# Standard Model Parameters and Renormalization

Computation of the strong coupling in $$N_f=4$$ QCD
Marina Marinkovic
Mon, 14:00, Seminar Room C -- Parallels 1C (Slides)

We present a non-perturbative computation of the running of $$N_f=4$$ QCD coupling with four flavours of O(a) improved Wilson fermions and Wilson plaquette action. The Schrödinger functional strategy is used to overcome the multi-scale problem in QCD and keep full control over the systematic errors. We check that cutoff effects in the step scaling function are weak by taking one more resolution compared to a previous computation. Finally, we show an improved result of the Lambda parameter in four flavor QCD in the units of hadronic scale $$L_{max}$$.

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Studying the gradient flow coupling in the SF
Patrick Fritzsch, Alberto Ramos
Mon, 14:20, Seminar Room C -- Parallels 1C (Slides)

We discuss the setup and features of a new definition of the running coupling in the Schroedinger functional scheme based on the gradient flow. Its suitability for a precise continuum limit in QCD is demonstrated on a set of $$N_f=2$$ gauge field ensembles in a physical volume of $$L\sim 0.4$$ fm. Moreover, we report on preliminary results of its step-scaling function at one value of the coupling in SU(3) pure gauge theory.

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Vector correlator and scale determination in lattice QCD
Harvey Meyer, Georg von Hippel, Fred Jegerlehner, Anthony Francis
Mon, 14:40, Seminar Room C -- Parallels 1C (Slides)

We implement a proposal made in 1107.4388 to determine the lattice spacing by matching the lattice vector correlator at a reference distance scale with the same correlator obtained by a dispersion relation based on the R ratio determined experimentally. We work with the isovector current, requiring a separation of the isovector hadronic final states on the phenomenological side. We also discuss the finite-size effect on the correlator, which must be controlled in order for the method to be applicable.

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On the $$N_f$$-dependence of gluonic observables
Mattia Bruno
Mon, 15:00, Seminar Room C -- Parallels 1C (Slides)

We compute gluonic observables at finite Gradient flow time for two flavour QCD. Despite significant autocorrelations, the use of the full CLS ensembles together with a careful error analysis allows to extract interesting quantities and to approach the continuum limit of the two flavour theory. A proper comparison to $$N_f=0$$ results shows the size of sea quark effects.

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Finite size effects in lattice RI-MOM
Francesco Di Renzo, Michele Brambilla
Mon, 15:20, Seminar Room C -- Parallels 1C (Slides)

RI-MOM (or its RI'-MOM variant) is one of the most polular renormalization schemes for Lattice QCD; being regulator independent, it can be effectively adopted in a lattice regularization. RI-MOM is defined in infinite volume. This is in principle a fundamental problem for the lattice, since any simulation is performed in a finite volume. From a practical point of view, one most often verifies a posteriori (by performing computations on different physical volumes) the expectation that renormalization constants, determined in the RI-MOM scheme at large momenta, should not be affected by significant finite size effects. In the context of Numerical Stochastic Perturbation Theory, we have in recent years devised a novel method to explicitly look and correct for finite size effects (in a convenient window). We review this method, discussing how it can be applied in a non-perturbative formulation as well.

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Renormalization of the momentum density on the lattice using shifted boundary conditions
Daniel Robaina, Harvey Meyer
Mon, 15:40, Seminar Room C -- Parallels 1C (Slides)

In order to extract transport quantities from energy-momentum-tensor (EMT) correlators in Lattice QCD there is a strong need for a non-perturbative renormalization of these operators. This is due to the fact that the lattice regularization explicitly breaks translational invariance, invalidating the non-renormalization-theorem. Here we present a non-perturbative calculation of the renormalization constant of the off-diagonal components of the EMT in SU(3) pure gauge theory using lattices with shifted boundary conditions. This allows us to induce a non-zero momentum in the system controlled by the shift parameter and to determine the normalization of the momentum density operator.

