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KTeV Determination of the CKM Parameter |Vus|
Nuclear Physics B (Proc. Suppl.) 142 (2005) 304–309 www.elsevierphysics.com
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m}{cwpg>x_{csCq wX}uxc:qaw{/JxYuzCysCzCZxYuy{c:zCwauzmu}wXV<x_{csmq/<xc"Au>y{cxcw zT >u>zv 1 Cqayau~Jwa¡T¢ wXzmV{csCqawXq5xcqawX
m}{cwa1£¤qJxcqawXqaz|{¥udzCq£Cq{cqxc5zmu>{c:z>f{csmq§¦2n_¨ vuxYu5q{cqx_© ªv«>¬:© ¡ ¼\8IKÀbv9]/DF78¾65G8H 8Å\Æ8=NOmDÄK|DÄS 8>=UVNZ;gKMLüF KC9 ®°¯±²>³|´ µ2¶ ·J²¸¹´± T U 8:KJ9[7=8¼°DF7859YNZÅÇ;gKM=hJ8:9cDÍdæL7=aKMO IaF NZO7h@-=aKJIDNZBCO 9] S7BC=ºUVBJ=8DF KJO°Dc»(B¼78I>KC¼\89]MDF78p½=9YD=B|»¾BJ@ DF78 E » 7 F e KJL7NZL LBJ¿6 BCL KÀbCKC9YF7NZ¿XÁKJ9Â|KÀ» K?Ãe 65ÁÄPU°K|D=NZÅVFKJ9 I>KÀbTN¼\Æ\8¿¿ 9[7hJhC89YD8:¼dKDc»(BJ¿9NZhCU°K§¼\Ng9I>=8Æ KMOIbVNZODF78 [7O7NZDKM=¿ NZDcbÇIBCO ¼\NZDNDÇD8D=F UVK|D NÙN<9¥imÚÛF7NZhCF78>=pDF KJODF78§Ü(Ý/Þ KÀ`C8>=aKMhJ8× ß|ÙÃàvDF78 =8:9Y[7;ZDNOmD O7I>KÀ8>b\[\9>Dà2=KJÍ ;f KMóVO ¼¼\8IaIFKÀKMb\=9¥hJ8F¼KÀ`JÂÀ8TKJBJO7O BM9/DKML =8>88O'L KC[ 9Y98:8¼¼#BC?-OÄLvbËÍ Ü óTÝ ¼\Þ58P¿ »ENZDF[7O7NZDKJ=NZDcbJ4fG BVKC¼7¼\=899(DF7859ND[ K|DNZBCO NÅvD=aKJID8¼Ç@-=BCUåÍdæ˼\8:I>KÀb\9>]765G 8>HFKJ9=8¿ ÆLBv8:I>BJKM=[;8=UVÍ NZ O7ó 8:¼1@-BJ4=pU8=@Î8KCI» DBJ8=:¼7]8KMDO8¼=UVF7N<8>O7O 8§I>á8â ã|äMõ á] @-=» BJKCU 9 I>8>OmD;UVN<;Z8Æ\DBCO7NgI°L7=aKMO IaF7N=`vNZ8» KMO ¼VDF78_I>BJO 9N<9YD8O IbTBM@DF7898EDc» B á âã|äMáC¼\8D8>=UTNÅvD=aKJIDNZBCO@-=BCUåBC[7=_=89[7;ZD9¥F KJ9_L88>O D =8>Æ BJ=D8:¼ÇN=:]7» 85hJN<`J85KTL7=NZ8>@¤¼\8>¿ 65NPpUVNg98>OmKMDO'9KJNZUV=8 Æ L BJKC=D9YKM8:Om¼ÇD5BCIO =BCF79N<9hJIaFF 89YIaDÂK|D4/N<9YGDNgF I>89 9I=NZÆ7DN4 9KJUTÆ ;Z8:95?cØj û Øj P]7KMO¼ » 8/DKJÂJ8 KJ¼\`|KMOmDaKMhJ8/BM@2DF 8 GF78dÍ æ ÐîÒï¤ðñfÖë?¹ÍVòó:P5¼\8:I>KÀbÄ=aK|D8VN<9§=8;=UTN¥IBJO9cDaKMOmD] ú õ N<9dDF78Â|KJBJOëU°KJ99>] ò þ1ÿ Ng9 9YNKÀbUTB\¼\8:9 KM=8 ¼\89I=NZL 8¼%8>;g98>»EF78=8ü× k ] èJÙÃ4 GF78ëB|`J8=KJ;Z;Vím[ KM;8/=aKJ¼7NOmDË;ZBCO7hM¿X¼\Ng9cDaKMO I>8Ñ=KC¼\NgK|DN<`J8ÑI>BJ==8:I¿ BM@ÄDF78ü9YNUV8>OmD NZOëDF78ļ7KMDKÑKJO ¼ëÁ'eå¼\8IKÀb `J8=YD8ž¼7N<9YD=NZL [\DNKJ;[7;8=ò B ?