Purpose The ICRU 89 recommends reporting a set of vaginal dose points for cervical cancer treatments in order to quantify the goodness of implant. This vaginal dose reporting method for combined external beam radiotherapy and brachytherapy has been adopted by the EMBRACE II study protocol. Large variations in dose between patients and centers have been reported. The aim of this study was to determine possible discrepancies with consensus observers from the same institution. Therefore, the inter- and intra-observer variability were analyzed. Material and methods For five patients, five experienced observers reported dose at the proposed vaginal points twice. The effect of inter- and intra-observer variations on total dose was analyzed by estimating biologically equivalent dose EQD2 (α/β = 3 Gy). Coefficient of variation (CV) was used to provide a measure of data dispersion as a proportion to the mean. Results The maximum inter-observer deviation among all patients and all points ranged from 0.5 Gy to 24.1 Gy in EQD2. The higher inter-observer discrepancies were found at points at 3 o’clock and at 6 o’clock, with respect to ovoids. In case of the maximum intra-observer deviation, it ranged from 0.5 Gy to 14.2 Gy, with higher deviation points at 12 o’clock and 9 o’clock, with respect to ovoids. Conclusions There is a need to ensure consistency in vaginal points reporting. The impact of the dosimetric inter- and intra-observer variability should also be considered when dealing with dose tolerances and limits due to the potential dose gradient.

Accurate measurements of K, D and B meson mixing amplitudes provide stringent constraints in the Unitary Triangle analysis, as well as useful bounds on New Physics scales. Lattice QCD provides a non perturbative tool to compute the hadronic matrix elements entering in the effective weak Hamiltonian, with errors at a few percent level and systematic uncertainties under control. I review recent lattice results for these hadronic matrix element performed with N-f = 2, N-f = 2 + 1 and N-f = 2 + 1 + 1 dynamical sea quarks.

D → π ν and D → K ν form factors with N f

We present precision lattice calculations of the pseudoscalar decay constants of the charmed sector as well as determinations of the bottom quark mass and its ratio to the charm quark mass. We employ Nf=2+1+1 dynamical quark gauge configurations generated by the European Twisted Mass Collaboration, using data at three values of the lattice spacing and pion masses as low as 210 MeV. Strange and charm sea quark masses are close to their physical values.

We present a lattice QCD determination of the vector and scalar form factors of the semileptonic $K \to \pi \ell \nu$ decay which are relevant for the extraction of the CKM matrix element $|V_{us}|$ from experimental data. Our results are based on the gauge configurations produced by the European Twisted Mass Collaboration with $N_f = 2+1+1$ dynamical fermions, which include in the sea, besides two light mass degenerate quarks, also the strange and the charm quarks. We use data simulated at three different values of the lattice spacing and with pion masses as small as $210$ MeV. Our final result for the vector form factor at zero momentum transfer is $f_+(0) = 0.9709 (46)$, where the uncertainty is both statistical and systematic combined in quadrature. Using the latest experimental value of $f_+(0) |V_{us}|$ from $K_{\ell 3}$ decays, we obtain $|V_{us}| = 0.2230 (11)$, which allows to test the unitarity constraint of the Standard Model below the permille level once the determination of $|V_{ud}|$ from superallowed nuclear $\beta$ decays is adopted. A slight tension with unitarity at the level of $\sim 2$ standard deviations is observed. Moreover we present our results for the semileptonic scalar $f_0(q^2)$ and vector $f_+(q^2)$ form factors in the whole range of values of the squared four-momentum transfer $q^2$ measured in $K_{\ell 3}$ decays, obtaining a very good agreement with the momentum dependence of the experimental data. We provide a set of synthetic data points representing our results for the vector and scalar form factors at the physical point for several selected values of $q^2$.

We present a lattice QCD determination of the vector and scalar form factors of the kaon semileptonic decay K →πℓν, which is relevant for the determination of the CKM matrix element |V_us| from experimental data. Our results are based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2+1+1 dynamical fermions. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV. Our estimate for the vector form factor at zero 4-momentum transfer is f_+(0) = 0.9709 (46), where the uncertainty is both statistical and systematic. By combining our result with the latest experimental value of f_+(0)|V_us| we obtain |V_us| = 0.2230 (11), which satisfies the unitarity constraint of the Standard Model at the permille level using the updated determination of |V_ud| coming from superallowed nuclear β decays. We present also the momentum dependence of the vector and scalar form factors in the whole range of values of the squared 4-momentum transfer measured in K_ℓ 3 decays, obtaining a good agreement with the experimental data.