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Combined Lattice and Continuum Analysis of the Light Quark $$V-A$$ Correlator at NNLO in ChPT
Kim Maltman, Peter Boyle, Luigi Del Debbio, Nicolas Garron, Jamie Hudspith, Eoin Kerrane, James Zanotti
Wed, 08:30, Seminar Room C -- Parallels 5C (Slides)

The light quark V-A correlator is analyzed at NNLO in the chiral expansion using a combination of continuum and lattice input. It is shown how lattice data with variable quark masses allows for a determination of a crucial combination on NNLO LECs inaccessible in the continuum approach, while the high precision determination of the correlator for physical quark masses provided by the dispersive continuum representation, plus additional continuum sum rule inputs for a second combination of NNLO LECs, further sharpens the lattice determination. The result is the first NNLO determination of the NLO LEC $$L_10$$ having all NNLO uncertainties under full, explicit control.

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Non-perturbative renormalization of overlap quark bilinears on domain wall fermion configurations
Zhaofeng Liu, Ying Chen, Shao-Jing Dong, Ming Gong, Anyi Li, Keh-Fei Liu, Yibo Yang
Wed, 08:50, Seminar Room C -- Parallels 5C (Slides)

We present calculations of the renormalization constants of overlap quark bilinear operators using the RI/MOM scheme. The matching to the MSbar scheme is then obtained by conversion ratios from continuum perturbation theory. The calculations are on $$24^3 \times 64$$ and $$32^3 \times 64$$ lattices with several valance and sea quark masses. The 2+1-flavor configurations are from the RBC/UKQCD collaboration.

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NPR of bilinear operators with improved staggered quarks
Jangho Kim, Jongjeong Kim, Weonjong Lee, Stephen Sharpe, Boram Yoon
Wed, 09:10, Seminar Room C -- Parallels 5C (Slides)

Matching introduces a significant systematic uncertainty in the lattice calculation of quark mass, and $$B_K$$ with improved staggered fermions. We present matching factors for the bilinear operators obtained using the non-perturbative renormalization method (NPR) for improved staggered fermions on the MILC asqtad lattices. We obtain the wave function renormalization factor from the conserved vector current. We also study the operator mixing. Preliminary results of bilinear matching are reported.

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Nonperturbative tests of the renormalisation of mixed clover-staggered currents in lattice QCD
Bipasha Chakraborty, Christine Davies, Gordon Donald, Rachel Dowdall, Jonna Koponen, G. Peter Lepage
Wed, 09:30, Seminar Room C -- Parallels 5C (Slides)

The Fermilab Lattice and MILC collaborations have shown in one-loop lattice QCD perturbation theory that the renormalisation constants of vector and axial-vector mixed Clover-Asqtad currents are closely related to the product of those for Clover-Clover and Asqtad-Asqtad (local) vector currents. To be useful for future higher precision calculations this relationship must be valid beyond one-loop. We test its validity nonperturbatively by using the temporal-axial and local vector currents made of Clover strange quarks, Highly Improved Staggered (HISQ) strange quarks and mixed Clover-HISQ strange quarks. We utilise the fact that the HISQ temporal-axial current is absolutely normalised and that the local vector currents can be normalised at zero momentum transfer. We have used three full lattice QCD ensembles with widely differing lattice spacings generated by the MILC collaboration. We find that the renormalisation of the mixed current differs from the square root of the product of the pure HISQ and pure clover currents by 2-3 %. This is small but nevertheless outside existing Fermilab/MILC error bars for this quantity. We also compare Clover, HISQ and mixed Clover-HISQ quark actions by comparing their approach to the continuum limit for the properties of the Phi meson.

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Perturbatively improving renormalization constants
Holger Perlt, Martha Constantinou, Marios Costa, Meinulf Goeckeler, Roger Horsley, Haralambos Panagopoulos, P.E.L. Rakow, Gerrit Schierholz, Arwed Schiller
Wed, 09:50, Seminar Room C -- Parallels 5C (Slides)

The determination of renormalization factors is of crucial importance in lattice QCD. They relate the observables obtained on the lattice to their measured counterparts in the continuum in a suitable renormalization scheme. Therefore, they have to be computed as precisely as possible. A widely used approach is the nonperturbative Rome-Southampton method. It requires, however, a careful treatment of lattice artifacts. We investigate a method to suppress these artifacts by subtracting one-loop contributions to renormalization factors calculated in lattice perturbation theory. We compare results obtained from a complete one-loop subtraction with those calculated for a subtraction of contributions proportional to the square of the lattice spacing.

