"!$#% '&( *),+- +
.0/21432576982:;5=<>/ ?@1A8CBD:;14EF1A?2EFGA:F1A/HBF1E:F<I82:DJLKNMO<>EFPQ13SRT8C/U325LKIVIEWKIPQP(1DBF1PQ?2:YX
1A:F?ZK\[1I]2^KIE_1a`C1AP(?CJ=1D?b<>82EcJLKd32GA:F5e/HBFGV>EFK\BW5e<>/,3SRf82/%gb<>:F<I/%321ih25=VIV>:j1A/lkdJ=1?mBW<>/2:
τ
ntemps espace
τ p + 0 ,s 0
τ p,s − h k
opJq:RTKIV>57Bj39RT82/,rtsOu2vqwxuZyzy|{}r~{-{~y|uZ]2 j1325LKIVIEWKIPQP(1j1:;Bj82/210BWEWK\3282[X
BF5=<>/%:;[h2GP(K\BF5=H821321JRTKIP(?CJ=5eBF823210321Z1A/2P(KI/S]
1:(:;P4gb<>J=1A:}8CBF5=Je5=:FGA:N?@<>8CE}J=1A:(3C5e6@GEF1A/BW:}Bp?b1:,321 ?ZKIEYBW5=[A82J=1A:O:F[KIJLKI5eEF1A:
MO1AEFPQ5=<>/C:Cgb<>:;<>/2:">1[BW1A82EF:W":;<>/B3C<>/2/2GA:3ZK\/2:"JLKdZV>8CEF1:F8257\KI/BW1
n
boson scalaire fermion (spineur) photon, W, Z
bosons de jauge (vecteurs) gluon
jhZK\8C1?@<>5e/BD3214[AEF<>5e:F1AP(1A/HBBWEWK\32825eB82/2145e/BW1EFK\BW5e<>/
n
[IRf1:YB82/>1AE;BW1a`@]1
l<m32AJ=1BWKI/23ZK\EF3l/21[<>/BW5e1/B0H8SRT8C/ /2<IP4g2EF1iZ/C5321i>1EYBW1a`|O><I5=EF1i:;1[BW5=<I/ :;8257X
\KI/BF1]^tKIE1`m1PQ?2J=1\5=J2/9RT1a`C5e:;BF1?ZK\:c321_I1E;BF1`(?b<>82E32G[AEF5eEF1"JLKi32576982:;5=<>/( j<>PQ?mX
BF<>/
γe − → γe −]xD/[A<>P4g25e/ZK"KIJ=<IEF:S321A8m`iI1E;BF1`
n
82/?2E;1PQ5=1AE328iBpm?b1
γe − → e −
K\8-BF1PQ?2:
t 1
1B082/ :;1[A<>/23
e − → γe − KI8%BW1AP(?C:
t 2 ≥ t 1
]
~<>82:J=1:325LK\V>EWKIPQPQ1:_321Z1m/CP}KI/ ?@1A8C>1A/BKI5=/C:F5~:F1d[A<>/2:YBWEF8C5=EF11/UK\:F:F1APNX
gCJLKI/Bt[1:I1EYBW1`4GJeGPQ1/BKI5eEF1A:t[A<>P(PQ1321:?C5=[A1:3C1j?282 A Je1I]>K3C5e6@82:F5e<>/ j<>PQ?mX
BF<>/-1:YBDKI5e/2:F5932G[AEF5eBF1i?ZKIEk4325LK\V>EWKIPQPQ1:
voie s voie t
q 2 = (p 1 − p 3 ) 2 = t q 2 = (p 1 + p 2 ) 2 = s
p 1
p 2
p 3
p 4
p 1
p 4
p 3
p 2
"!4 * # (# ~+l#-i#
D/UJe5=:;BF1d5e[5J RT1A/2:F1AP4g2Je1d321A:I1EYBW1` KI8CBW<IEF5=:;G:D32KI/2:DJe1N <32Je1NBK\/23ZKIE;3U321
JLK?2h:F5=H821321:?ZKIEYBW5=[A82J=1A:]2~<>8CBF15e/BW1EFKI[ABF5=<>/l328lP(<32AJ=1:;BWKI/23ZKIE;3 ?b18mB32<I/2[
