<p>An accurate calculation of the leading-order hadronic vacuum polarization (LOHVP) contribution to the anomalous magnetic moment of the muon (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math>) is key to determining whether a discrepancy, suggesting new physics, exists between the Standard Model and experimental results. This calculation can be expressed as an integral over Euclidean time of a current-current correlator <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> can be calculated using lattice QCD or, with dispersion relations, from experimental data for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><mtext>hadrons</mtext></math>. The BMW/DMZ collaboration recently presented a hybrid approach in which <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>G</mi><mo stretchy="false">(</mo><mi>t</mi><mo stretchy="false">)</mo></math> is calculated using lattice QCD for most of the contributing <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math> range, but using experimental data for the largest <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi></math> (lowest energy) region. Here we study the advantages of varying the position <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>t</mi><mo>=</mo><msub><mi>t</mi><mn>1</mn></msub></math> separating lattice QCD from data-driven contributions. The total LOHVP contribution should be independent of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>t</mi><mn>1</mn></msub></math>, providing both a test of the experimental input and the robustness of the hybrid approach. We use this criterion and a correlated fit to show that Fermilab/HPQCD/MILC lattice QCD results from 2019 strongly favor the CMD-3 cross section data for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo stretchy="false">→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> over a combination of earlier experimental results for this channel. Further, the resulting total LOHVP contribution obtained is consistent with the result obtained by BMW/DMZ, and supports the scenario in which there is no significant discrepancy between the experimental value for <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mi>μ</mi></msub></math> and that expected in the Standard Model. We then discuss how improved lattice results in this hybrid approach could provide a more accurate total LOHVP across a wider range of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>t</mi><mn>1</mn></msub></math> values with an uncertainty that is smaller than that from either lattice QCD or data-driven approaches on their own.</p>

United Kingdom

C.T.H. Davies

United States

A.S. Kronfeld

G.P. Lepage

C. McNeile

R.S. Van de Water

Utility of a hybrid approach to the hadronic vacuum polarization contribution to the muon anomalous magnetic moment

The Cabibbo-Kobayashi-Maskawa matrix elements <math><mrow><mo>|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>b</mi></mrow></msub><mo>|</mo></mrow></math> and <math><mo>|</mo><msub><mi>V</mi><mrow><mi>u</mi><mi>b</mi></mrow></msub><mo>|</mo></math> can be obtained by combining data from the experiments with lattice QCD results for the semileptonic form factors for the <math><mover><mi>B</mi><mo>¯</mo></mover><mo>→</mo><msup><mi>D</mi><mo>*</mo></msup><mo>ℓ</mo><mover><mi>ν</mi><mo>¯</mo></mover></math> and <math><mover><mi>B</mi><mo>¯</mo></mover><mo>→</mo><mi>π</mi><mo>ℓ</mo><mover><mi>ν</mi><mo>¯</mo></mover></math> decays. It is highly desirable to use the Oktay-Kronfeld (OK) action for the form factor calculation on the lattice, since the OK action is designed to reduce the heavy quark discretization error down to the <math><mi>O</mi><mo>(</mo><msup><mi>a</mi><mn>4</mn></msup><msup><mi>Λ</mi><mn>4</mn></msup><mo>)</mo><mo>≃</mo><mi>O</mi><mo>(</mo><msup><mi>Λ</mi><mn>4</mn></msup><mo>/</mo><mo>(</mo><mn>2</mn><msub><mi>m</mi><mi>Q</mi></msub><msup><mo>)</mo><mn>4</mn></msup><mo>)</mo></math> level in the power counting rules of the heavy quark effective theory (HQET). Here, we present a matching calculation to improve heavy-heavy and heavy-light currents up to the <math><msup><mi>λ</mi><mn>3</mn></msup></math> order in HQET, the same level of improvement as the OK action. Our final results for the improved currents are being used in a lattice QCD calculation of the semileptonic form factors for the <math><mover><mi>B</mi><mo>¯</mo></mover><mo>→</mo><msup><mi>D</mi><mo>*</mo></msup><mo>ℓ</mo><mover><mi>ν</mi><mo>¯</mo></mover></math> and <math><mover><mi>B</mi><mo>¯</mo></mover><mo>→</mo><mi>D</mi><mo>ℓ</mo><mover><mi>ν</mi><mo>¯</mo></mover></math> decays.

