We present a novel approach for investigating the spin structure of hadrons based on the two-point function in quantum field theory. In a rotating frame, we derive two independent expressions of the two-point function and identify their equivalence, which allows for a complete decomposition of the total spin of a composite system into the angular momenta of its constituent particles. Applying this approach to the proton, we analyze its spin structure in the massless quark limit. Our results indicate that the quark spin contribution accounts for approximately 27% of the total proton spin at a low-energy scale, significantly deviating from the prediction of the non-relativistic quark model.

Japan

HyungJoo Kim

Philipp Gubler

Poland

Chihiro Sasaki

Proton spin decomposition via QCD sum rules

<p>The degeneracy of chiral partners is an ideal signal for measuring the restoration of the spontaneously broken chiral symmetry in QCD. In this work we investigate the observability of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math> - <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>f</mi><mn>1</mn></msub><mrow><mo>(</mo><mn>1420</mn><mo>)</mo></mrow></mrow></math> degeneracy in the J-PARC E16 experiment, which measures dielectrons emitted from 30-GeV pA collisions. We for this purpose make use of an effective Lagrangian approach, which naturally incorporates the broken charge-conjugation symmetry in nuclear matter and the ensuing anomaly-induced mixing between vector and axial-vector mesons, to compute the spectral function relevant for the experimental measurement. The real-time dynamics of the pA collision is obtained from a transport simulation. Including experimental background and resolution effects on top of that, we find that a signal of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math> - <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msub><mi>f</mi><mn>1</mn></msub><mrow><mo>(</mo><mn>1420</mn><mo>)</mo></mrow></mrow></math> mixing can be observed at around 2.5 <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>σ</mi></math>, with the Run2 statistics planned for the J-PARC E16 experiment with an ideal mixing strength.</p>

Ren Ejima

Kenta Shigaki

Toward a direct measurement of partial restoration of chiral symmetry at J-PARC E16 via density-induced chiral mixing

<p>Production and in-medium modification of hidden strange <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math> mesons are studied in proton-nucleus reactions: <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">p</mi><mo>+</mo><mi mathvariant="normal">C</mi></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">p</mi><mo>+</mo><mi>Cu</mi></mrow></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">p</mi><mo>+</mo><mi>Pb</mi></mrow></math>, at 12 <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>GeV</mi><mo>/</mo><mi>c</mi></mrow></math>, partially measured by the KEK E325 Collaboration via the dilepton decay mode. This work is based on the off-shell microscopic parton-hadron-string dynamics transport approach, which provides the dynamical description of strongly interacting hadronic and partonic degrees of freedom in dense matter, and especially makes it possible to simulate in-medium off-shell dynamics of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math> meson in the reactions studied. Different in-medium scenarios for the modification of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math>-meson spectral function in nuclear matter are investigated: (i) dropping pole mass, (ii) collisional broadening, and (iii) simultaneous dropping pole mass and collisional broadening. Even though the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi></math> meson production in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi mathvariant="normal">p</mi><mo>+</mo><mi mathvariant="normal">A</mi></mrow></math> reactions occurs only at densities around or below normal nuclear matter density <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ρ</mi><mn>0</mn></msub></math>, we find visible modifications of the generated dilepton spectra for the in-medium scenarios compared to the vacuum distribution.</p>

Masaya Ichikawa

Germany

Taesoo Song

Elena Bratkovskaya

Production and in-medium modification of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>φ</mi></math> mesons in proton-nucleus reactions from a transport approach

The femtoscopic ϕN correlation function is studied within a hadronic effective Lagrangian approach with coupled channels, based on hidden local symmetry. The results are compared with the data recently reported by the ALICE collaboration. We find that the correlation function has very different features for the ϕN system in the spin 1/2 and 3/2 configurations, with the spin-averaged combination matching well with the experimental data. A strong attraction, leading to the formation of a ϕN bound state or a very prominent cusp is found in the spin 3/2 case. The correlation function for spin 1/2, on the other hand, is strongly impacted by the negative parity <math><msup><mrow><mi>N</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mo>(</mo><mn>1895</mn><mo>)</mo></math> nucleon resonance.

