Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://nuclphys.sinp.msu.ru/conf/lpp14/210809/Levy.pdf Äàòà èçìåíåíèÿ: Wed Sep 16 16:30:18 2009 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 00:39:06 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: hep-ex

Study of the quasi-elastic µ n /µ p scattering in ¯ the NOMAD experiment

µ
N
eutrino


O
scillation

MA

gnetic

D

etector

Jean-Michel Levy2 [for the NOMAD collaboration] arXiv:0812.4543 [hep-ex], to appear in Eur.Phys.J. C Vladimir Lyubushkin , 1 Boris Popov1,2 et al.
1 2

Joint Institute for Nuclear Research, DLNP, Dubna LPNHE, Univ. of Paris VI and VII, Paris

XIVth Lomonossov Conference

Moscow, August 21th , 2009


Outline

The NOMAD experiment and the detector The µ /µ - N total cross sections ¯ MC simulation and nuclear effects Selection of quasi-elastic events in NOMAD: topological and kinematical criteria Measurement of the quasi-elastic cross section and of the axial mass. Results and conclusions


NOMAD in a nutshell

Purpose: search for µ oscillations Method: identification of through the kinematics of its decay products into various channels Needed: a very precise momentum measurement and good par ticle identification Hardware: a massive but low Z , fine grained, active target with various subdetectors Output: a unique data set on which various analyses are still being performed ten years later


The NOMAD detector
Muon Chambers Front Calorimeter
V8

Dipole Magnet

TRD Modules Preshower

Neutrino Beam

Y

Z

1 metre

Veto Planes Drift Chambers

Trigger Planes Electromagnetic Calorimeter Hadronic Calorimeter

Drift Chambers (target and momentum measurement) Transition Radiation Detector for e
±

Position resolution < 200 µm (small angle tracks) Momentum resolution 3.5% (p < 10 GeV/c )

identification: rejection 103 for electron efficiency (E ) (3.22 ± 0.07)% Lead glass Electromagnetic Calorimeter = (1.04 ± 0.01)% + E E (GeV) Muon Chambers for µ± identification: efficiency 97% (pµ > 5 GeV/c ) Hadronic Calorimeter to veto n and K
0 L

90%


Neutrino fluxes on the NOMAD detector

Neutrinos / 1 GeV / 10 p.o.t.

10

6

NOMAD fiducial area: 2.6m x 2.6m 10
5

9

10

4

N / µ 1.0

- ,

GeV

i = Mode QEL RES DIS

24.3

Z

i (E )(E )dE Neutri 0.4 0.5 16.6 n 2 7 4 o 8 6 3 Antineutri 0.3 0.4 4.8 n 9 3 7 o 3 2 6

10

3

10

2

A A

0.068 0.010 0.0027

17.2 36.4 27.6

10

1

20

40

60

80

100

120

Neutrino energy (GeV)


View of a typical QEL candidate event in the NOMAD detector

E = Q2 = W2 = Ptmis=

57.00 GeV 2 0.60 GeV 2 1.44 GeV 0.05 GeV

Run 15049 Event 11514

Muon track:

P = 56.39 GeV;

Proton track:

P = 1.02 GeV;

Example of an event recognized as µ n µ- p (run 15049 event 11514). The long track is identified as a negatively charged muon, the short track is associated with the recoil proton.


The total µ CC cross section: mixture of QEL, RES and DIS contributions
cm / GeV)
1.2

2

µ N
1

/ E (10

-38

0.8

tot

0.6

0.4

0.2

QEL : MA = 1.03 ± 0.10 GeV RES : ExRS without BG MA = 1.03 ± 0.10 GeV Wcut = 2.0 GeV DIS : GRV98-LO Wcut = 1.4 GeV 1 10 50 100 150 200 250 300 350

E (GeV) tot /E , for the muon neutrino charged-current total cross section as function of neutrino energy. The straight line is the average value (0.677 ± 0.014) â 10-38 cm2 /GeV.