BWE;1d<>gmBW1/H8211/[A<>P4g25e/ZKI/B?2J=82:;5=1A82EF:0321d[A1:I1EYBW1`@][hZKIH821>1EYBW1a`<>/ 32<>5eB
<>g2:F1AE;I1E J RT1A/2:F1AP4g2Je1 3C1:lJ=<>5e:%321 [A<>/2:;1E;\K\BF5=<>/ 32GA[<>82J=KI/B 3C1:l5=/\KIEF5=KI/2[1A:-321
KI82V>1i328lPQ<m32AJ=1D1B0321JRf5=/\KIEF5=KI/2[1321<IEF1/BF I:WK ><I5=E
n
j<>/2:;1EYIK BW5=<I/ 321J=K482KI32EF5Xp5eP(?28CJ=:F5e<>/
j<>/2:;1EYIK BW5=<I/ 328l:F?C5=/
j<>/2:;1EYIK BW5=<I/ 321J=K4[hZKIEFVI1GAJ=1A[ABWE;5=H821
j<>/2:;1EYIK BW5=<I/ 321UJ=K :WK >1A82E 3C1:-H8ZKIEH:l1AB-321A: Je1?CBF<>/2: O:WKI8CMd?@<I82E%J=1A:
[<I82EWKI/BF:[hZK\EFV>GA:"MK\5=g2Je1:
j<>/2:;1EYIK BW5=<I/ 321J=K4[hZKIEFVI13C1[A<>82Je182E
^t<>82E:;5=PQ?2J=57Z1EJ RTGA[E;5eBW8CEF1_<>/Q/2<IBF1EWK:F8CEJe1:325=KIV>EWK\P(PQ1:
q
?@<>8CE8C/(H8ZKIEH821JX [<>/2H821\l − ?@<I82Ej82/%Je1?CBF<>/%[hZKIE;V>GD1B
ν l ?@<I82EjJe1/21A8CBWE;5=/2<NKI:;:F<[5eGI]m1A:"KI/BW5e?ZKIEYX BW5=[A82J=1A:DKI:;:F<[5eG1::F1E;<>/Bi/2<IBFG1A:
¯
q
l + 1AB ν ¯ l] /CZ/S93ZKI/2:DJe1d[KI:D3214J RT5e/BW1EFKI[ABF5=<>/
M KI5=g2Je1<>/-325e:;BF5=/2V>8C1EWK4Je1:_H8ZKIEH:321[hZK\EFV>1
2 3
u
c
1Bt
j/2<IBFG:q u 1B"J=1A:_82KIEH:
321[hZKIEFVI1
− 1 3
d
s
1Bb
j/2<\BWG:q d]
{{~w {wby|u2vbs{
opJ/SRf1`m5e:;BW1H8SRf82/-Bpm?b1321i>1AE;BW1a`lGJe1[ABFEF<>P(KIV>/CGABW5eH821i[<>8C?2JLKI/B"Je1:*MO1E;P(5e<>/2:
[h2KIEFV>GA:DKI8l?2h2<\BW<>/S]b1?2h2<IBF<>/ /C1?b<>E;BF1dK\82[82/C1[hZK\EFV>1\@5eJS1:YBD32<>/C[:FK(?2E;<>?2EF1
K\/HBF5=?ZK\E;BW5e[82Je1I]
q, l −
q, l ¯ +
∝ √ α EM γ
{{~wqw
Rf5=/BW1AEWKI[BW5=<I/ MO<>E;BF14/21[A<>/2[1AEF/21H821Je1:DH8ZK\EH:8C5?b<>E;BF1/B82/21321A:DBWE;<>5=:
[h2KIEFV>1A:(3C1 [A<>82J=1A82E ?ZK\EQ[A<>/>1A/HBF5=<>/
r
v
1ABb
]1:(KI/BW5eH8ZKIEH:Q?@<IE;BW1A/B(8C/21 [h2KIEFV>13SRTKI/BW5=[A<>82Je182EA]@KNBWh2GA<>EF5e1d321 KI82V>1321dJ RT5e/BW1EFKI[ABF5=<>/-MO<>EYBW1EF1?b<>:;1d:F8CEJ=1VIEF<>82?b1
SU (3)
