Towards a numerical solution of the "1/2 vs. 3/2" puzzle

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Lucinda Hardy
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1 Towards a numerical solution of the /2 s 3/2 puzzle Benoît Blossier DESY Zeuthen Motiations Hea Quark Effectie Theor Theoretical expectations Experimental measurements umerical computation of Conclusion outlook [D Bećireić et al, Phs Lett B 609, )] [B B et al, Phs Lett B 632, )] [I Bigi et al, hep-ph/052270]

2 Motiations Experimental data are well described b the CKM picture in the flaor sector Precision tests are made b CD, D0, B factories LHCb - hope of detecting phsics beond the SM in the flaor sector, especiall in transitions between the flaor famil - at present the uncertaint on fundamental parameters is dominated b theoretical errors one needs a deep understing of the current theor before using a theor beond the SM to analze data

3 - + % ) +, 9 < ; What is the composition of the hadronic final state in? # &% & Mass MeV) Width MeV) ) %3 is the main deca channel parit orbital momentum conseration the deca occurs with the pion in a wae or in a wae 76 # 6 S wae D wae S D wae are a priori allowed; howeer the S wae is forbidden b HQS 76 # 76 # An appropriate framework to stud transitions is the Hea Quark Effectie Theor HQET) it describes soft interactions between a hea quark the light cloud of quarks gluons within hea-light hadrons

4 L S i j P u r s r x u s r s r s Š Š Š Hea Quark Effectie Theor => HQET is an effectie theor whose the hard cut-off is Y L UM L S ST R? I XO W VB D QP M EG K HJI EG D BC?A@ ST R? fhg e cd ab ]_^` ) for Z\[ D Smmetr SU2 p o l n kml Hea-light meson Atom of hdrogen q Angular momentum Spectroscop hea-light mesons are put together in doublets w orbital excitation {} {} Uz L ƒ {} are defined u {, U in terms of HQET hadronic matrix elements u % MeV MeV u =Œ =Œ =ˆ =ˆ Ž = Œ = Œ Ž Š = ˆ = ˆ u u

5 u u I K I œ % u, I Ÿ Ÿ œ u, L Ÿ are expressed in terms of P With the trace formalism, transitions uniersal form factors the Isgur-Wise functions ) smmetr, their number is small Z [ Thanks to SU2 u u parameterizes the elastic transition I QP % u EG Ež I I I I QP % u EG Ÿ Ež P are not normalised at zero recoil; howeer,

6 ª Theoretical expectations Various quark models à la Bakamijan-Thomas, null plane, harmonic oscillator wae functions in a particular frame in the limit, models with approximate Lorentz boosts using wae functions with small components) predict hierarchies «contributions to do not change this picture Sum rules obtained b performing the hea quark expansion of a meson 2-pts function Bjorken,Uraltse, Voloshin, momenta) lead to the same hierarch «Sum rules à la SVZ [P Colangelo et al, Phs Re D 5, )]

7 ± Experimental measurements ALEPH DELPHI data indicate a big component of broad states in the latter lead to the hierarch ; In contradiction with quark models predictions with the OPE result /2 s 3/2 puzzle [V Morénas et al, hep-ph/00372, Uraltse, hep-ph/00925] One could fit the broad combinations # sstem as radial excitations or non resonant Measurements b BELLE are qualitatiel compatible with quark models predictions states dominate in the deca) States do not seem to saturate DELPHI) Theoreticall this saturation is not expected as well because of radiatie corrections A recent measurement b BABAR seems to confirm that hpothesis howeer, a determination of the resonant component of the inariant mass distribution is hoped # As is mainl goerned b confirm infirm) theoretical expectations of the hierarch between, their computation on the lattice can ±

8 I u I» ƒ u Ã % { ¾ Ð { Ï Ï ¾ Ë Ð { { Î ¾ ¾» µ µ ³ ³ umerical computation of One can not extract the required form factors from the computation of linear cancellation in ) # u º EG s Ež fh ¹ from Howeer, thanks to HQET equation of motion, one can extract ¼ ½ ¼ ½ ƒ s P # u the computation of [ A K Leiboich et al, Phs Re D 57, 30 99)] º E s E diergence) b the computation of À no ¼ ½ ¼ ½ ¼ ½ ¼ ½ ¾ Extraction of, Ã %»»» % the Ã %»È É» Ê»»È ÅÇÆ Computation of Ò Ñ Ö Ö Õ Æ Ó ÔÓ ¼ ½ Ò Ñ Ð Ö Ò Ñ Ê Í Ì ¼ ½ Ö Ö ratios À À lat DRMS Ê É Renormalisation of the operator»è É»»»» ÅÇÆ

9 á Ã Þ Ã Þ Ø á Ã Þ Ã Þ Ø á á ã, Ÿ x ç º Ù Ø» à Ê ÛÝ ß Ù Ø» ÛÝ Ú Ù Ù Ø» à Ê ÛÝ L Ù Ø» ÛÝ Ú Ù Ø»È» à Ê Û ß»È Ø» Ûâ Ú Ê Ø»È Ø» à Ê Û L»È Ø» Ûâ Ú Ê Ø E»» E Ÿ E»» E ã»» E ä ã Ÿ» comes from a spin-orbit coupling - The mass splitting = = L L L æs æs æs K 5 5» çqè ) ) J P =2 + 2 J P = 0 - J P = aeeff 06 aeeff 03 03» )» ) t/a t/a 0 are er short despite the use of state effectie mass of Plateaux of the é é HYP links smeared interpolating fields urther improements are needed

10 ã ë É í í Û í í % í óþ í ò Û ò Reduction of the coupling of radial excitations to the acuum ç ç E É Smearing of the interpolating field ðtñ Ö ï»» î É É É % É É 5 75 R0 + ) R2 + ) eff ae t/a t/a Plateaux are still er short ô Preliminar results

11 ± ö è À < Š M The composition of the final state 0 ears Conclusion outlook in has receied some attention since Theoreticall it is expected that states the P wae states do not saturate the total width Moreoer, coariant quark models sum rules extracted from the OPE in the hea quark limit lead to the hierarchies ± «@ D Experimentall it was found at LEP that the total width is saturated b the measured branching ratios read õc ± ± We hae proposed a method to compute on the lattice We obtained as a preliminar result «ø D Unfortunatel the noise pollutes significantl correlation functions of hea-light meson orbital excitations the coupling of radial excitations to the acuum is important Improements to reduce them hae been implemented but the are not sufficient et The search of methods to highl increase statistics is underwa one possibilit is to compute economicall the entire light propagator instead of a part To take account of all with À = # = º º corrections, we plan to compute form factors associated the quark is described b QCD discretisation effects fm to reduce

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