002242539 001__ 2242539
002242539 005__ 20230811061935.0
002242539 0247_ $$2DOI$$a10.22323/1.256.0197
002242539 0248_ $$aoai:cds.cern.ch:2242539$$pcerncds:FULLTEXT$$pcerncds:CERN:FULLTEXT$$pcerncds:CERN
002242539 035__ $$9arXiv$$aoai:arXiv.org:1701.03075
002242539 035__ $$9Inspire$$aoai:inspirehep.net:1508616$$d2023-08-10T06:47:18Z$$h2023-08-11T02:25:51Z$$mmarcxml$$ttrue$$uhttps://inspirehep.net/api/oai2d
002242539 035__ $$9Inspire$$a1508616
002242539 037__ $$9arXiv$$aarXiv:1701.03075$$chep-lat
002242539 037__ $$aCERN-TH-2016-262
002242539 037__ $$aDESY-17-007
002242539 041__ $$aeng
002242539 084__ $$2CERN Library$$aTH-2016-262
002242539 100__ $$aBruno, M.$$uBrookhaven
002242539 245__ $$9arXiv$$aThe $\Lambda$-parameter in 3-flavour QCD and $\alpha_s(m_Z)$ by the ALPHA collaboration
002242539 246__ $$9arXiv$$aThe $\Lambda$-parameter in 3-flavour QCD and $\alpha_s(m_Z)$ by the ALPHA collaboration
002242539 269__ $$c2017-01-11
002242539 260__ $$bSISSA$$c2016-12-23
002242539 300__ $$a21 p
002242539 500__ $$9arXiv$$a21 pages. Collects contributions of A. Ramos, S. Sint and R. Sommer to the 34th annual International Symposium on Lattice Field Theory; LaTeX input encoding problem fixed
002242539 520__ $$9arXiv$$aWe present results by the ALPHA collaboration for the $\Lambda$-parameter in 3-flavour QCD and the strong coupling constant at the electroweak scale, $\alpha_s(m_Z)$, in terms of hadronic quantities computed on the CLS gauge configurations. The first part of this proceedings contribution contains a review of published material \cite{Brida:2016flw,DallaBrida:2016kgh} and yields the $\Lambda$-parameter in units of a low energy scale, $1/L_{\rm had}$. We then discuss how to determine this scale in physical units from experimental data for the pion and kaon decay constants. We obtain $\Lambda_{\overline{\rm MS}}^{(3)} = 332(14)$ MeV which translates to $\alpha_s(M_Z)=0.1179(10)(2)$ using perturbation theory to match between 3-, 4- and 5-flavour QCD.
002242539 540__ $$barXiv$$uhttp://creativecommons.org/licenses/by-nc-sa/4.0/
002242539 540__ $$3Preprint$$aCC-BY-4.0
002242539 542__ $$3Preprint$$dCERN$$g2016
002242539 595__ $$aCERN-TH
002242539 65017 $$2arXiv$$ahep-ph
002242539 65017 $$2SzGeCERN$$aParticle Physics - Phenomenology
002242539 65017 $$2arXiv$$ahep-lat
002242539 65017 $$2SzGeCERN$$aParticle Physics - Lattice
002242539 690C_ $$aCERN
002242539 695__ $$2INSPIRE$$9bibclassify$$ascale: electroweak interaction
002242539 695__ $$2INSPIRE$$9bibclassify$$aK: decay
002242539 695__ $$2INSPIRE$$9bibclassify$$aquantum chromodynamics
002242539 695__ $$2INSPIRE$$9bibclassify$$aflavor
002242539 695__ $$2INSPIRE$$9bibclassify$$aALPHA
002242539 695__ $$2INSPIRE$$9bibclassify$$aperturbation theory
002242539 695__ $$2INSPIRE$$9bibclassify$$acoupling constant
002242539 695__ $$2INSPIRE$$9bibclassify$$astrong coupling
002242539 700__ $$aDalla Brida, M.$$iINSPIRE-00389600$$jORCID:0000-0001-7583-4067$$uINFN, Milan Bicocca$$uNIC, Zeuthen$$uMilan Bicocca U.$$uDESY, Zeuthen$$vDeutsches Elektronen-Synchrotron
002242539 700__ $$aFritzsch, [email protected]$$uCERN$$uMadrid, IFT
002242539 700__ $$aKorzec, T.$$uBergische U., Wuppertal (main)
002242539 700__ $$aRamos, A.$$uCERN$$vCERN
002242539 700__ $$aSchaefer, S.$$uNIC, Zeuthen$$uDESY, Zeuthen$$vDeutsches Elektronen-Synchrotron
002242539 700__ $$aSimma, H.$$uNIC, Zeuthen$$uDESY, Zeuthen$$vDeutsches Elektronen-Synchrotron
002242539 700__ $$aSint, S.$$uTrinity Coll., Dublin
002242539 700__ $$aSommer, R.$$iINSPIRE-00127745$$uNIC, Zeuthen$$uHumboldt U., Berlin$$uDESY, Zeuthen$$vDeutsches Elektronen-Synchrotron
002242539 773__ $$c197$$pPoS$$vLATTICE2016$$xPoS(LATTICE2016)197$$y2016
002242539 8564_ $$81271831$$s550941$$uhttps://cds.cern.ch/record/2242539/files/arXiv:1701.03075.pdf
002242539 8564_ $$81271830$$s11317$$uhttps://cds.cern.ch/record/2242539/files/lmaxt0p.png$$y00007 Preliminary continuum extrapolation of $({t_0^*})^{-1/2}\lmax$. The large volume simulation with the smallest lattice spacing is unfinished and the correction to shift it to the $\Phi_4=1.11$ point has not yet been included. It is only shown to illustrate where we are heading to. Extrapolations with 4,3 and 2 data points are shown together with a range for the continuum value covering all of them, see the text.