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Determination of $$c_A$$ in three-flavour lattice QCD with Wilson fermions and tree-level improved gauge action
Christian Wittemeier, John Bulava, Michele Della Morte, Jochen Heitger
Wed, 10:10, Seminar Room C -- Parallels 5C (Slides)

We report on an ongoing non-perturbative determination of the improvement coefficient of the axial current, $$c_A$$, with three flavours of dynamical O(a) improved Wilson quarks and tree-level Symanzik improved gauge action. Our computations are based on simulations with the openQCD code. The improvement condition for a range of couplings is formulated with Schrödinger functional boundary conditions and imposed along a line of constant physics in parameter space. Our analysis involves correlation functions with boundary wave functions such that a large sensitivity to $$c_A$$ can be reached by exploiting the PCAC relation with two different pseudoscalar states.

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A determination of the average up-down, strange and charm quark masses at $$N_f=2+1+1$$
Paolo Lami, for the ETM Collaboration
Fri, 14:00, Seminar Room C -- Parallels 9C (Slides)

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 0.06 fm, and with pion masses as small as 230MeV.

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A $$N_f = 2 + 1 + 1$$ “twisted” determination of the b quark mass
Eleonora Picca, for the ETM Collaboration
Fri, 14:20, Seminar Room C -- Parallels 9C (Slides)

I present a preliminary lattice QCD determination of the b quark mass performed with $$N_f = 2 + 1 + 1$$ twisted mass Wilson fermions. Simulations at three values of the lattice spacing and with light quark masses corresponding to $$M_\pi \approx 230$$ MeV have been performed, and the results are extrapolated to the continuum limit. The two point correlation functions used in the analysis are calculated with an optimized smearing technique. An interpolation in the heavy quark mass between the charm region and the infinite mass limit has been performed using suitable ratios with known static limit (the so called ratio method).

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Pseudoscalar decay constants $$f_K/f_\pi$$, $$f_D$$ and $$f_{D_s}$$ with $$N_f = 2 + 1 + 1$$ ETMC congurations
Lorenzo Riggio, for the ETM Collaboration
Fri, 14:40, Seminar Room C -- Parallels 9C (Slides)

We present a Lattice QCD calculation of the pseudoscalar decay constants $$f_\pi$$, $$f_K$$, $$f_D$$ and $$f_{D_s}$$ performed with $$N_f = 2+1+1$$ dynamical fermions by the European Twisted Mass Collaboration. We simulated at three di fferent lattice spacings, the smallest being apporximately 0,06 fm, and with pion masses down to 230 MeV.

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Chiral behaviour of the pion decay constant in $$N_f=2$$ QCD
Stefano Lottini
Fri, 15:00, Seminar Room C -- Parallels 9C (Slides)

As increased statistics and new ensembles with light pions have become available within the CLS effort, we complete previous work by inspecting the chiral behaviour of the pion decay constant. We discuss the validity of Chiral Perturbation Theory (ChPT) and examine the results concerning the kaon decay constant, the ratio $$f_K/f_\pi$$, and the ensuing lattice spacing determination; along the way, the relevant low-energy constants of SU(2) ChPT are estimated. All simulations were performed with two dynamical flavours of nonperturbatively O(a)-improved Wilson fermions, on volumes with $$m_\pi L \geq 4$$, pion masses $$\geq$$ 192 MeV and lattice spacings down to 0.047 fm. The careful error analysis takes into account the effect of slow modes in the autocorrelations.

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The chromomagnetic operator on the lattice
Haralambos (Haris) Panagopoulos, Martha Constantinou, Marios Costa, Roberto Frezzotti, Vittorio Lubicz, Guido Martinelli, Davide Meloni, Silvano Simula
Fri, 15:20, Seminar Room C -- Parallels 9C (Slides)

We study matrix elements of the "chromomagnetic" operator on the lattice. This operator is contained in the strangeness-changing effective Hamiltonian which describes electroweak effects in the Standard Model and beyond. Having dimension 5, the chromomagnetic operator is characterized by a rich pattern of mixing with other operators of equal and lower dimensionality, including also non gauge invariant quantities; it is thus quite a challenge to extract from lattice simulations a clear signal for the hadronic matrix elements of this operator. We compute all relevant mixing coefficients to one loop in lattice perturbation theory; this necessitates calculating both 2-point (quark-antiquark) and 3-point (gluon-quark-antiquark) Green's functions at nonzero quark masses. We use the twisted mass lattice formulation, with Symanzik improved gluon action.