1BM KI5eB5e/BW1EY>1A/25=E321A:t[A<>82?2J=KIV>1A::F82?2?CJ=GPQ1/BWKI5=E;1:] j<>/BWEWK\5=EF1AP(1A/B K\8 ?Ch2<IBW<I/S_J=1UV>Je82<>/ 1A:;Bl?@<IE;BW1A82E-3SRf82/21 [hZKIE;V>1 321 [<>82Je182E%1Bl3SRT8C/21 [hZKIEFVI139RKI/BF5=[<I82J=1A82E]SopJ 1a`m5=:;BF1(1A/ BF<>8CBhH825eBVIJ=82<>/C:1BJRTKI/BW5=?2KIE;BF5=[8CJ=1d39RT82/ V>Je82<>/ 1:YB
8C/ K\8CBWE;1DV>J=8C<>/S]CopJ@1`m5=:YBW1KI5e/2:F5@321:_5e/BW1EFKI[ABF5=<>/C:*1/BWE;1iJ=1A:_V>J=82<I/2:j1A8m`HXpP
PQ1:
:FK ><>5eE3C1:[<>82?CJLKIV>1A: BFEF<>5e: V>J=82<I/2: 1AB 82K\BWE;1V>Je82<>/2:A]1:[<>8C?2JLKIVI1: i82K\BWE;1
VIJ=82<>/C:*MO<>/B"5=/BW1AE;>1A/25=E"Je1i[ KIE;EFG321JLK4[A<>/2:;BWKI/BW1321[<>8C?2JLKIVI1I]
1:_I1E;BF1` 321JRf5=/BF1EWK\[ABW5e<>/}MO<>EYBW1i:;<>/B32<I/2[
n
g c 1 c ¯ 2
∝ √ α s
q c 1
¯ q ¯ c 2
g c 1 ¯ c 3 ∝ α s
g g c 1 ¯ c 2 g
g c 2 c ¯ 3
∝ √ α s
g g
KI/2:Q[1:N>1AE;BF1`@cJe1:N5=/C325=[A1:
c i 3CG:F5eV>/21A/HB(321A:([A<>82J=1A82EF:QK ?2EF5e<>EF5j325e6@GE;1/BW1A:
n
J RT5e/BW1EFKI[ABF5=<>/,MO<IE;BW1iPQ<325eZ1JLK4[hZKIE;V>1321[<>8CJ=18CE]
{{~w uZs O{
Rf5=/BW1AEWKI[BW5=<I/M KI5eg2J=1\ g2KI:FGA1_:F82EJ RT5e/IK\EF5LK\/2[1321 K\82V>1
SU(2)
MKI5eBKI?2?ZK\EWKeBWEF1 BFEF<>5e:cgb<>:;<>/2:j3C1 KI82VI1n
321A8m`,gb<>:;<>/2:jGAJ=1A[ABWE;5=H821AP(1A/HBj[hZKIE;V>G:
W + 1AB W −mK\/HBF57X
?ZKIE;BF5=[A82J=1_J RT82/N3210JRTKI8CBFEF1_1Bc8C/}gb<>:F<>/Q/21A8CBWE;1
Z
H825q1:YBj:FK?2E;<>?2E;1K\/HBF5=?ZK\E;BW5e[82Je1I]1A:c[A<>82EFKI/BW:j[h2KIEFV>GA:iOG[hZKI/CV>1321
W ±:F<>/BjJ=1::F1A82J=::F8C:F[1A?CBW5eg2J=1A:j3210PQ<m3257Z1E JLK :FK >18CE :FKI<>5=E321}BFEWKI/2:YMO<>EFPQ1E82/ H8ZKIE 321(Bpm?b1
d
1/ H8ZK\E|3C1}Bp?@1u
<>8-82/ Je1?CBF<>/-[hZKIE;V>G1A/ /C18CBFEF5=/C<Q1B05=/>1AEF:F1AP(1A/B ]@ j1:0[hZKI/2VI1PQ1/BW:0321:WK >1A82E
:F1NMO<>/B8C/25=H821AP(1A/HB -JRf5=/BWGAEF5e182ED39RT82/C1(P
PQ1M KIP(5eJ=Je1Iq:F<>57B
τ ↔ ν τ µ ↔ ν µ
e ↔ ν e d ↔ u
s ↔ c
b ↔ t
]c
j<>PQP(1%3ZK\/2:(Je1%[ KI:QGJe1[BWEF<IP}KIVI/2GABF5=H821%1AB
MO<>E;BJ=1:[A<>82EWK\/HBF:j/21A8CBWE;1:D gb<>:F<>/