002242539 8564_ $$81271832$$s10763$$uhttps://cds.cern.ch/record/2242539/files/cont_lim.png$$y00000 Continuum extrapolation of the step scaling function. The leftmost points are the continuum values, whereas the stars are obtained from perturbative scale evolution using the 3-loop $\beta$-function.
002242539 8564_ $$81271833$$s26037$$uhttps://cds.cern.ch/record/2242539/files/sigma_a4.png$$y00003 Continuum extrapolation of the step scaling function at the 9 target values of the coupling using as weights for the fit the uncertainty in $\Sigma$ and the systematic estimate of the ${\rm O}(a^4)$ effects.
002242539 8564_ $$81271834$$s8896$$uhttps://cds.cern.ch/record/2242539/files/Lambda-vs-alphasq-v6.png$$y00001 The extraction of the $\Lambda$-parameter using perturbation theory at different values of $\alpha$, plotted vs. $\alpha^2(1/L_n)$. The data points are, from top to bottom, for $\nu=-0.5,0,0.3$ and, from right to left, for $n=0,1,\ldots,5$ steps by a factor 2 in scale.
002242539 8564_ $$81271835$$s18977$$uhttps://cds.cern.ch/record/2242539/files/beta_all.png$$y00004 The non-perturbative $\beta$-functions in the SF-scheme from \cite{Brida:2016flw} and in the GF-scheme~\cite{DallaBrida:2016kgh}. The plotted 1,2-loop universal part of the perturbative expansion can be compared directly, but higher orders of the perturbative series are unknown for our finite volume GF-scheme. We give an impression of the typical magnitude of higher order perturbative terms in the form of the $\overline{\rm MS}$ scheme, for which we show curves up to 5-loops. On the other hand the 3-loop term is known for the SF scheme.
002242539 8564_ $$81271836$$s10211$$uhttps://cds.cern.ch/record/2242539/files/Lsw.png$$y00005 Continuum extrapolation of $\bar \gbar^2_{\rm GF}(2L_0)$ with the bare parameters determined by the condition $\bar g_{\rm SF}^2(L_0) = 2.012$. The continuum extrapolation is performed using both the Wilson flow/Clover discretization and our preferred setup Zeuthen flow/LW observable (the latter shows smaller discretization effects). The two types of error bars for each data point correspond to the inclusion or not of the propagated error for the SF coupling, cf.~text.
002242539 8564_ $$81271837$$s25570$$uhttps://cds.cern.ch/record/2242539/files/sigma.png$$y00002 Continuum extrapolation of the step scaling function at the 9 target values of the coupling using as weights for the fit the uncertainty in $\Sigma$. Note that different continuum extrapolations are systematically different.
002242539 8564_ $$81271838$$s1671$$uhttps://cds.cern.ch/record/2242539/files/ratio-fpik.png$$y00006 Chiral extrapolation of $f_{\pi K}$. In the horizontal axis we plot $\phi_2=8t_0m_\pi^2$, and we normalize the data with respect to the symmetric point. The data has been shifted to constant $\phi_4=1.11$.
002242539 8564_ $$81302621$$s628305$$uhttps://cds.cern.ch/record/2242539/files/PoS(LATTICE2016)197.pdf$$yFulltext
002242539 960__ $$a13
002242539 962__ $$b2228531$$k197$$nsouthampton20160724
002242539 980__ $$aArticle
002242539 980__ $$aConferencePaper
002242539 980__ $$aARTICLE