Electromagneticeffectsinη→3πarXiv:0910.0210v1 [hep-ph] 1 Oct 2009∗Speaker.
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Electromagneticeffectsinη→3πChristophDitsche
2
¯−uu(dd¯)(x),
(1.1)
whichareproportionaltothelight-quarkmassdifferencemd−mu,orelectromagneticinteractions,
H(x)=−
e2
QEDElectromagneticeffectsinη→3πChristophDitsche
3/4)×δ/(ms−mˆ)+O(δ3).Forthechargedchannel,theMandel-stamvariabless=(pη−pπ0)2,t=(pη−pπ+)2andu=(pη−pπ−)2arerelatedbys+t+u=
2+M2+2M2=3sc.ExpandinginisospinbreakingparametersuptoO(δ,e2,e2δ)andrewrit-Mηπ0π0
2,M2,∆M2andthepiondecayconstantFingeverythingintermsofphysicalobservableslikeMηπππ0
yieldsforthechargedamplitudeatleadingchiralorder
23(s−scB0δLO0)+2∆Mπ√Ac=−1+
23FπQ216
√√
Q216
Electromagneticeffectsinη→3πChristophDitsche
Electromagneticeffectsinη→3πChristophDitsche
3
T+−T−
3(u−t)
3
3i∑=1
3Ti
(MηQ−Mπ0)−s
c
−1=
32Electromagneticeffectsinη→3πChristophDitsche
GL0.0325−1.2790.3960.0744∆BKW(−1.1±0.9)%(+0.6±0.1)%(+1.4±0.2)%(+1.5±0.5)%∆DKM
(−2.4±0.7)%
(+0.7±0.4)%
(+1.5±0.7)%
(+4.4±0.4)%
Table1:Dalitznormalizationandslopesforη→π0π+π−resultingfromtheGLamplitudeandrelativeelectromagneticcorrectionsduetoBKWandDKMamplitudes.
|Nn|2102×αχ2/ndf
Electromagneticeffectsinη→3πChristophDitsche
r=Γn/Γc
rGL
∆ΓBKW∆ΓDKM(uc)∆QBKW∆QDKM(uc)
(−1.0±0.9)%(−1.0±0.5)%(+0.24±0.22)%(+0.24±0.12)%
(+0.28±0.22)%
Γc/n∝Q−4
(−1.1±0.9)%
∆rDKM
(−1.4±1.8)%
1.442
Electromagneticeffectsinη→3πChristophDitsche
Electromagneticeffectsinη→3πChristophDitsche
