Measurements of g at LHCb Mitesh Patel CERN
Measurements of g at LHCb Mitesh Patel (CERN) (on behalf of the LHCb Collaboration) 14 th December 2006 Mitesh Patel, CKM 06
Introduction • LHCb will use a number of methods to measure : – “ADS + GLW” • B±→D 0(K , KK, )K± • B 0→D 0(K , KK, )K*0 – “Dalitz” • B±→D 0(KS , KSKK)K± • B 0→D 0(KS , KSKK)K± – Four body “Dalitz” • B±→D(K , KK )K± – Bs→Ds. K – B→hh • [Jacopo Nardulli, WG 4, Friday, PM-1] Will present : – Expected sensitivity as a function of the relevant parameters – Signal selection/background estimate taking B±→D 0(K )K± as an example 14 th December 2006 Mitesh Patel, CKM 06 2
B±→DK± Decays – ADS Method • B- can decay into both D 0 and D 0, diagrams very different amplitudes B- b u s u c u KD 0 b Bu colour favoured • u c s u D 0 K- colour suppressed Decays of D 0, D 0 to same final state gives access to interference c 0 D u u s d u c d u s u u K+ - D 0 (doubly) cabibbo suppressed K+ cabibbo favoured • For ‘suppressed’ B-→(K+ -)DK- (+ c. c. ) decays : reversed suppression of D decays cf. B decays → ~ equal amplitudes → big interference effects • Counting experiment – no need for flavour tagging or t determination [For ‘favoured’ B-→(K- +)DK- (+ c. c. ) : higher rates, but smaller B± asymmetry] 14 th December 2006 Mitesh Patel, CKM 06 3
Interference parameters • Interference depends on a number of parameters : – From the B decays : D 0 K±) – because have b→u, b→c interference r. B – the ratio in magnitude of two diagrams (≤ 0. 1 for δB – a CP conserving strong phase difference – From the D decays : r. DK – the ratio in magnitude of two diagrams (0. 060) δDK – a CP conserving strong phase difference • Have 4 B± →D(K )K± rates we can measure : (1) (2) (3) (4) [+CP eigenstates → GLW Method] [+another D decay → ADS Method] – Two rates are favoured, (1) and (3) – Two rates are suppressed, (2) and (4) but these suppressed rates have order 1 interference effects as r. B ~ r. D 14 th December 2006 Mitesh Patel, CKM 06 4
B±→DK± Strategy : ADS+GLW • D 0→K : 3 observables from the relative rates of the 4 processes depends on the 4 unknowns: , r. B, d. DK – r. DK is already well measured – CLEO-c constraining cos(d. DK ) → Need an additional D 0 decay channel to solve for all unknowns • D 0→K : provides an additional 3 observables which depend only on one additional unknown: d. DK 3 (r. DK 3 also well measured) – At present have ignored resonant structure in D 0→K and just used rate for illustration, exploitation of sub-structure is under investigation • The CP eigenstate decays D 0→KK/ provide one more observable with no new unknowns: • Use the modes D 0→K , K 3 , KK, together to give best sensitivity 14 th December 2006 Mitesh Patel, CKM 06 5
Experimental Situation UTFIT best fit : r. B = 0. 08 ± 0. 03 • B-factories have not yet observed the suppressed modes • Dalitz analyses give r. B~0. 2 (BELLE) and r. B~0. 1 (BABAR) → Suggest suppressed modes should soon be observed • We take r. B=0. 08 (UTFIT), δB = 130 o (average B-factory results), r. DK =r. DK 3 =0. 06 (PDG), -25<d. DK <25 o, -180<d. DK 3 <180 o 14 th December 2006 Mitesh Patel, CKM 06 6
What can LHCb add. . . ? • 2 fb-1 in 107 sec → equivalent to 1012 bb, 0. 4 of which expected to be B± In both sign combinations signal yields then : -5 1012 bb × 0. 4 × 2 × e Favoured: BR = 1. 4× 10 Suppressed: BR = 1. 8× 10 -7 TOT × BR • Our total efficiency, e. TOT, and resulting sensitivity depend entirely on our ability to control the background – in very different environment to the B factories • Full simulation indicates that acceptance × trigger efficiency × selection efficiency gives e. TOT = 0. 5% (more in a moment) : – Favoured B±→D 0(K )K± – Suppressed B±→D 0(K )K± 14 th December 2006 → ~56, 000 events/2 fb-1 → ~700 events/2 fb-1 Mitesh Patel, CKM 06 7