ÎS2NZh45Ø:Pà DF78 Â|KMBCOê8>O78=hCb ¼\N<9YD=N=Ç@-BJ=ÇDF78ÄðÖ 9Yb\9YD8U]¥KMO ¼ õ KMhJ=8>8#» 8>;<;¹4 é 9NZhCO7N½ I>KMOmDìNUV8>OmD NZO DF 8 Ng9'DF78 Æ7FKJ98¿X9YÆ KCI8¾NZOmD8hJ=aKM;Ã]»EF NÆ 8>O¼79ìBJO á âã|äJáKMO KJ;Zb\9N<9_N<9 KdO 8>»üD=8KMDUV8>OmD BM@º=aKJ¼\NgK|DNZ`C88@A¿ UV8KC9Y[ =8:¼ 98>UVN<;Z8Æ\DBCO7N=aK|DBJ=(@-BJ=p98>UVN<;Z8Æ\DBCO7NKÀb UV8>OmDaKM;7NÆ\DBJO7NgIL7=aKMO IaF7NDN¿ UTB\¼\8:9>4¤GF78Æ7=BJhC=KJU8792:;Ä× iMÙvNg9¤[ 98¼§DB hJ8O78>=aK|D8 Í æ Ð Òï2ðñºÖ1?=<1Pà>79:?; NDNgI>KM;NZO7Æ [\DTN;Z[ ¼789=aKJ¼7NBJ==8:IDNDc»(88>O'DF78dIaFKM=hJ8¼ÄÆ KM=DNgI;<89] KJO ¼'NZO\¿ ¹ ? C j P 4 Ï O78>=EÈ =8U°99YD=aKMF7;<[7O7h?-WcÈEP(B&@DF 8/Æ NZBCO ]\;Z8Æ\DBCO KJO ¼ GBìND8=UVN
305
R. Kessler / Nuclear Physics B (Proc. Suppl.) 142 (2005) 304–309
LNMPOPQ4R+S MPTVU$MXWZY[]\M MX^_MPOXU$`ba&cd e8Q&T$Mfga`VUihjfgkla TIm U$Q nU]honpUI\qMbrtsvuwLMPOxQ4RgfgaNLNM>hjntyz\hoO \{d e|f aNLNhj}qM6` UI\M~Q OxOxMxkNU Q&nqOxMt2R2{Y "Q LNhQU$hjSMMX^_MPOGU `pQ&T$M Q&`VahofgkaTVU Q&nUihjn~UI\Mgc=aTIfcQ OGU$a TbfgMPQ`VT$MxfgMPnU ` M6O&Y A Y A Y
60
(a)
1.04
(b)
1.02
40
1
20
0.98
πππ
0.96 1.04
0
Data/MC ratio
Thousands of events / meter
0 0 0
20
Slope: −4 (-0.87 ± 1.20) × 10 /m
1.02
10
1
0.98
πeν 0
0.96 1.04
10
1.02
Slope: (-2.30 ± 1.30) × 10−4/m
1
5
0.98
πµν 0 30
0.96 1.04
20
1.02
10
0.98
Slope: (2.26 ± 2.06) × 10−4/m
1 + − 0
π ππ 0
130
0.96
140
150
Slope: −4 (2.37 ± 1.33) × 10 /m
130
140
150
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306
R. Kessler / Nuclear Physics B (Proc. Suppl.) 142 (2005) 304–309
high intensity beam with regenerator x10 lower intensity without regenerator
(B = ΓKe3/ΓL) (B = ΓKµ3/ΓL)
(ΓKµ3/ΓKe3)
(B = Γ000/ΓL) (B = Γ+−0/ΓL)
(Γ000/ΓKe3)
(B = Γ+−/ΓL) (B = Γ00/ΓL)
(Γ3π/ΓKe3) 0.9
(Γ2π/ΓKe3) (Γ00/Γ000) 0.98
0.985
0.99
0.995
1
1.005
1.01
1.015
1.02
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0.925
0.95
0.975
1
1.025
1.05
1.075
1.1
±k g«ÜI¦¨¯°b¦±£²bè'¿ÁS à ¯Ogka» Gg«g· ºO ª(k¥»Oª0O-¨#';k>k BKTEV / BPDG
decay rate ratio (arbitrary scale)
PDG 02
PDG 02
KTEV 0.38
0.39
0.4
KTEV
0.41
B(KL→πeν)
0.27
PDG 02
0.2
0
B(KL→3π )
0.21
0.124
0.126
B(KL→π+π−π0)
PDG 02 KTEV
0.275
PDG 02 KTEV
KTEV 0.19
0.2725
B(KL→πµν)
0.128
PDG 02 KTEV
>k OS5¦¨b#-·y9O #¸[¹¬º(ª(-¢»( ª0O- i #g©ºK¤a°b¦ ²w¼#-9®m O(½¾ ©»O À¿ÁS à y¼Ä £¬ªDkOª£-O½D 1.9
2
2.1
1000 × B(KL→π+π−)