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Renormalization of HQET $$\Delta B=2$$ operators: O($$a$$) improvement and $$1/m$$ matching with QCD
Mauro Lucio Papinutto, Anastassios Vladikas, Carlos Pena, Gregorio Herdoiza
Fri, 15:40, Seminar Room C -- Parallels 9C (Slides)

We determine a basis of dimension 7 operators which arise at O(a) in the Symanzik expansion of the DB=2 operators with static heavy quarks. Light quarks are either Wilson (including fully twisted mass) or Ginsparg-Wilson. In both these regularizations we have the same number of closely related O(a) counterterms. Only a subset of these operators has previously appeared in the literature. The O(1/m) operators contributing beyond the static approximation are also discussed.

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Perturbative renormalization of staggered fermion operators with stout improvement: Application to the magnetic susceptibility of QCD
Marios Costa, Gunnar S. Bali, Falk Bruckmann, Martha Constantinou, Gergely Endrodi, Sandor Katz, Haralambos (Haris) Panagopoulos, Andreas Schaefer
Poster Session

We calculate the fermion propagator and the quark-antiquark Green's functions for a complete set of ultralocal fermion bilinears using perturbation theory up to one-loop and to lowest order in the lattice spacing. We employed the staggered action for fermions and the Symanzik improved action for gluons. From our calculations we determine the renormalization factors for the quark field and for all ultralocal taste-singlet bilinear operators. The novel aspect of our calculations is that the gluon links which appear both in the fermion action and in the definition of the bilinears have been improved by applying a stout smearing procedure up to 2 times, iteratively. The renormalization functions are presented in the RI' scheme; the dependence on all stout parameters, as well as on the coupling constant, the number of colors, the lattice spacing, the gauge fixing parameter and the renormalization scale, is shown explicitly. We apply our results to a nonperturbative study of the magnetic susceptibility of QCD at zero and finite temperature.

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Quantifying Discretization Errors for the Gluon and Ghost Propagators using Stochastic Perturbation Theory
Jakob Simeth, Andre Sternbeck
Poster Session

The subtraction of hypercubic lattice corrections, calculated at 1-loop order in lattice perturbation theory (LPT), is common practice, e.g., for determinations of renormalization constants in lattice hadron physics. Providing such corrections beyond 1-loop order is however very demanding in LPT, and numerical stochastic perturbation theory (NSPT) might be the better candidate for this. Here we report on a first feasibility check of this method and provide the lattice corrections up to 3-loop order for the SU(3) gluon and ghost propagators in Landau gauge in an parametrization for arbitrary values of the lattice coupling. These propagators are ideal for this check as they are available from lattice calculations to high precision and can be combined to a renormalization group invariant product (Minimal MOM coupling) for which it has been seen that the corresponding 1-loop LPT corrections are insufficient to remove the bulk of the hypercubic lattice artifacts from the data.

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The Kaon Bag Parameter at Physical Mass
Julien Frison
Poster Session

We present preliminary results for the calculation of the Kaon Bag parameter $$B_K$$ in $$N_f=2+1$$ lattice QCD, using Möbius Domain Wall Fermion ensembles generated by the RBC-UKQCD collaboration. This computation is done directly at physical pion mass, so that we do not have to rely on chiral perturbation theory or any other mass extrapolation. In parallel, the four-quark operator is renormalised through the Rome-Southampton technique. Finally, we compare our value with previous results and draw some conclusions about the remaining dominant contributions in our error budget.

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Critical slowing down and the gradient flow coupling in the Schroedinger functional
Felix Stollenwerk
Poster Session

We study the sensitivity of the gradient flow coupling to sectors of different topological charge and its implications in practical situations. Furthermore, we investigate an alternative definition of the running coupling that is expected to be less sensitive to the inability of the HMC algorithm to sample all topological sectors.

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