First Measurement of Muon Neutrino Charged Current Quasielastic (CCQE) Double Differential Cross Section
aa r X i v : . [ h e p - e x ] S e p First Measurement of Muon Neutrino Charged CurrentQuasielastic (CCQE) Double Differential Cross Section
Teppei Katori for the MiniBooNE collaboration
Massachusetts Institute of Technology, Cambridge, MA Abstract.
Using a high statistics sample of muon neutrino charged current quasielastic (CCQE) events, we report thefirst measurement of the double differential cross section ( d s dT m d cos q m ) for this process. The result features reduced modeldependence and supplies the most complete information on neutrino CCQE scattering to date. Measurements of the absolutecross section as a function of neutrino energy ( s [ E QE , RFG n ] ) and the single differential cross section ( d s dQ QE ) are also provided,largely to facilitate comparison with prior measurements. This data is of particular use for understanding the axial-vector formfactor of the nucleon as well as improving the simulation of low energy neutrino interactions on nuclear targets, which is ofparticular relevance for experiments searching for neutrino oscillations. Keywords: axial mass, charged current quasi-elastic, neutrino, MiniBooNE, cross section
PACS:
CCQE EVENT SELECTION IN MINIBOONE
The MiniBooNE detector, a spherical tank filled with mineral oil, is surrounded by 1280 8” photomultiplier tubes(PMTs) to detect ˇCerenkov light from charged particles . In the 19.2 m s readout window, a “subevent” is defined as atiming cluster of PMT hits. The identification of n m CCQE interactions relies solely on the detection of the primarymuon ˇCerenkov light (first subevent) and the associated decay electron ˇCerenkov light (second subevent) in theseevents [4]: 1 : n m + n → m − + p m − → e − + ¯ n e + n m . (1)where each line in this equation identifies the subevent where each process occurs. Therefore, a CCQE candidate ischaracterized with a total of 2 subevents. After cuts, 146070 events are identified from 5 . × protons on targetcollected between August 2002 and December 2005. The cuts are estimated to be 26% efficient at selecting n m CCQEevents in a 550 cm radius, with a CCQE purity of 78%.The largest background is that from CC single-pion production (CC1 p + ). The CC1 p + interaction, proceeds as,1 : n m + p ( n ) → m − + p ( n ) + p + , p + → m + + n m m − → e − + ¯ n e + n m m + → e + + n e + ¯ n m . (2)Note this interaction results in total 3 subevents, the primary interaction and 2 muon decays resulting in an electron anda positron. Although these events can be removed from the CCQE sample by requiring only one muon decay (a totalof 2 subevents), there is still a significant number of CC1 p + events that contribute to the CCQE background becauseone of the muon decays may be missed for various reasons. Among them, p + absorption is a large effect (>40%) withlarge uncertainty ( ∼ p + backgrounds in the CCQE sample rely on the Reinand Sehgal’s model [5] and final state interactions (FSIs) in the NUANCE event generator [6] which are not sufficientlyaccurate for a precise background prediction to measure the absolute CCQE cross section. Ph.D thesis work at Indiana University, Bloomington, IN The mini-Booster neutrino experiment (MiniBooNE) at Fermi National Accelerator Laboratory (Fermilab) is designed to search for n m → n e appearance neutrino oscillations [1]. Detailed information about the Fermilab Booster neutrino beamline and the MiniBooNE neutrino detector are available elsewhere [2, 3]. E ve n t s (GeV QE2 Q dataMC totalCCQE + p CC1others E ve n t s (GeV QE2 Q w e i gh t + p CC E ve n t s (GeV QE2 Q dataMC totalCCQE + p CC1others E ve n t s (GeV QE2 Q FIGURE 1. (color online). The distribution of events in Q QE for the (a) 2 and (b) 3 subevent samples. Data and MC samples areshown along with the individual MC contributions from CCQE, CC1 p + , and other channels. The left side is before the applicationof the CC1 p + background correction. The inset in (b) shows the CC1 p + reweighting function as determined from the backgroundfit procedure. The right side is the same distribution after the application of the CC1 p + background correction and the new CCQEmodel parameters M e f fA and k as determined from the fit procedure described in the text. CC1 p + BACKGROUND MEASUREMENT
Because of uncertainties in the CC1 p + background predictions, we instead measure the CC1 p + rate in our CC1 p + data and the event generator is adjusted to match. By this, the predicted kinematic distribution of CC1 p + events ismodified, and the systematic error of CC1 p + cross section is reduced to the level of the p + absorption uncertainty.The left plot in of Figure 1 shows the Q QE distributions for data and Monte Carlo (MC) of the two samples beforethe reweighting of CC1 p + MC events. The 2-subevent sample shows good shape agreement between data and MC.
