<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

We study the impact of the top quark mass renormalized in the <math><mover><mrow><mtext>MS</mtext></mrow><mo>‾</mo></mover></math> scheme on the <math><mtext>t</mtext><mover><mrow><mtext>t</mtext></mrow><mrow><mo>¯</mo></mrow></mover></math>H production cross-sections as an alternative to theory predictions with the conventionally used pole mass scheme. The differential cross-sections at next-to-leading order in perturbative QCD with stable top quarks show a moderate decrease in scale uncertainties for the <math><mover><mrow><mtext>MS</mtext></mrow><mo>‾</mo></mover></math> mass renormalization scheme compared to the on-shell one. The shape of the differential distributions is not affected much, the largest differences being observed in the invariant mass distributions of the <math><mtext>t</mtext><mover><mrow><mtext>t</mtext></mrow><mrow><mo>¯</mo></mrow></mover></math> and the <math><mtext>t</mtext><mover><mrow><mtext>t</mtext></mrow><mrow><mo>¯</mo></mrow></mover></math>H systems.

Germany

Andrej Saibel

Sven-Olaf Moch

Maria Aldaya Martin

Cross-sections for H production with the top quark Mass

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

We discuss the different Kimber-Martin-Ryskin (KMR) prescriptions for unintegrated parton distribution functions (uPDFs). We show that the strong-ordering (SO) and the angular-ordering (AO) cutoffs lead to strong discrepancies between the obtained cross sections. While the result obtained with the AO cutoff overestimates the heavy-flavor cross section by about a factor of 3, the SO cutoff gives the correct answer. We also solve the issue of the KMR uPDF definitions mentioned by Golec-Biernat and Staśto [Phys. Lett. B 781, 633 (2018)] and show that, in the case of the AO cutoff, the KMR uPDFs are ill defined.

Chile

Benjamin Guiot

Pathologies of the Kimber-Martin-Ryskin prescriptions for unintegrated PDFs: Which prescription should be preferred?

