Unitarity Triangle fits Achille Stocchi LAL-Orsay (IN2P3/CNRS)

Collaboration RESULTS BASED ON THE WORK OF http://www.utfit.org M. Bona, M. Ciuchini, E. Franco, V. Lubicz, G. Martinelli, F. Parodi, M. Pierini, P. Roudeau, C. Schiavi, L. Silvestrini, A. Stocchi, V.Vagnoni Recent papers: M. Bona et al. hep-ph/0509219 accepted in JHEP M . Bona et al. (hep-ph/0501199) JHEP 0507 (2005) 028

How to fit the UT parameters and fit new physics From M.H. Schune plenary talk EPS2005 BDK : 3/ B// : 2/ bcℓ and buℓ Bd and Bs mixing K : CPV in K decays Bccs : 1 /b

Total Fit Dmd,Dms,Vub,Vcb,ek + cos2b + b + a + g + 2b+g r = 0.210 ± 0.036 [0.137, 0.279] @ 95% Prob. h = 0.347 ± 0.021 [0.306, 0.389] @ 95% Prob.

g sin(b+g) cos2b a b sin(2b) Sides + eK r = 0.218 ± 0.043 h = 0.385 ± 0.028 [0.,328, 0.440] @ 95% Prob. r = 0.218 ± 0.043 [0.129, 0.299] @ 95% Prob. Sides + eK UT with angles only h = 0.322 ± 0.025 [0.274, 0.373] @ 95% Prob. r = 0.187 ± 0.052 [0.090, 0.299] @ 95% Prob. sin(2b) a g sin(b+g) b cos2b

Test of SM (I) ? The presence of New Physics might appear as a disagreement between the new measurements and what the fit predicts (given by the color code). a and g (for the moment) are OK. The next validation will come from Dms for the bs sector. SM solution only ? SM solution only

From direct measurement from indirect determination Test of SM (II) sin2b=0.687±0.032 From direct measurement we have a weak sign of a disagreement sin2b =0.791±0.034 from indirect determination

Tension in the fit incl.+excl. Vub = (4.22 ± 0.20) 10-3 exclusive: BRs from HFAG; form factor from quenched LQCD Vub=(3.80±0.27±0.47)10-3 inclusive from HFAG Vub=(4.38±0.19±0.27)10-3 It can be interpreted as a problem with data, but it could be evidence of New Physics incl.+excl. Vub = (4.22 ± 0.20) 10-3 from all the other inputs: Vub = (3.48 ± 0.20) 10-3

Where do we really are on our knowledge of UT ? Fit with NP independent variables Fit in a NP model independent approach

Fit with NP independent variables If we use only Tree level processes -which can be assumed to be NP free- It is very important to improve Vub/Vcb from s.l decays g from tree level proceses r ± (0.18± 0.12) h ± (0.41 ± 0.05) (similar plot in Botella et al. hep-ph/0502133)

DF=2 Fit in a NP model independent approach r , h Cd,jd CeK Cs,js Parametrizing NP physics in DF=2 processes DF=2 Fit in a NP model independent approach r , h Cd,jd CeK Cs,js Vub/Vcb X Dmd eK ACP (J/Y K) a (rr,rp,pp) g (DK) Dms ACP (J/Y f) ~X g (DsK) 5 new free parameters Cs,js Bs mixing Cd,jd Bd mixing CeK K mixing Constraints Not yet available Today : fit possible with 6 contraints and 5 free parameters (r, h, Cd,jd ,CeK)

arbitrary phase or large Using Fit in a NP model independent approach Vub/Vcb Dmd ACP (J/Y K) g (DK) eK a cos2b ASL large NP with arbitrary phase NP solution 4% SM-like solution 96% SM or small NP with arbitrary phase or large NP with SM phase. NLO effects included

Fit in a NP model independent approach CBd = 1.27± 0.44 fBd = -(4.7 ± 2.3)o Ce = 0.95 ± 0.18 NP in DB=2 and DS=2 could be up to 50% wrt SM only if has the same phase of the SM

ANP/ASM vs fNP Artificially removing the present disagreement With present data ANP/ASM=0 @1s ANP/ASM ~1 only if fNP~0 ANP/ASM ~0-40% @95% prob. sensitive to small effects Artificially removing the present disagreement ~20% @ 95% prob for generic fNP

MFV New CP in bs What to do ? TWO SCENARIOS seems to be « favourite » - Improvements existing measurements - DF=1 Penguins transitions (just 1 transparency) - Rare decays (not discussed in this talk) - The Bs physics (LHCb/Tevatron)

Universal UTfit Buras et al. hep-ph/0007085 MFV = CKM is the only source of flavour mixing. eK and Dmd are not used (sensitive to NP). h = 0.319 ± 0.039 UUTfit r = 0.258 ± 0.066 UUTfit Almost as good as the SM !! Starting point for studies of rare decays see for instance : Bobeth et al. hep-ph/0505110

