We perform a rigorous analysis of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering at an unphysical pion mass 391 MeV using the Roy-Steiner equations, which satisfy unitarity, analyticity, and crossing symmetry, for the first time. Stable solutions of the Roy-Steiner equations with different quantum numbers of isospin and angular momentum are obtained in the elastic energy region, by taking inputs from the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> lattice data in the inelastic region, the lattice data from the crossed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>π</mi><mo stretchy="false">→</mo><mi>K</mi><mover accent="true"><mi>K</mi><mo stretchy="false">¯</mo></mover></math> channels, the masses of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>K</mi><mo>*</mo></msup></math> at the same pion mass from previous study, and the Regge model. Predictions on the elastic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering phase shifts and the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></math> pole content are made. Contrary to the virtual pole scenario obtained using the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>K</mi></math>-matrix method in the literature, we find that lightest strange scalar meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>K</mi></mrow><mrow><mn>0</mn></mrow><mrow><mo>*</mo></mrow></msubsup><mo stretchy="false">(</mo><mn>700</mn><mo stretchy="false">)</mo></mrow></math> remains a broad resonance at <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>m</mi><mi>π</mi></msub><mo>=</mo><mn>391</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>. The cross-channel dynamics is found to play a crucial role in deriving the proper pole position.

China

Xiong-Hui Cao

Feng-Kun Guo

Zhi-Hui Guo

Qu-Zhi Li

Rigorous Roy-Steiner equation analysis of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>π</mi><mi>K</mi></math> scattering at unphysical quark masses

We conducted a study using the modified Godfrey-Isgur quark model and quark pair creation model to investigate the spectrum and two-body strong decays of the newly discovered <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mo stretchy="false">(</mo><mn>2600</mn><mo stretchy="false">)</mo></math> resonance by the LHCb collaboration. Our analysis revealed that this resonance can be assigned as the fourth radial excitation within the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mn>0</mn><mo>+</mo></msup></math> light strange meson family. Furthermore, we predicted additional radial excitations in this meson family and systematically discussed their spectra, decay behaviors, and branching ratios. These results provide critical guidance for future to identify their signatures in experiments.

Cheng-Qun Pang

Hao Chen

Yun-Hai Zhang

Newly observed <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>κ</mi><mo stretchy="false">(</mo><mn>2600</mn><mo stretchy="false">)</mo></math> and the highly excited states of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msubsup><mi>K</mi><mn>0</mn><mo>*</mo></msubsup></math> family

The branching fractions of the axial vector meson decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">→</mo><msub><mi>a</mi><mn>0</mn></msub><mi>π</mi><mo>,</mo><mi>π</mi><mi>π</mi><mi>η</mi></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">→</mo><mi>ρ</mi><mi>π</mi><mo>,</mo><mi>π</mi><mi>π</mi><mi>π</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">→</mo><mi>K</mi><mi>K</mi><mi>π</mi></math> are calculated in the standard <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></math> quark Nambu–Jona-Lasinio model. The intermediate channels with the states <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>a</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>980</mn><mo stretchy="false">)</mo><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>0</mn></msub><mo stretchy="false">(</mo><mn>500</mn><mo stretchy="false">)</mo><mi>η</mi></math> are taken into account in the decay <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">→</mo><mi>π</mi><mi>π</mi><mi>η</mi></math>. In the case of the scalar mesons, the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mover accent="true"><mi>q</mi><mo stretchy="false">¯</mo></mover><mi>q</mi></math> representation as a chiral symmetric partners of the pseudoscalar mesons is used. It is shown that the decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">→</mo><mi>ρ</mi><mi>π</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>f</mi><mn>1</mn></msub><mo stretchy="false">→</mo><mn>3</mn><mi>π</mi></math> occur due to the mass difference of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>u</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>d</mi></math> quarks. All the results are obtained without using any additional arbitrary parameters and are in satisfactory agreement with the known experimental data.

