5! u/;¨F?,JF?@+,I^
AC(+*-.0(`149J7Q+7I¬2@67:Q1X,
!76 ±
Ã98
!;:=<
!
?>
= ,·ÃUfÄÉG0
¿VD5E(+F?j6>?(h5E(+7k3+([dK,8*-.a14VzGX14.:j6j+n Q+FK7:,P@+F45ª(21aG47c58(+7o`Vbc,·Ã<0ih B bc, ± 0il ,]dKnbne7I589Jd?^
*-5xQ+FK7:,(21aG471nx14@6*-N~7:,]5 bc,]±0x,JdKnbne7I589JdS.:F?9J987I,83=F?@+Q+*-@+>5EF!1V-*L@+7:149e.:F?n/;6*L@21X58*LF?@SF4N
>?7I@+7:981X5EF?9J, T @ " D $ Ã # ,·ÃUfF>"0
AC(+7I987
@
*-,<58(+7ª7:VL7I.I5898F?nb14>?@+7M5E*-.ª.0(+1498>?7X^A *L,i5E(+7T([dU3=7:9J.0(2149J>?74^C14@6Q,"
D
*L,i58(+7TA_7a14Z
*L,JF?,836*L@tf')(67N~7:9Jnb*-F?@+,_14987m5E(+7I@r3+Vw14.I7:Q*-@[5EFoV-7IN 5]\p(214@6Q+7:Q*-,8FX\ Q+F?j+;6VL7I58,W1X@+Q98*->?([5J\ (214@+Q+7IQ
*L,JFX\p,J*L@+>4VL7I58,Y.0(+149E14.M5E7I98*\WI7:Q;[d`58(+7/Ì}j214@[58j+n @}j+n/;=7:9J,"
D
1X@+QB ,,J7:7/'"14;+V-7<ÃUf°Ã<0M^=AC(+7:9J7
5E(67cV-7IN5]\p(214@6Q+7:QÅ14@+QÅ98*->?([5J\ (214@+Q+7IQÊ32149J58,rF4Ni1!>?7I@+7:9J*L.N~7I98ne*LF?@»¬27IVLQDC 149J7>?*-G47:@Å;}d
CUhEF ± Ã%,]±G< QIH 0JC`f
+ 14ne*LV-*L7:, " D
56
h
5 H
J h
5 K
O h ± 1 Ã
@B±
1 Ã
@q±
@q±
º
@q±
5
F
5 H
F
5 K
F º º º
F J F O F º @Ã @q±
h
h
h ± 1 Ã
@B±
1 Ã ± 1 |
± 1 | Ã 1 |
@q±
1 |
F
F F
F
F
F ºº É 1 |
@Ã
1 | Ã 1 |
@B±
1 |
'"14;+VL7YÃUf°ÃT^+27I98ne*LF?@iÌ}j214@[58j+n @Kj6n/;¨7I98,If')(+7*-@+.:V-j+,8*-F?@<F4Nt9J*L>?([5J\ (214@+Q67:Qx@67:j65898*D\
@+F?,C*-,),83=7:.:j6Vw1X58*-G?7 +5E(+7MdP149J7q@6F45C32149]5YFXN"58(+7BOK5014@6Q21498Q`RTFKQ+7:V·f
ÀÊ*-58(<58(+7:,J7Y3=F?,]5Ej+VL1X5E7IQi987:36987:,J7:@[501v5E*LF4@14,J,8*L>4@+nb7I@[5E,:^?58(+7)N~7:9Jnb*-F?@<14>?9E1X@+>?*w1X@/.a14@e;=7
AC98*D58587:@ª14,
6! #"
C Q H H C
$
H
' H $
H
d . H $
6 H
dd
!76
H # ,·ÃUf°Â<0
AC(+7I987z5E(+7N~7I98ne*LF?@6*L..Ij+989J7:@[5E,)58(21X5C.:F4j+3+VL7Y5EFi5E(+7z>?14j+>?7 \p;=F?,8F?@¬+7:VLQ6,
'
^-.B^+14@+Q ! 1X987"T
H
@ C Q H H
C&# ,·ÃUf´"0
H
d
Ã.:F?,-(+*
C Q H ,
@
Q H
02C # ,·ÃUf°²<0
6 H dd
à C h Q H " 6 CUh # ,·ÃUf°³<0
987I,83=7:.M5E*-G47:VDd?^+1X@+Qb58(+7Y,Jj+ne,WF4N C9Jj+@b58(+F?j+>?(x14VLV2V-7:3658F?@1X@+QxÌ}j2149JZ 1aG?F?9J,:f')(+7mN 14nb*-VL*L149
.:F4j+3+VL*-@+>i.:F4@+,J5E14@[5YFXN"58(+77:VL7I.I5898F?nb14>?@+7M5E*-.*L@[5E7I9E14.M5E*-F?@
*-,)>?*-G47:@P;[d
,J*L@)(+*^+AC(6*LVL7
5E(67kG47:.M5EF?9T14@+Q 1v¹U*w14Vy\ G?7I.I58F?932149]5E,ªF4Nq5E(+7k@+7Ij65E9814VzAW7:14Zh.:j+9J987I@}5T(21aG?7k5E(67.IF?j+3+V-*L@+>?,
" D
@Ã
@
,8*-@
(+*14@6Q
! " D
f_g 5m*L,C*-@}587:9J7:,J58*L@+><5EF<@+FX5E75E(21X5)58(+7AW7:14ZN~F?98.I7Q+FU7I,
@+F45m.IF?@+,87I9JG47B321X98*-5pd#" 5E(+7 ! ;=F?,8F4@ª*-@[5E7:9814.I58,CF?@+V-dxAC*-5E(r58(+7VL7IN5]\p(21X@+Q+7:QP321X9J5E*-.:V-7:,I,F49
98*->?([5J\ (214@+Q+7IQª14@[5E*L3+149J58*L.:V-7:,X0Mf
5E7I@+,8F498,Y14,
'&)(
"+*
u-,
!.!.!/
@ ±
É H
H
@ ±
É ! H
!
H
# , ÃUfD±HºG0
3+9J7:Q+*-.I5E*-@+>k5E98*-3+VL7P1X@+Q Ì}j2149]5E*-.ª;=F?,JF?@ .IF?j+3+V-*L@+>?,IfS')(67`.:F4j+3+VL*-@+>?,<;=7I5pA_7:7:@S5E(+7T@+7:j6589E14V
;=F?,8F?@6,B1X987/N~F?9J;+*LQ+Q67:@k14@+Q58(+7<F?@+V-d`14V-VLFHAW7IQ5E98*-3+VL7o14@+QcÌ}j2149J58*L./;=F?,JF?@G?7:9]5E*-.:7:,q987IÌ}j+*L9J7
1X5CV-7a14,]5)5pAWFb.0(21498>47:Qª;¨F?,JF?@+,If
-Ig!
')(+7_ÈY*->?>?,;¨F4,8F?@q*L,«1),83+*-@U\ ºC32149]5E*-.:VL7AC(6*L.0(q;+987:14Z},"5E(67V`bc,Ã"0ih BMbc,]± 0 l,JdKnenb7M5E9JdFXN65E(67
OK5E14@+Q2149JQRªFUQ+7IV;[dª14.:Ì}j+*-98*L@6><1<GX14.Ij+j+n7 ¹63=7:.M501X58*LF?@PGX14VLj674fl')(+7BÈY*L>4>?,¬27:V-QP*L,).0(+F?,J7:@
5EFb;¨7B1b.IF?ne3+VL7 ¹PQ+F?j+;6VL7I5:^2AC(+*L.0(*-,)5E(+7B,8*Lne3+V-7:,J5C3=F?,J,8*L;6VL7q@+F?@U\ 5E98*DGK*w14Vt9J7:3+9J7:,J7:@[501X58*LF?@TF4N
`bc, Ã<0CBobc,]±0M^ 14@+Qr58(+7qÈY*L>4>?,C14>?9E1X@+>?*w1X@r(214,)5E(+7zN~F?9Jn T
21
!*#*#/
,
H
0 , H
0U@',
0 # , ÃUfD±?± 0
AC(+7I9875E(+73=F45E7I@}58*w14V¨N~j+@+.I58*LF?@ *L,58(+7`bg,·Ã<0ihr*-@[G41X98*w1X@}53¨F4587:@[5E*L14VtF4N«5E(67BÈm*L>?>4,¬27:V-Q T
, 0 J
$
, 0 = , ÃUfD±®Ã<0
')(+7i3=F45E7I@[5E*w1XV"n/j6,J5*-@+.:9J7a14,J7oAC*-58($,
0M^¨(+7:@6.:7
º6^=AC(+*LV-7B58(+7/nb14,8,3+149E14ne7I587:9 J
.a1X@,J58*LVLV ;=7@+7I>[1X58*-G?7Xfgp@5E(6*L,.a14,J75E(+7Y3¨FX5E7:@[58*w14V (214,W1o@+F?@K\ 5E9J*-GK*w1XV2nb*-@+*Ln/j6n GX14VLj67
N~F?9
@ J
Ã
Ã
ºA# , ÃUfD±H|G0
AC(+7I987
21
Ã)*L,t58(+7G41X.:j+j+n 7M¹U3¨7I.I5E1X5E*-F?@qGX14V-j+7F4NK5E(+7_ÈY*->?>?,¦¬+7:VLQ¦f"')(+7V`bc, Ã<0 hz,JdKnbne7I589Jd
F4N58(+7ÈY*->?>?,W3=F4587:@[5E*L14V¨V-7a14Q6,_5EF<1qAC(+F?VL7YN 14nb*-V-diFXN©Èm*L>?>4,W>?9JF?j+@+Qr,]501X587:,:f¿mN 5E7I9.0(+FKF?,8*-@+>
1,83=7:.I*-¬2.rF4@+7P14,/5E(67G41X.:j+j+n >?98F4j+@+Q,J5E1X5E7X^_1>?14j+>?7r9JF4501X58*LF?@14VLV-F®AC,Bj+,/5EFAC9J*-587*-58,
7M¹U321X@+,8*-F?@`1X,
,0 ±
à º
$ ,0
# , ÃUfD±aÉA0
VL7:1aGU*-@+>F?@6V-dF?@+73+([dK,8*-.a14VCÈm*L>?>4,o;=F?,8F?@
, 0Mfk')(+*-,/GX14.:j+j6n7M¹U3=7:.M501X58*LF?@!;+9J7a14Z},i5E(67
`bc, Ã<0PB bc,]± 0,]dUnene7I5E9]dk14@+Qk9J7:,8j6V-5E,*-@1P14>?9814@+>?*L14@Q+7I,8.I98*L;6*L@+>P@+F45qF?@6V-d1rnb14,8,J*-G47
ÈY*->?>?,);=F?,8F4@ª;6j65Y14VL,JFenb14,J,8*-G47zG?7:.M5EF?9)¬27IVLQ+, ! 14@+Q .T
21
!*#*#/
±Ã ,
$
0
É . H . H $
É
,!