0 -1 10


The total µ CC cross section: mixture of QEL, RES and DIS contributions ¯
0.6

cm / GeV)

2

µ N
0.4

_

/ E (10

-38

0.2

tot

0 -1 10

1

10

50

100

150

200

250

300

350

E (GeV)
Baker et al., FNAL 1983 Seligman, CCFR 1997 Naples, NuTeV 2003 Colley et al., BEBC 1979 Bosetti et al., BEBC 1982 Allasia et al., BEBC 1984 Budagov et al., HLBC 1969 Eichten et al., GGM 1973 Ciampolillo et al., GGM 1979 Erriquez et al., GGM 1979 Morfin et al., GGM 1981 Abramowicz et al., CDHS 1983 Berge et al., CDHS 1987 Jonker et al., CHARM 1981 Allaby et al., CHARM 1988 Asratyan et al., IHEP-ITEP 1978 Baranov et al., IHEP SKAT 1979 Vovenko et al., IHEP-ITEP 1979 Asratyan et al., IHEP-ITEP 1984 Anikeev et al., IHEP-JINR 1996 Wu et al., NOMAD 2008

Barish et al., ANL 1979 Baltay et al., BNL 1980 Baker et al., BNL 1982 Benvenuti et al., HPWF 1974 Barish et al., CF 1975 Barish et al., CFR 1977 Barish et al., CFRR 1981 MacFarlane et al., CCFRR 1984 Auchincloss et al., CCFR 1990 Kitagaki et al., FNAL 1982 Taylor et al., HBF 1983

tot /E , for the muon antineutrino charged-current total cross section as function of neutrino energy. The straight line is the average value (0.334 ± 0.008) â 10-38 cm2 /GeV.


Monte Carlo simulation

Quasi-elastic neutrino scattering
based on the Smith-Moniz approach the vector form factors FV and FM are assumed to be known (GKex(05) parametrization) 2 the axial form factor is given the dipole form FA (Q 2 ) = FA (0)[1 + Q 2 /MA ]

-2

Single pion production via an intermediate resonant state
based on the Rein­Sehgal model set of 18 baryon resonances with masses below 2 GeV as in RS but with all relevant parameters updated.

Deep inelastic scattering
primary interaction described with a modified version of LEPTO 6.1 followed by JETSET 7.4 to account for the full hadron zoo structure functions are calculated at LO using the GRV 98 pdf

Coherent pion production Final State Interactions: Intra-nuclear cascade
simulated with the DPMJET package, based on the Formation Zone Intranuclear Cascade model the NUANCE event generator was used for a cross-check


Identification of QEL events in NOMAD

Required: an identified µ with/without a rather slow proton (mostly p < 1 GeV) at large angle (h > 600 ) Problem : slow protons in the upper hemisphere are bent back in a U-turn. Hence a reconstruction problem for which the software had not been optimized, and simulation difficulties making reliable estimation of efficiencies practically impossible. It was therefore decided to keep only upward going muons. The final errors being dominated by systematics, there is no loss in precision because of the lower statistics.


Identification of QEL events in NOMAD

Proton reconstruction efficiency, in %

Events
0 = 2.0 0 = 1.0 0 = 0.6

50 45 40 35 30 25 20 15 10 5 0 0 0.5 1 1.5
mc

1400 1200 1000 800 600 400 200 1-track sample 2-track sample MC prediction 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

2

0 0

h /



rec µ

/

Left : reconstruction efficiency of the proton track as a function of its azimuth h ; smoothed MC predictions for different values of the formation time 0 . Right: muon azimuth µ distributions in data and MC for 1-track and 2-track samples.


Intranuclear cascade and proton track reconstruction probability

Proton reconstruction efficiency, in %

Proton reconstruction efficiency, in %

Arbitrary events (logarifmic scale)

h = 40 ° h = 60 ° h = 70 °

1.0 GeV 0.5 GeV 0.4 GeV

before FSI after FSI

80

80

h = 80 °

60

60
ph = 0.3 GeV

40

40

before FSI after FSI 0 0.2 0.4 0.6 0.8 1 1.2 1.4

20

20

0

0

0

0.1

0.2

0.3

0.4

0.5

0.6

ph (GeV)

h /

Distributions of the leading proton momentum ph and emission angle h before (dash-dotted line) and after (solid line) the intranuclear cascade. The dashed lines show the reconstruction probability of the proton track.