MFV In models with one Higgs doublet or low/moderate tanb (D’Ambrosio et al. hep-ph/0207036) NP enters as additional contribution in top box diagram L0 is the equivalent SM scale dS0 = -0.03 ± 0.54 [-0.90, 1.79] @95% Prob. To be compared with tested scale using for instance b->sg (9-12Tev) D’Ambrosio et al. hep-ph/0207036

MFV 2Higgs + large tanb  also bottom Yukawa coupling must be considered dS0B ≠ dS0K dS0B dS0K Could give infomation on the tanb regime …not yet at the present L > 2.6 TeV @ 95% for dS0(xt) > 0 L > 4.9 TeV @ 95% for dS0(xt) < 0 L > 3.2 TeV @ 95% for dS0(xt) > 0 L > 4.9 TeV @ 95% for dS0(xt) < 0 Correlation coefficient =0.52

New physics in bs transitions DF=1 DF=2 B0d s d d K0 ~ g ~ ~ b b s s other information The SUSY option if Dms>31(38)ps-1 new physcis at 3(5)s

CKM Matrix in ≤2010-where we will be We have supposed that - B Factories will collect 2ab-1 - two years data taking at LHCb (4fb-1) Inputs b < 1° from charmonium ~ 7 ° ~ 5° (half B-factories/half LHCb) fBBB ~ 5% x ~ 3% BK ~ 5% Vub ~ 5% Vcb ~ 1% Dms at 0.3ps-1 (Tevatron or/and LHCb) Lattice sin2c ± 0.045 Outputs sin(2b) 0.694 ± 0.012 sin(2a) -0.543 ± 0.093 g[] 51.7 ± 3.0 r 0.240 ± 0.017 h 0.307 ± 0.010

Parenthesis for Lattice people Bands are 95% regions from angle measurements Bands are 95% regions from sides measurements Contours are 68%/95% regions from sides measurements Contours are 68%/95% regions from angle measurements An important point is that the relative precisions on CP-violating quantities are on phase with CP-conserving quantities IF fBBB ~ 5% x ~ 3% BK ~ 5% Lattice calculations at few % level

In the « sad » hypotesis the SM still work in 2010…. CKM2010 φBd = (-0.1 ± 1.3)o CBd = 0.98 ± 0.14 φBs = (0.0 ± 1.3)o CBs = 0.99 ± 0.12 in ≤ 2010 : same and impressive precision on b d and b s transitions VERY IMPORTANT

B → tn New comers soon.. ? SM expectation < 1.8 10-4 @ 90% CL exp. limit B → tn < 1.8 10-4 @ 90% CL BR(B → τ ν) = (1.03 ± 0.32)10-4 ([0.47,1.74] @ 95% prob.) Exp. likelkihood BR(B → τ ν) = (0.98 ± 0.49)10-4 [0.17,2.08] @ 95% prob.) fB = 0.178 ± 0.062 GeV from the exp+UTfit fB = 0.192 ± 0.026 ± 0.009 GeV Lattice QCD

Conclusions UTfits are in a mature age with recent precise measurement of UT sides and angles The SM CKM picture of CP violation and FCNC is strongly supported by data Generic NP in the b  d start to be quite constrained fBd ~ 0 At least in this sector, we are beyond the alternative to CKM picture, and we should look at « corrections ».

We need precision measurements to test NP and Studied presented in MFV. We start to test interesting NP scales. We need precision measurements to test NP and to push the NP scale in interesting ranges and to play the complementarity at LHC CKM2010 Bd sector What about the bs DB=2 sector ? Still large room for NP. LHCb plays the central role on it. CKM2010 Bs sector

and if SuperB….. See Report INFN-AE 05-08 and related talks at this conference

BACKUP SLIDES

BR(B → rg) BR(B → K*g) caveat: * SU(3) breaking effect * LQCD/mb corrections B(~cosa) to r/w g ( smaller for B0 than B+) Using the |Vtd/Vts| value from the SM, we can extract DR. |Vtd/Vts| = 0.10 ± 0.45 [0.02,0.18] @ 95% Prob. DR = -0.67 ± 0.24 [-0.99, 0.10] @ 95% using only B → r0g

} K± p±nn latest result from E949: BR(K±  p±nn) = 1.47 10-10 D'Ambrosio, Isidori hep-ph/0112135 K± p±nn with 3 signal events } ellipse centered in (r0, 0) latest result from E949: BR(K±  p±nn) = 1.47 10-10 +1.30 - 0.89 10% error with UTfit central value (BR = 0.83 10-10) 10% error with current central value

a a a a Using Vub/Vcb Dmd ACP (J/Y K) g (DK) eK SM-like Fit in a NP model independent approach Vub/Vcb Dmd ACP (J/Y K) g (DK) eK g Cd cos2(b+f) sin2(a-f) sin(2b+f) ASL SM-LIKE 60o 1 0.68 -0.23 0.96 OK NP1 -0.68 NP2 120o 0.4 -0.96 10-2 NP3 0.23 0K a a SM-like a a

In MFV CKM2010 Now  0.54 2010  0.26