Full MC Performance • LHCb uses full MC simulation to estimate the signal selection efficiency and the background : – PYTHIA - generation of p-p collisions at √s = 14 Te. V – GEANT - full detector response/spill-over and tracking through material – on/offline pattern recognition, full trigger chain, selections • Signal selection efficiency e. TOT(B±→D 0(K )K±)=0. 5%: B± mass /Me. V 8. 2% (geom. ) × 87. 8% (rec. ) × 28. 4% (seln. ) × 25. 0% (trig. ) • Si Sensors Mass resolutions RF foils – B± ~15 Me. V – D 0 ~6. 5 Me. V – Primary vertex sz ~ 50 mm – B decay vertex sz ~ 200 mm 14 th December 2006 R sensor Vertex resolutions f sensor • Interaction region Mitesh Patel, CKM 06 100 cm 8
Estimating the Background • From a large sample of minimum bias events find that no events are selected • To study background in more detail, focus on bb events where one b decays in 400 mrad – after the application of the trigger most likely source of background • Background sample 20 million bb events generated with above condition ( → factor 0. 434, sample equivalent to ~46 M bb events) • Still equivalent to only a few minutes of LHCb running ! 14 th December 2006 Mitesh Patel, CKM 06 9
• Favoured Modes – Background from D 0 decays dominates • Use RICH PID to separate D 0 and D 0 K • Use dedicated sample of D 0 to estimate B/S → Expect ~17 k bkgrd events /2 fb-1 from D 0 Efficiency / % Background Studies e(K K , p) = 93% e( K , p) = 4. 7% – Use bb sample to assess combinatorial bkgrd → Expect ~0. 7 k bkgrd events /2 fb-1 → ~28 k B+ signal events/2 fb-1 B/S~0. 6 → ~28 k B- signal events/2 fb-1 B/S~0. 6 MC B±→D 0(Kp)p± events 687 / 580 k pass all cuts except B mass • Suppressed Modes – bb sample → combinatorial bkgrd dominates → Expect ~0. 7 k bkgrd events /2 fb-1 → ~530 B+ signal events/2 fb-1 B/S~1. 5 → ~180 B- signal events/2 fb-1 B/S~4. 3 14 th December 2006 Momentum / Ge. V Mitesh Patel, CKM 06 387 / 580 k inside 3 s B mass cut B± mass 10 /Me. V
LHCb Sensitivity • • Toy MC used to generate 2 fb-1 data(*) d. DK , d. DK 3 Combine K with : w/o bkgrd – K 3 – similar yields and identical background level as K – KK and : • 4300 B+, 3350 B- decays with B/S ~ 2 [degrees] → s =5– 15 o with 2 fb-1 data d. DK , d. DK 3 Estimated bkgrd [degrees] (Non-Gaussian distribution of fit results highlighted …) 14 th December 2006 Mitesh Patel, CKM 06 (*) = 60º, r. B=0. 08, d. B= 130º, r. DK =r. DK 3 =0. 06, 25º<δDK < 25º and -180º< δDK 3 <180º 11
LHCb Sensitivity • • Toy MC used to generate 2 fb-1 data(*) d. DK , d. DK 3 Combine K with : w/o bkgrd – K 3 – similar yields and identical background level as K – KK and : • 4300 B+, 3350 B- decays with B/S ~ 2 [degrees] → s =5– 15 o with 2 fb-1 data d. DK , d. DK 3 Estimated bkgrd [degrees] (Non-Gaussian distribution of fit results highlighted …) 14 th December 2006 Mitesh Patel, CKM 06 (*) = 60º, r. B=0. 08, d. B= 130º, r. DK =r. DK 3 =0. 06, 25º<δDK < 25º and -180º< δDK 3 <180º 12
LHCb Sensitivity • • Toy MC used to generate 2 fb-1 data(*) d. DK , d. DK 3 Combine K with : w/o bkgrd – K 3 – similar yields and identical background level as K – KK and : • 4300 B+, 3350 B- decays with B/S ~ 2 [degrees] → s =5– 15 o with 2 fb-1 data d. DK , d. DK 3 Estimated bkgrd [degrees] (Non-Gaussian distribution of fit results highlighted …) 14 th December 2006 Mitesh Patel, CKM 06 (*) = 60º, r. B=0. 08, d. B= 130º, r. DK =r. DK 3 =0. 06, 25º<δDK < 25º and -180º< δDK 3 <180º 13
B±→D*K± Decays • B → D*K has attractive feature : – D*→D 0 0 – has CP cons. phase δB – D*→D 0 – CP cons. phase δB+ • Potentially very powerful : – Adding D* decays (w/o bkgrd) to prev. study: s =5 -15 o → s =2 -5 o – No phases with non-Gaussian fit results • Signal/bkgrd arbitary normaln One entry from BB sample corresponds to 5 k bkgrd evts/ 2 fb-1 B±→D*(D 0 )K± BB incl sample B± Mass /Me. V However, reconstruction efficiency for soft is small → large B/S B±→D*(D 0 0)K± • Ignore neutrals and fit DK mass shape ? – Fav. modes – yields 17 k ( 0) and 9 k ( ) / 2 fb-1 – Sup. modes – yields similar to D 0 K case - but bkgrd problematic → investigating use of event topology to reconstruct 0, momentum 14 th December 2006 Mitesh Patel, CKM 06 B±→D*(D 0 )K± D 0 K mass / Me. V 14