NUANCE uses the relativistic Fermi gas (RFG) model [7] for CCQE interactions. In the previous work, we adjusted 2parameters in RFG model, the effective axial mass M e f fA and Pauli blocking parameter k , to match the shape of the Q QE distribution to data [4]. Note that analysis did not consider the overall normalization of events. The 3-subevent sampleshows a large data-MC disagreement in both shape and normalization. Using these samples, a simultaneous fit wasperformed for the shape and normalization of the 3-subevent sample, and the normalization of the 2-subevent sample.These were then used to determine the CC1 p + reweighting function which is shown in the inset plot of Figure 1b (left).In order to reduce the sensitivity to the details of the shape of the 2-subevent sample, only the 0.2 < Q QE ( GeV ) < Q QE shape of the CCQE sample wasfit later although it has no impact on the cross section measurements. The effect of the CCQE normalization on the3-subevent sample was minimal since the background from CCQE in this Q QE region is small as can be seen in theleft plot of Figure 1b. As a final step, with the measured CC1 p + background incorporated, a shape-only fit to the2-subevent (CCQE) sample is performed in order to extract revised CCQE model parameters [4]. The normalizationof the CCQE sample is then extracted from the fit described above. The Q QE distributions of data from all subeventsamples is shown together with the MC prediction in the right plot of Figure 1. Data-MC agreement is good in bothsubevent samples. A fit to the 2-subevent sample provided adjusted CCQE model parameters, M e f fA and k . This wasa “shape-only” fit, that is, the MC was normalized with an arbitrary factor to have the same integrated event count asthe background subtracted data. The fit yielded, M e f fA = . ± .
17 GeV / c ; k = . ± .
012 ; c / do f = . / . The neutrino energy E QE n and 4-momentum transfer Q QE are reconstructed by assuming a CCQE interaction and neutron at rest, with averagednucleon binding energy = 34 MeV. (GeV QE2 Q E ve n t s datatotal errorshape error =1.000 k =1.03 GeV, effA MRFG model after fit k ( G e V ) e ff A M =47.0/38 c (GeV)=1.35 effA M=1.007 k contour s New fit with 1- contour s Old fit with 1- =1.000 k =1.03 GeV, effA M FIGURE 2. (Color online). Left plot is the Q QE distribution of the data, MC before, and MC after the fit with errors. Right plotis the 1 − s contour plot for the M e f fA − k fit. The filled star shows the best fit point and 1 − s contour extracted from this work.The open star indicates the best fit point and 1 − s contour from the previous work [4]. Two regions are shown from the previouswork, the larger area indicates the total uncertainty on the results including the background uncertainty [4]. The left plot of Figure 2 shows the Q QE distribution of data, MC before, and MC after the fit with all sources oferror. Data and MC after the fit agree within shape errors. The right plot of Fig. 2 is the 1 − s contour regions ofthis fit together with the results from the previous MiniBooNE analysis [4]. Note that the current result is consistent(to within 1 − s ) with k =
1. This is because the CC1 p + background resulting from the procedure in this work haschanged by an amount only just consistent with the error assigned on the background in the previous work. The valuefor k is quite sensitive to the CC1 p + background at low Q QE . However, the previous and current results are consistentat the 1 − s level.The effect of the new M e f fA is clearly seen in 2-dimensional plots. Figure 3 shows the data-MC ratio of CCQEcandidate events as a function of muon kinetic energy T m ( GeV ) and muon scattering angle cos m . Note the muon energyand muon scattering angle observables are the basis of all reconstructed kinematics variables in the n m CCQE channelin MiniBooNE. In the left plot, we use the world averaged nuclear parameters ( M e f fA = .
03 GeV / c , k = . Q . This is the same tendency observed in theprevious CCQE analysis in MiniBooNE [4], indicating that data-MC disagreement is more likely due to an incorrectcross section prediction (=function of Q ) than an incorrect flux prediction (=function of neutrino energy). Afterintroducing the new M e f fA and k ( M e f fA = .