Arbitrary events

100

100


Identification of QEL events: quality cuts

The reconstructed ver tex has to be in the fiducial volume. |X , Y | 100 cm, 25 Z 395 cm a single charged track originating from the ver tex has to be identified as a muon. The positive track must have P > .3GeV /c and at least 7 hits in the drift chambers, otherwise the event is retrograded to the 1 track set. For the 1-T set, the track is extrapolated back to the first DC and it is demanded that there be no hits in the veto chamber in the vicinity of the intersection. for µ- (1-T) it is required that P > .2GeV /c to suppress "inverse muon decay" events. (µ e- µ- e )


Identification of neutrino QEL events: µ n µ- p 2-T set

µ µ h
mis P

-

`2 ´ 21 Eµ = Pµ + mµ
h p
2

/2

E = Pµ cos µ + Ph cos

h

2 Q = 2E (Eµ - Pµ cos µ ) - mµ

proton identification: momentum ­ range relations for a subset. angle between the transverse components of the charged primary tracks: 0.8 / 1
m missing transverse momentum Pis

0. 8 G eV h / 0. 5

angle h between the proton momentum and the z axis: 0.2


Monte Carlo ­ data comparison for discriminating variables

Events

Events

2 / NDF = 32.35 / 40 400

800

2 / NDF = 13.31 / 20 NOMAD (7575 events) MC prediction QEL Signal

Events

2 / NDF = 20.04 / 30 400

300

600

300

200

400

200

100

200

100

0 0

0.2

0.4

0.6

0.8

1

0 0.7

0.75

0.8

0.85

0.9

0.95

1

0 0.1

0.2

0.3

0.4

0.5

0.6

P

mis

(GeV/c)

/

h /

m Distributions of Pis , and h Data vs simulation


Likelihood ratio
Events

600 500 400 300 200 100 0

2 / NDF = 18.88 / 28

-4

-2

0

2

4

L
m The final selection on = {Pis , h , } is imposed using a likelihood ratio:

L = ln

P ( |QEL) P ( |RES )

where P ( |QEL) and P ( |RES ) are the probability distribution functions of for signal and background events.


Identification/selection of QEL events: µ p µ+ n and 1-T µ ¯

Q 2 = 2M (E - Eµ )



E =

2 MEµ - mµ /2

M - Eµ + Pµ cos

µ

= Pµ cos µ + Ph cos

h

Only pµ and µ are available. The reconstructed recoil nucleon angle (h ) will play a role analogous to that of the likelihood ratio. It is demanded that 0.35
Events
250 3585 events 2 / NDF = 22.09 / 40 _ NOMAD µ data MC prediction QEL Signal

h /

0. 5

200

150

reconstructed neutrino energy: 3 E 100 G eV , muon emission angle µ : µ / 0.1

100

50

0 0.1

0.2

0.3

0.4

0.5

h /


QEL cross section measurement: normalization to DIS



qel

=

0

Nq e N0

l





qel

=

1 qe

l

» N

dat

0 N0

0

-

dis



dis

-

r es



r es

­

Selection of DIS events:
the primary vertex must be in the fiducial volume at least two charged tracks at the primary vertex, one of them identified as a muon (1) total visible energy in the event 1 E 300 GeV and reconstructed hadronic mass 1.4 GeV [A. Bodek et al., arXiv:hep-ex/0203009, hep-ex/0210024] squared W (2) the total visible energy in the event 40 E 200 GeV and the reconstructed hadronic 1.4 GeV [A. Bodek et al., same ref.] mass squared W (3) the total visible energy in the event 40 E


200 GeV [PDG value for t

ot

slope]

Mode (1) (2) (3)


0 16 6 6

0 .643 .462 .634

N0 792162 303791 310617
38

µ CC 0 0 /N0 2.101 2.127 2.136

0 4 2 2

0 .876 .133 .332

N0 16807 7129 7553
43

µ CC ¯ 0 0 /N0 29.012 29.924 30.872

the units used for 0 0 are 10-

cm2 while for 0 0 /N0 are 10-

cm2


QEL cross section measurement: normalization to IMD
The inverse muon decay (IMD) µ e- µ- e is purely leptonic and thus easier to analyze. In the Born approximation: !2 2 2 mµ 2me GF imd (E ) = as E 1 - , where as = = 1.723 â 10-41 cm2 /GeV 2me E imd = 1.017 â 10
2