s
H ! u H $ ! u
H ! s H 0 $ ,·Ã
J
0
$ === , ÃUfD± ><0
g 5,J(+F?j+V-Q`;=7o@+FX5E7:QT5E(21X5Y5E(+7B3+(+F458F?@`¬27IVLQ
'
987Inx1X*L@+,mnx1X,8,8V-7:,J,:fm')(+7/;=F?,8F?@Tnx1X,8,87I,z149J7
5E(67:@ª>?*-G47:@ª;}d
$3
à #
0
à #
ºA#
à J = , ÃUfD±HÂG0
R`14,J,5E7I98ne,mN~F?9C5E(67BN~7:9Jnb*-F?@+,Y14987q*L@[5898FKQ+j+.:7IQ`GK*w1 9j+Zv1HAW1x.IF?j+3+V-*L@+>?,mF4N58(+7BN~7I98ne*LF?@
¬27IVLQ+,)5EFi58(+7Q+F?j+;+V-7I5mÈm*L>?>?,¬+7:VLQ¦^ 14@+Qr5E(+79j+Zv1aAW1x14>?9814@+>?*L14@.a1X@ªAC9J*-58587:@T14,
'&54+6 (78(2 @
$
Ã
# , ÃUfD±®´<0
AC(+*-.0(*Lnenb7IQ+*w1v5E7:VDd>?*DG?7I,B5E(67bN~7:9Jnb*-F?@cnx14,J,87I,/14,
1
Ã}fT')(67x987Inx1X*L@+*-@+>`1v\
>?9814@+>?*L14@h5E7:9Jnb,P3+9JF?3=F?9J58*LF?@21XV5EF
Q+7:,J.:98*-;¨7k5E(67cN~7I98ne*LF?@U\pÈY*->?>?,*-@}587:9814.I58*LF?@+,AC*D5E( 1
.:F4j+3+VL*-@+>ª,J5E9J7:@+>X5E(
1
fr')(+7eN~7:9Jnb*-F?@knx14,J,87I,oQ+*¦7I9B;[dc,87MG?7:9814VWF498Q+7I98,oFXNnb14>?@+*D5Ej+Q+7
,,J7:7q'©1X;+VL7qÃUfD± 014@6Qª58(+7BOK5014@6Q21498QTRTFKQ+7IV.:F?@[501X*L@+,C@+Fe7M¹U3+VL14@21X58*LF?@N~F?958(+*L,)7 ¦7I.I5:f
J ) © +¤ ¢ ) l£ ¡2£ ¢C£
')(+7SOK5E14@+Q2149JQ RTFUQ67:V/(21X,(214Q½5E9J7:ne7:@+Q+F4j+,k,8j+.I.:7:,J,*-@½Q+7:,J.:9J*L;+*-@+>h5E(+7!.IF?@+,8*-Q+7:9814;+V-7
14neF?j+@[5FXNQ21X501kN~98F?n 14V-Vm(6*L>?(U\ 7:@+7I98>4d.IF?VLV-*LQ+7I9e7 ¹U3¨7I98*Lne7:@[58,:f¼')(+7kl lV-7:.M5E98FHA_7a14Z
ÀF?98Z}*L@6>/¾z98F?j63b.IF?n/;+*-@+7:,5E(67YneF?,J5*-nb3=F?9J5E14@[5lnb7:14,8j6987:ne7:@[58,N~9JF?n 5E(+7Yl"^}'"7MGX1X5E9JF?@
14@+QO6Y 7 ¹63=7:9J*Lne7:@[5E,*L@e1q,8*L@6>?VL7¬+55EF5E(67OK5E14@+Q21X98QxRTFUQ67:V"µy±aºX¶ f +©*L>?j6987mÃUf°Ã,J(+FHAC,W5E(67
3+j+V-V"Q6*L,J5898*-;+j65E*-F?@TN~F49o±H²xne7a1X,8j+9J7:ne7:@[5E,j6,87:Qk*-@`5E(+*-,Y¬+5:^¦*-@+.:V-j+Q+*L@6>b5E(67/Q+*L9J7:.M5ne7a14,Jj+987 \
S
Measurement Fit |O meas −O fit |/σ meas
0 1 2 3
0 1 2 3
∆α had (m Z )
∆α (5) 0.02758 ± 0.00035 0.02767 m Z [GeV]
m Z [GeV] 91.1875 ± 0.0021 91.1874 Γ Z [GeV]
Γ Z [GeV] 2.4952 ± 0.0023 2.4959 σ had [nb]
σ 0 41.540 ± 0.037 41.478 R l
R l 20.767 ± 0.025 20.742 A fb
A 0,l 0.01714 ± 0.00095 0.01643 A l (P τ )
A l (P τ ) 0.1465 ± 0.0032 0.1480 R b
R b 0.21629 ± 0.00066 0.21579 R c
R c 0.1721 ± 0.0030 0.1723 A fb
A 0,b 0.0992 ± 0.0016 0.1038 A fb
A 0,c 0.0707 ± 0.0035 0.0742 A b
A b 0.923 ± 0.020 0.935
A c
A c 0.670 ± 0.027 0.668
A l (SLD)
A l (SLD) 0.1513 ± 0.0021 0.1480 sin 2 θ eff
sin 2 θ lept (Q fb ) 0.2324 ± 0.0012 0.2314 m W [GeV]
m W [GeV] 80.410 ± 0.032 80.377 Γ W [GeV]
Γ W [GeV] 2.123 ± 0.067 2.092 m t [GeV]
m t [GeV] 172.7 ± 2.9 173.3
Summer 2005
+©*->?j+987WÃUf°ÃT"l9J7:.I*L,8*-F?@/7IVL7:.M5E9JF®A_7a1XZone7a14,Jj+987Inb7I@}58,14@+QB5E(+7I*L9©36j+VLV-,:^4Q67:98*DG?7IQ/N~98F?n
5E(67q>4VLF?;21XV¨¬+5C5EFi58(+7BOK5014@6Q21498Q`RTFKQ+7:V , 14,CF4NOUj+nenb7I9CÃ4º?ºG>"0Mf
1>?*DG?7:@k321X9E14ne7I587:9:^¨5E(+7i3+j6VLV©*-,Q+7M¬2@+7:Qc14,58(+7iQ+*¦7I987:@6.:7i;=7I5pA_7:7:@c5E(+7ine7a1X,8j+9J7:QGX14VLj+7
F4N"5E(+*-,m3+149E14ne7I587:9C14@6QT5E(67q;=7:,]5J\ ¬+5Q6*-GK*LQ+7IQP;}dP58(+7nb7:14,8j+9J7:ne7:@[5Y7:989JF?9, ,]5014@+Q+1498QªQ+7IGK*y\
1X58*LF?@ 0 f¿¼G?7I9JdP>?FKFKQT1X>?987I7:ne7:@[5C;¨7M5pAW7I7:@ª5E(+7z¬+5J5E7:QT14@+Qªne7a14,Jj+987IQª3+149E14ne7I587:9GX14V-j+7:,)*-,
F?;+,J7:9]G?7:Q¦f
')(+7W36987:.I*L,J*LF?@Bnb7:14,8j+9J7:ne7:@[5E,"F4N658(+7W7IVL7I.I5E9JFHAW7:14Z32149E1Xnb7M5E7:9J,"Q67:3=7:@+Q/V-F?>[149J*-58(+nb*-.a14V-V-d
F?@P5E(+7qÈm*L>?>?,C;=F?,8F4@Tnb14,8,)58(+98F?j6>?(T9814Q+*L1X5E*DG?7z.:F498987I.I58*LF?@+,If_')(67:987MN~F?987X^25E(+7q>?VLF4;214V¦¬+5m.:14@
;=7bj+,J7:Q58FT.IF?@+,J589E14*-@58(+7Èm*L>?>?,nb14,8,q*L@c5E(+7xOK5E14@+Q2149JQ!RTFKQ+7IV fj+©*->?j+987bÃUfÄ|T,J(+FHAC,o5E(67
F4N«5E(+7z¬+5:^+AC(+*L.0(ª>?*-G47:,)5E(67q36987IN~7I989J7:QPG41XVLj+7zF4N"5E(+7qÈm*L>?>?,Wnx14,J,m14,
³6±
s H
u:D
¾z7m.5# , ÃUfD±H²G0
0 1 2 3 4 5 6
100
30 300
m H [ GeV ]
∆χ 2
Excluded
∆α had =
∆α (5)
0.02758 ± 0.00035 0.02749 ± 0.00012 incl. low Q 2 data
Theory uncertainty
+©*->?j+987ÃUf°|T
FXNB58(+7k>?VLF?;+14VY¬+5r58F!5E(+7k3+9J7:.:*-,8*-F?@Ê7:VL7I.I5898FHAW7:14ZhQ21X5E114,P1
N~j+@+.M5E*-F?@F4Nl5E(67iÈY*->?>?,;=F?,8F4@nx14,J,g,14,zF4N_OUj+nene7:9zÃXº?ºG><0 fz')(+7i,8(21XQ+7:Qk987I>?*LF4@
F?@q5E(+7VL7MN5".IF?989J7:,J3¨F?@6Q+,©5EFC5E(67_V-*Lne*-5F?@q5E(+7_ÈY*->?>?,nb14,8,N~98F?n¼58(+7Q+*L9J7:.I5",87:1498.0(67:,
1X5mlÃUf
¬2Q+7I@+.:7ªVL7MG?7IVqµy±Hº®¶ f!g 5<,J(+F?j+V-QS;=7r@+F4587:Q5E(21v5<Q+*L9J7:.I5<,J7a149J.0(+7:,<N~F?9<Èm*L>?>?,i3698FKQ+j+.I58*LF?@1v5
l¼VL7a1XQk58Fª58(+7e.:F?@+.IVLj+,J*LF?@58(21X55E(+7bOK5E14@+Q21X98QU\ RTFUQ67:VÈY*->?>?,z,8(6F?j+VLQc;=7e(67a1aGK*L7:95E(+14@
±?±aÉ6fÄɾ7. ,·³G>¼.IF?@6¬2Q+7I@+.:7CV-7IG?7IV 0_µy±?±M¶ f"')(+7CÈY*->?>?,«Q+*L,J.:FHG?7I9Jdo*L,"58(+7nb14*L@B>?F[14V}F4N258(+7j+3K\
.:F4nb*-@+>o149J>?7YÈ14Q+9JF?@r{WF4VLVL*-Q+7:9 , È{ 036(}dK,J*L.:,W3+98F?>49E14nª^}14@+Qx58(+71X;¨FHG?7YVL*-nb*D5E,*-@+Q+*L.:1X5E7
5E(+1X5)5E(+7BOK5E14@+Q21X98Q`RTFUQ67:VÈY*->?>?,)*-,AW7IVLVtAC*-58(+*L@58(+7987:14.0(`F4N«5E(67BÈ{f
Y7:,J3+*-587o*-58,14363214987I@[5z,8j+.I.:7I,8,:^58(+7<OK5E14@+Q2149JQkRTFKQ+7:V"9E14*-,87I,nb14@[dTj6@214@+,]AW7I987:QcÌ}j+7:, \
5E*-F?@+,I^=7XfÄ>6f-^ *-5mQ+FK7:,m@+F45m7 ¹636Vw14*-@ª58(+7oVL1498>?7zQ6*¨7:987I@+.:7I,*-@T321X9J5E*-.:V-7znx14,J,87I,:^ AC(}dP58(+7:9J7/149J7
5E(6987:7bN~7:98ne*LF4@>?7I@+7:981X5E*-F?@+,:^AC(+1X5i*L,q5E(+7x,8F?j+9J.:7rF4NY{ÇGK*LF?VL1X5E*-F?@t^F?9/(+FHA 5EF`,8F?VDG?75E(67
(+*-7:9E1X98.0([dr3+9JF?;+VL7InF4N«5E(+7qÈm*L>?>?,)nb14,J,:f
G?7:@[58j214VLVDdkF?@+7iA_F?j+VLQ14V-,8FPVL*-Z47/5EFª*L@6.:VLj6Q+7i>?9E1aGK*-5pd*L@c1ªj6@+*-¬27IQc58(+7:F49Jdc14V-F?@+>AC*-58(
F458(+7:9q32149]5E*L.IVL7<*L@[587:9E1X.I5E*-F?@+,If')(+*L,q;+9J*L@+>?,qj+314@+F458(+7:9qÌ}j+7:,]5E*LF4@ ToAC([dk5E(+7bVw14@+.0Zk,J.a14V-7
,
.