0.85
0.9
0.95
1000 × B(KL→π0π0)
1
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307
R. Kessler / Nuclear Physics B (Proc. Suppl.) 142 (2005) 304–309
TVUXWHYNZ\[N]HTV^W`_,YbadcPeZ]gfhjiHTkWTVhjUblmTnio_pVZa ]pVqsrtTniTueNpuZ
Z]~dq iHhdpu{WHTuhdUbiWHYba W[NTk|}Z]etqm#hdU`a7rdZ],a ~jZddadUb[ _0hi#! ;b I _0hj]H]Z#iHfhdUb[Ni6Whxa I [{TV|}Z]ZUb_Zd
KTeV Form Factor Data 1st order fit
200
Data 2nd order fit
3
,,
10 × λ +
2
χ /dof = 13.7/ 16 0
2
4
t⊥π /M2π
13.73 A0 A1 A2
/ 14 1.000 -0.1351E-03 0.1872E-04
0.2494E-02 0.1905E-02 0.3084E-03
1.025
6
0.95 0
2
4
t⊥π /M2π
Tu~dN]Z`ðb«ña Wawa Ub[sÉwÊ[{Tni W]HTueN{WTVhjUbi^yhd]¶ò
Average Ke3 Kµ3
6
Òó
TuU
£
[{Z#_#a7qtiÐypuZ0^Wwa Ub[Ô[Na+W,aô+Éwʯ]a WHTuhjiÐy]TV~jYjW ¤ l ¬YbZx[ba+Wa*![{hdWi,3a ]ZLWHYbZ¶ia cxZ¶TVU*ehdWHY»WYNZxNfNfZ] adUb[mpuh v Z#]ÃfNpuh Wi#·Nhj]É*ÊÔ!YNTuiWHhj~d],a cgbWHYNZNfNfZ]
1
0 12
1.05
0.975 2
3
0.95
1
50 0
Data/MC ratio
2
χ /dof = 33.5/ 16
0
100
4
0.2503E-02 0.1910E-02 0.3095E-03
0.975
50
150
KTeV
/ 14 1.008 -0.7856E-02 0.1338E-02
1
100
6
14.69 A0 A1 A2
1.025
200
5
1.05
150
Thousands of entries per 0.4
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308
3
Methods
32
t⊥e t⊥π
30
DC1+50µm
22
−B, e−
−B, e+
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−B, e+
+B, e−
−B, e− +B, e+
24
+B, e+
26
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28
80
80
60
60
40
40
πeν
20 0
(b)
data MC
100
100
Alignment
Nominal
120
(a)
data MC
120
cos(θν) > 0.4
34
cos(θν) < 0.4
10 x λ+
Ke3 Form Factor Crosschecks (linear model)
Thousands of entries per 10 MeV/c2
R. Kessler / Nuclear Physics B (Proc. Suppl.) 142 (2005) 304–309
πµν
20
χ2/dof = 35.0/32
0.2
0.3 0.4 Mπe (GeV/c2)
χ2/dof = 22.9/25
0.5
0
0.2
0.3 0.4 Mπµ (GeV/c2)
0.5
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0.215
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0
Data/MC ratio
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0 0 0
20
Slope: −4 (-0.87 ± 1.20) × 10 /m
1.02
10
1
0.98
πeν 0
0.96 1.04
10
1.02
Slope: (-2.30 ± 1.30) × 10−4/m
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5
0.98
πµν 0 30
0.96 1.04
20
1.02
10
0.98
Slope: (2.26 ± 2.06) × 10−4/m
1 + − 0
π ππ 0
