We compute three-loop corrections to the three-point form factor of the operator <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>tr</mi><mo stretchy="false">(</mo><msup><mrow><mi>ϕ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo stretchy="false">)</mo></mrow></math> in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> supersymmetric Yang-Mills theory. In particular, our result is valid beyond the leading-color limit and will consequently be an important input towards extending the amplitude-bootstrap program beyond the leading-color approximation. We find that our analytic formulae are strikingly compact expressions in terms of integer linear combinations of generalized polylogarithms of weight six.

Xin Guan

Bernhard Mistlberger

Michael Ruf

Subleading Color Corrections at Three Loops to the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>tr</mi><mo stretchy="false">(</mo><msup><mi>ϕ</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> Three-Point Form Factor in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="script">N</mi><mo>=</mo><mn>4</mn></math> Supersymmetric Yang-Mills Theory

We present the first lattice QCD determination of the electromagnetic form factors of the exotic tetraquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow></msub><mo stretchy="false">(</mo><mi>b</mi><mi>b</mi><mover accent="true"><mrow><mi>u</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mover accent="true"><mrow><mi>d</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">)</mo></mrow></math> with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>I</mi><mo stretchy="false">(</mo><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0</mn><mo stretchy="false">(</mo><msup><mrow><mn>1</mn></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">)</mo></mrow></math>. The extracted form factors encode information about its internal structure, including the charge distribution and the magnetic dipole moments, determined separately for the light and heavy quarks. Our results provide evidence in favor of it being a bound state consisting of a compact heavy diquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">[</mo><mi>b</mi><mi>b</mi><mo stretchy="false">]</mo></math> in a color-antitriplet with spin one and a light antidiquark <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">[</mo><mover accent="true"><mrow><mi>u</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mover accent="true"><mrow><mi>d</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover><mo stretchy="false">]</mo></mrow></math> in a color-triplet with spin zero. The charge radius of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>T</mi><mrow><mi>b</mi><mi>b</mi></mrow></msub></math> is found to be significantly smaller than the combined charge radii of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>*</mo></msup></math> mesons. These two comprise the lowest-lying threshold <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>B</mi><msup><mi>B</mi><mo>*</mo></msup></math> in the channel that we are considering, and their electric charge form factors are also determined. The computations were performed on a single ensemble, generated by the Coordinated Lattice Simulations effort, with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>=</mo><mn>2</mn><mo>+</mo><mn>1</mn></mrow></math> dynamical quarks and a lattice spacing of approximately <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>a</mi><mo>≈</mo><mn>0.064</mn><mtext> </mtext><mtext> </mtext><mi>fm</mi></mrow></math> at the pion mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>m</mi></mrow><mrow><mi>π</mi></mrow></msub><mo>≈</mo><mn>290</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>.

Ivan Vujmilovic

Sara Collins

Luka Leskovec

Sasa Prelovsek

Electromagnetic Form Factors and Structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>T</mi></mrow><mrow><mi>b</mi><mi>b</mi></mrow></msub></mrow></math> Tetraquark from Lattice QCD

We report the first measurement of the semileptonic decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>μ</mi></mrow></msub></mrow></math>, using a sample of <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></math> annihilation data corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>7.33</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> collected at center-of-mass energies between 4.128 and 4.226 GeV with the BESIII detector at the BEPCII collider. The branching fraction of the decay is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>μ</mi></mrow></msub><mo stretchy="false">)</mo><mo>=</mo><mo stretchy="false">(</mo><mn>2.89</mn><mo>±</mo><mn>0.2</mn><msub><mrow><mn>7</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.1</mn><msub><mrow><mn>2</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, where the first uncertainty is statistical and the second is systematic. Based on a simultaneous fit to the partial decay rates in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> intervals measured in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>μ</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>μ</mi></mrow></msub></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi>K</mi><mn>0</mn></msup><msup><mi>e</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>e</mi></msub></math> decays, the product value of the form factor <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>f</mi><mo>+</mo><msup><mi>K</mi><mn>0</mn></msup></msubsup><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></math> and the Cabibbo-Kobayashi-Maskawa matrix element <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo stretchy="false">|</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>d</mi></mrow></msub><mo stretchy="false">|</mo></math> is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>f</mi></mrow><mrow><mo>+</mo></mrow><mrow><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup></mrow></msubsup><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo><mo stretchy="false">|</mo><msub><mrow><mi>V</mi></mrow><mrow><mi>c</mi><mi>d</mi></mrow></msub><mo stretchy="false">|</mo><mo>=</mo><mn>0.140</mn><mo>±</mo><mn>0.00</mn><msub><mrow><mn>8</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.00</mn><msub><mrow><mn>3</mn></mrow><mrow><mi>syst</mi></mrow></msub></mrow></math>, which is the most precise determination to date. In addition, lepton flavor universality is tested for the first time with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>D</mi></mrow><mrow><mi>s</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo stretchy="false">→</mo><msup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mo>ℓ</mo></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mo>ℓ</mo></mrow></msub></mrow></math> decays in full and separate <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>q</mi><mn>2</mn></msup></math> intervals. No violation is found.