±Hº : ¾7.I0*L,),8Fen/j+.0(ª;+*->?>?7:9_5E(214@P5E(67q7IVL7I.I5E9JFHAW7:14Zr,8.:14VL7 , *
±Hº ¾z7m.I0 f
')(+7:,J7z14@+QxF45E(+7I9_*-@+(+7I987:@[5W3+98F?;6VL7:ne,lF4Nt58(+7O}5014@+Q+1498QPRªFUQ+7IV .a14@+@6F45;=7Y,JF?V-G47:QxAC*D5E(U\
F?j655E(+7i*-@}5898FKQ+j+.M5E*LF4@F4Nl,8F4nb7 oµ±®Ãv¶·fq'AWFPF4N58(+7inbF4,J5z3=F?3+j+VL1497 ¹K5E7:@6,8*LF4@+,
F4N«5E(+7BOK5E14@+Q21X98QTRTFKQ+7:V·^2,8j+3=7:9J,JdKnbne7I589JdP1X@+QTneFKQ+7:V-,WAC*-58(ªVL1498>477M¹K5E981eQ6*Lne7:@+,J*LF?@+,I^2149J7
Q+*-,8.:j6,8,87IQ`*-@P58(+7@+7M¹K5Y.0(21436587:9If
m7I.:7I@}58V-d/58(+7¬29J,J5.:V-7a149,J*L>?@<F4N=3+([dK,8*-.:,;¨7Md?F?@6Qe58(+7mOK501X@+Q2149JQxRªFUQ+7IV2(214,;=7:7I@eN~F?j6@+Q
*L@z58(+7N~F498n¼F4NU@+7Ij65E9J*L@+FmF?,8.I*LV-Vw1X58*LF?@+,If©¹U3¨7I98*Lne7:@[58,"j+,J*L@+>m@+7Ij65E9J*L@+F?,>?7I@+7:981X5E7IQo;[d.:F4,8ne*L.M\
9E1adq*L@[587:9E1X.I5E*-F?@+,*L@5E(671X58nbF?,J3+(+7I9874^X;[dB@}j+.IVL7:149«N~j6,8*LF4@o*L@5E(67)OUj+@¦^?14@+QB;[do@}j+.IVL7a1X9«¬2,J,8*-F?@
*L@T987:14.I58F?98,(+1HG47/7:,]5014;6VL*L,J(+7:Q@67:j65898*L@6FX\ 1aG4F?9F?,J.:*-VLVw1v5E*LF4@+, T
5 H 5K
14@6Q
5 6 5 H1<5 K µy±a|X¶ f
¿,1x.:F4@+,87IÌKj67:@+.I74^5E(+7B@+7:jU5E98*-@+F?,Y,8(+F?j6VLQ(21aG47/@+F?@U\ W:7I98Fnb14,8,J7:,I^¦AC(+*L.0(TGU*-F?Vw1v5E7:,mF?@+7BF4N
5E(67OK5E14@+Q21X98QiRªFUQ+7IVK14,8,Jj+nb3U5E*LF4@+,:f©{WF?n/;+*-@+*L@6>C58(+7@+7:j65898*-@+FYF4,8.:*-VLVL1X5E*-F?@Q21X5E1CAC*D5E(qQ+*L9J7:.M5
VL*-nb*D5E,_F?@T58(+7B@67:j65898*L@6Fbnb14,8,J7:,-, ,J7:7o'"14;+V-7BÃUf-±0dK*-7:VLQ6,mnb14,J,87:,m*L@P5E(67B,Jj+;U\p7.$9E1X@+>?7bµy±:É4¶ f
')(+*-,,8(+F?j6VLQ<@+F45l(21aG4714@[do@+F45E*-.:7:14;+VL7)*-nb3+14.I5©F?@i5E(+7C3+([dK,8*-.:,l987I,8j+VD5E,l*L@/58(+*L,58(+7:,J*L,AC(+7:9J7
5E(67q@67:j65898*L@6F?,m1498714,J,8j+ne7:Qª5EF<;=7qnb14,J,8VL7I,8,I^ 14,)7M¹U3=7:.I587:Q*-@r5E(+7BOK5E14@+Q2149JQTRTFUQ67:V f
r `a PC:e q "!#
Y7Ij65E9J*L@+F321X*L9]\ 3+98FKQ+j+.M5E*-F?@/14.I.:F?ne3214@6*L7:Q<;[d/F4@+7CF?9neF?98736(+F45EF4@+,l*L,©58(+7CF?@+V-dB*L9J987IQ+j+.:*-;+VL7
;214.0Z}>?9JF?j+@+QN~F49B@+7MA 3+([dU,J*L.I,i3+98FK.:7I,8,87I,i*L@[G?F4V-GK*L@+>T3+(+F458F?@+,o14@+Qne*L,J,8*L@6>T7I@+7:9J>4d*-@5E(67
¬2@21XV«,]501X5874f ¸ @T58(+7BFX5E(+7I9Y(21X@+Qt^¨1b,J58j+Q6dªF4N"5E(+*-,Y3+9JFU.I7:,J,*L,m*L@[587:987I,J58*L@+>b*L@ª*-5E,J7:VDN,8*-@+.:7q*-5
14V-VLFHAC,F?@+7)5EFzG47:98*DNd/5E(67Y3+9J7:Q+*-.I58*LF?@+,FXN¨58(+7O}5014@+Q+1498QxRTFKQ+7:V 14@6QbQ+7M5E7I98ne*L@+758(+7Y@}j+no;¨7I9
F4N V-*L>?([5"@+7:j65898*-@+F,83=7:.I*L7I,:f¿»Q67IGK*w1X58*LF?@qN~98F?nÇ5E(67)OK5E14@+Q2149JQeRTFKQ+7:VKG41XVLj+7_F4N%$ |YA_F?j+V-Q
.:F4@+,J58*-5EjU5E7/1e.:V-7a149C*L@6Q+*L.:1X5E*-F?@PF4N@+7MAÇ3+([dU,J*L.I,:^t7XfÄ>+fD^=*-5CAWF4j+VLQT,8j+>?>47:,J55E(+7B7M¹U*L,]5E7:@6.:7oFXNl1
@+7MA¼N~7:9Jnb*-F?@>?7I@+7:981X5E*-F?@tf
gp@`5E(67iOK5E14@+Q2149JQRTFKQ+7IV"9J7a14.M5E*LF4@T7 s 7 u 5
5
QU, QZ0 ^=58(+7o3+(6F45EF?@6,149J7o9814Q+*w1v5E7:Qªnb14*L@+VDd
N~98F4n 58(+7*L@+.IF?ne*L@+>7:VL7I.I5898F?@+,14@+QÊ3¨F4,8*-5898F?@6,:^m13+98FK.:7I,8,r.:14VLV-7:Q&''())*+-,(.*(/102*43)*()56
,g]O F?98790:;<()02*6+-=>?0 f:
')(+7I987IN~F4987e1x3+9J7:.:*-,87ine7a14,Jj+987Inb7I@[5zF4Nl5E(+*-,3+9JFU.I7:,J,z3+98FHGK*LQ+7I,
1<j+@+*LÌ}j+7BF?3+3=F?9J58j+@+*D5pd5EF<5E7I,J5z1X@+Q`*-nb3+9JFHG?7z5E(+7q3+9J7:,87I@[5j+@+Q67:98,]5014@6Q+*L@+>xF4N©58(+7Bg]O 1X@+Q
F458(+7:9(6*L>?(+7I9]\ F?98Q+7I912z)Y 7 ¨7:.M5E,*L@`58(+7oN~7I98ne*LF?@`14@+Q;=F?,8F?@3698FKQ+j+.I58*LF?@`*L@(+*->?(U\ 7:@+7I98>4d
@BADCFE6GHJI'K)LGLMN.GOPCQGLCFRSETCQKUERLVGWHXHXRYZMO\[M2]2GW^6K_M`L_a6MEMb^L_NCFER9KUGWNM`EM2^PL_N.GWHdceGWN_L_CQ]BHXM2K2fghRYZM2iMbNjlkmRNVG
+©*->?j+987/ÃUfÆÉT*+27IdK@+nb14@Q+*L14>?9814nb,mF4Nl5E(67/5E987I7M\ VL7IG47:V3698FK.:7:,J,z7ast7®u
5
5
fBgp@5E(67
3EK.0(214@6@+7:V·^_1XVLV_58(+987I7r@+7:jU5E98*-@+F,83=7:.I*L7I,b1X987r3214*-9]\ 3+98FKQ+j+.I7:QGK*w1
S
7M¹U.0(21X@+>?7ª1G0M^
AC(+7I987a1X,WF?@+VDd<7:V-7:.I5898F?@b@+7:jU5E98*-@+F?,_14987Y14V-VLFHAW7IQb*-@e58(+7
E}.0(214@+@+7IV=À 7M¹U.0(214@+>47; 0Mf
7 s 7 u .:F?V-VL*L,J*LF?@6,:f¿Y@`14.I.:j+981X5E7Q+7I,8.I98*L3U5E*LF4@ªFXN,8j6.0(`.:F498987I.I58*LF?@+,C*-,)987:Ì}j+*-987IQªN~F?958(+7q3+987I.:*D\
,8*-F?@Pnb7:14,8j6987:ne7:@[58,1X5ml
1X@+Q`1v5)N~j65Ej+9J7(+*L>?(K\p7:@67:98>Xdr7as¦7®u.IF?VLV-*LQ+7I98,If
pJ ¥¦ 2§ ¢_
gp@Ê5E(+7OK5E14@+Q2149JQ RTFUQ67:V ^m5E(+7k9J7a14.M5E*LF4@Å7 s 7 u 5
5
3+9JFU.I7:7IQ+,r5E(+9JF?j+>?( 3EK.0(214@+@67:V
S
7M¹U.0(21X@+>?7oN~F?9Y14V-Vt5E(+9J7:7o@67:j65898*L@6F 1aG?F498,g,
5
5 6
#
5 H
#
5K
0C14@+Qª5E(+9JF?j+>?(
E}.0(214@+@+7IV«À 7 ¹}\
.0(214@6>?7YN~F?9l7IVL7:.M5E9JF?@x@+7Ij65E9J*L@+F4,_F?@6V-d?f©')(+7V-F®A_7:,]5F?9JQ+7:9P,q560! 4%0:5#"p'; *(_56:0Q+*L14>?9E1Xnb,
F4N)58(+*L,/3698FK.:7:,J,<14987x,8(+FHAC@*L@ +"*L>?j+9J7ÃKfÄÉ+f m,8*-@+>`5E(67j+ 7MdK@+nx1X@98j+V-7:,I^5E(+7r1Xnb3+V-*-58j+Q+7:,
$ 14@6Q $ 0 .:F?9J987I,83=F?@+Q+*-@+>e58Fi5E(+7I,87qQ+*w14>49E14ne,.a1X@ª;=7zAC98*D585E7I@`1X,
$&%
('%6
EH EK
Ã.IF?,
(+*
,
5
Q
H*)
h
5 0
H#+
@-,
H
, +
1
@.,
µ F 7 Q
+) F=7
$ h
73Q
+/) hU7t¶ #
$10
à , 7/Q
H/)
h
5 6 0
H#+
@., H0 , +
0 1
0
0
@-,
0 ,
56
Q
+*)
hK70 # , ÃUfD±H³G0
AC(+7I987
)
hEF ,]±< QIH30
1
ÃQ+7:@+FX5E7:,<5E(67ª.0(6*L9E1XV3+98F2J7:.I58*LF?@F?3=7:981X5EF?9J,<14@+Q
F , @
!
