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CC analysis – systematic errors

CC analysis – systematic errors.

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CC analysis – systematic errors

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  1. CC analysis – systematic errors • At the last collaboration meeting it was recognised that we needed to develop tools to enable us to properly assess the effect of systematic uncertainties on the CC analysis. Shortly after the meeting, a joint ND/CC meeting was convened at Boston to make headway on this issue: • Held at Tufts University, October 4-6 • Participants: H. Gallagher, E. Lartey, D. Petyt, C. Smith • Goals: • Discuss systematics relevant to the CC analysis • Identify tools & techniques that will allow these to be estimated using NearDet data and incorporated into the oscillation fit. • As a result of this meeting, a general-use package was developed which allows events to be re-weighted according to particular cross-section parameters. • I have used this package to study the effect of cross-section uncertainties on the all-event CC analysis. I have also started to look at how ND data can be used to constrain these (nuisance) parameters in oscillation fits.

  2. Event reweighting schemes • Many of the systematic uncertainties in the CC analysis can be studied using event reweighting. The parameters of the reweighting scheme can then be treated as nuisance parameters which are marginalised in the oscillation fit. • At the Boston meeting, we focussed mainly on cross-section uncertainties and started work on a package that will allow GMINOS events to be reweighted given a set of tweaked NEUGEN input parameters (see next slide) • Other uncertainties (such as hadron production uncertainties) might also be accounted for in this fashion. • However, estimating systematic errors due to hadronization models and intranuclear rescattering in this way may not be so straightforward. It will be necessary to conduct independent MC studies to determine how this might be done.

  3. Cross-section reweighting package • A working version of this package now exists (thanks to Chris Smith and Hugh Gallagher) • The package provides an interface to NEUGEN and allows the user to calculate a weight for a particular GMINOS event given a tweaked set of NEUGEN input parameters. • The parameters are: • MA for quasi-elastic scattering • MA for resonance production • DIS/Resonance scaling factors (8 parameters – 2 multiplicities, 4 initial states) • Parton distribution functions (from PDFLIB) • This package will enable us to assess the effect of cross-section uncertainties on the CC analysis • It is also required for the completion of the Mock Data Challenge • The code is largely complete (modulo a few minor bug-fixes) and has been made available for general use. • The source code currently lives in the NeugenInterface package in the minossoft CVS repository.

  4. Cross-section reweighting function • The weighting function has the following form: Double_t reweight( Float_t E_nu, Kinematic_variable_t::kv1, Float_t val1, Kinematic_variable_t::kv2, Float_t val2, Interaction I, process_t::proc neugen_config newconfig neugen_config oldconfig ) Neutrino energy Kinematic variables (x,y,q2 or W) relevant to this interaction and their values Includes: flavour, nucleus (A,Z), CC or NC, initial state (np, nn, nN …) These objects hold the values of the neugen config parameters (mA etc). The event weight is calculated based on these two sets of quantities QEL, RES, DIS, COH p

  5. The Physics Analysis Ntuple (PAN) • A simple ROOT ntuple that contains “all relevant quantities” for the CC analysis. • Truth information for MC events, including sufficient information to permit event reweighting (i.e. need at minimum E_nu, x, y, q2, W, E_mu, limited STDHEP information). Can be extended to accommodate other reweighting functions as required. • Reconstructed information necessary to perform oscillation fit • Quantities specific to the CC analysis, such as PID parameters and fiducial cuts, that enable CC-like events to be selected • Association of tracks/showers/slices in the Near Detector. Identical format for ND and FD events • An initial version of the PAN now exists with the quantities necessary for cross-section reweighting. A sample PAN for the far detector can be downloaded from the following website: • http://www.physics.umn.edu/~petyt/cc/PAN/ • Ed Lartey has provided code to produce a PAN object from within the Mad analysis framework

  6. PAN variables - 1 VariableDescription true_enu true neutrino energy (GeV) true_pmu true muon momentum (GeV/c) true_ehad true hadron energy (GeV) true_mudircos true muon z-direction cosine cc_nc cc/nc flag: 1-cc 2-nc flavour true flavour: 1-e 2-mu 3-tau process process: 1001-QEL 1002-RES 1003-DIS 1004-COH true_x true x true_y true y true_q2 true q^2 true_w true w initial_state initial state: 1-vp 2-vn 3-vbarp 4-vbarn ... nucleus target nucleus: 274-C 284-O 372-Fe run_num run number snarl snarl number evt_index event index within snarl mc_index mc index for this event numevt number of events/snarl numtrk number of tracks numshw number of showers evtvtx event vertex x-coord (m) Required for cross-section reweighting

