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RooFit toy MC sensitivity studies for g + f s and D m s from B s → D s p /K channels at LHCb

RooFit toy MC sensitivity studies for g + f s and D m s from B s → D s p /K channels at LHCb. Shirit Cohen NIKHEF MSc Colloquium May 11 th 2007. Outline. Introduction The LHCb detector & physics goals CP violation & interest in B s → D - s π + , B s →D Ŧ s K ± decay channels

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RooFit toy MC sensitivity studies for g + f s and D m s from B s → D s p /K channels at LHCb

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  1. RooFit toy MC sensitivity studies for g+fs and Dms from Bs→Dsp/K channels at LHCb Shirit Cohen NIKHEF MSc Colloquium May 11th 2007

  2. Outline • Introduction • The LHCb detector & physics goals • CP violation & interest in Bs→D-sπ+,Bs→DŦsK± decay channels • RooFit sensitivity studies: concept, experimental and physics input parameters, decay models and likelihood function description • Results from sensitivity studies • Summary & conclusions Shirit Cohen Master Colloquium

  3. Introduction • Matter dominated universe • Matter-anti matter difference in weak force, CP violating processes • In the Standard Model via the quark-mixing (CKM) matrix, via its phases • LHCb experiment designed to study CP violation, performing measurements in the b-quark sector • Motivation for measuring the CKM phase  Shirit Cohen Master Colloquium

  4. The LHCb detector ~ 10-250 mrad yz ~ 10-300 mrad xz p p  Shirit Cohen Master Colloquium Non bending plane view

  5. qb qb Detector detailed • Single arm forward spectrometer • Limited angular acceptance but very good time and mass resolutions • Optimal luminosity2∙1032cm-2s-1 • 1012 bb pairs produced per year • Bending magnet 4.2Tm bending power • VeLo very close to interaction point • Good separation of -K Shirit Cohen Master Colloquium

  6. NP * Vtb Vts t s b W W s b * Vts t Vtb SM Main LHCb physics goals • CKM matrix angles, a, b, g for example via time dependent CP asymmetry observable • fs mixing phase • Precision measurement of ms mass difference CDF measurement Δms = 17.77 ± 0.1(stat.) ± 0.07(syst.) ps-1 • DGs decay rate difference • Rare decays measurements • Signs of New Physics b→sg transitions through loop diagrams, sensitive to NP Shirit Cohen Master Colloquium

  7. * Vtb W Vts s b t t W s b * Vts Vtb Bs meson system flavour eigenstates Bs oscillations box diagram , mass eigenstates mass eigenstates time dependence decay amplitude into a final state f , if there is more than one contribution, the decay amplitudes can be written as a sum , Example: Bd → p+p- , strong phase keeps value, weak phase changes sign under CP transformation Shirit Cohen Master Colloquium

  8. Bs time dependent decay probability For charge conjugate final states: f→f, λf →λf, Af→Af, p/q → q/p decay oscillations Bs →Ds-K+ Bs →Ds-K+ Feynman calculus is in lf ! Bs →Ds+K- Bs →Ds+K- Shirit Cohen Master Colloquium * In this project we assume |p/q|=1

  9. CP violation in Bs meson system expected to be small ~10-2 in Bs section • In mixing, if |p/q|1, giving • In decay, if |Af||Af|, giving can occur only if two decay amplitudes with different strong and weak phases contribute to the same final state • In interference, when and possible, and there is a relative phase between mixing (e.g arg(q/p)=s) and decay (e.g. arg(Af/Af)) can occur also in charged mesons and baryons , Shirit Cohen Master Colloquium

  10. Single decay diagram → no CP violation Flavour specific decay Branching fraction: (3.4±0.7)·10-3 One diagram means λf=λf =0 (|Af|=|A f |), leading to Df=Sf=0, Cf=1. (two unique Bs→Dspequations) → Parameters to measure:Δms,ΔΓs d p+ u b c Bs 0 Ds - s s Bs→Dsp decay channel Shirit Cohen Master Colloquium

  11. Ds- Ds+ s s c c K+ s b u s b b u Bs Bs K- Bs K+ u s s s s b s + 0 b c 0 Ds- 0 Bs s s 0 Bs→DsK decay channel • Non flavour specific decay, four decay diagrams exist (four Eq.) • 2 diagrams and a relative phase → • Time dependent CP violation • |λf|=|λf | → Df, Cf, Sf coefficients non 0 → Parameters: |λf|, arg(λf), arg(λf ) to extractg+fs, ΔT1/T2 T1 T2 Branching fractions g+fs = [arg( l f ) - arg( l f )] /2 ΔT1/T2 = [arg( l f ) + arg( lf )] /2 Shirit Cohen Master Colloquium