35 GeV / c , k = . CCQE ABSOLUTE CROSS SECTION MEASUREMENTSFlux-averaged double differential cross section
Figure. 4 shows the flux-averaged double differential cross section, d s dT m dcos m , for the n m CCQE process. The flux-averaged total cross section, an integral of the double differential cross section ( − < cos m < + < T m ( GeV ) < ¥ ) is 9 . × − cm . The total normalization error on this measurement is 10 . T m and cos m , have been corrected for detector resolution effects only. This result is themost model-independent measurement of this process possible with the MiniBooNE detector. No cuts on the recoilnucleons are used to define this process. The neutrino flux is an absolute prediction and was not adjusted based onmeasured processes in the MiniBooNE detector. (GeV) m T mq c o s -1-0.8-0.6-0.4-0.2-00.20.40.60.81 0.80.850.90.9511.051.11.151.2 (a) (b) (c) (d)(e)(f)=0.4GeV QE n (a) E =0.8GeV QE n (b) E =1.2GeV QE n (c) E =0.2GeV QE2 (d) Q =0.6GeV QE2 (e) Q =1.0GeV QE2 (f) Q (GeV) m T mq c o s -1-0.8-0.6-0.4-0.2-00.20.40.60.81 0.80.850.90.9511.051.11.151.2 (a) (b) (c) (d)(e)(f)=0.4GeV QE n (a) E =0.8GeV QE n (b) E =1.2GeV QE n (c) E =0.2GeV QE2 (d) Q =0.6GeV QE2 (e) Q =1.0GeV QE2 (f) Q
FIGURE 3.
Ratio of MiniBooNE n m CCQE data/simulation as a function of measured muon angle and kinetic energy. Left plot,with world averaged M e f fA (=1 .
03 GeV / c ) and k (=1 . M e f fA (=1 .
35 GeV / c ) and k (=1 . E n and Q are overlaid. ( G e V ) m T m q c o s -1-0.8-0.6-0.4-0.2-00.20.40.60.810510152025 -39 · /GeV) (cm m q dcos m dT s d =10.8%) T N d MiniBooNE data (MiniBooNE data with shape error
FIGURE 4. (Color online). The flux-averaged double differential per nucleon ( n ) cross section for the n m CCQE process. Thedark bars indicate the measured values and the surrounding lighter bands show the shape error. The overall normalization (scale)error is 10.8%. (GeV QE2
Q0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ) / G e V ( c m Q E / d Q s d -39 · MiniBooNE data with shape error=1.000) k =1.03 GeV, effA RFG model (M =1.007) k =1.35 GeV, effA RFG model (M 1.10 · =1.007) k =1.35 GeV, effA RFG model (M
FIGURE 5. (Color online). The flux-averaged single differential per nucleon ( n ) cross section for the n m CCQE process. Themeasured values are shown as points with the shape error as shaded bars. Predictions from the
NUANCE
RFG model with differentvalues for the model parameters are shown as histograms.
Flux-averaged differential cross section
Figure. 5 shows the flux-averaged single differential cross section, d s dQ QE . The reconstructed 4-momentum transfer Q QE depends only upon the (unfolded) quantities T m and cos m .In addition to the experimental result, Figure 5 also shows the prediction for the CCQE process from the NUANCE simulation with three different variations of parameters in the underlying RFG model. The predictions are flux-averaged and absolutely normalized. The RFG model is plotted with both the world-averaged CCQE parameters( M A = .
03 GeV, k = . M A = .
35 GeV, k = . ≈ ≈ ≈ Flux-unfolded total cross section
The flux-unfolded total cross section ( s [ E QE , RFG n ] ) as a function of estimated neutrino energy E QE , RFG n is shownin Figure 6. The quantity E QE , RFG n is a model-dependent estimate of the neutrino energy obtained after correcting forboth detector and nuclear model resolution effects. These results depend on the details of the nuclear model used forthe calculation. The dependence is only weak in the peak of the flux distribution but becomes strong at E n < . E n > . NUANCE implementation of the RFG model with the world averagedparameter values ( M e f fA = .
