<p>We present analytical expressions for the transverse momentum dependent (unintegrated) gluon and quark densities in a proton derived at leading order of QCD running coupling and valid at both small and large <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>x</mi></math>. The calculations are performed using the Kimber-Martin-Ryskin/Watt-Martin-Ryskin prescription (in both differential and integral formulations) with different treatment of kinematical constraint, which reflects the angular and strong ordering conditions for parton emissions. As an input, the analytical solution of QCD evolution equations for conventional (collinear) parton distributions is applied, where the valence and nonsinglet quark parts obey the Gross-Llewellyn-Smith and Gottfried sum rules, and momentum conservation for the singlet quark and gluon densities is taken into account. Several phenomenological parameters are extracted from the combined fit to precision data on the proton structure function <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>F</mi><mn>2</mn></msub><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> collected by the BCDMS, H1, and ZEUS Collaborations, comprising a total of 933 points from 5 datasets. Comparison with the numerical results obtained by other groups is presented, and the phenomenological application to the inclusive <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>b</mi></math>-jet production at the LHC is given.</p>

JINR

A.V. Kotikov

Russia

A.V. Lipatov

Updating TMD parton densities in a proton within the Kimber-Martin-Ryskin approach

Romania

Victor E. Ambrus

France

Maxim N. Chernodub

Corrigendum to “Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism” [Physics Letters B 855 (2024) 138757/PLB 138795]

In this paper, we address the reduced beauty cross section [<math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math>] and the beauty structure function [<math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math>], to study the beauty content of a proton. We calculate <math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> and <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> in the <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization formalism by using the integral form of the Kimber-Martin-Ryskin and Martin-Ryskin-Watt unintegrated parton distribution function (KMR and MRW-UPDF) with the angular ordering constraint (AOC) and the <math><mi>M</mi><mi>M</mi><mi>H</mi><mi>T</mi><mn>2014</mn></math> <math><mi>P</mi><mi>D</mi><mi>F</mi></math> set as the input. Recently Guiot and van Hameren demonstrated that the upper limit, <math><msub><mi>k</mi><mi>max</mi></msub></math>, of the transverse-momentum integration performed in the <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization formalism should be almost equal to <math><mi>Q</mi></math>, where <math><mi>Q</mi></math> is the hard scale, otherwise it leads to an overestimation of the proton structure function [<math><msub><mi>F</mi><mn>2</mn></msub><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math>]. In the present work, we show that <math><msub><mi>k</mi><mi>max</mi></msub></math> cannot be equal to <math><mi>Q</mi></math> at low and moderate energy region, and also by considering the gluon and quark contributions to the same perturbative order and a physical gauge for the gluon, i.e., <math><msup><mi>A</mi><mi>μ</mi></msup><msubsup><mi>q</mi><mi>μ</mi><mo>′</mo></msubsup><mo>=</mo><mn>0</mn></math> in the calculation of <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> in the <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization formalism, we do not encounter any overestimation of the theoretical predictions due to different choices of <math><msub><mi>k</mi><mi>max</mi></msub><mo>&gt;</mo><mi>Q</mi></math>. Finally, the resulted <math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> and <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> are compared to the experimental data and the theoretical predictions. In general, the extracted <math><msubsup><mi>σ</mi><mi>red</mi><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> and <math><msubsup><mi>F</mi><mn>2</mn><mrow><mi>b</mi><mover><mi>b</mi><mo>¯</mo></mover></mrow></msubsup></math> based on the KMR and MRW approaches are in perfect agreement with the experimental data and theoretical predictions at high energies, but at low and moderate energies, the one developed from the KMR approach has better consistency than that of the MRW approach.

Iran

N. Olanj

Phenomenological investigation of the beauty content of a proton in the framework of <math><msub><mi>k</mi><mi>t</mi></msub></math>-factorization using Kimber-Martin-Ryskin and Martin-Ryskin-Watt unintegrated parton distributions

We discuss the imaginary-time formalism for field theories in thermal equilibrium in uniformly accelerating frames. We show that under a Wick rotation of Minkowski spacetime, the Rindler event horizon shrinks to a point in a two-dimensional subspace tangential to the acceleration direction and the imaginary time. We demonstrate that the accelerated version of the Kubo-Martin-Schwinger (KMS) condition implies an identification of all spacetime points related by integer-multiple rotations in the tangential subspace about this Euclidean Rindler event-horizon point, with the rotational quanta defined by the thermal acceleration, <math><mi>α</mi><mo>=</mo><mi>a</mi><mo>/</mo><mi>T</mi></math>. In the Wick-rotated Rindler hyperbolic coordinates, the KMS relations reduce to standard (anti-)periodic boundary conditions in terms of the imaginary proper time (rapidity) coordinate. Our findings pave the way to study, using first-principle lattice simulations, the Hawking-Unruh radiation in geometries with event horizons, phase transitions in accelerating Early Universe and early stages of quark-gluon plasma created in relativistic heavy-ion collisions.

