1. 10-Jun-161 LHCb MC data analysis  3µ Rare decays WG N.Sagidova Present limit : BR(  3µ) > 4·10 -8 Is it possible to improve this limit in LHCb ? How much ?

2. 2 CROSS SECTIONS Min.Bias σ tot (pp) = 102.9 mb σ incl (bb) = 698 µb σ incl (cc) = 3643 µb BRANCHING RATIOS Br(b → µ) incl = 10.7% Br(b → τ) incl = 2.9% Br(b → D s ) incl = 21% Br(D s → τν) = 6.4% D s PRODUCTION PROBABILITY FROM C P(c → D s ) = 0.11 Parameters of DC06 Monte Carlo production https://twiki.cern.ch/twiki/bin/view/LHCb/SettingsDc06?sortcol=0;table=3;up=0#sorted_table

3. 3 Tau Production Cross Sections (4π geometry) ChannelCross sections S1 b   (excluding b  c   ) σ 1 = σincl(bb) ∙2 ∙ Br(b → τ)incl 40µb S2 b  c   (cascade c-production) σ 2 = σ incl(bb) ∙2 ∙ Br(b → Ds) ∙ Br(Ds → τ) 19µb S3 c   (direct c-production) σ 3 ≈ σ 4 S4 Ds   (from direct c-production) σ 4 = σ incl(cc) ∙2 ∙ P(c → Ds)incl ∙ Br(Ds → τ) 51µb S5 X   (b&c excluding ) Main production channels Total σ (  ) = 110µb

4. 4 Estimation of background yield We assume that the main source of background is inclusive bb  2µ events Incl_b=DiMuon ~ 20M events 20M corresponds to luminosity = 3.9 pb -1 (1/500 from the yield per year) Signal events: DC06-phys-v2-lumi2 31113001 –   3µ ~50k events

5. 5 Estimation of  3µ yield  tot (  ) =110 µ b geometry LHCb acceptance ε acc_3 µ = 27%  yield per year in LHCb geometry acceptance (S1+S2+S3+S4 channels) N  (total) = 110µb ·2fb -1 · 0.27 = 5.9 ·10 10 If BR(  3µ) = 10 -8 then number of detected N(  3 µ ) = = (2.65%· 2.7·10 10 +0.5%· 3.2·10 10 ) ·BR(  3µ) = = 9 events per 2fb -1. N  (Ds  ) = 51µb ·2fb -1 · 0.27 = 2.7 ·10 10 However, separation of signals from background proved to be more effective for the Ds channel (S4-channel). Registration efficiency in S4-channel = 2.65% Registration efficiency in S1&S2-channels ≈ 0.5 % Therefore, our analysis was done mostly for S4-channel.

6. 6

7. 7 VariableNbgNsg Backg. Rej. Signal Eff.[%] 1Minmass(2µ) > 250 Mev597620002.799.4 2dLL (µ) > -3191016208.580.5 3 0 <IPS(  ) < 10 112136114467.7 4Cos(dira) > 0.999994195739447.6 50.07 < tdot < 1.03995441447.4 613GeV < maxP (µ) < 100GeV3184552142 70.3GeV < minPT (µ) < 5GeV8721201835.8 8L016251614431 Step-by-step cut application Backgound after stripping cuts Nbg = 16144 Ds sample with stripping cuts applied Nsg = 2012 Nbg – number of BG in mass window m  ±120 MeV Nsg – number of signals in mass window m  ±30 MeV after BG subtraction

8. 8 VariableNbgNsg Backg. Rej. Signal Eff.[%] 1Minmass(2µ) > 250 Mev597620002.799.4 2dLL (µ) > -3191016208.580.5 3 0.6 < IPS(  ) < 10 102116315857.8 4Cos(dira) > 0.999993177052138.3 50.07 < tdot < 1.03076853838.2 613GeV < maxP (µ) < 100GeV2469267334.4 70.3GeV < minPT (µ) < 5GeV2585807229.1 8L00506∞25.2 Step-by-step cut application Backgound After stripping Nbg = 16144 Ds sample with stripping cuts applied Nsg = 2012 Nbg – number of BG in mass window m  ±120 MeV Nsg – number of signals in mass window m  ±30 MeV after BG subtraction

9. 9 Results Background rejection and signal efficiency after all cuts applied. Nbg Signal efficiency S4 (Ds   )S1+S2 A12.65%0.5% B0 2.14% 0.4% Hopefully, the efficiency could be increased by a factor of 2 optimizing the preselection cuts Nbg – number of Bg events in mass window m  = ±120 MeV Signal efficiency in m  = ±30 MeV

10. 10 Results After cuts Nbg = 1 in mass window m  = ±120 MeV At L = 2fb -1 Nbg = 500 in mass window m  = ±120 MeV At L = 2fb -1 Nbg = 125 in mass window m  = ±30 MeV (1.67· √125 = 18) At L = 2fb-1 Nsg = 18 in mass window m  = ±30 MeV at BR(  3µ) = 2 · 10 -8 Hopefully, the UL can be pushed down by a factor of 2 by increasing the signal efficiency optimizing preselection cuts

11. 11 Conclusion The present analysis shows that at LHCb it might be possible to reach sensitivity up to BR(  3µ) = 10 -8 at L = 5-8 fb-1