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QCD is the fundamental theory of strong interactions ; however, at long distances (or equivalently, at low energies), the theory is non-perturbative. **Lattice QCD** (LQCD) is the only known method to treat QCD non-perturbatively from first principles. LQCD research (formal or more phenomenology oriented) is instrumental in modern particle physics, as it provides the only theoretical tool to compute a number of physical quantities (masses, branching fractions, …) and parameters of the SM (as decay constants and form factors) from first principles. Furthermore, in an era in which experimental data is becoming increasingly more precise, LQCD is crucial in bringing down theoretical uncertainties on par with the experimental ones.

One of the problems currently investigated concerns the so-called heavy flavours, most specifically the semi-leptonic decays of B mesons , where collectively denotes the set of first orbital excitations of the D mesons with angular momentum L=1 (P-states). While it is experimentally well known that these channels provide a non-negligible contribution to B decays, current theoretical knowledge on the form factors is far from satisfactory, since all existing treatments (such as heavy quark effective theory, quark models, etc.) are only approximate methods. In fact, the disagreement between theory and observation regarding the decay widths of B mesons to spin ½ and 3/2 D-states is such that it is known as the “P-states puzzle”. These decays are also mandatory for a more precise determination of the CKM matrix element , since they are non-negligible. These transitions are being studied within the European Twisted Mass Collaboration (ETMC) ; the approach is based on pure QCD and includes the dynamical quarks in the sea (“unquenched” approximation). First results include a feasibility proof of the determination of the branching ratios of (scalar) and at zero recoil (which allows to extract the ratio of the corresponding form factors at zero recoil). Although isolating excited states on the lattice is quite difficult, our study shows this to be possible for in general. This work has provided the first direct evidence in QCD of a non-vanishing transition amplitude of with finite mass heavy quarks : the extrapolated value in the continuum, 0.13, is already in very good agreement with the experimental findings, 0.10.

Such as in the continuum case, renormalisation is mandatory in LQCD : the computation of the renormalization factor of several operators (for instance local and non-local bilinear quark operators, and the quark propagator) is crucial to extract the physical quantities. The approach followed consists in computing the relevant correlation functions on the lattice using a non-perturbative renormalization scheme (RI-MOM), and then transferring the results to a more standard physical scheme. In order to do so, an analytical interpolation of the running of (which is indeed non-negligible) has to be carried, and lattice artifacts must be taken into account.

A final LQCD research topic is that of the estimation of the strong coupling in the scheme, , at the Z and mass scales (at which the coupling is experimentally estimated). The method used consists in computing the ghost-gluon vertex in the Landau gauge and in the Taylor scheme, the extracted value of then being transferred to the “physical” scheme. This approach relies on the gluon and ghost propagators produced by the ETMC, using 4 dynamical sea quarks (mass-degenerate u, d and non-degenerate s, c flavours). The results reveal an excellent agreement with experimental data, further showing that, as a consequence of including the c quark in the sea, there is no need to explicitly treat the Z mass threshold.

The study (which is done in a specific gauge – the Landau one) also allowed the confirmation that the only non-invariant operator playing a role is the Landau condensate moreover, the required Operator Product Expansion (OPE) to transfer the results to the scheme showed that the OP expansion was reliable and allowed to compute a particular Wilson coefficient on the lattice for the first time. Finally, the problem can be reversed, which allows one to actually extract the QCD scale from the lattice, again in excellent agreement with experimental data.

Other QCD related studies focused on spectra of 2 dimensional QCD-like theories, and pion couplings to scalar B mesons.

