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Marco Frasca
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We derive a low-energy quantum field theory from quantum chromodynamics (QCD) that holds in the limit of a very large coupling. All the parameters of the bare theory are fixed through QCD. Low-energy limit is obtained through a mapping theorem between massless quartic scalar field theory and Yang-Mills theory. One gets a Yukawa theory that, in the same limit of strong coupling, reduces to a Nambu-Jona-Lasinio model with a current-current coupling with scalar-like excitations arising from Yang-Mills degrees of freedom. A current-current expansion in the strong coupling limit yields a fully integrated generating functional that, neglecting quark-quark current coupling, describes all processes involving glue excitations and quark. Some processes are analyzed and we are able to show consistency of Narison-Veneziano sum rules. Width of the $sigma$ resonance is computed. The decay $etatoeta+pi^++pi^-$ is discussed in this approximation and analyzed through the more elementary processes $etatoeta+sigma$ and $sigmatopi^++pi^-$. In this way we get an estimation of the mass of the $sigma$ resonance and the value of the $eta$ decay constant. This $eta$ decay appears a possible source of study for the $sigma$ resonance.
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Low-energy limit of quantum chromodynamics (QCD) is obtained using a mapping theorem recently proved. This theorem states that, classically, solutions of a massless quartic scalar field theory are approximate solutions of Yang-Mills equations in the limit of the gauge coupling going to infinity. Low-energy QCD is described by a Yukawa theory further reducible to a Nambu-Jona-Lasinio model. At the leading order one can compute glue-quark interactions and one is able to calculate the properties of the $sigma$ and $eta-eta$ mesons. Finally, it is seen that all the physics of strong interactions, both in the infrared and ultraviolet limit, is described by a single constant $Lambda$ arising in the ultraviolet by dimensional transmutation and in the infrared as an integration constant.
Building upon the PDFSense framework developed in Ref. [1], we perform a comprehensive analysis of the sensitivity of present and future high-energy data to a number of quantities commonly evaluated in lattice gauge theory, with a particular focus on the integrated Mellin moments of nucleon parton distribution functions (PDFs), such as $langle x rangle_{u^+ - d^+}$ and $langle x rangle_{g}$, as well as $x$-dependent quark quasi-distributions -- in particular, that of the isovector combination. Our results demonstrate the potential for lattice calculations and phenomenological quark distributions informed by high-energy experimental data to cooperatively improve the picture of the nucleons collinear structure. This will increasingly be the case as computational resources for lattice calculations further expand, and QCD global analyses continue to grow in sophistication. Our sensitivity analysis suggests that a future lepton-hadron collider would be especially instrumental in providing phenomenological constraints to lattice observables.
The Dual QCD (DQCD) framework, based on the ideas of t Hooft and Witten, and developed by Bill Bardeen, Jean-Marc Gerard and myself in the 1980s is not QCD, a theory of quarks and gluons, but a successful low energy approximation of it when applied to $Ktopipi$ decays and $K^0-bar K^0$ mixing. After years of silence, starting with 2014, this framework has been further developed in order to improve the SM prediction for the ratio $epsilon/epsilon$, the $Delta I=1/2$ rule and $hat B_K$. Most importantly, this year it has been used for the calculation of all $Ktopipi$ hadronic matrix elements of BSM operators which opened the road for the general study of $epsilon/epsilon$ in the context of the SM effective theory (SMEFT). This talk summarizes briefly the past successes of this framework and discusses recent developments which lead to a master formula for $epsilon/epsilon$ valid in any extension of the SM. This formula should facilitate the search for new physics responsible for the $epsilon/epsilon$ anomaly hinted by 2015 results from lattice QCD and DQCD.
Correlations between the QCD coupling alpha_s, the gluon condensate < alpha_s G^2 >, and the c,b-quark running masses m_c,b in the MS-scheme are explicitly studied (for the first time) from the (axial-)vector and (pseudo)scalar charmonium and bottomium ratios of Laplace sum rules (LSR) evaluated at the mu-subtraction stability point where PT @N2LO, N3LO and < alpha_s G^2> @NLO corrections are included. Our results clarify the (apparent) discrepancies between different estimates of < alpha_s G^2> from J/psi sum rule but also shows the sensitivity of the sum rules on the choice of the mu-subtraction scale which does not permit a high-precision estimate of m_c,b. We obtain from the (axial-)vector [resp. (pseudo)scalar] channels <alpha_s G^2>=(8.5+- 3.0)> [resp. (6.34+-.39)] 10^-2 GeV^4, m_c(m_c)= 1256(30) [resp. 1266(16)] MeV and m_b(m_b)=4192(15) MeV. Combined with our recent determinations from vector channel, one obtains the average: m_c(m_c)= 1263(14) MeV and m_b(m_b) 4184(11) MeV. Adding our value of the gluon condensate with different previous estimates, we obtain the new sum rule average: <alpha_s G^2>=(6.35+- 0.35) 10^-2 GeV^4. The mass-splittings M_chi_0c(0b)-M_eta_c(b) give @N2LO: alpha_s(M_Z)=0.1183(19)(3) in good agreement with the world average (see more detailed discussions in the section: addendum). .
We calculate BSM hadronic matrix elements for $K^0-bar K^0$ mixing in the Dual QCD approach (DQCD). The ETM, SWME and RBC-UKQCD lattice collaborations find the matrix elements of the BSM density-density operators $mathcal{O}_i$ with $i=2-5$ to be rather different from their vacuum insertion values (VIA) with $B_2approx 0.5$, $B_3approx B_5approx 0.7$ and $B_4approx 0.9$ at $mu=3~GeV$ to be compared with $B_i=1$ in the VIA. We demonstrate that this pattern can be reconstructed within the DQCD through the non-perturbative meson evolution from very low scales, where factorization of matrix elements is valid, to scales of order $(1~GeV)$ with subsequent perturbative quark-gluon evolution to $mu=3~GeV$. This turns out to be possible in spite of a very different pattern displayed at low scales with $B_2=1.2$, $B_3=3.0$, $B_4=1.0$ and $B_5approx 0.2$ in the large $N$ limit, $N$ being the number of colours. Our results imply that the inclusion of meson evolution in the phenomenology of any non-leptonic transition like $K^0-bar K^0$ mixing and $Ktopipi$ decays is mandatory. While meson evolution, as demonstrated in our paper, is hidden in LQCD results, to our knowledge DQCD is the only analytic approach for non-leptonic transitions and decays which takes this important QCD dynamics into account.
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