  7. PAN variables - 2 evtvty event vertex y-coord (m) evtvtz event vertex z-coord (m) is_fid vertex fiducial volume flag: 0-fail 1-pass is_cev containment flag: 1-CEV 2-PCE trkpass track quality flag: 0-fail 1-pass evlength event length (planes) trklength track length (planes) trkrange track momentum range (GeV/c) trkqp track momentum q/p trkeqp error on fitted q/p trkdircos track z-direction cosine shwph summed shower pulse height (shw.ph.gev) reco_pmu reconstructed muon momentum (GeV/c) (range or q/p) reco_eshw reconstructed shower energy (shw.ph.gev/1.23) reco_enu reconstructed neutrino energy (GeV) phfrac track pulse height fraction (uses sigcor) phplane track pulse height per plane ( " " ) pid1 pid parameter - Super-K definition pid2 pid parameter (probmu/(probmu+probnc)) neural neural network output is_cc cc-like flag: 0-nc-like 1-cc-like The only cut required to select cc-like events

  8. The CC-like sample R1.9 • A CC-like event is defined by the following cuts: • At least 1 reconstructed track with trkpass=1 • Pid parameter>-0.4 (>-0.1 in ND) • Selected sample consists of: • 55.4% (61.1%) DIS • 25.9% (23.0%) RES • 16.5% (13.2%) QEL • 2.2% (2.7%) NC (numbers in parentheses are for dmsq=0.002,s2t=1.0) NCQELRESDIS

  9. Event reweighting ma_qel+10% ma_res+10% • Cross-section weighting is performed on an event-by-event basis using the NeugenInterface package. The cross-section parameters that can be changed are: • ma_qel, ma_res, RES-DIS acceptance factors, PDFs • Events are reweighted according to the following parameters: • True enu, initial_state, CC/NC, flavour, target nucleus and the following kinematic variables: • q2 (QEL) • q2, W (RES) • x,y (DIS) Disfact-25%

  10. Shape & normalisation weight • The plot at right shows the weighting factors for QE,RES&DIS events as a function of visible energy calculated for the following parameters: • ma_qel + 5% • ma_res + 5% • Disfact + 5% • The QEL (and to a lesser extent, the RES) weights are approximately flat versus Evis. • DIS weights much smaller than QEL/RES QEL RESDIS Visible energy (GeV)

  11. “Error band” for ma_qel10% 19.5e20 p.o.t FD only nominal Note asymmetry. Protons? unoscillated 10% dmsq=0.002,s2t=1 NC included NC subtracted

  12. “Error band” for ma_res10% 19.5e20 p.o.t Lots of NC RES in this bin?

  13. Fitting cross-section uncertainties • Cross-section uncertainties can be treated as nuisance parameters in oscillation fit. • Define c2 as a function of oscillation parameters and cross-section parameters. Minimise chisq with respect to cross-section parameters to yield dmsq,s2theta contours • Can also apply ‘penalty terms’ to c2 in order to constrain the values of these nuisance parameters. FD c2 therefore looks like this: • Can add additional c2term for ND which depends only on the nuisance parameters. The idea here is that the ND will help to constrain these parameters since they will, in general, be correlated with dmsq,s2t in FD-only fits.

  14. Parameter measurement 6.5e20 p.o.t nominal sma=5%sma=10% unconstrained note positive correlation

  15. ND-FD fit – constrained ma_qel FD onlyND only ND+FD 6.5e20 p.o.t FD, ~10000 ND snarls

  16. ND-FD fit – unconstrained ma_qel FD onlyND only ND+FD

  17. Future work • Need to look at other cross-section parameters. Only considered QEL weights so far and these affect just ~15% of the total CC-like dataset • What are the correlations/degeneracies between the various parameters? To what extent can ND data resolve them? How much ND data will be required? • Are there additional ND variables, such as pm,qm, and particular ND event samples, such as a QEL-rich sample, that will help to further constrain the cross-section parameters? • Should increase size of FD dataset. At what pot value do systematic errors exceed statistical errors? • Resolve question mark hanging over DIS weights • Can then perform a MDC-style study with 3 of the 4 systematics in place (the 3 cross-section parameters) to test the fitting machinery - in advance of tackling the real MDC once beam weighting code is available.

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