-4 0

cm2

90 80 70 60 50 40 30 20 10 0 0 0.01 0.02 0.03
2

Events / 10

NOMAD data 1 parameters fit IMD signal

-3

- only one negatively charged track identified as a muon - no veto chamber hits in the vicinity of the intersection of the extrapolated muon track and the first drift chamber (same as for 1-track events from the QEL sample) -E Result
µ 2 2 mµ +me 2me

GeV

= 10.93 GeV

2 p

2me E

µ

0.04

P , (GeV/c)

2

2 A 1-parameter fit to the p distribution then yields N0 = 496.6 ± 32.5 events


Measured cross-section µ n µ- p: dependence from FSI
The simulation of the re-interaction between particles produced at the primary neutrino collision off the target nucleon and the residual nucleus has been done with the DPMJET package There are two important parameters in DPMJet: The formation time 0 controls the development of the intranuclear cascade. With increasing 0 the number of cascade generations and the number of low-energy particles will be reduced. Its default value is 0 = 2.0. The correction factor F od . In DPMJet the momenta of the spectator nucleons are sampled m from the zero temperature Fermi distribution. The nuclear surface effects and the interaction between nucleons reduce this momentum. This is accounted for by F od = 0.6 m
cm ) A , 10
1 3 2 1 0
1-track sample 2-tracks sample 1+2-tracks sample
-2 2

1.1

6 5 4


0.9

QEL

(10

-38

-1 -2 -3

0.8

0.7 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8

2

2.2

-4 0.4 0.6 0.8

1

1.2 1.4 1.6 1.8

2

2.2



1 - 2 A= 2(1 + 2 ) where 1 and 2 - measured cross-section qel for 1- and 2-track samples.

0



0


Systematic uncer tainties in QEL cross section
(1) QEL Identification procedure. The corresponding errors can be estimated by varying the selection criteria with in reasonable limits (likelihood L = -2 Â 1.2 and pr / = 0.3 Â 0.4) (2) Uncer tainty in the DIS cross-section, used both for normalization and DIS background subtraction. Errors are 2.0% for µ and 2.5% for µ . ¯ (3) Uncer tainty of the single pion production cross-section. We assume 10% error in res . (4) Nuclear reinteractions (Intranuclear cascade). (5) Shape of neutrino spectrum. (6) Neutral Current contribution. (7) Muon misidentification. (8) Coherent Diffractive Pion Production (µ + Z µ- + Z + + )
Source 1 2 3 4 5 6 7 8 total qel 3.5 2.9 4.0 1.8 0.2 < 0.1 < 0.1 0.8 6.5
µ

MA from qel

µ

3.2 2.6 3.6 1.6 0.2 < 0.1 < 0.1 0.7 5.9

MA from d /dQ 2 2.4 0.2 0.6 6.5 0.1 ­ ­ < 0.1 7.0

qel

µ ¯

MA from qel

µ ¯

4.3 4.2 7.6 ­ 0.9 1.1 1.0 1.1 9.9

4.2 4.2 7.4 ­ 0.9 1.1 1.0 1.1 9.5


Summary of the cross section measurements
NEUTRINO QEL scattering
We have analyzed 751.000 µ CC events and identified 14021 QEL candidates with about 49.7% of background contamination from DIS (29.8%) and RES (19.9%). The total efficiency of the QEL selection is about 34.6%. We obtain the following values for the µ n µ- p cross section and axial mass:
qel = [0.92 ± 0.02(stat ) ± 0.06(syst )] · 10 -3 8

cm2
2

MA = [1.05 ± 0.02(stat ) ± 0.06(syst )] GeV/c

ANTINEUTRINO QEL scattering
We have analyzed 23.000 µ CC events and identified 2237 QEL ¯ candidates with about 62.0% of background contamination from DIS (33.5%) and RES (28.5%) events. The total efficiency of the QEL selection is about 64.4%. We obtain the following values for the µ p µ+ n cross section and axial ¯ mass:
¯ qel = [0.81 ± 0.05(stat ) ± 0.08(syst )] · 10 -3 8

cm2
2

MA = [1.06 ± 0.07(stat ) ± 0.10(syst )] GeV/c


NOMAD results in comparison with previous experimental data

cm )

2

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 10
-1

CERN HLBC 69, C3 H8 CERN GGM 77, CF3 Br CERN GGM 79, C3 H8 / CF3 Br ANL 69, Fe IHEP 85, Al IHEP SKAT 90, CF3 Br NuTeV 04, Fe NOMAD 08, Carbon MA error 0.06 GeV MA = 1.05 GeV

µ + n ¡ µ + p

-

(10

-38

1

10

10

2

E (GeV)

Comparison with previous experimental data on µ scattering off heavy nuclei. The solid line and error band correspond to the MA value obtained in the NOMAD experiment. Nuclear effects are included into the calculations according to the Smith and Moniz relativistic Fermi gas model.


