form factors and determination of V us from decays Emilie Passemar Los Alamos National Laboratory The 11th International Workshop on Chiral Dynamics Jefferson Laboratory, Virginia, USA August 7, 01
Outline : 1. Introduction and Motivation. Dispersive representation of the form factors 3. Fits to the and l3 decays 4. Conclusion and outlook
1. Introduction and Motivation
1.1 Test of New Physics : Vus Studying and l3 decays indirect searches of new physics, several possible high-precision tests: Extraction of V us l l l e, V us W l, e l l 1 3 / 0 N f (0)V / 0 l 3 us I /0 with I dt F t, f ( t), f 8 0( t) m /0 f (0) f (0) V us V us From Lattice QCD Test of unitarity V V V 1 ud us ub? 0 + 0 + decays l3 decays Negligible (B decays) 4
1.1 Test of New Physics : Vus Studying and l3 decays indirect searches of new physics, several possible high-precision tests: Extraction of V us l l l e, V us W l, e l l 1 3 / 0 N f (0)V / 0 l 3 us I /0 with I dt F t, f ( t), f 8 0( t) m /0 nowledge of the two form factors: ( p ) s u (p ) = p p p p f ( t) p p f0( t) t t f0, () t t q ( p p ) ( p p ), f 0, () t f (0) vector scalar 5
1.1 Test of New Physics : Callan-Treiman theorem Callan-Treiman (CT) theorem : Bernard, Oertel, E.P., Stern 06 C us F F V 1 ud f 0( ) V r ud us F f(0) F V f(0) V m CT CT m Very precisely known from Br(l/l), (e3) and V ud In the Standard Model : r 1 lncsm 0.141(73) In presence of new physics, new couplings : r 1 6
1.1 Test of New Physics Test of New Physics : u s g V us W,e g,e SUSY loops Z, Charged Higgs, Right-Handed Currents,. [E.g. Bernard et al 06, 07, Deschamps et al 09, Cirigliano et al 10, Jung et al 10, Buras et al 10 ] 7
1. Determination of the form factors f () t accessible in e3 and 3 decays f () t 0 only accessible in 3 (suppressed by m l /M ) + correlations difficult to measure Data from Belle and BaBar on decays (Belle II, SuperB soon!) Use them to constrain the form factors and especially decays V us Hadronic matrix element: Crossed channel W s u 0 = p p p p f ( s) p p f0( s) s s f 0 with s q ( p p ) vector scalar 8
. Dispersive Representation of the form factors
.1 Introduction Parametrization to analyse both l3 and Vector form factor: Dominance of *(89) resonance f f s l 3 decays s ' '' ( s) 1... m m 1 s decays f( s) ibw ( s) i m m m m m m s [GeV] 10
.1 Introduction Parametrization to analyse both l3 and f0 Scalar form factor: No obvious dominance of a resonance s l 3 decays decays f s s ( s) 1... ' '' 0 0 0 m m f ( s)? 0 CT m m m m m s [GeV] 11
. Dispersive representation Parametrization to analyse both l3 and Use dispersion relations Omnès representation: f,0 s ( s) exp ds' ( s') s' s' s i,0 s th +,0 (s): phase of the form factor - s s : ( s) ( s) in,0 scattering phase sth m m - s s : ( s) unknown in,0 ( s) ( s) f ( s) 1/ s,0,0,0as [Brodsky&Lepage] Subtract dispersion relation to weaken the high energy contribution of the phase. Improve the convergence but sum rules to be satisfied! 1
. Dispersive representation Dispersion relation with n subtractions in : f,0( s) exp Pn 1( s) n s s ds' s th s' s s n Bernard, Boito, E.P., in progress,0( s') s' s i f () s 0 dispersion relation with 3 subtractions: in s=0 and 1 in s= s lnc f 0( s) exp lnc s ' 0 m s s 0 m m [Callan-Treiman] ds' ( s') s' s' s' s i For s<s in : scattering phase extracted from the data Buettiker, Descotes-Genon, & Moussallam 0 parameters to fit to the data lnc ln f( ) and ' 0 13