Brazil

Luciano M. Abreu

K.P. Khemchandani

A. Martínez Torres

Atsushi Hosaka

A study of the Correlation Function

We study the recently observed <math><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> baryon in quantum chromodynamics (QCD) sum rules. We construct the <math><mi>P</mi></math>-wave <math><mi>Ω</mi></math> baryon currents with a covariant derivative, and perform spin projection to obtain the currents with total spin <math><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></math> and <math><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow></math>. We then apply the parity-projected QCD sum rules to separate the contributions of the positive and negative parity states. We extract the masses of <math><mrow><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><mn>1</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> and <math><mn>3</mn><mo>/</mo><msup><mn>2</mn><mo>−</mo></msup></math> states to be <math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup></mrow></msub><mo>=</mo><msubsup><mrow><mn>2.07</mn></mrow><mrow><mo>−</mo><mn>0.07</mn></mrow><mrow><mo>+</mo><mn>0.07</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math> and <math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mn>3</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup></mrow></msub><mo>=</mo><msubsup><mrow><mn>2.05</mn></mrow><mrow><mo>−</mo><mn>0.10</mn></mrow><mrow><mo>+</mo><mn>0.09</mn></mrow></msubsup><mtext> </mtext><mtext> </mtext><mi>GeV</mi></mrow></math>. Both results are in good agreement with the experimental result. Therefore, it is likely that the <math><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> is a negative parity state, which is interpreted as a <math><mi>P</mi></math>-wave excited state in the quark model. However, its spin is not determined in the present analysis, which can be done by detailed study on its decay properties.

China

Niu Su

Hua-Xing Chen

Investigation on the <math><mi>Ω</mi><mo>(</mo><mn>2012</mn><mo>)</mo></math> from QCD sum rules

Observing the mass shifts of chiral partners will provide invaluable insight into the role of chiral symmetry breaking in the generation of hadron masses. Because both the <math><msup><mi>K</mi><mo>*</mo></msup></math> and <math><msub><mi>K</mi><mn>1</mn></msub></math> mesons have vacuum widths smaller than 100 MeV, they are ideal candidates for realizing mass shift measurements. On the other hand, the different momentum dependence of the longitudinal and transverse modes smear the peak positions. In this work, we analyze the angular dependence of the two-body decays of both the <math><msup><mi>K</mi><mo>*</mo></msup></math> and <math><msub><mi>K</mi><mn>1</mn></msub></math>. It is found that the longitudinal and transverse modes of the <math><msup><mi>K</mi><mo>*</mo></msup></math> can be isolated by observing the pseudoscalar decay in either the forward or perpendicular directions, respectively. For the <math><msub><mi>K</mi><mn>1</mn></msub></math> decaying into a vector meson and a pseudoscalar meson, one can accomplish the same goal by further observing the polarization of the vector meson through its angular dependence on the two pseudoscalar meson decay.

South Korea

In Woo Park

Hiroyuki Sako

Kazuya Aoki

Su Houng Lee

Identifying the transverse and longitudinal modes of the <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math> and <math><msub><mi>K</mi><mn>1</mn></msub></math> mesons through their angular-dependent decay modes

Angular distributions of <math><mrow><mi>ϕ</mi></mrow></math> meson decay amplitudes of <math><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> and <math><mrow><msup><mrow><mi>K</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>K</mi></mrow><mrow><mo>−</mo></mrow></msup></mrow></math> channels are computed using both specific interaction Lagrangians and simple arguments relying on angular momentum conservation. Based on the obtained results, we assess methods to experimentally disentangle the longitudinal and transverse polarization modes of the <math><mi>ϕ</mi></math> meson and discuss advantages and disadvantages of employing either the leptonic or hadronic decay modes for this task.

Disentangling longitudinal and transverse modes of the <math><mi>ϕ</mi></math> meson through dilepton and kaon decays

The modification of the <math><mi>ϕ</mi></math> meson spectrum in nuclear matter is studied in an updated QCD sum rule analysis, taking into account recent improvements in properly treating the chiral invariant and breaking components of four-quark condensates. Allowing both mass and decay width to change at finite density, the QCD sum rule analysis determines certain combinations of changes for these parameters that satisfy the sum rules equally well. A comprehensive error analysis, including uncertainties related to the behavior of various condensates at linear order in density, the employed renormalization scale and perturbative corrections of the Wilson coefficients, is used to compute the allowed ranges of these parameter combinations. We find that the <math><mi>ϕ</mi></math> meson mass shift in nuclear matter is especially sensitive to the strange sigma term <math><mrow><msub><mrow><mi>σ</mi></mrow><mrow><mi>s</mi><mi>N</mi></mrow></msub></mrow></math>, which determines the decrease of the strange quark condensate in nuclear matter. Specifically, we obtain a linear relation between the width <math><msub><mi>Γ</mi><mi>ϕ</mi></msub></math> and mass shift <math><mrow><mi>Δ</mi><msub><mrow><mi>m</mi></mrow><mrow><mi>ϕ</mi></mrow></msub></mrow></math> given as <math><mrow><msub><mrow><mi>Γ</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mo>=</mo><mi>a</mi><mi>Δ</mi><msub><mrow><mi>m</mi></mrow><mrow><mi>ϕ</mi></mrow></msub><mo>+</mo><mi>b</mi><msub><mrow><mi>σ</mi></mrow><mrow><mi>s</mi><mi>N</mi></mrow></msub><mo>+</mo><mi>c</mi></mrow></math> with <math><mrow><mi>a</mi><mo>=</mo><mo>(</mo><msubsup><mrow><mn>3.947</mn></mrow><mrow><mo>−</mo><mn>0.130</mn></mrow><mrow><mo>+</mo><mn>0.139</mn></mrow></msubsup><mo>)</mo></mrow></math>, <math><mrow><mi>b</mi><mo>=</mo><mo>(</mo><msubsup><mrow><mn>0.936</mn></mrow><mrow><mo>−</mo><mn>0.177</mn></mrow><mrow><mo>+</mo><mn>0.180</mn></mrow></msubsup><mo>)</mo></mrow></math> and <math><mrow><mi>c</mi><mo>=</mo><mo>−</mo><mo>(</mo><msubsup><mrow><mn>7.707</mn></mrow><mrow><mo>−</mo><mn>5.679</mn></mrow><mrow><mo>+</mo><mn>4.791</mn></mrow></msubsup><mo>)</mo><mtext> </mtext><mtext> </mtext><mi>MeV</mi></mrow></math>.