Victor E. Ambruş

Acceleration as a circular motion along an imaginary circle: Kubo-Martin-Schwinger condition for accelerating field theories in imaginary-time formalism

The study of the rare decays <math><mi>B</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math> offers a window into the dynamics operating at the electroweak scale, allowing studies of the Standard Model and searches for heavy new physics. However, the analysis of these decays is also potentially sensitive to the on shell production of new light bosons <math><mi>X</mi></math> through the process <math><mi>B</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mi>X</mi></math>. In particular, Belle II has recently measured <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>K</mi><mo>+</mo></msup><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math>, finding a <math><mn>2.8</mn><mi>σ</mi></math> excess under the assumption of heavy new physics. Since this excess is rather localized in the kaon energy, a fit that includes the decay mode <math><msup><mi>B</mi><mo>+</mo></msup><mo>→</mo><msup><mi>K</mi><mo>+</mo></msup><mi>X</mi></math> to the kinematic distributions prefers <math><msub><mi>m</mi><mi>X</mi></msub><mo>≈</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> with branching fraction <math><mi>Br</mi><mo>[</mo><mi>B</mi><mo>→</mo><mi>K</mi><mi>X</mi><mo>]</mo><mo>=</mo><mo>(</mo><mn>8.8</mn><mo>±</mo><mn>2.5</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math> and a significance of <math><mo>≈</mo><mn>3.6</mn><mi>σ</mi></math>. However, no excess was found in the BABAR measurements of <math><mi>B</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mi>ν</mi><mover><mi>ν</mi><mo>¯</mo></mover></math>, and a global analysis of the Belle II and BABAR data leads to <math><mi>Br</mi><mo>[</mo><mi>B</mi><mo>→</mo><mi>K</mi><mi>X</mi><mo>]</mo><mo>=</mo><mo>(</mo><mn>5.1</mn><mo>±</mo><mn>2.1</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>6</mn></mrow></msup></math> with a reduced significance of <math><mo>≈</mo><mn>2.4</mn><mi>σ</mi></math>. We then study various simplified dark-flavored models and present a possible UV completion based on a gauged <math><msub><mi>B</mi><mn>3</mn></msub><mo>−</mo><msub><mi>L</mi><mn>3</mn></msub></math> symmetry, highlighting the discovery potential of dedicated searches for <math><mi>B</mi><mo>→</mo><msup><mi>K</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mi>X</mi></math> at Belle II.

United States

Wolfgang Altmannshofer

Switzerland

Andreas Crivellin

Austria

Huw Haigh

Gianluca Inguglia

Spain

Jorge Martin Camalich

Light new physics in <math><mrow><mi>B</mi><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mi>ν</mi><mover><mrow><mi>ν</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math>?

Protoneutron stars formed during core-collapse supernovae are hot and dense environments that contain a sizable population of muons. If these interact with new long-lived particles with masses up to roughly 100 MeV, the latter can be produced and escape from the stellar plasma, causing an excessive energy loss constrained by observations of SN 1987A. In this article we calculate the emission of light dark fermions that are coupled to leptons via a new massive vector boson, and determine the resulting constraints on the general parameter space. We apply these limits to the gauged <math><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></math> model with dark fermions, and show that the SN 1987A constraints exclude a significant portion of the parameter space targeted by future experiments. We also extend our analysis to generic effective four-fermion operators that couple dark fermions to muons, electrons, or neutrinos. We find that SN 1987A cooling probes a new physics scale up to <math><mo>∼</mo><mn>7</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>, which is an order of magnitude larger than current bounds from laboratory experiments.