. Dispersive representation Dispersion relation with n subtractions in : f,0( s) exp Pn 1( s) n s s ds' s th s' s s n Bernard, Boito, E.P., in progress,0( s') s' s i f () s dispersion relation with 3 subtractions in s=0 f ' s 1 '' ' s s ( s) exp + 7 parameters to fit to the data: ' and can be combined with l3 fits Resonance parameters: 3 m m m m s' s' s i '' 3 * * *' *' ds' ( s' ) Extracted from a model including resonances *(89) and *(1414) m,, m,, Boito, Escribano, Jamin 09, 10 Jamin, Pich, Portolés 08 Mixing parameter 14
3. Fits to the and l3 decays
3.1 form factors from and l3 decays Fit to the decay data from Belle [Epifanov et al 08] (BaBar?) from simulated SuperB data [Antonelli, Lusiani, E.P. in progress] N N b Number of events/bin events tot w 1 bin width d d s N N events bins N with 3 3 3 F C (0) 1 1 ( ) ( ) ( ) 3 SEW f Vus q s f s q s f0( s) s 3 s m m 4s d G m s s d Normalization disappears by taking the ratio 1 d d s fit independant of V us 16
3.1 form factors from and l3 decays Fit to the decay data from Belle [Epifanov et al 08] (BaBar?) from simulated SuperB data [Antonelli, Lusiani, E.P. in progress] N N b Number of events/bin events tot w 1 bin width d d s N N events bins N with 3 3 3 F C (0) 1 1 ( ) ( ) ( ) 3 SEW f Vus q s f s q s f0( s) s 3 s m m 4s d G m s s d Possible combination with l3 decay data fits [Flavianet aon WG 10] T l 3 3 1 ln ln l C C l3 V lnc with ' '' 17
3.1 form factors from and l3 decays Preliminary results : Bernard, Boito, E.P., in progress Antonelli, Lusiani, E.P. in progress Only statistical errors but the dominant ones! 18
3.1 form factors from and l3 decays Bernard, Boito, E.P., in progress Antonelli, Lusiani, E.P. in progress 19
3. Applications: V us Very precise knowledge of the form factors in the whole range of energy I ds F s, f ( s), f 0( s) V us from l3 decays: very precise determination see Cirigliano s talk l 1 3 with I /0 dt F 8 t, f ( t), f 0( t) l N f (0)V l 3 us I /0 /0 V 0.54 0.0013 (0) 0.163 0.0005 f V us us m /0 Similarly, V us from but not competitive yet! N f (0)Vu s I with I ds F s, f ( s), f 0( s) f (0)Vus 0.111 0.0037 V 0.01 0.0040 us 0
From Unitarity Flavianet aon WG 10 BaBar & Belle HFAG 1
3. Applications: Callan-Treiman Very precise knowledge of the form factors in the whole range of energy I ds F s, f ( s), f 0( s) V us from l3 decays: very precise determination see Cirigliano s talk l 1 3 with I /0 dt F 8 t, f ( t), f 0( t) l N f (0)V l 3 us I /0 /0 V 0.54 0.0013 (0) 0.163 0.0005 f V us us m /0 Callan-Treiman test: lnc 0.00(55) ~1.5 from the SM : lnc 0.141(73) SM
3. Applications: * pole Very precise knowledge of the form factors in the whole range of energy I ds F s, f ( s), f 0( s) V us from l3 decays: very precise determination see Cirigliano s talk l 1 3 with I /0 dt F 8 t, f ( t), f 0( t) l N f (0)V l 3 us I /0 /0 V 0.54 0.0013 (0) 0.163 0.0005 f V us us m /0 Precise extraction of scattering phase and good determination of *: m* 89.01 0.1 MeV and * 46.493 0.436 MeV PDG: m* 891.66 0.6 MeV and * 50.8 0.9 MeV 3
3. Applications: V us Antonelli, Lusiani, E.P. in progress Very precise knowledge of the form factors in the whole range of energy Use the form factors and the aon Brs to try to reconcile the extraction of V us from exclusive and inclusive modes Exclusive mode : / PDG 10: Need lattice input f f see V.Cirigliano s talk FLAG 11 Vus 0.55 0.004 f 1.193 0.005 f 4
3. Applications: V us Antonelli, Lusiani, E.P. in progress Very precise knowledge of the form factors in the whole range of energy Use the form factors and the aon Brs to try to reconcile the extraction of V us from exclusive and inclusive modes Inclusive modes: s V us 00, S 00 R, V A 00 R, th V ud R data: PDG 10: 00 R S, 0.161(38) Vud and 0.9745() 00 R, V A 3.467(11) 00 R,th computed from phenomenology Gámiz, Jamin, Pich, Prades,Schwab 0 03 Maltman et al. 09 00 R, th 0.40(3) Vus 0.173 0.000 exp 0.0010 th 3.4 away from unitarity! 5
