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Analysis of the Kl3K form factors l3 IPNO Participation: Véronique Bernard, Jan Stern (malheureusement décédé au cours du travail) Collaboration : Bern (Suisse), LUTH, Valence (Espagne) Une paramétrisation dispersive du facteur de forme scalaire changeant l’étrangeté a été introduite, guidée par le théorème de Callan-Treiman, permettant de tester le Modèle Standard (MS). Elle a été étendue au facteur de forme vecteur. Sa robustesse a été étudiée en détail. En particulier, la dépendance en cut-off, les effets de brisure d’isospin et la présence possible de zéro ont été discutés. Les résultats publiés de KTeV ont été réanalysés à l’aide de cette paramétrisation et un bon accord avec le MS a été obtenu. La connaissance de la valeur du facteur de forme vecteur à zéro moment transféré permet de déterminer l’élément de matrice CKM, V us et conduit donc à un test supplémentaire du MS. Cette valeur a été obtenue en QCD sur réseau. Toutefois une extrapolation chirale est nécessaire pour passer des valeurs des masses de quarks atteintes aujourd’hui sur réseau aux valeurs physiques. Une première étude exploratoire a été faite dans le cadre de la théorie chirale des perturbations (théorie effective du MS) à deux boucles. Experimental information on the shape of the strangeness changing vector and scalar form factors f 0 and f + can be obtained from the study of K l3 decays. These quantities indeed enter the differential decay rates of these semi-leptonic processes. One of the main aim of these experiments is the extraction of the CKM matrix element V us providing a test of the Standard Model (SM). A dispersive parameterization of f 0 [1] allows for another test by the measurement of its only parameter, the the two collaborations of 2.1σ. We have, in collaboration with KTeV [3], reanalyzed their data confirming the KLOE result with a value of lnC= 0.195 ± 0.0122 in good agreement with the SM. At the same time that these efforts are put in testing the SM, lots of progress has been made in QCD lattice calculations. One important progress in the light quark sector concerns the values of the quark masses that can now be reached. These are very close to the physical ones making a controlled, i.e. trustable, chiral extrapolation of the lattice results to the physical points possible. A very powerful model-independent framework to perform this extrapolation is Chiral Perturbation Theory (ChPT), the Effective Field Theory of QCD at low energies. Indeed it allows to calculate low-energy QCD processes in terms of the light pseudoscalar meson masses. The scalar form factor has been studied on the lattice [4]. Some parameterization of its momentum-dependence plus the knowledge of the one-loop ChPT result at zero momentum trans- Fig.1: Dispersive representation of the scalar form factor. The blue lines delimits the physical region of K l3 decays. For comparison two different values of lnC have been used. The black/red band take care of all the uncertainties discussed. value of the form factor at the so-called Callan- Treiman point, f 0 (Δ Kπ )≡C where Δ Kπ ≡ m 2 K -m 2 π with m π and m K the pion and kaon mass respectively. This value is indeed known from a soft pion theorem derived in the sixtees by Callan and Treiman. Due to the importance of such a measurement it is mandatory to make a detailed study of the robustness of the dispersive parameterization [2]. Fig.1 shows the result of such an analysis. Experimentally a reanalysis of the data by the NA48 and KLOE collaboration with the dispersive parameterization was done with a difference in the result of Fig.2 Momentum dependence of the scalar form factor. The result of the fit is shown (solid line) as well as the convergence of the chiral expansion. The dash dotted line is the result at leading order, the dashed line displays the one up to next to leading order. 87
fer is used to extract f + (0). We have done a first exploratory study [5] using a two-loop ChPT calculation [6] to fit the lattice data. We have not only considered the scalar form factor but at the same time we have fitted the ratio of the kaon to the pion decay constants F K /F π since similar low energy constants (LECs) enter the two quantities. This allowed us to determine some LECs at two loop order and thus not only obtain f + (0) and determine V us but also the value of the scalar form factor at the Callan-Treiman point and at its soft-kaon analog. Results are in good agreement with the determination from experiment using the standard couplings of quarks to the W boson. The slope of the form factors is however rather large. A study of the convergence of the chiral expansion is also performed and the result is shown on Fig.2. Also displayed on the figure is the result of the fit (solid line) and the lattice data. References [1] V. Bernard, M. Oertel, E. Passemar and J. Stern, Phys. Lett B638 (2006) 480 [2] V. Bernard, M. Oertel, E. Passemar and J. Stern, Phys. ReV. D80 (2009) 034034 [3] E. Abouzaid et al., Phys. Rev. D81 (2010) 052001 [4] P. A. Boyle, J. M. Flynn, A. Juttner, C. T. Sachrajda and J. M. Zanotti, JHEP 0705 (2007) 016 [5] V. Bernard and E. Passemar, to be published in JHEP, arXiv:0912.3792 [6] J. Bijnens and P. Talavera, Nucl. Phys. B669 (2003) 341 88
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EXOTIC NUCLEI STRUCTURE AND REACTIO
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in the spectra by analyzing their t
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were taken from ref. [5]. Concernin
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keV -ray with the particles and the
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the 605.9 keV line of the 74 Zn 2+
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Figure 2 a n d analysis. Figure 2 s
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ing particles was thus obtained by
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First p-p p collisions in the ALICE
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Quarkonia physics with ALICE IPNO P
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NA50 updated puzzle IPNO Participat
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Status of the HADES experiment (I):
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Status of the HADES experiments (II
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Status of the HADES experiment (III
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Page 29 and 30: Hadron Electrodynamics IPNO Partici
Page 31 and 32: G0 experiment at Jefferson Lab. IPN
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Page 35 and 36: Exotic low mass narrow baryons from
Page 37 and 38: The PVA4 parity violation experimen
Page 39 and 40: Etude des Distributions de Partons
Page 41 and 42: Latest Results from GRAAL IPNO Part
Page 43 and 44: Persistence of the Polarization in
Page 45 and 46: The northern site of the Pierre Aug
Page 47 and 48: The Pierre Auger southern Observato
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Page 51 and 52: THEORETICAL PHYSICS Research in the
Page 53 and 54: transfer reaction, the 34 Si(d, 3 H
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Page 57 and 58: Pairing and nuclear incompressibili
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Page 61 and 62: Evaporation-residue residue cross s
Page 63 and 64: Extending the VMI model: normal and
Page 65 and 66: Alpha particle condensation in nucl
Page 67 and 68: Collective Modes in Ultracold Trapp
Page 69 and 70: Exploring key unknown neutrino prop
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Page 73 and 74: After a term by term Borel resummat
Page 75 and 76: Chiral expansions of the π 0 lifet
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Page 83 and 84: A pseudo Coulombian potential in D=
Page 85 and 86: The many-body problem with an energ
Page 87 and 88: The rotational spectrum and the att
Page 89 and 90: Z-identification of very heavy nucl
Page 91 and 92: The Pegase project, a new solid sur
Page 93 and 94: But at 80 keV total energy ( 200 eV
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Page 105 and 106: ENERGY AND ENVIRONMENT The increasi
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Page 111 and 112: 3D coupling of Monte-Carlo neutroni
Page 113 and 114: Fission cross sections of actinides
Page 115 and 116: Studies and synthesis of specific m
Page 117 and 118: Chemistry and Electrochemistry of T
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