The study of neutral $\textit{D}$-meson mixing provides a unique probe of long-distance effects in the charm sector, where Standard Model contributions are dominated by nonperturbative effects. In this work, we investigate the feasibility of using spectral reconstruction techniques within lattice QCD to compute the long-distance contributions to $\textit{D}$ − $$ {\overline{D}}^0 $$ mixing. After outlining the general formalism describing neutral meson mixing in the charm sector, we focus on the determination of the mixing amplitudes and the dimensionless parameters $\textit{x}$ = ∆$\textit{m}$ $\textit{/}$Γ and $\textit{y}$ = ∆Γ $\textit{/}$(2Γ ), which respectively encode the mass and width differences between the $\textit{D}$-meson mass eigenstates. We discuss in detail the required theoretical and computational framework, including the definition and renormalization of the four-quark operators entering the ∆$\textit{C}$ = 1 weak Hamiltonian, and strategies for evaluating the relevant correlation functions employing variance-reduction techniques. To extract the mixing ampli- tudes, we explore methods for reconstructing the spectral density from lattice correlators, providing preliminary assessments of the data quality required to reach the scaling regime, where the smearing width is small enough to yield physically meaningful results. Our findings lay the groundwork for future precision determinations of long-distance contributions to $\textit{D}$-meson mixing from first principles.

Switzerland

Matteo Carlo

Felix Erben

United Kingdom

Maxwell Hansen

Long distance contributions to neutral $\textit{D}$-meson mixing from lattice QCD

<p>We measure the time-integrated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> decays reconstructed in <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><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow></math> events collected by the Belle and Belle II experiments. The corresponding data samples have integrated luminosities of 980 and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>428</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>, respectively. To infer the flavor of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup></math> meson, we exploit the correlation between the flavor of the reconstructed decay and the electric charges of particles reconstructed in the rest of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup></mrow><mo stretchy="false">→</mo><mrow><mi>c</mi><mover accent="true"><mi>c</mi><mo stretchy="false">¯</mo></mover></mrow></math> event. This results in a sample which is independent from any other previously used at Belle or Belle II. The result, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msub><mo stretchy="false">(</mo><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>1.3</mn><mo>±</mo><mn>2.0</mn><mo>±</mo><mn>0.2</mn><mo stretchy="false">)</mo><mo>%</mo></mrow></math>, where the first uncertainty is statistical and the second systematic, is consistent with previous determinations and with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> symmetry.</p>

I. Adachi

Y. Ahn

N. Akopov

S. Alghamdi

M. Alhakami

A. Aloisio

N. Althubiti

K. Amos

M. Angelsmark

N. Anh Ky

C. Antonioli

D.M. Asner

H. Atmacan

T. Aushev

M. Aversano

R. Ayad

V. Babu

H. Bae

N.K. Baghel

S. Bahinipati

P. Bambade

Sw. Banerjee

M. Barrett

M. Bartl

J. Baudot

A. Baur

A. Beaubien

F. Becherer

J. Becker

J.V. Bennett

F.U. Bernlochner

V. Bertacchi

M. Bertemes

E. Bertholet

M. Bessner

S. Bettarini

B. Bhuyan

F. Bianchi

T. Bilka

D. Biswas

A. Bobrov

D. Bodrov

A. Bondar

J. Borah

A. Boschetti

A. Bozek

M. Bračko

P. Branchini

R.A. Briere

T.E. Browder

A. Budano

S. Bussino

M. Campajola

L. Cao

G. Casarosa

C. Cecchi

P. Cheema

B.G. Cheon

K. Chilikin

J. Chin

K. Chirapatpimol

H.E. Cho

K. Cho

S.J. Cho

S.K. Choi

S. Choudhury

I. Consigny

L. Corona

J.X. Cui

E. De La Cruz-Burelo

S.A. De La Motte

G. de Marino

G. De Pietro

R. de Sangro

M. Destefanis

A. Di Canto

J. Dingfelder

Z. Doležal

I. Domínguez Jiménez

T.V. Dong

M. Dorigo

G. Dujany

P. Ecker

D. Epifanov

R. Farkas

P. Feichtinger

T. Ferber

T. Fillinger

C. Finck

G. Finocchiaro

A. Fodor

F. Forti

B.G. Fulsom

A. Gabrielli

A. Gale

E. Ganiev

M. Garcia-Hernandez

R. Garg

G. Gaudino

V. Gaur

Measurement of the time-integrated <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup></mrow></math> decays using opposite-side flavor tagging at Belle and Belle II

<p>A first determination of the strong-phase difference between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> is performed using <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><mi>ψ</mi><mo stretchy="false">(</mo><mn>3770</mn><mo stretchy="false">)</mo><mo stretchy="false">→</mo><mi>D</mi><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover></math> data collected by the BESIII detector corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>20.3</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The measurements are made in four pairs of bins in phase space, which are chosen to provide optimal sensitivity to the angle <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>γ</mi></math> of the unitarity triangle in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>±</mo></msup><mo stretchy="false">→</mo><mi>D</mi><msup><mi>K</mi><mo>±</mo></msup></math> decays. From these measurements, it follows that the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math>-even fraction of the decay is <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mo>+</mo></msub><mo>=</mo><mn>0.754</mn><mo>±</mo><mn>0.01</mn><msub><mn>0</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mspace linebreak="goodbreak"></mspace><mn>0.00</mn><msub><mn>8</mn><mrow><mi>syst</mi></mrow></msub></math>. In addition, the branching fraction of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mn>0</mn></msup><mo stretchy="false">→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">(</mo><mn>2.863</mn><mo>±</mo><mspace linebreak="goodbreak"></mspace><mn>0.02</mn><msub><mn>8</mn><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.04</mn><msub><mn>5</mn><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, which is twice as precise as previous results obtained at other experiments.</p>

China

M. Ablikim

Russia

M.N. Achasov

Sweden

P. Adlarson

Germany

O. Afedulidis

X.C. Ai

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

JINR

O. Bakina

I. Balossino

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

E. Bianco

A. Bortone

I. Boyko

United States

A. Brueggemann

H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

G. Chelkov

C. Chen

C.H. Chen

Chao Chen

G. Chen

H.S. Chen

H.Y. Chen

M.L. Chen

S.J. Chen

S.L. Chen

S.M. Chen

T. Chen

X.R. Chen

X.T. Chen

Y.B. Chen

Y.Q. Chen

Z.J. Chen

Z.Y. Chen

South Korea

G. Cibinetto

F. Cossio

J.J. Cui

H.L. Dai

J.P. Dai

A. Dbeyssi

R.E. de Boer

D. Dedovich

C.Q. Deng

Z.Y. Deng

A. Denig

I. Denysenko

F. De Mori

B. Ding

X.X. Ding

Y. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. Duan

Z.H. Duan

P. Egorov

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Measurement of the strong-phase difference between <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mover accent="true"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> in bins of phase space