2004 Oscillation Analysis Summary

Official Numbers

Best fit result:

	sin²(2θ)	Δm² [eV²]	Δln(L_null)≡ ln(L_null)-ln(L_min^phys)	Null oscillation probability	remarks
	Normalization (# of FCFV events) & Energy spectrum fit
Best fit in all region	1.53	2.12×10^-3			ln(L_min^phys)-ln(L_min)=0.64
Best fit in physical region	1.00	2.73×10^-3	9.09	0.011% (3.86σ)	ln(L_min^phys)-ln(L_min)=0.64
	Normalization (# of FCFV events) fit
Best fit in all region	0.81	3.00×10^-3	4.32	0.33% (2.94σ)
	Energy spectrum fit
Best fit in all region	1.40	2.45×10^-3			ln(L_min^phys)-ln(L_min)=0.88
Best fit in physical region	1.00	2.92×10^-3	4.46	1.1% (2.53σ)	ln(L_min^phys)-ln(L_min)=0.88
	K2K-I
Best fit in all region	1.02	2.69×10^-3			ln(L_min^phys)-ln(L_min)=0.0013
Best fit in physical region	1.00	2.73×10^-3	4.33	1.3% (2.48σ)	ln(L_min^phys)-ln(L_min)=0.0013
	K2K-II
Best fit in all region	2.02	1.93×10^-3			ln(L_min^phys)-ln(L_min)=1.70
Best fit in physical region	1.00	2.72×10^-3	5.19	0.56% (2.77σ)	ln(L_min^phys)-ln(L_min)=1.70

Energy spectrum.
- Energy spectrum distortion: Kolmogorov-Smirnov Goodness-of-Fit Test (KS test)
  
  KS probability(%) Data and best fit Data and null oscillation
  
  K2K-I 43% 4.4%
  
  K2K-II 40% 1.2%
  
  ALL 52% 0.11%
- Spectrum shape consistency between K2K-I & K2K-II
  KS test between K2K-I & K2K-II data = 66.5%
N_SK (expected # of events in null oscillation case): Revised: '04/06/08

K2K-I & K2K-II K2K-I K2K-II

FCFV 150.85 +11.61 79.08 +6.22 71.77 +5.93

-10.04 -5.38 -5.09
Allowed region of Δm²

CL = 68% 1.99 × 10^-3 ≤ Δm² ≤ 3.33 × 10^-3 [eV²]

CL = 90% 1.72 × 10^-3 ≤ Δm² ≤ 3.51 × 10^-3 [eV²]

KS probability(%)	Data and best fit	Data and null oscillation
K2K-I	43%	4.4%
K2K-II	40%	1.2%
ALL	52%	0.11%

	K2K-I & K2K-II	K2K-I	K2K-II
FCFV	150.85	+11.61	79.08	+6.22	71.77	+5.93
-10.04	-5.38	-5.09

CL = 68%	1.99 × 10^-3 ≤ Δm² ≤ 3.33 × 10^-3 [eV²]
CL = 90%	1.72 × 10^-3 ≤ Δm² ≤ 3.51 × 10^-3 [eV²]

Official Plots

Reconstructed neutrino energy of 1-Ring mu-like events & MC expected spectrum assuming null oscillation
K2K-I & K2K-II	K2K-I	K2K-II

Reconstructed neutrino energy of 1-Ring mu-like events & Best fit
K2K-I & K2K-II	K2K-I	K2K-II

Reconstructed neutrino energy of 1-Ring mu-like events & Best fit in physical region
K2K-I & K2K-II	K2K-I	K2K-II

Allowed region in Δm² .vs. sin²(2θ)
K2K-I & K2K-II	K2K-I	K2K-II

K2K-I & K2K-II Normalization Revised: '04/06/07	K2K-I & K2K-II energy spectrum shape Revised: '04/06/07	K2K-I & K2K-II: linear scale for Δm²

N_SK (expected # of events in null oscillation case) distribution in Toy MC Revised: '04/06/08
K2K-I & K2K-II	K2K-I	K2K-II