Claudio Andrea Manzari

CERN

Germany

Jonas Spinner

Robert Ziegler

Supernova limits on muonic dark forces

We compute the axion-pion scattering <math><mi>a</mi><mi>π</mi><mo>→</mo><mi>π</mi><mi>π</mi></math>, relevant for the axion thermalization rate in the early Universe, within unitarized next-to-leading-order chiral perturbation theory. The latter extends the range of validity of the chiral expansion of axion-pion scattering and thus provides a crucial ingredient for the reliable determination of the relic density of thermal axions, whenever the axion decoupling temperature is below that of the QCD phase transition. Implications for cosmological observables are briefly discussed.

Italy

Luca Di Luzio

Guido Martinelli

José Antonio Oller

Gioacchino Piazza

Axion-pion thermalization rate in unitarized NLO chiral perturbation theory

The discrepancies between <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> data and the corresponding Standard Model predictions constitute one of the most significant hints for new physics currently available. In fact, many scenarios that can account for these anomalies have been proposed in the literature. However, only a single light new physics explanation, i.e., with a mass below the <math><mi>B</mi></math> meson scale, is possible: a light <math><mrow><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> boson. In this article, we aim at excluding any light <math><msup><mi>Z</mi><mo>′</mo></msup></math> model as a solution to <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> data, using a minimal and conservative setup. Considering the improved limits on <math><mrow><mi>B</mi><mo>→</mo><msup><mrow><mi>K</mi></mrow><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mi>ν</mi><mi>ν</mi></mrow></math>, including the experimental sensitivities required for a proper treatment of the necessarily sizable <math><msup><mi>Z</mi><mo>′</mo></msup></math> width, together with the forthcoming Belle II analyses of <math><msup><mi>e</mi><mo>+</mo></msup><msup><mi>e</mi><mo>−</mo></msup><mo>→</mo><msup><mi>μ</mi><mo>+</mo></msup><msup><mi>μ</mi><mo>−</mo></msup><mo>+</mo><mtext>invisible</mtext></math>, can rule out a <math><msup><mi>Z</mi><mo>′</mo></msup></math> explanation of <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> data with a mass below <math><mo>≈</mo><mn>4</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. Importantly, such a light <math><msup><mi>Z</mi><mo>′</mo></msup></math> is the only viable single particle solution to the <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math> anomalies predicting <math><mi>R</mi><mo>(</mo><msup><mi>K</mi><mrow><mo>(</mo><mo>*</mo><mo>)</mo></mrow></msup><mo>)</mo><mo>&gt;</mo><mn>0</mn></math> in high <math><msup><mi>q</mi><mn>2</mn></msup></math> bins, therefore providing an essential consistency test of data.

Paul Feichtinger

Toward excluding a light <math><mrow><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> explanation of <math><mi>b</mi><mo>→</mo><mi>s</mi><msup><mo>ℓ</mo><mo>+</mo></msup><msup><mo>ℓ</mo><mo>−</mo></msup></math>

Dark sector particles at the GeV scale carrying baryon number provide an attractive framework for understanding the origin of dark matter and the matter-antimatter asymmetry of the universe. We demonstrate that dark decays of hadronic states containing strange quarks—hyperons—offer excellent prospects for discovering such dark baryons. Building up on novel calculations of the matrix elements relevant for hyperon dark decays, and in view of various collider, flavor, and astrophysical constraints, we determine the expected rates at hyperon factories like BESIII and LHCb. We also highlight the interesting theoretical connections of hyperon dark decays to the neutron lifetime anomaly and mesogenesis.

Canada

Gonzalo Alonso-Álvarez

Gilly Elor

Miguel Escudero

Bartosz Fornal

Benjamín Grinstein

Strange physics of dark baryons

In this work, we study the structure of the leading order Martin–Ryskin–Watt (MRW) unintegrated parton distribution function (UPDF) and explain in detail why there exists discrepancy between the two different definitions of this UPDF model, i.e., the integral (I-MRW) and differential (D-MRW) MRW UPDFs. We perform this investigation with both angular and strong ordering cutoffs. The derivation footsteps of obtaining the I-MRW UPDF from the D-MRW ones are numerically performed, and the reason of such non-equivalency between the two forms is clearly explained. We show and find out that both methods suggested in the papers by Golec-Biernat and Staśto as well as that of Guiot have shortcomings, and only the combination of their prescriptions can give us the same UPDF structure from both of these two different versions of the MRW UPDF, namely I-MRW and the D-MRW UPDFs.

Ramin Kord Valeshabadi

M. Modarres

On the ambiguity between differential and integral forms of the Martin–Ryskin–Watt unintegrated parton distribution function model