We present precise lattice computations for the b-quark mass, the quark mass ratios m(b)/m(c) and m(b)/m(s) as well as the leptonic B-decay constants. We employ gauge configurations with four dynamical quark flavors, up-down, strange and charm, at three values of the lattice spacing (a similar to 0.06-0.09 fm) and for pion masses as low as 210 MeV. Interpolation in the heavy quark mass to the bottom quark point is performed using ratios of physical quantities computed at nearby quark masses exploiting the fact that these ratios are exactly known in the static quark mass limit. Our results are also extrapolated to the physical pion mass and to the continuum limit and read m(b)((MS) over bar, m(b)) = 4.26(10) GeV, m(b)/m(c) = 4.42(8), m(b)/m(s) = 51.4(1.4), f(Bs) = 229(5) MeV, f(B) = 193(6) MeV, f(Bs)/f(B) = 1.184(25) and (f(Bs)/f(B))/(f(K)/f pi) = 0.997(17).

We investigate the vector form factor relevant for the Kℓ3 semileptonic decay using maximally twisted-mass fermions with 4 dynamical flavours (Nf=2+1+1). Our simulations feature pion masses ranging from 210 MeV to approximately 450 MeV and lattice spacing values as small as 0.06fm. Our main result for the vector form factor at zero 4-momentum transfer is f+(0)=0.9683(65) where the uncertainty is both statistical and systematic. By combining our result with the experimental value of f+(0)|Vus| we obtain |Vus|=0.2234(16), which satisfies the unitarity constraint of the Standard Model at the permille level.

We present a lattice QCD determination of the vector and scalar form factors of the semileptonic decays D->πl νand D -> K l νwhich are relevant for the extraction of the CKM matrix elements |Vcd| and |Vcs| from experimental data. Our analysis is based on the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2+1+1 dynamical fermions. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV. Our preliminary estimates for the vector form factor at zero 4-momentum transfer are f+(D -> π)(0) = 0.610 (23) and f+(D -> K)(0) = 0.747 (22), where the uncertainties are only statistical. By combining our results with the experimental values of f+(D -> π)(0) |Vcd| and f+(D -> K)(0) |Vcs| we obtain |Vcd| = 0.2336 (93) and |Vcs| = 0.975 (30), which together with the PDG determination of |Vcb| are in agreement with the unitarity constraint of the Standard Model.

N. Carrasco(a), P. Lami∗(a,b), V. Lubicz(a,b), E. Picca(a,b), L. Riggio(a), S. Simula(a), C. Tarantino(a,b) (a) INFN, Sezione di Roma Tre, Rome, Italy. Email: carrasco@fis.uniroma3.it, lorenzo.riggio@gmail.com, simula@roma3.infn.it (b) Dipartimento di Matematica e Fisica, Università Roma Tre, Rome, Italy. Email: lamipaolo@gmail.com, lubicz@fis.uniroma3.it, e.picca88@gmail.com, tarantino@fis.uniroma3.it

We present unquenched lattice QCD results for the matrix elements of four-fermion operators relevant to the description of the neutral K and D mixing in the Standard Model and its extensions. We have employed simulations withNf = 2+1+1 dynamical sea quarks at three values of the lattice spacings in the interval 0.06 { 0.09 fm and pseudoscalar meson masses in the range 210 { 450 MeV. Our results are extrapolated to the continuum limit and to the physical pion mass. Renormalization constants have been determined non-perturbatively in the RI-MOM scheme. In particular, for the Kaon bag-parameter, which is relevant for the K 0 K 0 mixing in the Standard Model, we obtain B RGI = 0:717(24).

