Jet observables at hadron colliders feature “super-leading” logarithms, double-logarithmic corrections resulting from a breakdown of color coherence due to complex phases in hard-scattering amplitudes. While these effects only arise in high orders of perturbation theory and are suppressed in the large- limit, they formally constitute leading logarithmic corrections to the cross sections. We present the first analysis of the corresponding contributions to a hadronic cross section, including all partonic channels and interference effects. Interestingly, some interference terms in partonic $$ q\overline{q} $$ → $$ q\overline{q} $$ scattering are only linearly suppressed in 1 . Our results for the → 2 jets gap-between-jets cross section demonstrate the numerical importance of super-leading logarithms for small values of the veto scale , showing that these contributions should be accounted for in precision studies of such observables.

Switzerland

Thomas Becher

Germany

Patrick Hager

Giuliano Martinelli

United States

Matthias Neubert

Dominik Schwienbacher

Michel Stillger

Super-leading logarithms in

A new strategy is presented for systematically treating super-leading logarithmic contributions including higher-order Glauber exchanges for non-global LHC observables in renormalization-group (RG) improved perturbation theory. This represents an important improvement over previous approaches, as it allows for the consistent inclusion of the scale dependence of the strong coupling, thereby providing more reliable estimates of the scale uncertainties in theoretical predictions. The key idea is to rearrange the relevant RG evolution operator in such a way that all double-logarithmic corrections are exponentiated from the outset. This forms the starting point for the first resummation of super-leading logarithms at leading order in RG-improved perturbation theory for arbitrary 2 → M scattering processes. Moreover, the asymptotic scaling of subleading logarithmic corrections from higher-order Glauber exchanges is determined, demonstrating their parametric suppression.

Philipp Böer

Xiaofeng Xu

Renormalization-group improved resummation of super-leading logarithms

The Glauber series for non-global jet observables at hadron colliders simultaneously includes the super-leading logarithms alongside an arbitrary number of Glauber phases. Building on the formalism of [1], it is shown that the leading terms in this series for large N  c  can be resummed in closed form in renormalization-group improved perturbation theory. This remarkable observation suggests that large-N  c  methods might also be helpful to study other aspects of non-global logarithms at hadron colliders, and to combine our analytic results with amplitude-level parton showers.

Resummation of Glauber phases in non-global LHC observables for large N  c

The resummation of the “Glauber series” in non-global LHC observables is extended to processes with gluons in the initial state. This series simultaneously incorporates large double-logarithmic corrections, the so-called “super-leading logarithms”, together with higher-order exchanges of pairs of Glauber gluons associated with the large numerical factor (iπ)2. On a technical level, the main part of this work is devoted to the systematic reduction of the appearing color traces and construction of basis structures, which consist of thirteen elements for gg and eleven elements for qg scattering. Numerical estimates for wide-angle gap-between-jet cross sections at the parton level show that, in particular for gg scattering at relatively small vetoes Q 0, the contribution involving four Glauber exchanges gives a sizeable correction and should not be neglected.

Glauber phases in non-global LHC observables: resummation for gluon-initiated processes

We present a systematic formalism based on a factorization theorem in soft-collinear effective theory to describe non-global observables at hadron colliders, such as gap-between-jets cross sections. The cross sections are factorized into convolutions of hard functions, capturing the dependence on the partonic center-of-mass energy   <math> <msqrt> <mover> <mi>s</mi> <mo>̂</mo> </mover> </msqrt> </math>  $$ \sqrt{\hat{s}} $$ , and low-energy matrix elements, which are sensitive to the low scale Q 0 ≪   <math> <msqrt> <mover> <mi>s</mi> <mo>̂</mo> </mover> </msqrt> </math>  $$ \sqrt{\hat{s}} $$  characteristic of the veto imposed on energetic emissions into the gap between the jets. The scale evolution of both objects is governed by a renormalization-group equation, which we derive at one-loop order. By solving the evolution equation for the hard functions for arbitrary 2 → M jet processes in the leading logarithmic approximation, we accomplish for the first time the all-order resummation of the so-called “super-leading logarithms” discovered in 2006, thereby solving an old problem of quantum field theory. We study the numerical size of the corresponding effects for different partonic scattering processes and explain why they are sizable for pp → 2 jets processes, but suppressed in H/Z and H/Z + jet production. The super-leading logarithms are given by an alternating series, whose individual terms can be much larger than the resummed result, even in very high orders of the loop expansion. Resummation is therefore essential to control these effects. We find that the asymptotic fall-off of the resummed series is much weaker than for standard Sudakov form factors.