0 1 Ã ,J*L@
(014@6Q
h ,
$
0 1 Ã @ : $ ,8*-@
(0149J758(+7q.:F?j+36VL*L@6>b.IF?@+,J5E14@[5E,mF4N
5E(67q9J*L>?([5]\14@+QªVL7MN 5J\p(+14@+Q+7IQª7IVL7I.I5E9JF?@+,)5EFi58(+7 .Ç;=F?,8F4@tf
3 ARSN M54GWnocHXMj LaM ^E6]bMbN_LGWCXE9L76 RE L_aMqL_a6MbRNMBLCX]2GWH OPMK_]bN_CXcPL_CXRE RWkULaM CFE6CJLCXGHJI GE6O986EeGWHFIK)LGWL_MqNGWI
OPCQGLCFRSE CXE LaMoN_MG]/LCFRSE M;:rM=<> u?:u@<>.ACBDFEHGhCXKGWE CFnocRN_LGESLK_R^N.]BM RWkZKI6PKLMbn GLCX] MbNNRN.KURE L_a6M
')(+7 WF?98@K\pVL7MG?7IV.:98F4,8,C,87I.I5E*-F?@ª*L,5E(67:@ª>?*-G47:@ª;}dkµy±HÂv¶
6<6
, 0 $
Â
,
F
$3
h 0
µ, R@
0 $ , 0
¶
@
h
0
, R@
0
, R@
0 $ , 0
, $
0 0
VLF?>
$
0
0 @
0
@ |
Ã
$
0 $
Ã
0
Ã)
@
0
$
0
V-F?>
$
0
0 # , ÃUf°Ã4ºG0
AC(+7I987 r*L,q5E(+7x.:7:@[587:9]\ F4Nw\pnb14,J,/7:@+7I98>4d4^ª*L,q5E(+7xAC*-Q65E(!FXN)5E(+7
S
;=F?,JF?@t^l14@+Q
*-,
5E(671+27:98ne*=.:F?j+36VL*L@6>/.:F?@6,J501X@}5,
1 Ã 1 ²
0
0Mf')(675E(+9J7:75E7I98ne,*L@lÌ}j21v5E*LF4@ªÃUfÃXº
F?9J*L>?*-@21X5E7N~9JF?n 5E(67,8Ì}j21X987FXNt5E(+7
S
@1Xnb3+V-*-58j+Q+74^?58(+7YÀ @ S
*-@}587:9]N~7:987I@+.:7X^214@+Qe5E(+7Y,8Ì}j2149J7
F4Nm5E(+7rÀ @Y14ne3+VL*D5Ej+Q+7X^l987:,J3¨7I.I58*-G?7IV-d4fS')(+7P¬29J,J5<5E7I98n*-,/5E(+7ªF?@+VDdF?@+7P,J7:@+,J*-5E*DG?7r5EFk5E(67
@}j+n/;=7:9F4N=V-*L>?([5"@+7:j65898*-@+Fz,83=7:.I*L7:,$ ,8*-@+.:7)F?@6V-dq5E(+77IVL7I.I5E9JF?@<@+7:jU5E98*-@+F?,.:14@<;¨7W3+98FKQ+j+.I7:Q
*L@i58(+7
EK.0(214@+@67:V f©g 5_,J(+F?j+V-Qb;=7C@+F4587:Q<5E(21X5l*-@i5E(+7YOK5E14@+Q2149JQRªFUQ+7IV ^?58(+7C.:98F4,8,,87:.M5E*-F?@+,lF4N
5E(67
5H
5H 14@+Q
5 K
5 K
3214*-9]\p3698FKQ+j+.I58*LF?@r.:14@ª;¨7q14,J,8j+ne7:QP5EFe;¨7*-Q+7:@[5E*-.a14V¦,8*L@6.:7,8nb14VLV¦7 ¨7:.I58,
149J*L,8*-@+>/N~98F4n3=F?,8,J*L;+VDd@+F?@%W:7:9JFb@67:j65898*L@6Fbnb14,8,J7:,m149J7zj+@+Q+7M5E7:.M5014;6VL7B1X5m«f
')(+7 WF?9J@U\pV-7IG47:V«.:98F4,8,,J7:.I58*LF?@FXN5E(+7/9J7a14.M5E*-F?@`7 s 7 u 5
5
*-,,J(+FHAC@c*-@f+©*->?j+987oÃUf?>416fD
¿5e7:@+7I98>?*-7:,b1498F4j+@+Q!5E(+7
S
3¨F?V-74^ ³U±`¾z7m. ,·l)±T7I@+7:9J>4d9E14@6>?70 ^58(+7
56
5 6 1X@+Q
5 H
5 H
.I98F?,J,,87I.I5E*-F?@+,14987o14VLneF?,J5C58(+7o,814nb7B987:14.0(+*L@6>x5E(+7Bnx1®¹6*-n/j+nGX14V-j+7qF4N|6fijb@};t^t1X@+Q
5E(67
EK.0(+14@+@+7IV«.IF?@[5E9J*L;+j658*LF?@P5EF<5E(67
56
5 6
.I98F?,J,Y,J7:.I58*LF?@`14neF?j+@[5E,)5EFeF?@+VDdP14;=F?j65± f_')(+7
,8*D5Ej21v5E*LF4@/.0(214@+>47:,1X5llÃz7I@+7:9J>?*L7I,:^ ½Ã4º?º¾z7m.<^?AC(+7I98758(+75iEK.0(+14@+@+7IV2.:F?@[5E9J*L;+jU5E*LF4@
.:V-7a149JV-dxQ+F?ne*L@21X587:,I^
! #"
, 5 6
56
0 É[ºi3+;`1X@+Q
"
, 5 H
5 H
0 ±3+;f
')(+7W*-@+.:V-j+,8*-F?@F4N658(+7g]O 14@+QoFX5E(+7I9"(+*->?(+7I9]\pF498Q+7I9 2)Y .IF?989J7:.M5E*LF4@+,"*-,G?7:9]dq*Lne3¨F?9]5014@[5
N~F?958(+*L,z3+9JFU.I7:,J,:f +©*L>?j6987<ÃUf?>X;c,8(+FHAC,5E(+7<.I98F?,J,q,J7:.M5E*LF4@F4N5E(67e9J7a14.M5E*-F?@k7 s 7 u 5
5 , QZ0M^
14,Y3+987IQ+*L.M5E7:Q`;}dª5E(67%$$'&(r3+9JF?>?9814n µy±H´v¶"AC(6*L.0(`5E14Z47I,*L@[5EFx14.:.IF?j+@[558(+7og]O 7 ¦7I.I5E,g, ,87I7
OU7I.I5E*-F?@!ÃKfÃUfÄ|G0 f`{WF4nb321X98*L@6>ª58(+7g]O \p.IF?989J7:.I587:Q!1X@+Q WF?9J@U\pV-7IG47:Vl.:9JF?,8,/,J7:.M5E*LF4@+,:^©A_7.:14@
,87I7/5E(21v5z1X5«lÃb5E(67/*L@+.IVLj+,J*LF?@TF4Nlg]O *L@+.I987a1X,87:,58(+7B58F4501XV
5 H
5H
,Q 0m.:98F4,8,,J7:.I58*LF?@;[d`1
N 14.M5EF?9CF4N,J7IG47:@t^
!)+*
F ,
5 H
5 H
0, ´<36;f')(+*L,m7 ¨7:.M5.:14@`;=7B7:14,8*-V-drj6@+Q+7:9J,J58FUFKQ`;[dª7M¹614ne*L@U\
- gUM2N_M`GWEeO\CXE\LaM kmRHXHFRY CXEwejSLaMCFEeOPM 4/.>kmRSNZLaM`OPC10M2N_M2ESLUE6Mb^PLN_CXERoK)cM2]bCFMKsCXKsRSn CFL)LM2OqGWE6OqG K)^n"RWk
GWHXH4wM2EMbN.GLCFRSE6KCXKhOPMbERL_MOTGSK32#4654pf7
e + e − → νν _ e + e − → ν e ν _ e e + e − → ν µ ν _ µ
√s (GeV)
Cross section (nb)
LEP1-LEP2 (Born)
a)
10 -3 10 -2 10
-1 1 10
80 100 120 140 160 180 200
e + e − → νν _ (γ) e + e − → ν e ν _ e ( γ ) e + e − → ν µ ν _ µ (γ)
√s (GeV)
Cross section (nb)
LEP1-LEP2 (KKMC)
b)
10 -3 10 -2 10
-1 1 10
80 100 120 140 160 180 200
√s = 200 GeV
c) ν µ ν _ µ (γ) + ν τ ν _ τ (γ) ν e ν _ e (γ)
Invariant Mass (GeV)
∆σ / ∆ M inv (pb/4 GeV)
10 -3 10 -2 10 -1 1 10
0 50 100 150 200
+©*->?j+987rÃUfF>:Tr'"F45E14V.I98F?,J,e,J7:.M5E*LF4@SF4NC58(+7P987a1X.I5E*-F?@7as¦7®u
5
5 , QZ0/14,<1N~j+@+.M5E*-F?@
F4N5E(67c.I7:@[5E7I9]\ F4Nw\pnb14,8,r7I@+7:9J>4dÊ1G0b1X5 WF?9J@U\pV-7IG?7IVz14@+QÊ; 01X,r3+987IQ+*L.M5E7:QÅ;[d»5E(67
$$'&(3+9JF?>?9E1XnTfÅ.0b')(67
5
5
*L@[GX149J*w14@[5bnx14,J,xQ+*-,J5898*L;6j65E*-F?@»1X5
Ã4º4º¾z7m.