B 0→DK*0 Decays • For B 0→DK*0 decay r. B ~ 0. 4 (both diagrams colour suppressed) • Treat with the same (“ADS+GLW”) method, so far have used K , KK, modes • Removes bias from DCS decays seen using traditional ‘GLW’ approach Yield / 2 fb-1 B/S favoured B 0 (K+ -)D K*0 + c. c. 3400 < 0. 3 suppressed B 0 (K- +)D K*0 + c. c. 500 < 1. 7 B 0 (K+K-/ + -)D K*0 + c. c. 600 < 1. 4 Mode → s =7 -10 o with 2 fb-1 data (taking r. B=0. 4, -180<d. B<180 o, -180< d. DK <180 o) 14 th December 2006 Mitesh Patel, CKM 06 15
B±→D(KS + -)K± Decays – Dalitz • Three body decay D 0→Ks + - fully parameterized with parameters m+2=m 2(Ks +) and m-2=m 2(Ks -) • Use pre-determined model to describe D 0 decay amplitudes as a function of (m+2, m-2) • Total B decay amplitude is sum of contributions via D 0 and D 0 : N: number of resonances aj, aj: amplitude and phase parameters from B factories • Interference has sensitivity to Aj: model-dependent parameterization of matrix element G(m-2, m+2) = |f(m-2, m+2)|2 + r. B 2 |f(m+2, m-2)|2 + 2 r. B Re [ f(m-2, m+2)f*(m+2, m-2)ei (-g+d. B) ] 14 th December 2006 Mitesh Patel, CKM 06 16
B±→D(KS + -)K± – Sensitivity Signal selection gives : – 5 k events/2 fb-1 assuming “good” KS efficiency(*) – Combinatorial bkgrd B/S < 0. 7 @ 95% C. L. – D(KS ) bkgrd B/S = 0. 2± 0. 1 → 0. 2<B/S<1. 0 @ 90% C. L. m-2(Ge. V 2/c 4) • • Model parameters from B and charm factories • With r. B = 0. 08, s( ) ~ 8º (signal only and w/o acceptance effect in fit) + model uncertainty • Similar method will be used for D 0→KSK+K- decays: reduced BR but less bkgrd (PID from RICH) • B 0→D(KS + -)K*0 decays also under investigation (*) Assuming all K LHCb generator studies D 0/D 0 r(770) K* and DCS K* m+2(Ge. V 2/c 4) S found offline can be reconstructed online 14 th December 2006 Mitesh Patel, CKM 06 17
Four-body “Dalitz” Analyses • Idea for 3 -body D 0 decays can be extended to 4 -body D 0 decays • Five parameters are then needed to describe the decays • Two modes are presently being investigated: – B±→D(KK )K± • For =60º, d. B=130º, r. B=0. 08, expect 1. 7 k events/2 fb-1 • B/S=0. 9± 0. 4 (Combinatorial, D 0 ) → s( ) ~ 15º (signal only) [hep-ph/0611272] – B±→D(K )K± (as used in ADS+GLW analysis) • Take into account strong phase dependence across “Dalitz” space • Sensitivity under study 14 th December 2006 Mitesh Patel, CKM 06 18
Bs→Ds. K Decays • Interference between tree level decays via Bs mixing • Measures + fs (fs from Bs J/y f decays) • Main background from Ds : – Factor 10 higher branching ratio – Suppressed using kaon id from RICH detectors – B/S < 1 @ 90% CL • Expect 5. 4 k signal events/ 2 fb-1 • Excellent proper-time resolution (st~40 fs) allows to resolve Bs oscillations → s( ) ~ 13 from 2 fb-1 data [ ms = 17. 3 ps– 1 ] • Parallel analysis possible with Bd→DŦ ± (~790 k events/2 fb-1 with B/S ~ 0. 3, extraction requires r. D or combined Bs→ Ds. K U-spin analysis) 14 th December 2006 Mitesh Patel, CKM 06 19
Summary of Performance B mode D mode s( ) B+→DK+ K + KK/ + K 3 5º - 15º B+→D*K+ K Under study B+→DK+ Ks 8º B+→DK+ KK 15º B+→DK+ K Under study B 0→DK*0 K + KK + 7º - 10º B 0→DK*0 Ks Under study Bs→Ds. K KK 13º Signal only, no accep. effect • Combining all modes, with a nominal year of data (~2 fb-1), LHCb will be able to extract from combined analysis B→DK with the ~5º precision required to match the indirect determination • Comparison of from B→DK and indirect determination will become a stringent test of the SM 14 th December 2006 Mitesh Patel, CKM 06 20
Measuring : B+ D 0(K 0π+π-)K+ Giri, Grossman, Soffer, Zupan (PRD 68, 054018 (2003)) • Use three body Cabibbo allowed decays of the D 0/D 0 • BR(D 0 K 0π+π-)=(5. 97± 0. 35)% m-2(Ge. V 2/c 4) • Large strong phases between the intermediate resonances allow the extraction of r. B , d and by studying the Dalitz distribution of events LHCb generator studies D 0/D 0 r(770) where K* and DCS K* 14 th December 2006 Mitesh Patel, CKM 06 m+2(Ge. V 221 /c 4)
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