e ↔ ν e d ↔ u
s ↔ c
b ↔ t
]c
j<>PQP(1%3ZK\/2:(Je1%[ KI:QGJe1[BWEF<IP}KIVI/2GABF5=H821%1AB
MO<>E;BJ=1:[A<>82EWK\/HBF:j/21A8CBWE;1:D gb<>:F<>/
Z
/210P(<325e21/B?ZKI:JLKi:WK >1A82E]mopJq1`m5=:YBW1032<>/B BWEF<I5=:dI1E;BF1` 321-[A<>82?2J=KIV>1-KI8m`zMO1EFPQ5=<I/2:n
1:MO1AEFPQ5=<>/2:3C8 l<m32AJ=1lBWKI/23ZK\EF3
q ¯ d , l +
∝ √ α w
q ¯ u , ν ¯ l q, l ¯ + , ¯ ν l
W − Z
W +
q, l − , ν l
q d , l − q u , ν l
GABK\/HBQP(KI:F:;5eMO:A<>/ P(<I/HBFEF1%H821-J=1A:NGABK BW:?2E;<>?2EF1A:(3C1%JRf5=/BW1AEWKI[BW5=<I/zMO<>E;BF1%1ABQJ=1A:
GABK BW:"?2EF<I?2EF1A:321?2E;<>?ZKIV>K\BW5e<>/ ?ZK\E;BW5e[82Je1:_Je5=g2E;1:j/C1:;<>/B?2KI:"J=1:"P PQ1:A]ZopJ1/
EFG:;82JeBF18C/ PQGJLK\/2V>1i321A::FKI182E;:DH825~[<>/23C825eB NJLKN?@<>:;:F5eg25=Je5eBWG321BFEWKI/C:F5eBF5=<>/-?ZK\E
[<>82EFKI/B[hZKIEFVIG(1A/HBFEF1(3218m` M K\P(5eJ=J=1A:D325769GAEF1/BF1:]t j1A[5/SRK 691A[ABW1QH821QJ=1N:F1A[ABW1A82E
321H8ZKIEH:CJe1:/218mBWEF5e/2<>:cGABK\/HBj:WKI/C:jP(KI:F:;13ZKI/C:jJ=1 <32Je1iBWKI/23ZK\EF3S]m RKIPQ?2Je57X
BW82321d3214[1A:DBWEFKI/2:F57BW5e<>/2:01:;BD[ KIEFKI[ABFGEF5e:FGA14?ZKIED8C/P}K BWEF5e[13214PQGJLK\/2V>182/25eBWKI5=E;1I
JLK4P(K\BWE;5=[1321 *KIg2g25eg@<\X<>g2K>KI:FhC57XY KI: K*KN<>8-P(K\BWE;5=[1i
n
V CKM =
V ud V us V ub V cd V cs V cb V td V ts V tb
=
0.974 0.226 0.004 0.226 0.973 0.042 0.009 0.041 0.999
^~<>82E82/ >1AE;BF1`
W q u q d JRKIPQ?2Je5eBW8C321i3214Z1m/CP}KI/lMKI5eB05e/HBF1EY>1/C5=E8C/ BW1AEFPQ1
∝ V q u q d
√ α w]21A:*BW1E;P(1A:*325=KIV><>/ZK\8m`(321iJLKP}K\BFEF5e[1:;<>/B"J=1A:*?2J=8C:*5=PQ?@<IE;BK\/HBF:c1B J=1:0[<I82?2JLK\V>1:"M KI5=gCJ=1:":;1MO<>/B?2EF5e/2[5e?ZKIJ=1AP(1A/B QJRf5=/BWGAEF5e182E_3SRf82/21dP
P(1iM KIPQ5=JeJ=1
32182KIEH:]@1[A<>82?2J=KIV>1i1A/HBFEF13218` M K\P(5eJ=J=101:YBPQ<>5e/2:_?2EF<IgZKIg2Je1[A1H825?b1E;P(1B
3SRT1a`m?2J=5e8C1EJLKV>EWKI/C3213C82EFGA13210m5e13C1:j?2KIE;BF5=[8CJ=1:[A<>/BW1/2KI/B*82/(82KIENGABFEWKI/CV>1
