Probing the New Physics scale with the Unitarity Triangle fit

Transcription

1 Probing the New Physics scale with the Unitarity Triangle fit Denis Derkach University of Oxford On behalf of UTfit group Adrian Bevan, Marcella Bona, Marco Ciuchini, Denis Derkach, Enrico Franco, Vittorio Lubicz, Guido Martinelli, Fabrizio Parodi, Maurizio Pierini, Carlo Schiavi, Luca Silvestrini, Viola Sordini, Achille Stocchi, Cecilia Tarantino, Vincenzo Vagnoni ICHEP 2014 Valencia, Spain 04 July 2014

2 Method Use the Bayesian statistics to obtain the most probable values and credibility intervals from the current data (before ICHEP 2014) Before the observation B, our degree of belief of A is P(A) (prior probability) Having observed B, our degree of belief changes into P(A B) (posterior probability) We use likelihoods of measurements for prior probabilities where possible. Gaussian PDFs are used to represent statistical and systematic uncertainties otherwise. γ0 The posterior uncertainties are obtained using Highest Probability Density method. k γ1 γ2 Δγ 2

3 Constraints used (angles) In the Wolfenstein parameterisason, one can represent the Unitarity CondiSons in graphical way. We now want to test this picture using different possible constraints. cos(2β) B DK, B Dπ α B ππ, B ρρ, B ρπ 2β+γ B DK, B Dπ sin(2β) B J/ΨK γ B DK 3

4 Alpha from B ππ B π + π -, B π 0 π 0, B π + π 0 decays are connected from isospin relasons. Tree Penguin We can construct the observables, like CP asymmetries and branching fracsons from amplitudes and solve the equason on α. The same method also can be used for the B ρρ system Another point is adding the B ρπ analysis This is a completely different analysis:the Sme- dependent Dalitz plot analysis of the decays of the neutral B allows one to infer the value of α without any dependence on the hadronic parameter. 4 Phys. Rev. D76 (2007) PRL 65 (1990) 3381

5 Beta results B 0 J/ΨK 0 The decay is dominated by a single (tree level) amplitude, thus a can be simplified: We also analise to obtain the theorescal uncertainty related to the penguin poluson in data- driven way. This gives us an addisonal correcson: ΔS [- 0.02,0.00] at 68% prob. 5 Phys. Rev. Lett. 95, (2005)

6 Gamma inputs We use the available informason coming from the three methods: GLW (M. Gronau, D. London, D. Wyler, PLB253,483 (1991); PLB 265, 172 (1991)) ADS (D. Atwood, I. Dunietz and A. Soni, PRL 78, 3357 (1997)) GGSZ (A. Giri, Yu. Grossman, A. Soffer, J. Zupan, PRD 68, (2003)) For the decays: B + D (*) K (*)+ and B 0 D (*) K (*)0 The combinason is performed starsng from the HFAG averages. The main problem is treatment of the nontrivial likelihoods for {γ, δ B, rb} observables. δ B is the strong phase of the decay; rb is the amplitude raso GLW ADS We also use CLEOc results in the ADS reconstrucson. Currently, we do not include D 0 mixing in the combinason, as the effect is small in B DK system GLW+ADS 6

7 Results of CombinaSon B+ DK+ B+ DK+ We also are able do determine strong phase δd- >Kπ = (18±14) Which can be compared with charm sector (see later). γ = (68.3±7.5) DK+ D*K+ DK*+ DK*0 δb (117.9±8.8) (-49±13) (126±34) (-53 ±46) rb (0.100±0.007) (0.12±0.02) (0.13±0.06) (0.25±0.06) It is very important to understand that construcsng predicsons observables out of values of {γ, δb, rb} requires a similar likelihood analysis (for example, asymmetries will not be gaussian). D. Derkach UTFIT@ICHEP2014 7

8 History of Combination After a decade of study by experimentalists and almost 50 papers published, the world average uncertainty has decreased by a factor 3 in 10 years 8

9 Constraints used (sides constraints) V ub / V cb exclusive B Dlν (B π(ρ)lν) determinason inclusive b c (b u) determinason Δm d /Δm s B d,s mixing ε K indirect CP violason in K L decays Δm d B d mixing Rare decays B τν, B μμ 9