JINR

M.K. Volkov

A.A. Pivovarov

Kazakhstan

K. Nurlan

Decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><msub><mrow><mi>f</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">→</mo><msub><mrow><mi>a</mi></mrow><mrow><mn>0</mn></mrow></msub><mi>π</mi><mo>,</mo><mi>π</mi><mi>π</mi><mi>π</mi></mrow><mo stretchy="false">(</mo><mi>η</mi><mo stretchy="false">)</mo></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>f</mi></mrow><mn>1</mn></msub><mo stretchy="false">→</mo><mi>K</mi><mi>K</mi><mi>π</mi></mrow></math> in the chiral <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo><mo>×</mo><mi>U</mi><mo stretchy="false">(</mo><mn>3</mn><mo stretchy="false">)</mo></mrow></math> quark NJL model

We measure the spin-density matrix elements (SDMEs) for the photoproduction of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ϕ</mi><mo>(</mo><mn>1020</mn><mo>)</mo></mrow></math> off of the proton in its decay to <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>L</mi><mn>0</mn></msubsup></mrow></math>, using 105 <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>pb</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup></math> of data collected with a linearly polarized photon beam using the GlueX experiment. The SDMEs are measured in nine bins of the squared four-momentum transfer <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> in the range <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mo>−</mo><mi>t</mi><mo>=</mo><mn>0.15</mn><mo>−</mo><mn>1.0</mn></mrow></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>GeV</mi></mrow><mn>2</mn></msup></math>, providing the first measurement of their <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi></math> dependence for photon beam energies of <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>E</mi><mi>γ</mi></msub><mo>=</mo><mn>8.2</mn><mo>−</mo><mn>8.8</mn></mrow></math> GeV. We confirm the dominance of Pomeron exchange in this region and put constraints on the contribution of other Regge exchanges. We also find that helicity amplitudes where the helicity of the photon and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ϕ</mi><mo>(</mo><mn>1020</mn><mo>)</mo></mrow></math> differ by two units are negligible.

Germany

F. Afzal

United States

C.S. Akondi

M. Albrecht

M. Amaryan

S. Arrigo

V. Arroyave

A. Asaturyan

A. Austregesilo

Z. Baldwin

F. Barbosa

J. Barlow

E. Barriga

R. Barsotti

D. Barton

V. Baturin

V.V. Berdnikov

T. Black

W. Boeglin

M. Boer

W.J. Briscoe

T. Britton

R. Brunner

S. Cao

E. Chudakov

G. Chung

P.L. Cole

O. Cortes

V. Crede

M.M. Dalton

United Kingdom

D. Darulis

A. Deur

S. Dobbs

Russia

A. Dolgolenko

M. Dugger

R. Dzhygadlo

D. Ebersole

M. Edo

H. Egiyan

T. Erbora

P. Eugenio

A. Fabrizi

C. Fanelli

S. Fang

A.M. Foda

M. Fritsch

S. Furletov

L. Gan

H. Gao

A. Gardner

A. Gasparian

D.I. Glazier

C. Gleason

V.S. Goryachev

B. Grube

J. Guo

L. Guo

J. Hernandez

K. Hernandez

N.D. Hoffman

Canada

D. Hornidge

Chile

G. Huber

P. Hurck

W. Imoehl

D.G. Ireland

M.M. Ito

I. Jaegle

N.S. Jarvis

T. Jeske

M. Jing

R.T. Jones

Armenia

V. Kakoyan

G. Kalicy

V. Khachatryan

Greece

C. Kourkoumelis

A. LaDuke

I. Larin

D. Lawrence

D.I. Lersch

H. Li

B. Liu

K. Livingston

L. Lorenti

V. Lyubovitskij

A. Mahmood

H. Marukyan

V. Matveev

M. McCaughan

M. McCracken

C.A. Meyer

R. Miskimen

R.E. Mitchell

K. Mizutani

P. Moran

V. Neelamana

L. Ng

E. Nissen

S. Orešić

A.I. Ostrovidov

Z. Papandreou

C. Paudel

Measurement of spin-density matrix elements in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>ϕ</mi><mrow><mo>(</mo><mn>1020</mn><mo>)</mo></mrow><mo>→</mo><msubsup><mi>K</mi><mi>S</mi><mn>0</mn></msubsup><msubsup><mi>K</mi><mi>L</mi><mn>0</mn></msubsup></mrow></math> photoproduction with a linearly polarized photon beam at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>E</mi><mi>γ</mi></msub><mo>=</mo><mn>8.2</mn><mo>–</mo><mn>8.8</mn><mo> </mo><mi>GeV</mi></mrow></math>