K 0 K ± Λ
]]A]i/ :WKI57BDKI8 <>82EF39RThH825~H8214J=1A:/C18CBFEF5=/C<>::;<>/BDP(KI:F:;5eMO:01ABDH8SRf5=J
1`m5=:YBW1"GVK\J=1PQ1/B82/C1P(K\BWE;5=[A1_321"P(GAJLKI/2VI1_3ZKI/2:J=1_:;1[BW18CEj321A:cJe1?CBF<>/2:HK\?2?@1AJ=GA1
Λ
]]A]i/ :WKI57BDKI8 <>82EF39RThH825~H8214J=1A:/C18CBFEF5=/C<>::;<>/BDP(KI:F:;5eMO:01ABDH8SRf5=J 1`m5=:YBW1"GVK\J=1PQ1/B82/C1P(K\BWE;5=[A1_321"P(GAJLKI/2VI1_3ZKI/2:J=1_:;1[BW18CEj321A:cJe1?CBF<>/2:HK\?2?@1AJ=GA1P}K\BFEF5e[1i^ ^t<>/BW1A[<>EY><\X K K XK KIVKjK XYmK K\BKa]
j<IP(PQ13ZKI/2:J=1[ KI:0321dJ RT5e/BW1EFKI[ABF5=<>/%MO<>EYBW1\b5eJ1`m5=:YBW1dGAVKIJe1PQ1/B0321:0BW1E;P(1A:
321j[A<>82?2J=KIV>1:~1/BFEF1jgb<>:;<>/2:3C1 KI82VI1DBWEF<I5=:~1ABt82K\BWE;1jgb<>:F<>/C:~5e/2[Je8ZKI/BtJ=1?2h2<IBF<>/
?2825=:;H821J=1:
W ± ?@<IE;BW1A/B8C/21[hZKIEFVI1GAJ=1A[ABWE;5=H821
n
Z/γ W −
W +
W +
W − W +
W −
W − W +
Z/γ Z/γ
{{~w}r~{ sOvbv
Rf8CBW5eJ=5=:FK\BW5e<>/N321iPQG[ K\/25=:;P(13215eV>V>:c?@<>8CE*g2EF5e:F1AE*JLK:;P(GBWE;5=1DGAJ=1[BWE;<IM KI5=gCJ=1
[A<>/2328C5eB iJRTKI?2?ZK\EF5eBF5=<>/d3SRT8C/(gb<>:F<I/Q:;[ KIJ=KI5=E;1*/21A8CBWE;1IHJ=1_gb<>:F<I/Q3C105=V>VI:>[A<>82?2JeG
BF<>8CBF1:_J=1A:_?ZKIEYBW5=[A82J=1A:*P(KI:F:;5e>1A:
n
BW<I82:"J=1:cMO1EFPQ5=<I/2:4JRf1`m[A1?CBF5=<>/-321A:0/C18CBFEF5=/C<>:
Je1:(g@<>:;<>/2:(321 KI82VI1 321 JRf5=/BW1AEWKI[BW5=<I/ MKI5eg2J=1
W ± 1B Z
1B,J=1lgb<>:F<>/ 3215eV>V>:
Je8257X P
P(1dOBF1E;P(1A:_3SRK\8CBW<[<>8C?2JLKIVI1D3ZKI/2:_Je1i?@<\BW1/BF5=1JL]m RT5e/HBF1/2:;5eBFGi328-[<>82?CJLKIV>1
K\8m`}MO1AEFPQ5=<>/C:1A:;B_?CEF<>?b<>E;BF5=<>/C/21JeJ=1 dJLKP}K\:F:F1328}MO1AEFPQ5=<>/}KIJ=<>E;:cH821J=10[<>82?CJLKIV>1
K\8m` g@<>:;<>/2:321 KI8CV>1}1A:;B4?CEF<>?b<>E;BF5=<>/C/21JKI8z[KIEFE;G}321(JLK-P}K\:F:F1(328zgb<>:F<I/S]1A:
3C5e6@GEF1A/BW:_>1AE;BW1a`l:F<>/BKI5=/C:F5
n
q, l ¯ + q, l −
∝ M 2
h h
∝ m h h
W + , Z W + , Z
W − , Z W − , Z
1B0?@<>8CE_J=1:"K\8CBW<[<>8C?2JLKIVI1:
n