N~F?9z1X@c7MG?7I@}5B,E1Xnb3+V-7/>?7I@+7:981X5E7IQcAC*D5E(5E(+7 $$'&6(`3+9JF?>?9E1XnTf/{WF?@[5E98*-;+j658*LF?@+,YN~98F?n
Q+*¦7I987:@[5m@+7Ij65E9J*L@+F<,83=7:.I*L7I,149J7z,8(+FHAC@T,87:3+149E1X587:VDd?f
*L@6>5E(+7<*L@[GX149J*w14@[5nb14,J,zQ+*L,]5E98*-;+j658*LF?@FXN_58(+7
5
5
3214*L9J, ,,J7:7 +©*L>4j+987<ÃKfF>X. 0Mfg+2F?9Y5E(+7in/j6F?@
@+7Ij65E9J*L@+F?,I^5E(+7xnx12JF498*-5pdkFXNC>?7:@+7I9E1X587:Q!7MG?7:@[58,e(+1HG475E(+7b*L@[GX1498*L14@[5/nb14,8,B.:V-F?,87e5EF`58(+7
S
nb14,8,/T
, 5 H
5 H
0 ofo')(}j+,I^«58(+7i3+(+FX5EF?@c7:ne*L,J,8*LF4@(214,z5E(67i7 ¨7:.I5qF4N9J7:Q+j+.I*L@+>P5E(67
7 ¨7:.M5E*DG?7.:7I@}587:9 \pF4Nw\ nx14,J,)7:@+7I98>4dbN~98F?nÃ4º?º<¾z7m.Ç5EFe14;=F?j65)³6±q¾7.<^6AC(+7I987z5E(+7 _F?98@U\ VL7MG?7:V
.:9JF?,8,,87:.M5E*-F?@`*-,n/j+.0(`(+*L>?(67:9:fC')(+7
S
;¨F4,8F?@+,Y*L@ª5E(+7 /E}.0(214@+@+7IV149J7B3698FKQ+j+.:7IQ3+987IQ+F?ne*D\
@214@[58V-dPF?@U\ ,8(+7IVLV·f_')(+*-,Y7 ¦7I.I5:^¨.:14VLV-7:Q ( 02*43)*() 0()=0 (/5 ( ^2A1X,YF?;6,87:9]G?7IQN~F?9m14VLV
N~7:9Jnb*-F?@k3214*-9]\p3698FKQ+j+.I58*LF?@3698FK.:7:,J,87I,i1X5BÃUfx')(+7b9J7:,Jj+V-58*L@+>ª3¨7:14Z*L@58(+7e5pA_FX\ N~7:98ne*LF4@
+"*L>?j+9J7qÃUfÄÂ%TlF®A_7:,]5J\ F?98Q+7I9P+27MdU@6nx14@PQ+*L14>?9814nb,_N~F?95E(+79J7a14.M5E*LF4@ª7 s 7 u 5
5
Q«f
,8(6F®AC,"5E(21X558(+7W7IVL7:.M5E9JF?@o@+7Ij65E9J*L@+F4,©149J7_3698FKQ+j+.:7IQ/3+9J7:Q+F?ne*L@+14@[5EV-d*L@5E(+7
EK.0(214@6@+7:V·^4AC(+7:9J7
, 5 6
56
0 ?f
pp ¡2¢C£¤¥¦ +§]¢_ ¢ Y§] l£ ¤ +§ ¢l 6¢_ '« ©
¿,<,J(+FHAC@ *L@$+©*->?j+9J7ªÃUf°ÂU^58(+7P987a1X.I5E*-F?@7ast7®u
5
5
Qh3+9JFU.I7:7:Q6,bnb14*L@6V-dcGU*L1*L@+*D5E*w1XV_,]501X587
9E1XQ+*w1X58*LF?@bN~98F?n58(+7*L@+.IF?ne*L@+>i7IVL7:.M5E9JF?@+,m14@+QP3=F?,8*D5E98F4@+,:flgp@T14Q+Q+*D5E*LF4@t^+1i,8nb14V-V¦N~9E14.M5E*-F?@rF4N
3+(+FX5EF?@+,*,#¼º%=?> 0.:14@x;=77Inb*D58587:Qx*-@b58(+7
EK.0(+14@+@+7IV¨À ;=F?,8F4@xN~j+,8*-F?@f,+©*L>4j+987ÃUfÄÂ470mµy±a²X¶ f
OU*-@+.:7C5E(+7m3+9JFUQ+j6.:7:Qx@+7:j65898*-@+F?,14987mj+@+Q67I5E7I.I5E14;+VL7X^H),Jj+.0(7MG?7:@[58,WAWF4j+VLQbVL7a1XQe58Fq58(+7Y,J*L@+>4VL7M\
3+(+FX5EF?@14@6Q!nb*-,8,8*-@+>7I@+7:9J>4d,J*L>?@21v5Ej+9J74fk')(+7:9J7IN~F?9J74^5E(675EF45E14V_981X5E7xF4NC5E(+7*-@+*-58*w14Vl,]501X587
9E1XQ+*w1X58*LF?@e14,lA_7:VLV¨14,l5E(+7Y7:@+7I98>4db14@6Q14@+>4j+Vw149lQ+*-,J5898*L;6j65E*-F?@+,F4Nt58(+77Inb*D58587:Qe3+(+F458F?@+,W(+1HG47
5EF<;=7ZK@6F®AC@ª5EFe1i(+*L>4(ª36987:.I*L,J*LF?@tf
¿ >47:@+7I9E14V«14@+Qª,8*-nb36VL7143+3698F[14.0(ª5EF<5E(+*-,)3+98F4;+VL7In*L,5EF"!JQ+9J7:,J,$#x58(+7_F?98@U\ VL7MG?7:V.I98F?,J,
%'& EH6TG L_CXE 6 kmN.G]BL_CXRE9D)( P+*<-,5GRk P$*.*0/ M21 EM2^PL_NCXERSKsYR^HQOqCFE9LMbN.G]/L Y CFL_a LaMn GLMbNCXGH4RWkDL_aM J43
OPMbL_M2]BL_RSN OP$5TS f
,87I.I58*LF?@ªF4N«5E(+7
5
5
3214*-9)3+98FKQ+j+.M5E*LF4@ , , 0 0_AC*D5E(ª1i9E14Q6*w1X58F?9WN~j+@+.M5E*-F?@
, #?( 0zµÄÃ4ºv¶ T
à ±
à ± $
,]±R@ "0
,J*L@
( $ É
6 1 @ # , ÃUf°ÃU± 0
AC(+7I987
1
^ 6
*-,W5E(67q7IVL7I.I5E9JF?@rnb14,8,I^214@+Q *L,_5E(+7I2z)Y .IF?j+3+V-*L@+>o.:F?@+,]5014@[5:f
')(+7qQ+*¨7:9J7:@[5E*L14V¦.I98F?,J,Y,J7:.M5E*LF4@TF4N«5E(67q9J7a14.M5E*-F?@P7as¦7®u
5
5
Q.a14@P5E(67:@ª;¨77IGX14V-j21X587:Qª14,
.:F?,(
,Jµy± @ ®¶8 0U8
, # ( 0Z= , ÃUf°Ã?Ã<0
©¹+1Xnb*-@+*L@+>lÌ}j21v5E*LF4@<ÃUf°ÃU±?^4A_7).a14@<,J7:75E(+1X55E(67Q+*¨7:9J7:@[5E*L14VK.:98F4,8,,87I.I58*LF?@i*-,7M¹U3=7:.I587:Q
5EFo3¨7:14Zx1v5VLFHAÊ3+(6F45EF?@r7I@+7:9J>?*L7I,)14@+Qx3¨F?VL149_14@+>?V-7:,:f©gp@P14Q+Q+*D5E*LF4@t^KlÌ}j21v5E*LF4@ªÃUfÃ4Ãq7M¹U3+VL14*L@6,
5E(67i143+3=7a149814@+.I7iF4N5E(+7
S \ 987M5Ej+9J@3¨7:14Z fgp@5E(+7 3EK.0(21X@+@+7:V·^¦5E(67 WF?9J@U\pV-7IG?7IV©.I98F?,J,z,87:.M5E*-F?@
, 0"*-,G?7I9Jdi(+*->?(i@+7:1495E(+7
S
3=F?VL7W,8Fz5E(21v55E(+7)Q6*¨7:987I@[5E*w1XV6.:9JF?,8,l,J7:.I58*LF?@<(21X,l1nx1v¹U*-n/j+n
N~F?93+(+FX5EF?@+,zAC*D5E("056'+`; *6.:V-F?,87<5EFP5E(67
S
;¨F4,8F?@cnx1X,8,:fb')(+7e3+(+F458F?@9J7:.IF?*LVnb14,8,*-,
Q+7M¬2@+7:Q`14,)5E(+7*-@}GX149J*w14@[5)nb14,J,)987:.IF?*LV-*L@+><1X>[14*L@6,J558(+73+(+F458F?@, ,X0)14@+Qª*L,)>?*DG?7:@ª;[d
\6
8 @ >
@
# , ÃUf°Ã4|G0
AC(+7I987 /14@6Q
o149J7`5E(675EF45E14V7I@+7:9J>4dÊ14@+QhneF?ne7:@[5Ej6n F4N5E(67
3+(+FX5EF?@+,If +2F?9C,8*-@+>?VL7 \p3+(6F45EF?@P7MG?7:@[58,:^tÌ}j21X58*LF?@ÃUf°Ã4|e,J*Lne3+VL*D¬27:,_5EF
\6
R@Ã
Wf
')(+7)3=F?,8*D5E*-F?@/F4N 5E(67
S
\p987M5Ej+9J@i3¨7:14Zo*-@/5E(+7)9J7:.IF?*LVUnx14,J,Q+*-,J5E9J*L;+jU5E*LF4@/*L,*-@+Q+7I3¨7I@+Q+7:@[5F4N 5E(67
.:F4VLVL*-,8*-F?@T7I@+7:9J>4d?f')(+7I987MN~F?987X^t*L@+,]5E7:14QF4Nj+,8*-@+>x58(+7/3+(+FX5EF?@7I@+7:9J>4d`GX149J*w14;+V-74^ 5E(+7o3+(+F458F?@
987I.:F?*-Vtnb14,8,C*L,)j6,8j214V-V-dxj+,87IQtf
')(+7z9E1XQ+*w1X58F?9lN~j+@+.I58*LF?@143+3+9JF[14.0(r*L,W.a14321X;+VL7YF4N.a14V-.:j+VL1X5E*-@+>B58(+758F45014V=.:9JF?,8,),J7:.M5E*LF4@F4N
5E(67),8*L@6>?VL7 \p3+(+FX5EF?@B3+98FKQ+j+.M5E*LF4@/AC*-5E(<136987:.I*L,J*LF?@/FXN¦1X;¨F?jU5É µÄÃU±M¶ f©')(+*L,V-7IG47:V+F4N¨14.I.:j+9814.Id
*L,)@6F45m,E1X58*L,JN 1X.I5EF49JdxN~F49)nodP14@21XV-dK,8*-,:f')(+7I987IN~F49874^2g_j+,87q,83=7:.I*w14V-V-dbQ+7IG47:V-F?3¨7IQRªF?@[5E7o{1498V-F
3+9JF?>?9E1Xnb,5EFT,8*Lnoj+Vw1X587i5E(+77:s¦7vu
5
5
QU, QZ03698FK.:7:,J,j,,J7:7@67M¹K5i,87I.I58*LF?@ 0 fT')(67xN~F?VLV-FHAC*L@+>