  12. /K Bs 0 Ds K SV K ~6mm Primary Vertex ~1cm  btag Event topology Bs→Dsh decay channels • The topology of the decay channels Bs→Ds-π+ and Bs→DsŦK± is very similar • Bs→Ds-π+ can be used for Δms measurement • Bs→DsŦK± can be used to extract the CP angle g+fs • Standard Model prediction g ≈ 60° • s ≈ 0.02° can be determined by Bs→J/channel Shirit Cohen Master Colloquium

  13. Toy MC sensitivity studies • Goal - • Obtain expected sensitivity for measuring ms and +s at LHCb from Bs→Dsp and Bs→DsK decay channels • Approach – • Define decay models Probability Distribution Functions (PDF’s) according to decay equations & including experimental effects • Generate events for all decay flavours, simulating 5 years of data taking • Fit decay models back to the events. Simultaneous fit of both decay channels in order to achieve best sensitivities and have correlations taken care of • Repeat experiment many times, estimate sensitivities from collected output • Input data - • Experiment-related parameters from full LHCb GEANT4 simulation • Physics parameter values agreed with WG • Tools - • RooFit toolkit for data modeling & ROOT data analysis framework • Ganga, LHC(b) interface for running jobs on the GRID/ CERN Shirit Cohen Master Colloquium

  14. Experimental parameters (1/2) • Common Bs→Dsh selection, topological cuts • For Dsπ: require bachelor particle reconstructed as π For DsK: require bachelor particle reconstructed as K and a cut on ΔLKπ in order to get rid of misidentified π’s • Signal event yields • Bs reconstructed mass from Ds-π+and DsŦ K± channels (after the trigger) • Reconstructed Bs mass resolution 14MeV • B/S limits and central values • Specific central values used for toy MC Bs reconstructed mass from Bs→Dsπ, signal and major background Results for B/S ratios Bs reconstructed mass from Bs→DsK, signal and major background Event yields for 2fb-1(define as 1y) Shirit Cohen Master Colloquium

  15. Experimental parameters (2/2) mean value 33fs most probable value 30fs • Proper time per-event error distribution • Due to detector resolutions on vertices, tracking, momenta etc. • PT per-event error distribution parameterization used in toy MC • Acceptance function after triggers and offline selection • Low PT Bs’s rejected due to misplaced vertex requirements and low significance impact parameter • Fraction of high PT Bs’s rejected due to high impact parameter • Acceptance parameterization used in toy MC • Tagging efficiency etag=0.5812, mistag fraction w=0.328 Proper time per-event error distribution Shirit Cohen Master Colloquium Acceptance function

  16. Following previous work done with FORTRAN (LHCb-2003-103) Building PDF components using the RooFit package From the components we construct a decay PDF described by PDFB→f(trec,mrec|Δtrec) for the Bs→Dsp and Bs→DsK decay channels (and for the different flavours) Events are generated according to decay PDF, meaning an event is a set of “trec,mrec,Δtrec” RooFit sensitivity studies (1/2) Shirit Cohen Master Colloquium

  17. The components that are used in PDFB→f(trec,mrec|Δtrec): Signal trec distribution– Bs decay equation, include ω smearing Signal mrec distribution– Gaussian distribution Background trec distribution – decaying particle with t=tBs/2 Background mrec distribution – flat distribution Resolution function: per-event proper time error (with scale factor) Acceptance function on trec Construction Implementing the acceptance function on signal proper time distribution (and same for background) Constructing PDFsig = PDFsig(trec,mrec| Δtrec)and same for background Adding signal and background with fsig, fbg (calculated from B/S ratios) Generate events from each decay flavour separately, fit the desired parameters from all decay flavours simultaneously RooFit sensitivity studies (2/2) Shirit Cohen Master Colloquium

  18. Likelihood description Likelihood function with , acceptance function resolution function: proper time per-event error, with signal scale factor signal proper time including mistagged events bg proper time resolution function: proper time per-event error, with bg scale factor bg reconstructed Bs mass signal reconstructed Bs mass Shirit Cohen Master Colloquium

  19. Physics and experimental input parameters for toy MC • central values of specific background used for B/S estimation • acceptance function • per-event proper time error distribution Physics Experimental Shirit Cohen Master Colloquium

  20. Example for single decay flavor PDF Bs→Ds-π+ projections on (trec,mrec,Δtrec) (5y) trec mrec Δtrec Bs→Ds-K+ projections on (trec,mrec,Δtrec) trec mrec Δtrec Shirit Cohen Master Colloquium

  21. Sensitivity results from tagged events • Two Dsπ equations, four DsK equations, simultaneous fit performed • Collected data from many “experiments” of 5y tagged data, scaled results to 1y • Fit a Gaussian to the fitted values from all the “experiments”, make pull distribution Data from 400 “experiments” Shirit Cohen Master Colloquium

  22. Example for distributions for 400 exper. Δms (ps)-1 values g +fs° values # events # events Δms pull # events g +fs pull # events Shirit Cohen Master Colloquium

