Fragmentation in a Positive Light

The organizers of the present symposium demonstrated a keen sense of topicality when they chose Diversity or Cacophony? New Sources of Norms in International Law? as the subject-matter of the 25th Anniversary Symposium of the Michigan Journal of International Law. For the last decade or so, the question whether the international legal order finds itself in the process of fragmentation, and if so, what the consequences of this development will be, has been a popular area of study for many jurists; most of them expressing their concern about what they consider to constitute a threat to the unity of international law-a unity which they believe to have existed or to still exist, or towards which, in their view, both the law-maker and the practitioner/judge ought at least to strive

Tribute to Eric Stein

My first encounter with Eric dates back forty years. In 1971 he taught a course at the Hague Academy of International Law. At that time, I was an assistant lecturer at the University of Innsbruck, had just submitted my Habilitationsschrift to the Law Faculty there, and, while waiting for my venia legendi to come forward, I wanted to spend a few weeks at what was-and probably still is-the most exciting place for young international law scholars to get together with hundreds of like-minded individuals and some of the most inspiring teachers worldwide. Eric certainly lived up to my expectation of what a leading American law professor would be like: His lectures were sharp and challenging, as was the entire man. I remember him as prim in his appearance, crystal clear in the presentation of his subject, but what I also remember (and what in retrospect, having known Eric and his gentle, Old Worldish manners for decades, I find surprising) is that in the afternoon seminars accompanying his lectures he struck me as extremely tough in his attempt to employ what I later got to know as the Socratic method vis-ii-vis an international student population more used to looking up in awe at the great figures in the field and not daring to say a word. Well, I did not let myself be intimidated; I took the floor a couple of times and must at least have made the impression of not being too shy to survive intellectual slugouts at U.S. law schools, because at the end of one session Eric called me to the podium, inquired who I was and where I came from, and then invited me to apply for admission to the LL.M. program at Michigan. I intended to follow this up after completing my Habilitation procedure, but immediately after I had done so I was offered the Chair of International Law at the University of Munich, and so I wrote to Eric begging him to understand my career choice, which he generously did

Fragmentation in a Positive Light

The organizers of the present symposium demonstrated a keen sense of topicality when they chose Diversity or Cacophony? New Sources of Norms in International Law? as the subject-matter of the 25th Anniversary Symposium of the Michigan Journal of International Law. For the last decade or so, the question whether the international legal order finds itself in the process of fragmentation, and if so, what the consequences of this development will be, has been a popular area of study for many jurists; most of them expressing their concern about what they consider to constitute a threat to the unity of international law-a unity which they believe to have existed or to still exist, or towards which, in their view, both the law-maker and the practitioner/judge ought at least to strive

Tribute to Eric Stein

My first encounter with Eric dates back forty years. In 1971 he taught a course at the Hague Academy of International Law. At that time, I was an assistant lecturer at the University of Innsbruck, had just submitted my Habilitationsschrift to the Law Faculty there, and, while waiting for my venia legendi to come forward, I wanted to spend a few weeks at what was-and probably still is-the most exciting place for young international law scholars to get together with hundreds of like-minded individuals and some of the most inspiring teachers worldwide. Eric certainly lived up to my expectation of what a leading American law professor would be like: His lectures were sharp and challenging, as was the entire man. I remember him as prim in his appearance, crystal clear in the presentation of his subject, but what I also remember (and what in retrospect, having known Eric and his gentle, Old Worldish manners for decades, I find surprising) is that in the afternoon seminars accompanying his lectures he struck me as extremely tough in his attempt to employ what I later got to know as the Socratic method vis-ii-vis an international student population more used to looking up in awe at the great figures in the field and not daring to say a word. Well, I did not let myself be intimidated; I took the floor a couple of times and must at least have made the impression of not being too shy to survive intellectual slugouts at U.S. law schools, because at the end of one session Eric called me to the podium, inquired who I was and where I came from, and then invited me to apply for admission to the LL.M. program at Michigan. I intended to follow this up after completing my Habilitation procedure, but immediately after I had done so I was offered the Chair of International Law at the University of Munich, and so I wrote to Eric begging him to understand my career choice, which he generously did

The Λ\Lambda-parameter in 3-flavour QCD and αs(mZ)\alpha_s(m_Z) by the ALPHA collaboration

We 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.Comment: 21 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 fixe

The determination of αs\alpha_s by the ALPHA collaboration

We review the ALPHA collaboration strategy for obtaining the QCD coupling at high scale. In the three-flavor effective theory it avoids the use of perturbation theory at $\alpha > 0.2$ and at the same time has the physical scales small compared to the cutoff $1/a$ in all stages of the computation. The result \Lambda_\overline{MS}^{(3)}=332(14)~MeV is translated to \alpha_\overline{MS}(m_Z)=0.1179(10)(2) by use of (high order) perturbative relations between the effective theory couplings at the charm and beauty quark "thresholds". The error of this perturbative step is discussed and estimated as $0.0002$.Comment: 7 pages, proceedings of FPCapri2016 conferenc

The strong coupling from a nonperturbative determination of the Λ\Lambda parameter in three-flavor QCD

We present a lattice determination of the $\Lambda$ parameter in three-flavor QCD and the strong coupling at the Z pole mass. Computing the nonperturbative running of the coupling in the range from $0.2\,$GeV to $70\,$GeV, and using experimental input values for the masses and decay constants of the pion and the kaon, we obtain $\Lambda_{\overline{\rm MS}}^{(3)}=341(12)\,$MeV. The nonperturbative running up to very high energies guarantees that systematic effects associated with perturbation theory are well under control. Using the four-loop prediction for $\Lambda_{\overline{\rm MS}}^{(5)}/\Lambda_{\overline{\rm MS}}^{(3)}$ yields $\alpha^{(5)}_{\overline{\rm MS}}(m_{\rm Z}) = 0.11852(84)$.Comment: Correction in the comparison to the LHC value for alpha(1.5TeV) which was given by CMS in the 5-flavor theory. The agreement is improved. Also 1 Reference added and a few typos correcte