Q+*¦7I987:@[58*w14VtQ6*L,J5898*-;+j65E*-F?@+,WA_7:9J7BF4;65014*-@+7:QPj+,J*L@+>i58(+7;$ $'&6(3+9JF?>?9E1XnTf
¿,CQ+*-,8.:j6,8,87IQ`*-@ª{W(21436587:9mÂ6^658(+7nx14*-@GX1498*L14;+VL7I,Wj+,J7:QT*L@5E(67q,J7:V-7:.I58*LF?@PF4N«,J*L@+>?V-7M\1X@+Q
n/j+VD5E*y\p3+(+FX5EF?@7IG47:@[5E,rA_7:98758(+73+(6F45EF?@ 3¨F?VL149b14@+>?V-7 ,( "0e14@+Q»589E14@+,]G?7I98,87neF?ne7:@[5Ej6nT^
)
",8*-@)( KfW7:.:14j+,87z58(+77e.:*-7:@+.MdrF4N5E(+7q|o5E9814.0Z47I9CQ+7:.I987a1X,87:QT9E1436*LQ+VDdbAC*D5E(P3¨F4Vw149
a)
e + e − → ν e ν _ e γ e + e − → ν µ ν _ µ γ
√s = 205 GeV
|cos θ γ |
∆σ / ∆ |cos θ γ | (pb/0.02)
10 -3 10 -2 10 -1 1 10
0 0.2 0.4 0.6 0.8 1
b)
e + e − → ν e ν _ e γ e + e − → ν µ ν _ µ γ
θ γ > 14 o X T = P γ T / E beam
X T
∆σ / ∆ X T (pb/0.02)
10 -2 10
-1 1
0 0.2 0.4 0.6 0.8 1
c) ν e ν _ e γ ν µ ν _ µ γ
√s = 205 GeV P γ T > 0.02√s θ γ > 14 o
Recoil Mass (GeV)
∆σ / ∆ M rec (pb/4 GeV)
0 0.1 0.2 0.3
0 50 100 150 200
d)
s-channel
t-channel + interference e + e − → ν e ν _ e γ
|cosθ γ |
∆σ / ∆ |cos θ γ | (pb/0.05)
0 0.05 0.1 0.15
0 0.2 0.4 0.6 0.8 1
+©*->?j+987ªÃKf´TY*-,J5E9J*L;+jU5E*LF4@+,/F4N1G0o5E(+7P3=F?Vw1X9<14@+>?V-7P14@+Q; 0o5E(+7r5E9814@+,]G?7:9J,87TnbFX\
ne7:@[5Ej+n$N~F?9_,8*-@+>?VL7 \p3+(6F45EF?@e7IG47:@[5E,C>?7I@+7:981X5E7IQxAC*-58(r1B58(+987I,8(+F?V-Q
±¾7.<^61v5
Ã4ºG>B¾7.<f')(+7z1X9898FHAC,_*L@+Q+*-.a1X587m58(+7 !],87:V-7:.M5E*LF4@#o.Ij65E,IfY*-,J5898*L;6j65E*-F?@+,F4N. 0
5E(67q9J7:.IF?*LVtnb14,J,Y1X@+QPQ 0W5E(+73=F?Vw14914@+>?V-71XN5E7I95E(+7q143+36VL*L.:1X5E*-F?@F4N«5E(67:,87q.:jU5E,:f
14@+>4VL74^X1CVLFHAW7I9".Ij65"F?@B58(+7_3=F?VL14914@+>?V-7lF4N+5E(67_3+(6F45EF?@B(214Q5EFY;¨7_143+3+V-*L7IQ9_±:É 7 ( g7 ±HÂ?Â:f
')(+7nb14*-@o;214.0Z}>?9JF?j+@+Qi58F5E(+*-,"58F?3¨F4VLF?>4d,]5E7Inbne7:Q/N~9JF?n½5E(+79814Q+*L1X5E*DG?7 W(214;+(+1,8.a1v585E7I98*-@+>
3+9JFU.I7:,8,I^¦7:st7vu
7ast7®uQ«^=AC(67:987B;¨FX5E(`7IVL7I.I5E9JF?@+,mAW7I987/V-F?,J5Y*L@P5E(+7B;¨7:14n 3+*L3=74^=14@6Q`F?@+VDdª1
3+(+FX5EF?@AW14,i,8.:1X58587:9J7:Q1X5<1VL1498>?7e3=F?Vw149o14@+>?V-74f'«F9872J7:.I5/,8j+.0(7IG47:@[5E,I^58(+75E9814@+,JG47:9J,87
neF?nb7I@[5Ej+n#FXNW5E(67e36(+F45EF4@AW14,B9J7:Ì}j+*-987:Qk5EFª;=7x14;=FHG?7bº%=ĺ[à [fb')(+7:,J7b5pA_F !J,J7:V-7:.I58*LF?@#
.:jU5E,CQ+7I¬+@+7:Qª5E(+73+(21X,87q,83214.I7B9J7:>?*-F?@rF4N"nodr,J*L@+>?V-7M\ 3+(+F458F?@r,87IVL7:.M5E*-F?@tf
¿,",8(+FHAC@/*-@-+©*->?j+9J7WÃKf´41U^v58(+7W1X@+>?j+VL149.:j65"9872J7:.M5E7:Q<1X;¨F?jU5©²4º F4N2;=F458(q58(+7
5H
5H Qe1X@+Q
5 6
56
Q7IG47:@[5E,Ifi')(+7iQ+*-,J5E9J*L;+jU5E*LF4@F4Nl5E(+7i,J.a14V-7:Q589E14@+,]G?7I98,87eneF?nb7I@[5Ej+nª^ )
1
^
a)
Recoil Mass (GeV)
∆σ / ∆ M rec (pb/4 GeV)
0 0.2 0.4 0.6 0.8 1 1.2 1.4
0 50 100 150 200
b)
√s = 200 GeV e + e − → νν _ γ
E γ > 1 GeV θ γ > 9.9 o P γ T > 0.02√s θ γ > 14 o
cos θ γ
∆σ / ∆ cos θ γ (pb/0.05)
0 0.2 0.4 0.6 0.8 1
-1 -0.75 -0.5 -0.25 0 0.25 0.5 0.75 1
√ s (GeV)
Cross section (pb)
LEP2 (KKMC)
c) Σ n ν n ν _ n γ(γ) n=e,µ,τ Σ m ν m ν _ m γ ( γ ) m= µ , τ ν e ν _ e γ ( γ )
P γ(γ) T > 0.02√s θ γ > 14 o
0 5 10 15 20
140 160 180 200
+©*->?j+987ÃUfIJ%TUY*¦7I987I@}58*w14V}.I98F?,J,,87:.M5E*-F?@+,F4N258(+7987:14.I58*LF?@i7:s¦7vu
5
5
Q14,"N~j+@+.I58*LF?@6,
F4Nq1G0/5E(67987I.:F?*-Vmnb14,J,r14@+Q»;0e.:F4,-( K^).a14V-.:j+VL1X5E7IQSAC*-58( 5E(67 $$&6(3+98F4>?9E14n 1v5
Ã4º?ºe¾z7m.ifl. 0)'«F45E14Vt.:9JF?,8,m,87I.I58*LF?@PF4N«5E(+79J7a14.M5E*LF4@ª7
s 7 u 5
5
QU, Q 0 f
1XN587:9r5E(+*-,r.:j65T*L,r,J(+FHAC@¼*L@ +©*->?j+9J7cÃUf´v;tf ')(+7cGK*-,8*L;6VL73=7a14Z»,]5E9Jj+.I58j+9871X5 º%=°º?Ã
.:F4nb7I,YN~98F4n 58(+7o7MG?7I@}58,z*L@ª5E(+7
S \ 987M5Ej+9J@`3=7a14Z f')(67/.:j65F?@`58(+7B589E14@+,]G?7I98,87ineF?ne7:@[5Ej6nT^
)
º%=ĺ[à ?^987 2J7I.I587:QF?@+VDd1X;¨F?jU5± >F4N)58(+7
5 H
5 H
QS7IG?7I@[5E,e14@+Q14;=F?j65oÉ[º #F4NC5E(67
5 6
56
Q7IG47:@[5E,If
+©*L>4j+987I,<ÃUf°´X.4^ÆQ!,8(+FHA 5E(+7x987:.IF?*LVnb14,8,i1X@+Q!3¨F4Vw149B14@+>?V-7xQ+*-,J5898*L;6j65E*-F?@+,oFXN)5E(+7,J*L@+>4VL7M\
3+(+FX5EF?@7MG?7:@[58,q3+14,8,J*L@+>58(+7:,J7"!],87:V-7:.M5E*LF4@#.:jU5E,:fÀÊ(+*-VL7B58(+7
S \ 987I58j+98@3=7a1XZT*-,3+987I,87I@}5q*-@
;=F45E(ª5E(+7q7:V-7:.I5898F?@K\)14@6Q`n/j+F4@U\p@+7Ij65E9J*L@+Fe9E1XQ+*w1X58*-G47q,J3¨7I.I589E16^=5E(+7
5 6
5 6
Qk3+9JFUQ6j+.I58*LF?@ªQ+F?ne*D\
@21X587:,C*L@r58(+7987:>4*LF?@PF4N"(+*L>4(ª9J7:.IF?*LVtnb14,J,87:,,~VLFHA 36(+F45EF4@T7I@+7:9J>?*L7I, 0Mf
OU*L@6.:7_58(+7@+7Ij65E9J*L@+F4,©7:,J.a143=7:QiQ67I5E7I.I58*LF?@t^XF?@+7.IF?j+V-Qo@+F45©Q+*L,]5E*-@+>?j+*-,8(q;¨7M5pAW7I7:@i5E(+7
5 6 5 6
Q
+©*->?j+987iÃUf°³TFHAW7I,J5J\ F?98Q67:9I+27IdK@+nb14@Q+*w1X>?9E14ne,YN~F495E(+7i9J7a14.M5E*-F?@7as¦7®u
5
5 Q Q"f
¸ @+V-db5pAWFeF4N"5E(+7<±H³<14V-VLFHAW7IQrQ+*w1X>?9E14ne,)149J7,8(+FHAC@tf
14@+Q
5H
5H
Q¬2@21XVW,J5E1X5E7I,:fc')(+7r.:F4n/;+*L@67:Q
5
5
QSQ+*L,]5E9J*L;+j658*LF?@6,BF4NC58(+73+(+FX5EF?@!9J7:.:F4*LVWnb14,J,
14@+Qr3=F?VL149W1X@+>?VL714987,8(+FHAC@P*L@n+"*L>?j+9J7:,ÃUf°²416^Ä;¦f)+ F49W.:F4nb321X98*L,JF?@t^}5E(+7I,87¬2>4j+987I,C14VL,JF/,8(+FHA
5E(67,E14ne7xQ6*L,J5898*-;+j65E*-F?@+,qF?;65E14*L@+7IQ!1XN587:9o9J7:VL1v¹U*L@+>ª5E(+7 !],87:V-7:.M5E*LF4@#.:jU5E,o58F
±P¾z7m.