  23. Bs→DsK untagged events • Meaning events with no information if the decaying meson was a Bs or a Bs • Decay equations for Bs→DsK untagged events: • One cannot observe the Bs oscillations using untagged events • Untagged events still hold information on the phases through Ref, Ref • Add untagged events to the analysis in order to increase the sensitivities to the phases Shirit Cohen Master Colloquium

  24. Adding untagged DsK events Projections over proper time (ps) Shirit Cohen Master Colloquium

  25. Results from tagged+untagged events • Two Dsπ equations, four DsK equations + two untagged DsK equations. Collected data from 400 “experiments” of 5y tagged+untagged data, scaled results to 1y • Fit a Gaussian to the fitted values from all the experiments, check pulls Δms (ps)-1 values g+fs° values # events # events Shirit Cohen Master Colloquium

  26. Results with different input values • Including tagged+untagged events, similar as in last section • Running with different strong phase values (all other parameters unchanged; g +fs= 60° ) • Running with different B/S ratios for Bs→ DsK channel (all other parameters unchanged; g +fs =60°,Bs→Ds-π+ B/S value = 0.2 ) Different strong phase input value DifferentB/S input value for Bs→DsK Shirit Cohen Master Colloquium

  27. Extra check: fitting mistag fraction & signal scale factor simultaneously • Signal scale factor used for checking PT error estimation • Mistag fraction and PT errors damp the Bs oscillations • Fitting both parameters simultaneously could be problematic, correlated effects • Fitting the five regular floating parameters + signal scale factor • Running 400 “experiments”, fits converge • Decreased resolution on ω, signal scale resolution of ~10%. Weak, strong phase and Δms resolutions remain unchanged. Shirit Cohen Master Colloquium

  28. Summary & conclusions • Code for RooFit toy MC sensitivity studies developed • Sensitivity results look good, pulls are fine • Including untagged events improves the g+fsresolution 12° → 10° • Expect LHCb to measure s(Δms) = 0.007(ps)-1 and s(g+fs) = 10.3° for nominal input values CDF measurement Δms = 17.77 ± 0.1(stat.) ± 0.07(syst.) ps-1 • Obtained resolutions with different input values for strong phase and Bs→DsK B/S ratio • LHCb-2007-041, results quoted in the “Flavour at the era of LHC” Yellow Report Shirit Cohen Master Colloquium

  29. Backup slides Shirit Cohen Master Colloquium

  30. Outlook • A possible scenario before the LHCb measurement of g: Shirit Cohen Master Colloquium

  31. Outlook • A possible scenario after the LHCb measurement of g: Shirit Cohen Master Colloquium

  32. Backup I likelihood description Likelihood function for B→f Physics parameters that go in PDF models, smearing: mistag fraction, background, detector’s acceptance & resolution extract from LHCb-2007-041 Shirit Cohen Master Colloquium Total likelihood

  33. Backup II w pull • Fitting signal scale factor and mistag fraction simultaneously - pull distributions g+fs pull Ssig pull Shirit Cohen Master Colloquium

  34. The LHCb detector Shirit Cohen Master Colloquium Non bending plane view

  35. Interesting parameters • Dsπcase: flavor specific decay, two decay diagrams exist. For this channel: λf=λf =0 (|Af|=|A f |), leads to Df=Sf=0, Cf=1. → Parameters to measure:Δms,ΔΓ • DsK case: non flavor specific decay, 4 decay diagrams exist, time dependent CP violation. |λf|=|λf |. → Parameters: |λf|, arg(λf), arg(λf ) to extractg+fs, ΔT1/T2 • arg(λf) = ΔT1/T2 - (g+fs) • arg(λf ) = ΔT1/T2 + (g+fs) • Assume |p/q|=1 • Only 2 unique Dsπ equations • 4 unique DsK equations Estimated branching fraction % (used for DC04 selection study) Shirit Cohen Master Colloquium

  36. * Vtb Vts t s b W W s b * Vts t Vtb * Vtb W Vts s b t t W s b * Vts Vtb Bs meson system flavour eigenstates Bs oscillations box diagrams , mass eigenstates mass eigenstates time dependence decay amplitude into a final state f , decay amplitudes can be written as a sum , strong phase keeps value, weak phase changes sign under CP transformation Shirit Cohen Master Colloquium

  37. Bs→Dsπ physics decay model Bs→Ds- π+ Bs→Ds-π+ Bs decay equations f : final state, Ds-π+ or Ds-K+ For charge conjugate final states: B → B ,f→f, λf →λf, Af→Af , p/q → q/p Shirit Cohen Master Colloquium * In this project we assume |p/q|=1

  38. Matter dominated universe • Matter-anti matter difference in weak force, CP violating processes • In the Standard Model via the quark-mixing (CKM) matrix, via its phases • LHCb experiment designed to study CP violation, performing measurements in the b-quark sector • Motivation for measuring the CKM phase  Shirit Cohen Master Colloquium

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