130
0.96
140
150
Slope: −4 (2.37 ± 1.33) × 10 /m
130
140
150
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high intensity beam with regenerator x10 lower intensity without regenerator
(B = ΓKe3/ΓL) (B = ΓKµ3/ΓL)
(ΓKµ3/ΓKe3)
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(Γ000/ΓKe3)
(B = Γ+−/ΓL) (B = Γ00/ΓL)
(Γ3π/ΓKe3) 0.9
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0.99
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PDG 02
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0.39
0.4
KTEV
0.41
B(KL→πeν)
0.27
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0
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0.21
0.124
0.126
B(KL→π+π−π0)
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0.275
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0.128
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307
R. Kessler / Nuclear Physics B (Proc. Suppl.) 142 (2005) 304–309
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KTeV Form Factor Data 1st order fit
200
Data 2nd order fit
3
,,
10 × λ +
2
χ /dof = 13.7/ 16 0
2
4
t⊥π /M2π
13.73 A0 A1 A2
/ 14 1.000 -0.1351E-03 0.1872E-04
0.2494E-02 0.1905E-02 0.3084E-03
1.025
6
0.95 0
2
4
t⊥π /M2π
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1
0 12
1.05
0.975 2
3
0.95
1
50 0
Data/MC ratio
2
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0
100
4
0.2503E-02 0.1910E-02 0.3095E-03
0.975
50
150
KTeV
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1
100
6
14.69 A0 A1 A2
1.025
200
5
1.05
150
Thousands of entries per 0.4
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308
3
Methods
32
t⊥e t⊥π
30
DC1+50µm
22
−B, e−
−B, e+
+B, e−
−B, e+
+B, e−
−B, e− +B, e+
24
+B, e+
26
t⊥π (Born MC) t⊥e (Born MC)
28
80
80
60
60
40
40
πeν
20 0
(b)
data MC
100
100
Alignment
Nominal
120
(a)
data MC
120
cos(θν) > 0.4
34
cos(θν) < 0.4
10 x λ+
Ke3 Form Factor Crosschecks (linear model)
Thousands of entries per 10 MeV/c2
R. Kessler / Nuclear Physics B (Proc. Suppl.) 142 (2005) 304–309
πµν
20
χ2/dof = 35.0/32
0.2
0.3 0.4 Mπe (GeV/c2)
χ2/dof = 22.9/25
0.5
0
0.2
0.3 0.4 Mπµ (GeV/c2)
0.5
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