M. Ablikim

M.N. Achasov

P. Adlarson

X.C. Ai

R. Aliberti

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

V. Batozskaya

K. Begzsuren

N. Berger

M. Berlowski

M. Bertani

D. Bettoni

F. Bianchi

E. Bianco

A. Bortone

I. Boyko

R.A. Briere

A. Brueggemann

H. Cai

M.H. Cai

X. Cai

A. Calcaterra

G.F. Cao

N. Cao

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

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

X.Y. Chen

Y.B. Chen

Y.Q. Chen

Z. Chen

Z.J. Chen

Z.K. Chen

S.K. Choi

X. Chu

G. Cibinetto

F. Cossio

J. Cottee-Meldrum

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

M. Destefanis

F. De Mori

B. Ding

X.X. Ding

Y. Ding

Y.Q. Ding

Y.X. Ding

J. Dong

L.Y. Dong

M.Y. Dong

X. Dong

M.C. Du

S.X. Du

Y.Y. Duan

P. Egorov

G.F. Fan

J.J. Fan

Y.H. Fan

J. Fang

S.S. Fang

W.X. Fang

Y.Q. Fang

R. Farinelli

L. Fava

F. Feldbauer

G. Felici

C.Q. Feng

J.H. Feng

L. Feng

First Measurement of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>D</mi><mi>s</mi><mo>+</mo></msubsup><mo stretchy="false">→</mo><msup><mi>K</mi><mn>0</mn></msup><msup><mi>μ</mi><mo>+</mo></msup><msub><mi>ν</mi><mi>μ</mi></msub></math> Decay

The decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></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><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math>, with a <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetry expected to be close to zero in the standard model, is theoretically clean and sensitive to potential new physics. An analysis of the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></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><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>B</mi><mo>±</mo></msup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi mathvariant="normal">S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>±</mo></msup></math> is performed using proton-proton collision data collected by the LHCb experiment at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>5.4</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> asymmetries are determined to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="script">A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msup><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></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><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mo>−</mo><mn>0.028</mn><mo>±</mo><mn>0.009</mn><mo>±</mo><mn>0.009</mn></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="script">A</mi></mrow><mrow><mi>C</mi><mi>P</mi></mrow></msup><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></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><msup><mrow><mi>K</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0.118</mn><mo>±</mo><mn>0.062</mn><mo>±</mo><mn>0.031</mn></mrow></math>, and the branching fraction ratio is measured to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></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><msup><mrow><mi>K</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></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><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo><mo>=</mo><mn>0.055</mn><mo>±</mo><mn>0.004</mn><mo>±</mo><mn>0.002</mn></mrow></math>, where the first uncertainties are statistical and the second are systematic. These results are the most precise measurements of these quantities to date. A search for the rare decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>B</mi><mi>c</mi><mo>±</mo></msubsup><mo stretchy="false">→</mo><msubsup><mi>K</mi><mi mathvariant="normal">S</mi><mn>0</mn></msubsup><msup><mi>K</mi><mo>±</mo></msup></math> is also performed. No significant signal is observed, and the upper limit on the product of the branching fraction ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi mathvariant="normal">S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo><mo>/</mo><mi mathvariant="script">B</mi><mo stretchy="false">(</mo><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></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><msup><mrow><mi>π</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">)</mo></mrow></math> and the fragmentation-fraction ratio <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mi>c</mi></msub><mo>/</mo><msub><mi>f</mi><mi>u</mi></msub></math> is set to be 0.015 (0.016) at the 90% (95%) confidence level.

R. Aaij

A.S.W. Abdelmotteleb

C. Abellan Beteta

F. Abudinén

T. Ackernley

A.A. Adefisoye

B. Adeva

M. Adinolfi

C. Agapopoulou

C.A. Aidala

Z. Ajaltouni

S. Akar

K. Akiba

M. Akthar

P. Albicocco

J. Albrecht

R. Aleksiejunas

F. Alessio

P. Alvarez Cartelle

R. Amalric

S. Amato

J.L. Amey

Y. Amhis

L. An

L. Anderlini

M. Andersson

P. Andreola

M. Andreotti

S. Andres Estrada

A. Anelli

D. Ao

C. Arata

F. Archilli

Z. Areg

M. Argenton

S. Arguedas Cuendis

L. Arnone

A. Artamonov

M. Artuso

E. Aslanides

R. Ataíde Da Silva

M. Atzeni

B. Audurier

J.A. Authier

D. Bacher

I. Bachiller Perea

S. Bachmann

M. Bachmayer

J.J. Back

P. Baladron Rodriguez

V. Balagura

A. Balboni

W. Baldini

Z. Baldwin

L. Balzani

H. Bao

J. Baptista de Souza Leite

C. Barbero Pretel

M. Barbetti

I.R. Barbosa

R.J. Barlow

M. Barnyakov

S. Barsuk

W. Barter

J. Bartz

S. Bashir

B. Batsukh

P.B. Battista

A. Bay

A. Beck

M. Becker

F. Bedeschi

I.B. Bediaga

N.A. Behling

S. Belin

A. Bellavista

K. Belous

I. Belov

I. Belyaev

G. Benane

G. Bencivenni

E. Ben-Haim

A. Berezhnoy

R. Bernet

S. Bernet Andres

A. Bertolin

F. Betti

J. Bex

O. Bezshyyko

S. Bhattacharya

M.S. Bieker

Precision Measurement of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>C</mi><mi>P</mi></math> Violation and Branching Fractions in <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>B</mi></mrow><mrow><mo>±</mo></mrow></msup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>h</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math> (<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>h</mi><mo>=</mo><mi>π</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>K</mi></mrow></math>) Decays and Search for the Rare Decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>B</mi></mrow><mrow><mi>c</mi></mrow><mrow><mo>±</mo></mrow></msubsup><mo stretchy="false">→</mo><msubsup><mrow><mi>K</mi></mrow><mrow><mi>S</mi></mrow><mrow><mn>0</mn></mrow></msubsup><msup><mrow><mi>K</mi></mrow><mrow><mo>±</mo></mrow></msup></mrow></math>