Using <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> data taken at the center-of-mass energy of 3.773 GeV with 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>, we report the first measurement of the decay dynamics of the semileptonic decays <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msup><mo stretchy="false">→</mo><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><mn>0</mn><mo stretchy="false">(</mo><mo>−</mo><mo stretchy="false">)</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math>. The amplitude analysis gives the hadronic form factors of the semileptonic <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi></math> transitions into the axial-vector meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></mrow></math> to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi>A</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mo>−</mo><mn>11.2</mn><mo>±</mo><msub><mrow><mn>1.0</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><msub><mrow><mn>0.9</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>r</mi></mrow><mrow><mi>V</mi></mrow></msub><mo>=</mo><mo stretchy="false">(</mo><mo>−</mo><mn>4.3</mn><mo>±</mo><msub><mrow><mn>1.0</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><msub><mrow><mn>2.5</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>2</mn></mrow></msup></mrow></math>. This is the first in the semileptonic decays of heavy mesons into axial-vector mesons. The angular analysis yields an up-down asymmetry <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi mathvariant="script">A</mi></mrow><mrow><mi>ud</mi></mrow><mrow><mo>′</mo></mrow></msubsup><mo>=</mo><mn>0.01</mn><mo>±</mo><mn>0.11</mn></mrow></math>, which is consistent with the standard model prediction. In addition, the branching fractions of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math> and <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><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math> are determined with improved precision to be <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>2.27</mn><mo>±</mo><mn>0.1</mn><msub><mrow><mn>1</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.0</mn><msub><mrow><mn>7</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo>±</mo><mn>0.0</mn><msub><mrow><mn>7</mn></mrow><mrow><mtext>input</mtext></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mo stretchy="false">(</mo><mn>1.02</mn><mo>±</mo><mn>0.0</mn><msub><mrow><mn>6</mn></mrow><mrow><mi>stat</mi></mrow></msub><mo>±</mo><mn>0.0</mn><msub><mrow><mn>6</mn></mrow><mrow><mi>syst</mi></mrow></msub><mo>±</mo><mn>0.0</mn><msub><mrow><mn>3</mn></mrow><mrow><mtext>input</mtext></mrow></msub><mo stretchy="false">)</mo><mo>×</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></math>, respectively. No significant signals of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>D</mi></mrow><mrow><mo>+</mo></mrow></msup><mo stretchy="false">→</mo><msub><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1400</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mn>0</mn></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math> and <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><msub><mrow><mi>K</mi></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1400</mn><msup><mrow><mo stretchy="false">)</mo></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math> are observed and their branching fraction upper limits are set as <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>1.4</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mn>0.7</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math> at 90% confidence level, respectively.

M. Ablikim

M.N. Achasov

Sweden

P. Adlarson

X.C. Ai

R. Aliberti

Italy

A. Amoroso

Q. An

Y. Bai

O. Bakina

Y. Ban

H.R. Bao

Poland

V. Batozskaya

Mongolia

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

Türkiye

S.A. Cetin

X.Y. Chai

J.F. Chang

G.R. Che

Y.Z. Che

G. Chelkov

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.K. Chen

South Korea

S.K. Choi

X. Chu

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

First Measurement of the Decay Dynamics in the Semileptonic Transition of <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mo>+</mo><mo stretchy="false">(</mo><mn>0</mn><mo stretchy="false">)</mo></mrow></msup></mrow></math> into the Axial-Vector Meson <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mover accent="true"><mrow><mi>K</mi></mrow><mrow><mo stretchy="false">¯</mo></mrow></mover></mrow><mrow><mn>1</mn></mrow></msub><mo stretchy="false">(</mo><mn>1270</mn><mo stretchy="false">)</mo></mrow></math>