N_obs (observed # of events in null oscillation case) distribution in Toy MCRevised: '04/06/08
K2K-I & K2K-II	K2K-I	K2K-II

log Likelihood curve
Δ ln(L) .vs. Δm²	Δ ln(L) .vs. sin²(2θ)

Reference (Internal information for collaborators)

Toy MC Revised: '04/06/09

ΔlnL threshold (from lnL_min in physical region)
K2K-I & K2K-II	68%	90%	95%	99%
K2K-I	1.685	2.8916	3.59937	5.22062
K2K-I & K2K-II	1.121995	2.274490	2.960860	4.551075
K2K-II	2.30599	3.541985	4.260910	5.9025
K2K-I & K2K-II Normalization	1.0	1.71	3.84	6.63
K2K-I & K2K-II energy spectrum shape	1.837405	3.051860	3.762115	5.391155

Summary table of sub-sample analysis.: For experts

Normalization
		K2K-I	K2K-II	ALL
		Best fit in all region
sin^2(2theta) (MINOS ERROR)		0.88144 +- 1.8182	0.67325 +- 1.8843	0.80531 +- 0.68391
sin^2(2theta) (MINOS ERROR)		-0.59935 +at limit	-0.42895	-0.49089 +at limit
dm^2 (MINOS ERROR)		0.28559E-02 +- 0.10010E-01	0.33976E-02 +- 0.18258E-01	0.30006E-02 +- 0.80923E-02
dm^2 (MINOS ERROR)		-0.17465E-02	-0.23707E-02	-0.10117E-02
log likelihood minimum (lnL_min)		2.9331025	2.8961629	3.2607758
FCFV Nexp	K2K-Ia	3.19991002	----------	3.23848428
	K2K-Ib	52.80009236	----------	53.37036551
	K2K-II	----------	52.00000026	51.39115118
KS prob	ALL-MC	0.3038639426	0.0960950181	0.2118454874
	K2K-I-MC	0.5516881943	0.4449231029	0.6160905361
	K2K-II-MC	0.2714127898	0.1219806150	0.2105851024
		Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)
		Best fit in Null oscillation case
log likelihood minimum (lnL_min_null)		5.6487416	5.0734892	7.5824101
FCFV Nexp	K2K-Ia	4.46624543	----------	4.47942609
	K2K-Ib	67.67733947	----------	65.99431184
	K2K-II	----------	65.82925787	63.71957571
KS prob	ALL-MC	0.0009778294	0.0010304055	0.0006585165
	K2K-I-MC	0.0410539694	0.0422007069	0.0333526991
	K2K-II-MC	0.0107701076	0.0110458946	0.0088866362
		Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)
		Null oscillation probability
dlnL = lnL_min_null - lnL_min		2.7156391	2.1773263	4.3216351
Null Osc Prob		0.0197791960	0.0369079895	0.0032827160
1.0- Null osc. Prob		0.9802208040	0.9630920105	0.9967172840
Spectrum shape
		K2K-I	K2K-II	ALL
		Best fit in all region
sin^2(2theta) (MINOS ERROR)		1.0563 +- 0.35260	2.2760 +- 1.8440	1.3960 +- 0.38259
sin^2(2theta) (MINOS ERROR)		-0.41532 +0.82055	at limit	-0.30036 +0.93585
dm^2 (MINOS ERROR)		0.28891E-02 +- 0.94240E-03	0.21347E-02 +- 0.50749E-03	0.24500E-02 +- 0.63452E-03
dm^2 (MINOS ERROR)		-0.12905E-02 +0.88996E-03	-0.29414E-03	-0.82032E-03 +0.57180E-03
log likelihood minimum (lnL_min)		29.8693403	19.8849344	52.3139851
KS prob	ALL-MC	0.6353842616	0.0000004910	0.2593989074
	K2K-I-MC	0.2895430326	0.0000174620	0.1495971084
	K2K-II-MC	0.5484489799	0.0009968145	0.6289703250
		Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)
		Best fit in physical region