**LQCD at the LPC : computational resources and collaborations**

The computations are done relying on (among others) the resources of the IN2P3 computation centre; V. Morénas is head manager - “Czar” – of the lattice QCD group at the IN2P3CC. | ||

LQCD studies are partially done in the framework of the ETM Collaboration. |

**Recent publications :**

- M. Atoui, V. Morénas, D. Bečirević and F. Sanfilippo, " near zero recoil in and beyond the Standard Model”, Eur. Phys. J. C 74 (2014) 5 [arXiv:1310.5238 [hep-lat]].
- M. Atoui, B. Blossier, V. Morénas, O. Pène and K. Petrov, “Semileptonic mesons decays in Lattice QCD : a feasibility study and first results”, arXiv:1312.2914 [hep-lat].
- B. Blossier et al., “Renormalisation of quark propagators from twisted-mass lattice QCD at ”, Phys. Rev. D 83 (2011) 074506 [arXiv:1011.2414 [hep-ph]].
- B. Blossier, M. Brinet, P. Guichon, V. Morénas, O. Pène, J. Rodríguez-Quintero and S. Zafeiropoulos, “Renormalization constants for twisted mass QCD”, arXiv:1411.0053 [hep-lat].
- B. Blossier et al. [ETM Collaboration], “Renormalization of quark propagator, vertex functions and twist-2 operators from twisted-mass lattice QCD at "”, arXiv:1411.1109 [hep-lat].
- B. Blossier et al. [ETM Collaboration], “Ghost-gluon coupling, power corrections and from twisted-mass lattice QCD at ”, Phys. Rev. D 82 (2010) 034510 [arXiv:1005.5290 [hep-lat]].
- B. Blossier et al., “Ghost-gluon coupling, power corrections and from lattice QCD with a dynamical charm”, Phys. Rev. D 85 (2012) 034503 [arXiv:1110.5829 [hep-lat]].
- B. Blossier et al., “The Strong running coupling at and mass scales from lattice QCD”, Phys. Rev. Lett. 108 (2012) 262002 [arXiv:1201.5770 [hep-ph]].
- B. Blossier, P. Boucaud, M. Brinet, F. De Soto, V. Morénas, O. Pène, K.Petrov and J.Rodríguez-Quintero, “Testing the OPE Wilson coefficient for from lattice QCD with a dynamical charm”, Phys. Rev. D 87 (2013) 074033 [arXiv:1301.7593 [hep-ph]].
- B. Blossier et al. [ETM Collaboration], “High statistics determination of the strong coupling constant in Taylor scheme and its OPE Wilson coefficient from lattice QCD with a dynamical charm”, Phys. Rev. D 89 (2014) 1, 014507 [arXiv:1310.3763 [hep-ph]].
- P. Boucaud, M. Brinet, F. De Soto, V. Morénas, O. Pène, K. Petrov and J. Rodríguez-Quintero, “Three-gluon running coupling from lattice QCDat : a consistency check of the OPE approach”, JHEP 1404 (2014) 086 [arXiv:1310.4087 [hep-ph]].
- B. Blossier, P. Boucaud, M. Brinet, F. De Soto, V. Morénas, O. Pène, K. Petrov and J. Rodríguez-Quintero, “Novel method for the physical scale setting on the lattice and its application to simulations”, Phys. Rev. D 89 (2014) 3, 034026 [arXiv:1312.1514 [hep-lat]].
- B. Blossier, N. Garron and A. Gérardin, “Pion couplings to the scalar B meson”, arXiv:1410.3409 [hep-lat].

CKMFitter aims at probing and ultimately validating the Cabibbo-Kobayashi-Maskawa model of quark flavour transitions, but also has the potential of identifying the most crucial measurements to be carried out, and pointing the way to SM extensions capable of alleviating the tension between theory and experiment. In this program, we performed a critical study of the theoretical uncertainties in the decay of the extremely rare process , which has recently been measured.

**Recent publications :**

- [J. Charles et al., “Predictions of selected flavour observables within the Standard Model”, Phys. Rev. D 84 (2011) 033005 [arXiv:1106.4041 [hep-ph]].
- J. Charles et al., “Current status of the Standard Model CKM fit and constraints on New Physics”, arXiv:1501.05013 [hep-ph].