10 La ce For most of other CKM fit inputs we need several parameters calculated on la ce. We use: B- parameter in the Kaon sector K, D, and B mesons decay constants fbs, fb, fd, fk Matrix elements for K, B, and D mixing s quark mass, Vus, Vud (FlaviaNet values) We take the most updated values from FLAG working group and our averages for the full basis of K- Kbar, D- Dbar and B- Bbar mixing 10 Nuovo Cim.B123: ,2008

11 Vub/Vcb The relative ratio of CKM elements is easily calculable: QCD corrections to be considered inclusive measurements: OPE exclusive measurements: form-factors from lattice QCD There is still an inconsistency between inclusive and exclusive measurements. We take this into account inflating the combined uncertainty (a-la PDG). Vub(excl) = (3.42 ± 0.22) 10 3 Vub(incl) = (4.40 ± 0.31) 10 3 Vub = (3.75 ± 0.46) 10 3 ~1.9σ discrepancy Vcb(excl) = (39.55 ± 0.88) 10 3 Vcb(incl) = (41.7 ± 0.7) 10 3 Vcb = (40.9 ± 1.0) 10 3 ~2.5σ discrepancy 11

12 εk Indirect CP violation in the Kaon system is usually expressed in terms of εk parameter which is the fraction of CP violating component in the mass eigenstates. S0 - Inami Lim functions for c c, c t, e t t contributions (from perturbative calculations) We also have a corrections for long-distance effects (Phys.Rev.D78:033005, PLB688 (2010) 309). We use: Introducing the NNLO charm-top-quark contribution (from PRL108 (2012) ) increases the uncertainty by 0.01 and does not affect a global fit. 12

13 Δms or Δmd We include the oscillation of Bd and Bs as inputs of the fit using two observables Δmd and Δmd/Δms We use the following approximation 13

14 Rare decays We use the combinason of B τν measurements by BaBar and Belle We use: Brand new constraint from B(s) μμ measurements by LHCb and CMS Experimental value needs to be corrected for the Bs oscillason to be compared to the theorescal predicsons (see De Bruyn PRL 109, (2012)) We use LHCb+CMS combinason: 14

15 Charm mixing for generic new physics fit We perform a fit to the charm sector results allowing for CP violation in the singly-cabibbo suppressed decays and receive the following results. For the purpose of constraining NP, it is useful to express the fit results in terms of the ΔC = 2 effective Hamiltonian matrix elements. Charm average gives δd- >Kπ = (8±13), compasble with gamma combinason q/p -1=0.016 ± ɸ=(-0.5 ± 0.6) x = (3.6 ± 1.6) 10-3 y = (6.1 ± 0.7) 10-3 M12 =(0.0044±0.002) ps -1 Γ12=(0.0149±0.0016) ps -1 ϕ12=(2.0±2.7) 15 JHEP 1403 (2014) 123

16 Outlook Some more results did not make it inside the talk: lifetimes, their differences and quark masses. vs. 16

17 Full Fit results Measurement Prediction (remove parameter from the fit) Pull, º (90.8±7.5) (87.2±3.9) <1 sin(2 ) (0.680±0.023) (0.756±0.042) -1.5, º (68.4±7.5) (69.5±3.9) ~0 V ub, 10-3 (3.75±0.46) (3.62±0.13) +0.3 V cb, 10-3 (40.9±1.0) (42.1±0.7) -1.0 K,10-3 (2.228±0.011) (2.04±0.19) +1.0 m s, ps -1 (17.768±0.024) (17.5±1.1) -0.3 B(Bu ),10-4 (1.14±0.22) (0.805±0.07) -1.4 B(Bs ),10-9 (2.9±0.7) (3.90±0.16) 1.3 B(Bd ),10-9 (0.37±0.15) (0.114±0.007) -1.7 The full CKM matrix now looks as following: s, rad (not in the SM fit) (0.005±0.035) ( ±0.0008) <1 17

18 La ce in the Full Fit Observables Measurement Prediction Pull (σ) B K 0.766± ±0.076 <1 f Bs ± ± <1 f Bs /f Bd 1.202± ±0.06 <1 B Bs 0.875± ±0.045 <1 B Bs /B Bd 1.06± ±0.076 <1 Color code: agreement between the predicted values and the measurements at beƒer than 1, 2,...nσ. The cross has the coordinates (x,y) =(central value, error) of the direct measurement. 18