Jisu Kim

<math><mrow><mi>ϕ</mi></mrow></math> meson properties in nuclear matter from QCD sum rules with chirally separated four-quark condensates

The contribution of the CP violating three-gluon Weinberg operator,   <math> <mfrac> <mn>1</mn> <mrow> <mn>3</mn> <mo>!</mo> </mrow> </mfrac> <mi>w</mi> <msup> <mi>f</mi> <mi>abc</mi> </msup> <msup> <mi>ϵ</mi> <mtext>νραβ</mtext> </msup> <msubsup> <mi>G</mi> <mi>μν</mi> <mi>a</mi> </msubsup> <msubsup> <mi>G</mi> <mi>αβ</mi> <mi>b</mi> </msubsup> <msubsup> <mi>G</mi> <mi>ρ</mi> <mi>cμ</mi> </msubsup> </math>  $$ \frac{1}{3!}w{f}^{abc}{\epsilon}^{\nu \rho \alpha \beta}{G}_{\mu \nu}^a{G}_{\alpha \beta}^b{G}_{\rho}^{c\mu} $$ , to the atomic and nuclear EDMs is estimated using QCD sum rules. After calculating the transition matrix element between the pion and the vacuum through the Weinberg operator, we obtain the long-range CP-odd nuclear force by determining the isovector CP-odd pion-nucleon vertex, using chiral perturbation theory at NLO. The EDMs of 199Hg, 129Xe, and 225Ra atoms, as well as those of 2H and 3He nuclei are finally given including comprehensive uncertainty analysis. While the leading contribution of the 199Hg EDM is given by the intrinsic nucleon EDM, that of 129Xe atom may be dominated by the one-pion exchange CP-odd nuclear force generated by the Weinberg operator. From current experimental data of the 199Hg atomic EDM, we obtain an upper limit on the Weinberg operator magnitude of |w| &lt; 4 × 10 −10GeV −2 if we assume that it is the only source of CP violation at the scale μ = 1 TeV.

Naohiro Osamura

Nodoka Yamanaka

Contribution of the Weinberg-type operator to atomic and nuclear electric dipole moments

The spectrum of the negative-parity spin-1/2 Λ baryons is studied using lattice QCD and hadronic effective theory in a unitarized coupled-channel framework. A direct comparison between the two approaches is possible by considering the hadronic effective theory in a finite volume and with hadron masses and mesonic decay constants that correspond to the situation studied on the lattice. Comparing the energy level spectrum and <math><mi>S</mi><mi>U</mi><mo>(</mo><mn>3</mn><mo>)</mo></math> flavor decompositions of the individual states, it is found that the lowest two states extracted from lattice QCD can be associated with one of the two <math><mi>Λ</mi><mo>(</mo><mn>1405</mn><mo>)</mo></math>-poles and the <math><mi>Λ</mi><mo>(</mo><mn>1670</mn><mo>)</mo></math> resonance. The quark mass dependences of these two lattice QCD levels are in good agreement with their effective theory counterparts. However, as current lattice QCD studies still rely on three-quark operators to generate the physical states, clear signals corresponding to the meson-baryon scattering states, that appear in the finite volume effective theory calculation, are not yet seen.

Spain

Rafael Pavao

Pedro Fernandez-Soler

Juan Nieves

Makoto Oka

Toru T. Takahashi

The negative-parity spin-1/2 Λ baryon spectrum from lattice QCD and effective theory