3. Inclusive decays from kaon decays Modes measured in the strange channel for : Antonelli, Lusiani, E.P. in progress s HFAG 1 6
3. Inclusive decays from kaon decays Modes measured in the strange channel for : Antonelli, Lusiani, E.P. in progress s HFAG 1 ~70% of the decay modes crossed channels from aons! 7
3. Inclusive decays from kaon decays The Brs of these 3 modes can be predicted using aon Brs very precisely measured + form factor information : Antonelli, Lusiani, E.P. in progress B (0.715 0.003)% uni : precise knowledge of phase space required (dispersive ff in I ) B uni uni 0 (0.4376 0.0106)% and B 0 (0.875 0.01)% Preliminary 8
3. Inclusive decays from kaon decays s Modes measured in the strange channel for : Antonelli, Lusiani, E.P. in progress HFAG 1 0.715 0.003. 10 0.4376 0.0106. 10 0.875 0.01. 10.9543 0.049. 10 9
Antonelli, Lusiani, E.P. in progress From Unitarity Flavianet aon WG 10 BaBar & Belle HFAG 30
4. Conclusion and outlook
4. Conclusion and outlook Possibility to get interesting constraints on the form factors from decays New data available from Belle and BaBar Build a parametrization using dispersion relations to have a precise parametrization and theoretically well motivated to fit the data Dispersive parametrization possible combination with l3 data to have constraints from different energy regions Possibility to test the Standard Model: V us Possibility to reconcile the different determinations of V us using kaon data Work still in progress High precision era in : - more precise data with Belle II, SuperB - theoretical: EM, IB corrections 3
5. Back-up
Exclusive decays: decays vs. / Emilie Passemar SuperB Physics Meeting, Frascati, Dec. 11 011 34
For + (s): In this case instead of the data, use of a parametrization including resonances *(89) and * (1414) : Jamin, Pich, Portolés 08 f m* * Re H (0) Re H (0) s s ( s) - Dm*, * Dm*', *' P,1/ Im f( s) tan Re f ( s) with D m, m s Re H im ( s) n n n n n n Parametrization that takes into account the loop effects : * *' * *', * 0 0 0, *' Loops with *(89) dominant decay channel of * (1410) (>40%) also included but not in Jamin, Pich, Portolés 08, Boito, Escribano, Jamin 08 10 E. Passemar 35 35 H * 0 0 0
3. Inclusive decays V us can also be determined from inclusive decays hadrons kl kl (0) kl( D) kl( D) R NC SEW Vus V ud 1 Vud ud Vus us D Use instead R kl R kl kl, V A, S V ud R V us N S - kl( D) kl( D) C EW ud us D kl ms ( m ) R 4 kl S ms and/or m Vus 36
3. Inclusive decays V us can also be determined from inclusive decays hadrons kl kl (0) kl( D) kl( D) R NC SEW Vus V ud 1 Vud ud Vus us D Use instead R kl R kl kl, V A, S V ud R V us N S - kl( D) kl( D) C EW ud us D kl ms ( m ) R 4 kl S ms and/or m Vus 37
3. Inclusive decays 00 R, S Vus 00 00 data: R and R, S 0.1615(40), V A 00 R, th V PDG 10: 0.9745() ud Vud 00 R, V A 3.479(11) V 0.10(3) 00 R, th 0 us 00 R,th computed from phenomenology Gámiz, Jamin, Pich, Prades,Schwab 0 03 00 R, th 0.16(16) Vus 0.164 0.007 exp 0.0005 th dominated by experimental uncertainties V us from unitarity: V 0.55 0.0010 3 away! us 38
3. Inclusive decays from kaon decays Possible normalization problem: R,S Smaller branching ratios smaller smaller Vus 00 R, S old 0.1686(47) 00 R, S new 0.1615(40) V 0.14 0.0031 0.0005 us old exp th V 0.164 0.007 0.0005 us new exp th Missing modes at B factories? 39
3. Inclusive decays Missing modes at B factories? PDG 010: «Fifteen of the 16 B-factory branching fraction measurements are smaller than the non-b-factory values. The average normalized difference between the two sets of measurements is -1.36» Los Alamos, March 6 th 01 40