We present a lattice QCD calculation of the pseudoscalar decay constants fK, fD and fDs performed using the gauge configurations produced by the European Twisted Mass Collaboration with Nf = 2 + 1 + 1 dynamical quarks, which include in the sea, besides two light mass degenerate quarks, also the strange and charm quarks with masses close to their values in the real world. The simulations are based on a unitary setup for the two light mass-degenerate quarks and on a mixed action approach for the strange and charm quarks. We use data simulated at three different values of the lattice spacing in the range 0.06 - 0.09 fm and at pion masses in the range 210 - 450 MeV. Our main results are: fK+ / fpi+ = 1.184 (16), fK+ = 154.4 (2.0) MeV, which incorporate the leading strong isospin breaking correction due to the up- and down-quark mass difference, and fK = 155.0 (1.9) MeV, fD = 207.4 (3.8) MeV, fDs = 247.2 (4.1) MeV, fDs / fD = 1.192 (22) and (fDs / fD) / (fK / fpi) = 1.003 (14) obtained in the isospin symmetric limit of QCD. Combined with the experimental measurements of the leptonic decay rates of kaon, pion, D- and Ds-mesons our results lead to the following determination of the CKM matrix elements: |Vus| = 0.2269 (29), |Vcd| = 0.2221 (67) and |Vcs| = 1.014 (24). Using the latest value of |Vud| from superallowed nuclear beta decays the unitarity of the first row of the CKM matrix is fulfilled at the permille level.

We present a lattice QCD determination of the vector form factor of the kaon semileptonic decay K -> pi l nu which is relevant for the extraction of the CKM matrix element |V_{us}| from experimental data. Our result is based on the gauge configurations produced by the European Twisted Mass Collaboration with N_f=2+1+1 dynamical fermions. We simulated at three different values of the lattice spacing and with pion masses as small as 210 MeV. Our preliminary estimate for the vector form factor at zero momentum transfer is f_+(0)=0.9683(65), where the uncertainty is both statistical and systematic. By combining our result with the experimental value of f_+(0)|V_{us}| we obtain |V_{us}|=0.2234(16), which satisfies the unitarity constraint of the Standard Model at the permille level.

In this paper, for the first time to our knowledge, a method is proposed to compute electromagnetic effects in hadronic processes, such as decays, using lattice simulations. The method can be applied, for example, to the leptonic and semileptonic decays of light or heavy pseudoscalar mesons. For these quantities the presence of infrared divergences in intermediate stages of the calculation makes the procedure much more complicated than is the case for the hadronic spectrum, for which calculations already exist. In order to compute the physical widths, diagrams with virtual photons must be combined with those corresponding to the emission of real photons. Only in this way do the infrared divergences cancel as first understood by Bloch and Nordsieck in 1937. We present a detailed analysis of the method for the leptonic decays of a pseudoscalar meson. The implementation of our method, although challenging, is within reach of the present lattice technology.

We present unquenched lattice QCD results for the matrix elements of four-fermion operators relevant to the description of the neutral $K$ and $D$ mixing in the standard model and its extensions. We have employed simulations with ${N}_{f}=2+1+1$ dynamical sea quarks at three values of the lattice spacings in the interval 0.06--0.09 fm and pseudoscalar meson masses in the range 210--450 MeV. Our results are extrapolated to the continuum limit and to the physical pion mass. Renormalization constants have been determined nonperturbatively in the RI-MOM scheme. In particular, for the kaon bag parameter, which is relevant for the ${\overline{K}}^{0}\ensuremath{-}{K}^{0}$ mixing in the standard model, we obtain ${B}_{K}^{\mathrm{RGI}}=0.717(24)$.

We present a lattice QCD determination of the average up-down, strange and charm quark masses based on simulations performed by the European Twisted Mass Collaboration with N_f = 2 + 1 + 1 dynamical fermions. We simulated at three different values of the lattice spacing, the smallest being approximately 0.06fm, and with pion masses as small as 210 MeV. Our results are: m_ud(2GeV)=3.70(17)MeV, m_s(2GeV)=99.2(3.9)MeV, m_c(m_c)=1.350(49)GeV, m_s/m_ud=26.64(30) and m_c/m_s=11.65(12).

We discuss a lattice QCD computation of the $B$-meson decay constants by the ETM collaboration where suitable ratios allow to reach the bottom quark sector by combining simulations around the charm-quark mass with an exactly known static limit. The different steps involved in this ratio method are discussed together with an account of the assessment of various systematic effects. A comparison of results from simulations with two and four flavour dynamical quarks is presented.