14@+Q ( (
,)¾ ¸ 0 ±Hº ^«AC(+*L.0(98F?j+>4(+V-d.IF?989J7:,J3¨F?@6Q+,o5EFª5E(+7b7:@+7I98>4d14@6Q14@+>4j+Vw149
14.I.:7:3U5014@+.I7BFXN"58(+7 )¾ ¸ 7:V-7:.I5898F?nb14>?@67I5E*-..a1XVLF?9J*Lne7I5E7I94, ,J7:7B{W(2143U5E7:9J,YÉb14@+Q ><0 f
')(+7P5EF45E14V.:9JF?,8,e,87I.I58*LF?@F4NY5E(+7P,8*-@+>?V-7M\q14@6QSn/j6V-5E*y\p3+(6F45EF?@3+98FKQ+j+.M5E*LF4@3698FK.:7:,J,87I,b*-,
,8(6F®AC@x*L@ +©*L>?j6987YÃUfIJ4.4^}AC(+7:9J77MG?7:@[58,WAC*-58(bneF?987C5E(+14@xF?@67Y3+(6F45EF?@eAC*-58(
±¾z7m.Ç1X@+Q
( %,]±a²?º @ ( "0
±aÉW1X987m14VL,JF*L@+.IVLj+Q+7IQtf')(+*-,_36VLF45l,J(+FHAC,_5E(+1X5_1X5_«là , ½ÃXº?ºq¾7.0
5E(67B9814Q+*w1v5E*-G47z3+98FKQ+j+.M5E*-F?@TFXN©5E(67q7IVL7I.I5E9JF?@`@67:j65898*L@6F?,)A14,Y14,mVw149J>?714,C5E(+7q.:F4n/;+*L@67:Qª3+98FX\
Q+j+.M5E*-F?@PF4N"58(+7n/j+F?@T14@+Qr5E14jT@67:j65898*L@6F?,:^ ,
5 6
56
QU, Q 0e0 ,
5H
5H QU, Q 0e0
$ ,
5 K
5 K QU, QZ0e0Mf
X $ !" # m kZ :
¿,YAC*LVLV;=7/Q+*-,8.:j6,8,87IQ*-@T58(+7/@+7 ¹U5.0(+14365E7I9:^t,J7IG47:9E1XV,8j+3=7:9J,JdKnenb7M5E98*-./3+9JFU.I7:,8,J7:,.a1X@VL7a1XQ
5EFr58(+7 ; =>+-()',56(/56 *%3 ; '?10? ¬2@21XV,J501v5E7/GK*w17:st7vu
9 9
Q Q«^AC(+7:9J7
14@+Q 914987<@+7MA @+7Ij65E9814Vl*L@[GK*L,8*-;+VL7o32149J58*L.IVL7:,Ifi')(+7:9J7IN~F?9J74^"*-5z*-,q*-@[5E7:9J7:,]5E*L@6>P58FT.IF?@+,J*LQ+7I9
5E(67q3698FKQ+j+.I58*LF?@PF4N"n/j+VD5E*y\p3+(+FX5EF?@7MG?7I@}58,*-@P58(+7BOK501X@+Q2149JQ`RªFUQ+7IV ^27 s 7 u 5
5 Q QU,QZ0Mf
')(+*L,©3+98FK.:7I,8,.:F498987I,83=F?@+Q+,58F1Y5EFX5014VUF4N=Â1+27IdK@+nb14@/Q+*L14>?9E1Xnb,N~F?9"58(+7
5 H
5 H
Q Qb3+98FKQ+j+. \
5E*-F?@B14@+Qx±a³P+27IdK@+nb14@oQ6*w14>?9814ne,N~F4958(+7
56
5 6
Q Qe3+98FKQ+j+.M5E*LF4@tf"')(67:,87WQ+*w14>49E14ne,.:F?9J987I,83=F?@+Q
5EFx14VLV3=F?,J,8*L;6VL7q.:F?n/;6*L@21X58*LF?@6,mFXN©5pA_F3+(+F458F?@+,Y7:ne*-58587:QªN~98F?n58(+7o*-@+.:F?ne*L@6>e7IVL7I.I5E9JF?@1X@+Q
3=F?,8*D5E98F4@14,A_7:V-V14,N~9JF?n 58(+7oÀ ;=F?,8F?@k3+9JF?3214>?1X5EF?9Y*L@`58(+7
EK.0(+14@+@+7IV fq¿,z14@7 ¹614nb36VL74^
a)
Recoil Mass (GeV)
∆σ / ∆ M rec (pb/4 GeV)
0 0.02 0.04 0.06 0.08
0 50 100 150 200
b)
√ s = 200 GeV e + e − → νν _ γγ
P γγ T > 0.02 √ s E γ2 > 1 GeV
E γ2 (GeV)
∆σ / ∆ E γ 2 (pb/2 GeV)
0 0.01 0.02 0.03 0.04 0.05 0.06
0 10 20 30 40 50 60
+©*->?j+987oÃUfD±Hº%T Y*¨7:9J7:@[5E*L14V.:9JF?,8,,J7:.M5E*LF4@+,F4N58(+7/7 s 7 u 5
5 Q Q3+98FK.:7I,8,z1X,N~j+@+. \
5E*-F?@+,F4N¦1G0"58(+7C987:.IF?*LV6nx14,J,l14@+Qe; 0"5E(67m7I@+7:9J>4d<F4N=5E(+7C,J7:.:F4@+Qb36(+F45EF4@t^}.a14V-.:j+VL1X5E7IQ
AC*-58(r5E(+7;$$'&(3698F?>?9814n1v5
Ã4º?ºe¾7.<f
¿hn/j+VD5E*D\ 3+(+F458F?@B14@+Qine*L,8,J*L@+>7:@+7I98>4do7IG?7I@[5_*-,Q+7M¬2@+7:Qb14,(+1HGK*-@+>1X5V-7a14,]55pAWFz36(+F45EF4@+,
AC*-58(
±x¾z7m.14@+Q$( %,]±a²?º @ ( "0
±:É f<gp@1XQ+Q+*-58*LF?@¦^¦5E(+7i589E14@+,]G?7I98,87eneF?nb7I@[5Ej+n
F4Nz58(+7n/j+VD5E*y\p3+(+FX5EF?@,JdK,J587:n ,J(+F?j+V-Q»,E1v5E*L,]N d )
º%=ĺ[Ã8 ?f +©*L>?j6987`ÃUf-±aº,8(+FHAC,r5E(67
Q+*¦7I987:@[58*w14VY.:98F4,8,P,87I.I5E*-F?@+,PF4Nq5E(+*-,987:14.I58*LF?@Å14,N~j6@+.I58*LF?@+,rFXNB58(+7k987:.IF?*LVYnx1X,8,P14@+QÊ5E(67
7:@67:98>XdxF4N¦5E(+7Y,87:.IF?@+QrneF?,J5_7:@67:98>47I5E*-.3+(+FX5EF?@[,
0 f©ÀÊ(+*-VL7C5E(+7Y987:.IF?*LV nb14,8,_Q+*L,]5E9J*L;+j658*LF?@
(214,)58(+7N 14ne*LVL*L149N~7a1X58j+987F4N«5E(67
S
\p987M5Ej+9J@P3¨7:14Z ^+5E(+7 ,J3¨7I.I5E9Jj+n*L,)Q6F?nb*-@21X587:Qr;[dr,8FXN5
3+(+FX5EF?@+,I^¦7 ¹6(6*L;+*D5E*L@6>b5E(67o;=7:(21aGK*LF?9Y7M¹U3=7:.I587:QN~98F4nÁÌ}j21X58*LF?@6,zÃUf°ÃU±i14@6QkÃUf°Ã?ÃUfm¿5zl_ÃK^
5E(67/5EF45E14V©.I98F?,J,z,87:.M5E*-F?@kF4Nl5E(+7i7:s¦7vu
5
5 Q Q3698FK.:7:,J,A1X,B1X;¨F?jU5i± >b5E*-nb7I,,Jnx14V-VL7I9Y5E(+14@
5E(+1X5CF4N«5E(+77 s 7 u 5
5
Q3+9JFU.I7:,J,:f
p ¢_W ¡0]¢ '"W «¡© 6¢_¡
gp@PF?98Q67:9)5EFi7I,J5E*-nx1v5E75E(67z7e.:*-7:@+.MdPF4N5E(+77as¨7vu
5
5
QU, QZ0W7IG47:@[5Y987:.IF?@+,]5E98j6.I5E*-F?@ª14@+Qª,87 \
VL7I.I58*LF?@t^4g"9J7:V-doF?@bRTF?@[5E7Y{149JVLF ,·R{ 0,8*Lnoj+Vw1X58*LF?@6,:f«g©14V-,8Fzj+,J7YR{3+9JF?>?9814nb,"5EF.a14V-.:j+VL1X5E7
5E(67q7 ¹U3¨7I.I5E7IQ`981X5E7F4N«5E(+7z,J*L@+>4VL7M\l14@+Qªn/j+V-58*D\ 3+(+F458F?@3+9JFUQ+j6.I5E*-F?@r*L@r58(+7BOK5014@6Q21498QTRTFKQ+7IV
14@+Qi58Fz7:,J58*Lnb1X5E7W,JdK,J587:nb1X5E*-.)7:989JF?98,.:14j+,J7:Qe;}d/j+@+.:7I9J5E14*L@[5E*-7:,*-@/5E(+758(+7:F?9J7I58*L.a1XV6neFUQ+7IVLV-*L@+>
F4N«5E(+7I,87q3+98FK.:7I,8,J7:,:f
Yj+98*-@+>`58(+7x¬2@21XV_d?7:1498,<F4N)58(+7Pl_Ã`3698F?>?9814nª^©N~98F?n ±H³4³?²T5EFcÃXº?º?º6^©58(+7N~F?j+9o
7M¹U3=7:9J*Lne7:@[5E,).IF?VLV-7:.I587:Qr1X;¨F?jU5mÃUf?>BN~; u F4NQ21X5E1i1X5 ±H²4³M@Ã4º?²i¾z7m.<f')(67z,J501v5E*L,]5E*-.a14V
7:9J98F?9_F4Nt58(+7.IF?989J7:,83=F?@+Q6*L@+>
5
5 Q , QZ0.:9JF?,8,_,87I.I5E*-F?@ne7a14,Jj+987Inb7I@[5)*L,7M¹U3=7:.I587:Qr5EFB;¨7Y;¨7IVLFHA
Ãf')(}j+,I^U5E(67Y7 ¹63=7:.M5E7IQr.:98F4,8,W,J7:.M5E*LF4@b(21aG47Y5EFB;¨7CZ}@+FHAC@xAC*D5E(1987IVw1X58*-G47m36987:.I*L,J*LF?@eF4N1v5
VL7:14,J5o± ^t14@6Q5E(+7B.:F?9J987:,J3¨F4@+Q+*L@6>rQ+*¨7:9J7:@[5E*L14VQ+*L,]5E98*-;+j658*LF?@+,m(21aG?7/58F;=7o,8*-n/j+VL1X5E7IQTAC*-58(
1i,8*-nb*-Vw149_VL7IG47:VF4N©14.I.:j+9814.Id4f
Y3i5EFz58(+7d?7:149Ã4º?º?ºU^?nbF4,J5F4N=5E(67C«lc7M¹U3¨7I98*-nb7I@}58,l(214Qij+,J7:Q<5E(+73$iR{!7IG47:@[5
>?7I@+7:981X5EF?9mµÆÃ?Ãv¶·fg 5AW14,lF?98*->?*L@+14VLVDdzAC98*-5J5E7I@<58F,8*Lnoj+Vw1X587_58(+7 O
O
3214*-9]\p3698FKQ+j+.I58*LF?@/14@+QeQ+7:.:1Hd
1X5<7I@+7:9J>?*L7I,e@67a149/58(+7
S
3=F?VL7f,·lC±0<1X@+Q!A14,<VL1X5E7I9i7M¹K5E7I@+Q+7:Q5EFk*L@6.:VLj6Q+7x5E(67
5 5 Q ,QZ0
3+9JFU.I7:,8,Ifx')(+7$ `>?7:@67:9E1v5EF?9Q+*-Q@+FX5Bj6,87<5E(+7e7M¹614.M5o.I98F?,J,B,J7:.I58*LF?@cF4N_5E(+7i5E9J7:7 \pVL7MG?7IV
987:14.I58*LF?@ª7as¨7vu
5
5
Q,JFb5E(+1X5m.:F?@[5E9J*L;+jU5E*LF4@+,)N~98F?n58(+7
E}.0(214@+@+7IV«À 7M¹U.0(214@6>?7/Q+*L14>?9E1Xnb,
A_7:98714Q+Q+7IQj+,8*-@+>`981X5E(67:9o,J*Lne3+VL7e14363+98Fa¹U*Lnb1X5E*-F?@+,eµÆÃ4|X¶·fP')(+*L,B987:,Jj+V-587:Q*-@1ª,JdK,J587:nb1X5E*-.