China

Ding Shao

Factorization of non-global LHC observables and resummation of super-leading logarithms

It has been known for many years that jet cross sections at hadron colliders exhibit double-logarithmic corrections starting at four-loop order, arising from two soft Glauber-gluon interactions between the two colliding partons. The resummation of these “super-leading logarithms” has been achieved only recently by means of a renormalization-group treatment in soft-collinear effective theory. We generalize this result and, within the same framework and for quark-initiated processes, resum the double logarithms arising in the presence of an arbitrary number of Glauber-gluon exchanges. For typical choices of parameters, the higher-order Glauber terms give rise to corrections which are expected to be numerically of the same magnitude as the super-leading logarithms. However, we find that the Glauber series for jet cross sections is dominated by the two-Glauber contribution, if the colliding partons are quarks or anti-quarks.

Glauber phases in non-global LHC observables: resummation for quark-initiated processes

We present the first measurement of the Michel parameter <math><msup><mi>ξ</mi><mo>′</mo></msup></math> in the <math><msup><mi>τ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>μ</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>μ</mi></msub><msub><mi>ν</mi><mi>τ</mi></msub></math> decay using the full data sample of <math><mn>988</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> collected by the Belle detector operating at the KEKB asymmetric energy <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></math> collider. The method is based on the reconstruction of the <math><msup><mi>μ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>e</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>e</mi></msub><msub><mi>ν</mi><mi>μ</mi></msub></math> decay-in-flight in the Belle central drift chamber and relies on the correlation between muon spin and its daughter electron momentum. We study the main sources of the background that can imitate the signal decay, such as kaon and pion decays-in-flight and charged particle scattering on the detector material. Highly efficient methods of their suppression are developed and applied to select 165 signal-candidate events. We obtain <math><msup><mi>ξ</mi><mo>′</mo></msup><mo>=</mo><mrow><mn>0.22</mn><mo>±</mo><mn>0.94</mn><mo>±</mo><mn>0.42</mn></mrow></math> where the first uncertainty is statistical, and the second one is systematic. The result is in agreement with the Standard Model prediction of <math><msup><mi>ξ</mi><mo>′</mo></msup><mo>=</mo><mn>1</mn></math>.

D. Bodrov

P. Pakhlov

I. Adachi

H. Aihara

S. Al Said

D. M. Asner

H. Atmacan

T. Aushev

R. Ayad

V. Babu

Sw. Banerjee

P. Behera

K. Belous

J. Bennett

M. Bessner

B. Bhuyan

T. Bilka

D. Biswas

A. Bobrov

A. Bondar

J. Borah

A. Bozek

M. Bračko

P. Branchini

T. E. Browder

A. Budano

M. Campajola

D. Červenkov

M.C. Chang

B. G. Cheon

K. Chilikin

K. Cho

S.J. Cho

S.K. Choi

Y. Choi

S. Choudhury

D. Cinabro

S. Das

G. De Nardo

G. De Pietro

R. Dhamija

F. Di Capua

J. Dingfelder

Z. Doležal

T. V. Dong

D. Epifanov

T. Ferber

D. Ferlewicz

B. G. Fulsom

V. Gaur

A. Garmash

A. Giri

P. Goldenzweig

E. Graziani

D. Greenwald

T. Gu

Y. Guan

K. Gudkova

C. Hadjivasiliou

S. Halder

K. Hayasaka

H. Hayashii

M. T. Hedges

D. Herrmann

W.S. Hou

C.L. Hsu

T. Iijima

K. Inami

N. Ipsita

A. Ishikawa

R. Itoh

M. Iwasaki

W. W. Jacobs

E.J. Jang

Q. P. Ji

S. Jia

Y. Jin

K. K. Joo

D. Kalita

A. B. Kaliyar

K. H. Kang

T. Kawasaki

C. Kiesling

C. H. Kim

D. Y. Kim

K.H. Kim

Y.K. Kim

H. Kindo

K. Kinoshita

P. Kodyš

A. Korobov

S. Korpar

P. Križan

P. Krokovny

T. Kuhr

M. Kumar

R. Kumar

K. Kumara

Y.J. Kwon

J. S. Lange

Study of the muon decay-in-flight in the <math><msup><mi>τ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>μ</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>μ</mi></msub><msub><mi>ν</mi><mi>τ</mi></msub></math> decay to measure the Michel parameter <math><msup><mi>ξ</mi><mo>′</mo></msup></math>