sin^2(2theta) (MINOS ERROR)		1.00000 +- 0.87998	1.00000 +- 0.12715	1.00000 +- 0.11050
sin^2(2theta) (MINOS ERROR)		(-0.36373 +at limit)	-0.13697 +at limit	-0.10813 +at limit)
dm^2 (MINOS ERROR)		0.29721E-02 +- 0.77662E-03	0.28887E-02 +- 0.60402E-03	0.29226E-02 +- 0.47627E-03
dm^2 (MINOS ERROR)		-0.94456E-03 +0.81869E-03	-0.68467E-03 +0.56367E-03	-0.52667E-03 +0.44759E-03
log likelihood minimum (lnL_min_phys)		29.8819852	23.2945066	53.1950762
KS prob	ALL-MC	0.6830764413	0.6462269425	0.6439630985
	K2K-I-MC	0.3347403705	0.3509394825	0.3584465683
	K2K-II-MC	0.4591656625	0.4483641982	0.4471776187
		Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)
		Best fit in Null oscillation case
log likelihood minimum (lnL_min_null)		31.5149570	26.2042861	57.6628930
KS prob	ALL-MC	0.0018435231	0.0023058825	0.0025578325
	K2K-I-MC	0.0574903078	0.0634440258	0.0672317073
	K2K-II-MC	0.0147293797	0.0168418474	0.0177538656
		Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)
		Null oscillation probability
dlnL = lnL_min_null - lnL_min_phys		1.6329718	2.9097795	4.4678168
Null Osc Prob		0.1953481883	0.0544877388	0.0114723342
1-Null osc. Prob		0.8046518117	0.9455122612	0.9885276658
Combined
		K2K-I	K2K-II	ALL
		Best fit in all region
sin^2(2theta) (MINOS ERROR)		1.0240 +- 0.45862	2.0234 +- 0.28623E-16	1.5286 +- 0.68362
sin^2(2theta) (MINOS ERROR)		-0.39451 +1.0611	at +limit at limit	-0.48032 +at limit
dm^2 (MINOS ERROR)		0.26921E-02 +- 0.97534E-03	0.19342E-02 +- 0.80256E-19	0.21229E-02 +- 0.73992E-03
dm^2 (MINOS ERROR)		-0.11486E-02 +0.10200E-02	at +limit at limit	-0.70617E-03 +???????
log likelihood minimum (lnL_min)		32.8871379	24.5729987	55.9707077
FCFV Nexp	K2K-Ia	3.11500220	----------	3.03655552
	K2K-Ib	51.30399717	----------	50.89002017
	K2K-II	----------	46.28360289	48.98728907
KS prob	ALL-MC	0.5521001220	0.0779760703	0.5107437372
	K2K-I-MC	0.4310561121	0.0673559383	0.2512494922
	K2K-II-MC	0.4221234620	0.3513624966	0.8306059837
		Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)
		Best fit in physical region
sin^2(2theta) (MINOS ERROR)		1.00000 +- 0.88624	1.00000 +- 0.16325	1.00000 +- 0.15545
sin^2(2theta) (MINOS ERROR)		-0.36888 +at limit	-0.15961 +at limit	-0.13590 +at limit
dm^2 (MINOS ERROR)		0.27342E-02 +- 0.53893E-03	0.27203E-02 +- 0.48184E-03	0.27299E-02 +- 0.36684E-03
dm^2 (MINOS ERROR)		-0.57790E-03 +0.97948E-03	-0.51133E-03 +0.46220E-03	-0.38364E-03 +0.37414E-03
log likelihood minimum (lnL_min_phys)		32.8885267	26.2709589	56.6077034
FCFV Nexp	K2K-Ia	3.11903967	----------	3.12351750
	K2K-Ib	51.35251335	----------	51.80548967
	K2K-II	----------	50.18847990	49.86845034
KS prob	ALL-MC	0.5158003569	0.5264701247	0.5213258862
	K2K-I-MC	0.4434316754	0.4253791571	0.4349086881
	K2K-II-MC	0.3990996778	0.4019556046	0.4011933506
		Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)
		Best fit in Null oscillation case
log likelihood minimum (lnL_min_null)		37.2162153	31.4622349	65.6952735
FCFV Nexp	K2K-Ia	4.46559305	----------	4.47499754
	K2K-Ib	67.86360776	----------	66.83817668
	K2K-II	----------	66.48253632	64.51994955
KS prob	ALL-MC	0.0011319100	0.0015118229	0.0011482574
	K2K-I-MC	0.0445423201	0.0507625937	0.0441038497
	K2K-II-MC	0.0115808453	0.0136862956	0.0119844535
		Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)	Spectrum & fit results (PS),(EPS files 1,2,3,4)
		Null oscillation probability
dlnL = lnL_min_null - lnL_min_phys		4.3276886	5.1912760	9.0875701
Null Osc Prob		0.0131980171	0.0055649010	0.0001131
1.0- Null osc. Prob		0.9868019829	0.9944350990	0.9998869
Changing FD flux / MC model
		Standerd NEUT (W/O θ cut for FD flux determination)	Coherent π supression
		Best fit in all region
sin^2(2theta) (MINOS ERROR)		1.2437 +- 0.29075	1.5723 +- 0.71775
sin^2(2theta) (MINOS ERROR)		-0.27671 +0.38688	-0.49564 +at limit
dm^2 (MINOS ERROR)		0.23647E-02 +- 0.46862E-03	0.21008E-02 +- 0.74853E-03
dm^2 (MINOS ERROR)		-0.51397E-03	-0.67572E-03 0.64233E-03
log likelihood minimum (lnL_min)		56.2063390	56.0224930
FCFV Nexp	K2K-Ia	3.12308311	3.02455934
	K2K-Ib	49.62113086	50.89305506
	K2K-II	47.77855046	48.98881554
KS prob	ALL-MC	0.7781293988	0.4589156806
	K2K-I-MC	0.3966858685	0.2319755852
	K2K-II-MC	0.5929255486	0.8039594293
		Best fit in physical region
sin^2(2theta) (MINOS ERROR)		1.00000 +- 0.14761	1.00000 +- 0.14648
sin^2(2theta) (MINOS ERROR)		-0.12422 +at limit	-0.13007 at limit
dm^2 (MINOS ERROR)		0.26544E-02 +- 0.34316E-03	0.27446E-02 +- 0.36679E-03
dm^2 (MINOS ERROR)		-0.35906E-03 +0.34203E-03	-0.38293E-03 +0.36975E-03
log likelihood minimum (lnL_min_phys)		56.5929467	56.7454907
FCFV Nexp	K2K-Ia	3.19032858	3.11940531
	K2K-Ib	50.74964660	51.87673217
	K2K-II	48.86619419	49.93453124
KS prob	ALL-MC	0.3447558880	0.5329799056
	K2K-I-MC	0.5735797882	0.4264678359
	K2K-II-MC	0.3070581853	0.4066191316
		Best fit in Null oscillation case
log likelihood minimum (lnL_min_null)		66.5123366	65.9715278
FCFV Nexp	K2K-Ia	4.47492411	4.47482004
	K2K-Ib	66.83219323	66.87239559
	K2K-II	64.54009849	64.54880848
KS prob	ALL-MC	0.0002979948	0.0011400280
	K2K-I-MC	0.0217640772	0.0439221412
	K2K-II-MC	0.0055233669	0.0119512463
		Null oscillation probability
dlnL = lnL_min_null - lnL_min_phys		9.9193899	9.2260371
Null Osc Prob		0.0000492112	0.0000984426
1.0- Null osc. Prob		0.9999507888	0.9999015574

Allowed region in Δm² .vs. sin²(2θ)
Standerd NEUT (W/O θ cut for FD flux determination)	Coherent π supression

Allowed region in Δm² .vs. sin²(2θ)
K2K-I (δm² linear scale)	K2K-II (δm² linear scale)

Nakadaira Takeshi(nakadair@scphys.kyoto-u.ac.jp)

Last modified: Fri Jun 11 11:17:47 JST 2004