j+@+.I7:9]5014*-@}5pdqF4N214;¨F4j65©É ½F4@B5E(67W,8*-@+>?V-7M\p36([email protected]?,J,,87I.I5E*-F?@t^vAC(+*LV-7N~F?95E(67Wn/j+VD5E*y\p3+(+FX5EF?@
¬2@21XV,J501v5E7:,)58(+7,JdK,J587:nb1X5E*-.qj6@+.:7I9J501X*L@[5pdP.:F?j6VLQP;¨71X,m(6*L>?(ª14,±Hº ÁµÄÃvÉ4¶ f
gp@rÃ4º4º?º6^?5E(67 $/7MG?7:@[5W>?7:@+7I9E1X58F?9A1X,_9J7:3+VL14.:7IQb;[de1nbF?9J7C14Q6GX14@+.I7:Qx14@+Qe3+987I.:*L,J7
R{3+9JF?>?9814nT^$$&6( µy±H´®¶·fÅgp@6*-5E*L14VLVDd?^l*-5b.:F4j+VLQS;¨7ªj+,87IQ»5EF,8*Lnoj+Vw1X587ª14@[dN~7I98ne*LF?@321X*L9]\
3+9JFUQ+j6.I5E*-F?@x3698FK.:7:,J,87I,:^27as¨7vu
,QZ0M^67 ¹U.:7:3U5N~F?9 _(214;+(21B,8.a1v585E7I98*-@+>i14@+Qx@+7:j65898*-@+Fo321X*L9]\
3+9JFUQ+j6.I5E*-F?@tfB')(+7
5
5
QU, QZ0Y3+9JFUQ+j6.I5E*-F?@k3+98FK.:7I,8,zAW14,Vw1X587:9*-@+.:F?9J3¨F49E1X587:Q*L@58(+*L,3+98F?>49E14n
14@+Q1qN~j+9]5E(+7I9]\p*-nb3698FHG?7IQxG?7I98,8*-F?@xAW14,9J7:VL7:14,87IQ*L@OU7:3U5E7:no;¨7I9CÃ4º?º[Ãq14, $$'&6(+fl')(+*-,
G?7I98,J*LF?@FXNt5E(+7 $$'&(<>?7I@+7:981X5EF?9lAW14,_58(+7nb14*L@<,JF?j+98.I7F4N¦,8*L@6>?VL7 \1X@+Qxn/j6V-5E*y\p3+(6F45EF?@bRTF4@}587
{149JVLF<7IG47:@[5E,CN~F?9)nodP1X@214V-dK,J7:,:f
')(+7 $$&6(Å3+98F?>49E14n *L@+.IVLj+Q67:,`58(+7!.:F?ne3+V-7I5E7j,
0T.:14VL.Ij+Vw1v5E*LF4@+,TN~F?9T5E(+7!9J7a14.M5E*LF4@
7as¨7vu
5
5
Q AC*D5E(
±# ÃK^*L@+.IVLj+Q+*-@+>.IF?@[5E98*-;+j658*LF?@+,BN~98F?n Q+*w14>49E14ne,BAC*D5E(5E(67r7:ne*L,]\
,8*-F?@F4NF?@+7i9J7a14V©14@+QkF?@+7BGU*-9J58j214V©36(+F45EF4@tfo')(+7i(6*L>?(+7I9]\ F?98Q+7I9g]O 14@+QkF45E(67:942z)Y$.:F?9 \
987I.I58*LF?@+,b149J7T.:14VL.Ij+Vw1X587:Qj+,8*-@+>k5E(+7;94+O}\ *L@+,J3+*L9J7:QS{WF?(+7I987I@}5r¹U.IVLj+,J*-G?7`©¹63=F?@+7I@[5E*w1v5E*LF4@
,8.0(67:ne7eµÄÃ<>®¶ ^21X,Q+*L,J.:j+,J,87IQT*-@ªOU7:.M5E*LF4@r¿ofÄ|6f')(+7z.:F4nb3+V-7I587n, 07:VL7I.I5898FHAW7:14Z.IF?989J7:.I58*LF?@6,
AC*-58(P(+*L>?(67:9]\ F?98Q67:9)7M¹K587:@+,J*LF?@+,Y149J7z*Lne3+VL7Inb7I@}587:QPj+,J*L@+>i5E(67PVL*L;69E149]dµÆÃ4Âv¶·f
')(+7k,JdK,J587:nb1X5E*-.7:9J98F?9J,r149877I,J58*Lnb1X5E7IQ»5EF!;=7k14;¨F4j65Pº6fIJ ^B±4f°| ^Y14@+Q >N~F?95E(67
5 H
5 H Q«^
5 6
5 6 Q«^=14@+Q
5
5 Q Qk3+98FKQ+j+.M5E*LF4@T3+9JFU.I7:,J,87:,I^¦9J7:,83=7:.M5E*DG?7:VDdµÄÃXÉX¶ f')(}j+,I^¨58(+7 $$'&6(r3+98FX\
>?9814n 14.0(+*L7MG?7IQ5E(+7b>?F[14VF4NC1`F4@+7x3=7:9J.:7:@[5i36987:.I*L,J*LF?@F?@5E(67x5EF45E14Vl.:9JF?,8,/,J7:.M5E*LF4@F4N)5E(67
7as¨7vu
5
5
QU, QZ0W3+9JFU.I7:,8,If
√s (GeV) σ νν _ γ (pb)
KKMC NUNUGPV KORALZ a)
<√ s > = 198 GeV
σ kkmc / σ nunugpv = 1.002 ± 0.002 σ koralz / σ nunugpv = 1.016 ± 0.003 e + e − → νν _ γ , νν _ γγ
3.75 4 4.25 4.5 4.75 5
190 195 200 205
√s (GeV) σ νν _ γγ (pb)
KKMC NUNUGPV KORALZ b)
e + e − → νν _ γγ
<√ s > = 198 GeV
σ kkmc / σ nunugpv = 1.03 ± 0.01 σ koralz / σ nunugpv = 1.06 ± 0.01 0.26
0.28 0.3 0.32 0.34
190 195 200 205
+©*->?j+987)ÃUf-±4±<T"'«F45E14V+.:9JF?,8,,87I.I58*LF?@+,l1<0©F4N¨58(+7C.:F?no;+*L@+7IQ<,8*L@6>?VL7 \14@+Q<n/j6V-5E*y\p3+(6F45EF?@
3+9JFUQ+j6.I5E*-F?@3698FK.:7:,J,i14@+Q; 0FXN5E(+7bn/j+VD5E*D\ 3+(+F458F?@c3+98FKQ+j+.M5E*LF4@3+9JFU.I7:,J,:^l14,B3+987 \
Q+*-.I5E7IQT;[d58(+7;$$&6(2^ "$ "$# %&¨^=14@6Q $x7MG?7:@[5>?7:@+7I9E1X58F?98,If
*L@6.:VLj6Q+7:,58(+7<7M¹614.I5nb1X5898*D¹`7:V-7:ne7:@[5E,N~F495E(+7<987:14.I58*LF?@6,7ast7®u
5
5
Q«^AC*D5E(
±#0Ã #0|6f
')(+7Bg]O 1X@+Q`F458(+7:9m(+*->?(+7:9 \pF?9JQ+7:9P2z)Y.:F?9J987I.I5E*-F?@+,Y14987q.a1XVL.:j6Vw1X587:Qªj+,8*-@+>b58(+7iOK5898j+.M5Ej+9J7
+2j+@+.M5E*LF4@P587:.0(+@6*LÌ}j+7:,-, ,J7:7BOU7I.I5E*-F?@ª¿of°Ã<0Mf')(+7nb14*L@rV-*Lne*-5E1X5E*-F?@<F4N"58(+7 "$ "$# %&P3+98F?>49E14n
*L,_5E(+714;6,87:@6.:7zF4N5E(67z7M¹614.I5 n, 0_7:V-7:.M5E98FHA_7a14Zx.:F?9J987:.M5E*-F?@+,:^KAC(+*L.0(P9J7:,8j6V-5E,)*-@P1/3+987I.:*-,8*LF4@
F4N_±3E6Ã$N~F?9W58(+7,8*Lnoj+Vw1X58*LF?@xF4N5E(+7,8*-@+>?V-7M\p36(+F45EF4@r3+98FKQ+j+.M5E*LF4@r3+98FK.:7I,8,oµÄÃ4²v¶ fgp@T14Q+Q+*D5E*-F?@t^
.:F4@}589E149]do58F5E(+7,$$'&6(o>?7I@+7:981X5EF?9I^45E(67 " "$# %&/3+98F?>49E14n .a14@6@+F45;=7)j+,87IQiN~F?9©5E(67*L@+.IVLj+,J*-G47
987:14.I58*LF?@P7:st7vu
5
5 , Q 0 f_')(67Bnb14*L@P1XQ6GX14@[5014>?7F4N"5E(+7 " " # %&ª*L,)*D5E,m14;+*-VL*-5pde5EF<,J*Ln/j+VL1X5E7
5E(67),8*L@6>?VL7 \«14@+Q<n/j+VD5E*y\p3+(+FX5EF?@B3+98FKQ+j+.M5E*LF4@e3698FK.:7:,J,87I,_*-@/5E(+7)3+9J7:,J7:@+.I7F4N¨14@+F4nx14V-F?j+,«5E98*-3+VL7
14@+QÌ}j21X9J5E*-.o>[1Xj+>?7M\ ;¨F4,8F?@.IF?j+3+V-*L@+>4,:fz')(+7I987IN~F49874^¦gCAC*-VLV«j+,87B5E(+*-,3+98F4>?9E14n *-@nodT,87a1X98.0(
N~F?9C14@6F?nx1XVLF?j+,W;¨F?,JF?@ª.:F?j+36VL*L@6>?,:f
+©*L>4j+987xÃUfD±?±x,J(+FHAC,<1`.:F?ne32149J*L,JF?@;=7I5pA_7:7I@!5E(+7 $$'&6(2^ " "$# %&=^14@+Q $7IG47:@[5
>?7I@+7:981X5EF?9J,W*-@b5E(677:@67:98>Xdb9814@+>?7Y,J58j+Q+*L7IQ*L@e5E(+*-,58(+7:,J*L,I^
±H²?³C@Ã4º?²B¾7.<f')(+7.I98F?,J,
,87I.I58*LF?@P.:j69JG?7I,C3+987IQ+*L.M5E7:QP;[dx58(+7$$'&(b14@+Q " "$# %&r,8(6F®A¼14@r7M¹U.I7:VLV-7:@[5m14>?9J7:7Inb7I@}5:^6A_7:VLV
AC*-58(+*L@!58(+7P7M¹U3¨7I.I587:Q 58(+7:F?9J7I58*L.a1XV3+987I.:*-,8*LF4@tf¿ .IVL7:149i*Lne3+98FHG47:ne7:@[5eF®G47:9<5E(+7ª14.I.:j+9814.Id
VL7MG?7IVF4N"58(+7;$ x*L,m14V-,8FiF?;+,J7:9]G?7:Q¦f
')(+7z,83=7:.I*-¬2.1XVL>?F?9J*-58(+nb,lj+,J7:QP*L@b5E(+7$$'&6(b14@6Q " "$# %&rRTF?@[5E7q{149JVLF/3698F?>?9814ne,149J7