We report the first measurement of the Michel parameter <math><msup><mi>ξ</mi><mo>′</mo></msup></math> in the <math><mrow><msup><mrow><mi>τ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>μ</mi></mrow></msub><msub><mrow><mi>ν</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math> decay with a new method proposed just recently. The measurement is based on the reconstruction of the <math><msup><mi>τ</mi><mo>−</mo></msup><mo>→</mo><msup><mi>μ</mi><mo>−</mo></msup><msub><mover><mi>ν</mi><mo>¯</mo></mover><mi>μ</mi></msub><msub><mi>ν</mi><mi>τ</mi></msub></math> events with subsequent muon decay in flight in the Belle central drift chamber. The analyzed data sample of <math><mn>988</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> collected by the Belle detector corresponds to approximately <math><mrow><mn>912</mn><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>6</mn></mrow></msup></mrow></math> <math><msup><mi>τ</mi><mo>+</mo></msup><msup><mi>τ</mi><mo>−</mo></msup></math> pairs. We measure <math><mrow><msup><mrow><mi>ξ</mi></mrow><mrow><mo>′</mo></mrow></msup><mo>=</mo><mn>0.22</mn><mo>±</mo><mn>0.94</mn><mo>(</mo><mrow><mi>stat</mi></mrow><mo>)</mo><mo>±</mo><mn>0.42</mn><mo>(</mo><mrow><mi>syst</mi></mrow><mo>)</mo></mrow></math>, which is in agreement with the standard model prediction of <math><msup><mi>ξ</mi><mo>′</mo></msup><mo>=</mo><mn>1</mn></math>. Statistical uncertainty dominates in this study, being a limiting factor, while systematic uncertainty is well under control. Our analysis proved the practicability of this promising method and its prospects for further precise measurement in future experiments.

H. E. Cho

S. C. Lee

First Measurement of the Michel Parameter <math><mrow><msup><mrow><mi>ξ</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> in the <math><mrow><msup><mrow><mi>τ</mi></mrow><mrow><mo>−</mo></mrow></msup><mo>→</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo></mrow></msup><msub><mrow><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>μ</mi></mrow></msub><msub><mrow><mi>ν</mi></mrow><mrow><mi>τ</mi></mrow></msub></mrow></math> Decay at Belle

We analyse the effects of Dirac and Majorana neutrinos on leptonic decays of muon and tau leptons using the most general four-lepton effective interaction Hamiltonian of dimension six. We calculate the specific energy and angular distribution of the final charged lepton, including the polarizations of the initial and final charged leptons. We discuss the new generalized Michel parameters and focus on the effects of the heavy neutrino masses that would lead to sizable contributions on scenarios where the new sterile neutrinos have non-negligible mixing. Specifically, the most promising scenario is found for the case of τ decay with one heavy final-state neutrino with a mass around 102 − 103 MeV, where the linear term suppression could be of order 10 −4, low enough to be measured in current and forthcoming experiments.

Mexico

Juan Márquez

Gabriel Castro

Pablo Roig

Michel parameters in the presence of massive Dirac and Majorana neutrinos

This paper provides a detailed description of the method for the first direct measurement of all Michel parameters in the τ  −  → μ  −    <math> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\nu} $$   μ  ν  τ  decay related to the polarization of the daughter muon. An application of the suggested method in the existing and future experiments at e + e  −  colliders is considered. We have performed a feasibility study for the future Super Charm-Tau Factory and Belle II experiments. For the first one, the sensitivity to the Michel parameters ξ′, ξ′′, η′′, α′/A, and β′/A is estimated. For the latter, only one Michel parameter, ξ′, for which the sensitivity is maximum, is considered.

Russia

A new method for the measurement of the Michel parameters that describe the daughter muon polarization in the τ  −  → μ  −    <math> <mover> <mi>ν</mi> <mo>¯</mo> </mover> </math>  $$ \overline{\nu} $$   μ  ν  τ  decay