19 Some Comments on the Full Fit Combined Vub and Vcb have two components: exclusive and inclusive. We perform the fits with only inclusive and only exclusive components to test the pulls. This have some influence to the connected observables. inclusive exclusive inclusive exclusive Also affects B(Bu τν) and ε K. predicson: sin2β = ± sin2β = ±

20 More Comments on the Full Fit Experimental values BR(Bs µµ) = (2.9 ± 0.7)10-9 BR(Bd µµ) = (3.7 ± 1.5)10-10 ) ) indirect determinasons from UT BR(Bs ll) = (3.91 ± 0.16)10-9 BR(Bd ll) = (1.15 ± 0.07)10-10 Sme- integrason included 20 D. Derkach UTFIT@ICHEP2014

21 Generic NP parameterization Since the fit is over constrained, we can introduce new parameters added in order to parameterize generic NP ΔF=2 processes in all sectors In case of absence of NP effects, C i =1, φ i =0 21

22 Generic NP specific constraints semileptonic asymmetries:sensisve to NP effects in both size and phase ASL(Bd)[10-3 ] = 3.2 ± 2.9, ASL(Bs)[10-3 ] = ± 5.2 B factories,cdf + D0 + LHCb same- side dilepton charge asymmetry:admixture of Bs and Bd so sensisve to NP effects in both systems Aμμ[10-3 ] = ± 2.0 D0 arxiv: lifesme τ FS in flavour- specific final states:average lifesme is a funcson to the width and the width difference (independent data sample) τ FS =1.417 ± HFAG φs=2βs vs Γs from Bs J/ψφ angular analysis as a funcson of proper Sme andb- tagging. AddiSonal sensisvity from the Γs terms φ s: LHCb: Gaussian Γs: average: Gaussian 22

23 Generic NP Fit results SM: We thus obtain the following results. NP: CBd = 1.07 ± 0.17 φbd = (- 2.0 ± 3.2) CBs = 1.05 ± 0.08 φbs = (0.7 ± 2.0) CεK = 1.05 ± 0.16 The uncertainty in d- sector is larger than that in s- sector. This can be interpreted using different observables: No real tension in any place D. Derkach UTFIT@ICHEP

24 Scale Analysis StarSng from previous results, we can put the limits to the generic New physics scenarios. The most general effecsve Hamiltonians for F = 2 processes beyond the SM have the form. NP effects are in the Wilson Coefficients Ci. Ci in general can be presented as: Fi : funcson of the NP flavour couplings Li: loop factor (in NP models with no tree- level FCNC) Λ: NP scale (typical mass of new parscles mediasng F=2 transisons) The dependence of C on Λ changes with flavour structure. We can consider different flavour scenarios: where Generic: C(Λ) = α/λ 2 ; Fi~1, arbitrary phase NMFV: C(Λ) = α FSM /Λ 2 ; Fi~ FSM, arbitrary phase To obtain the PDF for the Wilson coefficients Ci(Λ) at the new- physics scale, we switch on one coefficient at a Sme in each sector and calculate its value from the result of the NP analysis. 24 JHEP 0803:049,2008 arxiv:

25 Scale Analysis Generic C(Λ) = α/λ 2, Fi~1 NMFV C(Λ) = α FSM /Λ 2 α~1 α~1 To obtain the lower bound for loop- mediated contribusons, one simply mulsplies the bounds by αs ( 0.1) or by αw ( 0.03). α ~ αw in case of loop coupling through weak interacsons NP in αw ( 0.1) loops Λ > TeV NP in αw ( 0.1) loops Λ > 3.4 TeV Non- perturbasve NP Λ > TeV Non- perturbasve NP Λ > 113 TeV JHEP 0803:049,2008 arxiv:

26 Conclusion SM analysis displays good overall consistency SSll open discussion on semileptonic inclusive vs exclusive UTA provides determinason also of NP contribusons to F=2 amplitudes. It currently leaves space for NP at the level of 15-20% Scale analysis points to high scales for the generic scenario and even above LHC reach for weak cou pling. Indirect searches become essensal. 26