03 GeV, k = . M e f fA = .
35 GeV, k = . ∼
20% higher than the RFG model prediction with world average parameter values at the flux peak (700 −
800 MeV).The prediction with the RFG parameter values extracted from the shape-only fit to MiniBooNE CCQE data reproducesthe data significantly better, to within 1 s for every point over the entire measured energy range.Figure 6(b) shows the CCQE results from the LSND [9] and NOMAD [10] experiments. It is interesting to note thatNOMAD results are better described with the world-average M e f fA and k values. .4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ) ( c m s -39 · MiniBooNE data with shape errorMiniBooNE data with total error =1.000 k =1.03 GeV, effA RFG model with M =1.007 k =1.35 GeV, effA RFG model with M (GeV)
RFG n E(a) (GeV)
RFG n E -1
10 1 10 ) ( c m s -39 · MiniBooNE data with total errorNOMAD data with total errorLSND data with total error =1.000 k =1.03 GeV, effA RFG model with M =1.007 k =1.35 GeV, effA RFG model with M (b)
FIGURE 6. (Color online). The flux-unfolded total per nucleon (n) cross section with total errors and bin widths plotted indicatedwith the data points. In (a) shape errors are shown as shaded boxes. In (b), a larger energy range is shown along with results from theLSND [9] and NOMAD [10] experiments. Predictions from the
NUANCE simulation with two different RFG parameter variationsare shown in both plots.
At this time, a solution to this growing mystery is not evident. Although there are tremendous efforts to modelthis process [11], no models seem to be able to produce the (1) large observed M e f fA and (2) large observed total crosssection, while keeping the “bare” M A = .
03 GeV (the world averaged value). Model-independent cross section resultsfrom the MINOS near detector [12], running with E n ∼ < E n <
20 GeV could help shed further light on this subject.
REFERENCES
1. A. A. Aguilar-Arevalo et al. [MiniBooNE Collaboration], Phys. Rev. Lett. , 231801 (2007); Phys. Rev. Lett. , 101802(2009); arXiv:0904.1958 [hep-ex].2. A. A. Aguilar-Arevalo et al. [MiniBooNE Collaboration], Phys. Rev. D79 , 072002 (2009).3. A. A. Aguilar-Arevalo et al. [MiniBooNE Collaboration], Nucl. Instr. Meth.
A599 ,28 (2009).4. A. A. Aguilar-Arevalo et al. [MiniBooNE Collaboration], Phys. Rev. Lett. , 032301 (2008); Teppei Katori, AIP Conf.Proc. , 123 (2007); FERMILAB-THESIS-2008-645. D. Rein and L. M. Sehgal, Nucl. Phys.
B223 , 29 (1983).6. D. Casper, Nucl. Phys. Proc. Suppl. , 161 (2002)7. R. A. Smith and E. J. Moniz, Nucl. Phys.
B43 , 605 (1972); erratum: ibid.
B101 , 547 (1975)8. V. Bernard et al. , J. Phys.
G28 , R1 (2002).9. L. B. Auerbach et al. [LSND Collaboration], Phys. Rev. C , 015501 (2002).10. K. S. Kuzmin, V. V. Lyubushkin, and V. A. Naumov, Eur. Phys. J. C , 517 (2008); V. V. Lyubushkin et al. [NOMADCollaboration], arXiv:0812.4543 [hep-ex].11. J. E. Amaro et al. , Phys. Rev. C71 , 015501 (2005); Phys. Rev.
C75 , 034613 (2007); T. Leitner et al. , Phys. Rev.
C73 ,065502 (2006); Phys. Rev.
C79 , 065502 (2006); O. Benhar et al. , Phys. Rev.
D72 , 053005 (2005); arXiv:0903.2329 [hep-ph];A. Butkevich et al. , Phys. Rev.
C72 , 025501 (2005); Phys. Rev.
C76 , 045502 (2007); Phys. Rev.
C80 , 014610 (2009);S. K. Singh et al. , arXiv:0808.2103 [nucl-th]; J. Nieves et al. , Phys. Rev.
C73 , 025504 (2006); N. Jachowicz et al. , Phys. Rev.
C73 , 024607 (2006); A. M. Ankowski et al. , Phys. Rev.
C77 , 044311 (2008).12. M. Dorman, FERMILAB-THESIS-2008-72; in these proceedings13. David Boehnlein, AIP Conf. Proc.967