NOMAD results in comparison with previous experimental data

cm )

2

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 10
-1

CERN BEBC 90, D2 ANL 73, D2 ANL 77, D2 BNL 81, D2 FNAL 83, D2 NOMAD 08, Carbon MA error 0.06 GeV MA = 1.05 GeV

µ + n ¡ µ + p

-

(10

-38

1

10

10

2

E (GeV)

Comparison with previous experimental data from deuterium filled bubble chambers. The solid line and error band correspond to the MA value obtained in the NOMAD experiment. All experimental data are corrected for nuclear effects.


NOMAD results in comparison with previous experimental data

cm )

2

1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 10
-1

CERN GGM 77, CF3 Br CERN GGM 79, C3 H8 / CF3 Br IHEP 85, Al IHEP SKAT 90, CF3 Br NuTeV 04, Fe NOMAD 08, Carbon MA error 0.12 GeV MA = 1.06 GeV

µ + p ¡ µ + n

_

+

(10

-38

1

10

10

2

E (GeV)

Total cross-section for µ p µ+ n extracted from data on µ scattering off heavy nuclei ¯ ¯ Nuclear effects are included into calculations according to the standard relativistic Fermi gas model. The solid line and error band correspond to the MA value obtained in the NOMAD experiment.


Axial mass measurement from the Q 2 distribution

300 250 200 150 100 50 0
NOMAD data MC (DPMJet) BackGround

300 250 200 150 100 50 0
NOMAD data MC (NUANCE) BackGround

2

N events / 0.05 GeV

0

0.5

1

1.5
2 2

2

N events / 0.05 GeV

2

0

0.5

1

1.5
2 2

2

Q (GeV )

Q (GeV )

Q 2 distribution for the identified QEL events in the MC and in the data. MA = 1.07 ± 0.05 GeV/c
2


Axial mass: NOMAD and previous neutrino experiments
ANL SC 69 ANL 73 ANL 77 ANL 82 BNL 81 BNL 90 FermiLab 83 NuTeV 04 CERN HLBC 64 CERN HLBC 67 CERN SC 68 CERN HLBC 69 CERN GGM 77 CERN GGM 79 CERN BEBC 90 IHEP 82 BNL 80 BNL 88 FermiLab 84

Deuterium filled bubble chambers Heavy liquid bubble chambers and other experiments d / dQ 2 d / dQ

2

MA world average value

IHEP SKAT 88 IHEP SKAT 90 K2K SciFi 06 K2K SciBar 08 MiniBooNE 07 NOMAD 08 0.2 0.4 0.6 0.8 1 1.2

neutrino experiments

IHEP 85

NuTeV 04 CERN GGM 77 CERN GGM 79 IHEP 85 IHEP SKAT 88 IHEP SKAT 90 NOMAD 08 1.6 0.2 0.4 0.6 0.8 1

1.4

1.2 1.4 1.6

MA (GeV)

MA (GeV)

antineutrino


Conclusion

We have performed the most accurate measurement to date of the µ n µ- p cross-section on a bound nucleon. The result obtained from the combined 1-track and 2-track samples has the best statistical precision and limited systematic uncer tainties, since in this case the results are almost insensitive to FSI effects. The axial mass parameter MA has been extracted from the QEL cross-section measurement, with the result MA = 1.05 ± 0.02(stat ) ± 0.06(syst ) GeV/c 2 , consistent with the values calculated from the antineutrino cross-section and from the Q 2 shape analysis based on the sample of µ QEL 2-track events. These results are in good agreement with those obtained in previous bubble chamber experiments, but they do not corroborate the MA measurements published recently by the K2K and MiniBooNE collaborations, which repor ted somewhat larger values, however compatible with our results within their large errors.