South Korea

Jon A. Bailey

Yong-Chull Jang

Sunkyu Lee

Weonjong Lee

Jaehoon Leem

Improvement of heavy-heavy and heavy-light currents with the Oktay-Kronfeld action

The OktayâKronfeld (OK) action extends the Fermilab improvement program for massive Wilson fermions to higher order in suitable power-counting schemes. It includes dimension-six and -seven operators necessary for matching to QCD through order O(ÎQCD3/mQ3) in HQET power counting, for applications to heavyâlight systems, and O(v6) in NRQCD power counting, for applications to quarkonia. In the Symanzik power counting of lattice gauge theory near the continuum limit, the OK action includes all O(a2) and some O(a3) terms. To assess whether the theoretical improvement is realized in practice, we study combinations of heavyâstrange and quarkonia masses and mass splittings, designed to isolate heavy-quark discretization effects. We find that, with one exception, the results obtained with the tree-level-matched OK action are significantly closer to the continuum limit than those obtained with the Fermilab action. The exception is the hyperfine splitting of the bottomâstrange system, for which our statistical errors are too large to draw a firm conclusion. These studies are carried out with data generated with the tadpole-improved Fermilab and OK actions on 500 gauge configurations from one of MILCâs aâ0.12 Â fm, Nf=2+1 -flavor, asqtad-staggered ensembles.

Carleton DeTar

Germany

Andreas S. Kronfeld

Mehmet B. Oktay

Heavy-quark meson spectrum tests of the Oktay–Kronfeld action

A comprehensive review of physics at an e+e- linear collider in the energy range of s=92 Â GeVâ3Â TeV is presented in view of recent and expected LHC results, experiments from low-energy as well as astroparticle physics. The report focusses in particular on Higgs-boson, top-quark and electroweak precision physics, but also discusses several models of beyond the standard model physics such as supersymmetry, little Higgs models and extra gauge bosons. The connection to cosmology has been analysed as well.

G. Moortgat-Pick

H. Baer

M. Battaglia

France

G. Belanger

Japan

K. Fujii

Poland

J. Kalinowski

Spain

S. Heinemeyer

Y. Kiyo

K. Olive

F. Simon

P. Uwer

D. Wackeroth

P.M. Zerwas

A. Arbey

M. Asano

Canada

J. Bagger

P. Bechtle

A. Bharucha

J. Brau

F. Brümmer

S.Y. Choi

A. Denner

K. Desch

S. Dittmaier

U. Ellwanger

C. Englert

A. Freitas

Russia

I. Ginzburg

S. Godfrey

N. Greiner

C. Grojean

Ireland

M. Grünewald

J. Heisig

CERN

A. Höcker

S. Kanemura

K. Kawagoe

R. Kogler

M. Krawczyk

J. Kroseberg

S. Liebler

J. List

F. Mahmoudi

Y. Mambrini

S. Matsumoto

J. Mnich

K. Mönig

M.M. Mühlleitner

R. Pöschl

W. Porod

S. Porto

K. Rolbiecki

M. Schmitt

P. Serpico

M. Stanitzki

Sweden

O. Stål

T. Stefaniak

D. Stöckinger

G. Weiglein

G.W. Wilson

Netherlands

L. Zeune

F. Moortgat

Denmark

S. Xella

J. Ellis

S. Komamiya

M. Peskin

D. Schlatter

A. Wagner

H. Yamamoto

Physics at the e+e- linear collider

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.