We previously investigated the compatibility of the $${\textit{Kimber}}$$ <math><mi>Kimber</mi></math> –$${\textit{Martin}}$$ <math><mi>Martin</mi></math> –$${\textit{Ryskin}}$$ <math><mi>Ryskin</mi></math>  ($${\textit{KMR}}$$ <math><mi>KMR</mi></math> ) $${\textit{unintegrated}}$$ <math><mi>unintegrated</mi></math>  parton distribution functions ($${\textit{UPDF}}$$ <math><mi>UPDF</mi></math> ) with the experimental data on the proton (longitudinal) structure functions ($${\textit{PSF}}$$ <math><mi>PSF</mi></math>  ($${\textit{PLSF}}$$ <math><mi>PLSF</mi></math> )). Recently $${\textit{Golec-Biernat}}$$ <math><mrow><mi>Golec</mi><mo>-</mo><mi>Biernat</mi></mrow></math>  and $${\textit{Stasto}}$$ <math><mi>Stasto</mi></math>  ($${\textit{GBS}}$$ <math><mi>GBS</mi></math> ) demonstrated that the differential version of $${\textit{KMR}}$$ <math><mi>KMR</mi></math>  prescription and the implementations of angular (strong) ordering ($${\textit{AOC}}$$ <math><mi>AOC</mi></math>  ($${\textit{SOC}}$$ <math><mi>SOC</mi></math> )) constraints, cause the negative-discontinuous $${\textit{UPDF}}$$ <math><mi>UPDF</mi></math>  with the ordinary parton distribution functions ($${\textit{PDF}}$$ <math><mi>PDF</mi></math> ) as the input, which leads to a sizable effect on the calculation of $${\textit{PSF}}$$ <math><mi>PSF</mi></math> . In the present work, we use the new $${\textit{MMHT2014}}$$ <math><mrow><mi>MMHT</mi><mn>2014</mn></mrow></math> -$${\textit{LO}}$$ <math><mi>LO</mi></math> -$${\textit{PDF}}$$ <math><mi>PDF</mi></math>  as the input and focus on the $${\textit{UPDF}}$$ <math><mi>UPDF</mi></math>  behaviors as was raised by $${\textit{GBS}}$$ <math><mi>GBS</mi></math> . The resulting $${\textit{PSF}}$$ <math><mi>PSF</mi></math>  and $${\textit{PLSF}}$$ <math><mi>PLSF</mi></math>  are compared with the $${\textit{MSTW2008}}$$ <math><mrow><mi>MSTW</mi><mn>2008</mn></mrow></math> -$${\textit{LO}}$$ <math><mi>LO</mi></math> -$${\textit{PDF}}$$ <math><mi>PDF</mi></math>  and $${\textit{MRST99}}$$ <math><mrow><mi>MRST</mi><mn>99</mn></mrow></math> -$${\textit{PDF}}$$ <math><mi>PDF</mi></math>  and the 2014 data given by the $${\textit{ZEUS}}$$ <math><mi>ZEUS</mi></math>  and $${\textit{H1}}$$ <math><mrow><mi>H</mi><mn>1</mn></mrow></math>  collaborations. The calculated $${\textit{PSF}}$$ <math><mi>PSF</mi></math>  and $${\textit{PLSF}}$$ <math><mi>PLSF</mi></math>  based on the integral prescription of the $${\textit{KMR}}$$ <math><mi>KMR</mi></math> -$${\textit{UPDF}}$$ <math><mi>UPDF</mi></math>  with the $${\textit{AOC}}$$ <math><mi>AOC</mi></math>  and the ordinary $${\textit{PDF}}$$ <math><mi>PDF</mi></math>  as the input are reasonably consistent with the experimental data. Therefore, they are approximately independent to the $${\textit{PDF}}$$ <math><mi>PDF</mi></math>  (no need to impose cutoff on the $${\textit{PDF}}$$ <math><mi>PDF</mi></math> ). At very small x regions because of the excess of gluons in the $${\textit{MMHT2014}}$$ <math><mrow><mi>MMHT</mi><mn>2014</mn></mrow></math> -$${\textit{LO}}$$ <math><mi>LO</mi></math> -$${\textit{PDF}}$$ <math><mi>PDF</mi></math>  and $${\textit{MSTW2008}}$$ <math><mrow><mi>MSTW</mi><mn>2008</mn></mrow></math> -$${\textit{LO}}$$ <math><mi>LO</mi></math> -$${\textit{PDF}}$$ <math><mi>PDF</mi></math> , an increase in $${\textit{PSF}}$$ <math><mi>PSF</mi></math>  and $${\textit{PLSF}}$$ <math><mi>PLSF</mi></math>  is achieved. Finally, according to the $${\textit{GBS}}$$ <math><mi>GBS</mi></math>  report the differential version by using the cutoff independent $${\textit{PDF}}$$ <math><mi>PDF</mi></math>  produces results far from the experimental data.

A phenomenological investigation of the integral and the differential versions of the $${\textit{Kimber}}$$ <math><mi>Kimber</mi></math> –$${\textit{Martin}}$$ <math><mi>Martin</mi></math> –$${\textit{Ryskin}}$$ <math><mi>Ryskin</mi></math>  $${\textit{unintegrated}}$$ <math><mi>unintegrated</mi></math>  parton distribution functions using two different constraints and the $${\textit{MMHT}}2014$$ <math><mrow><mi>MMHT</mi><mn>2014</mn></mrow></math>  $${\textit{PDF}}$$ <math><mi>PDF</mi></math>

A natural star product for 4-d <math><mi>κ</mi></math>-Minkowski space is used to investigate various classes of <math><mi>κ</mi></math>-Poincaré invariant scalar field theories with quartic interactions whose commutative limit coincides with the usual <math><msup><mi>ϕ</mi><mn>4</mn></msup></math> theory. <math><mrow><mi>κ</mi></mrow></math>-Poincaré invariance forces the integral involved in the actions to be a twisted trace, thus defining a Kubo-Martin-Schwinger (KMS) weight for the noncommutative (<math><mrow><msup><mrow><mi>C</mi></mrow><mrow><mo>*</mo></mrow></msup></mrow></math>-)algebra modeling the <math><mi>κ</mi></math>-Minkowski space. In all the field theories, the twist generates different planar one-loop contributions to the 2-point function which are at most UV linearly diverging. Some of these theories are free of UV/IR mixing. In the others, UV/IR mixing shows up in non-planar contributions to the 2-point function at exceptional zero external momenta while staying finite at nonzero external momenta. These results are discussed together with the possibility for the KMS weight relative to the quantum space algebra to trigger the appearance of KMS state on the algebra of observables.

Timothé Poulain

Jean-Christophe Wallet

<math><mi>κ</mi></math>-Poincaré invariant quantum field theories with Kubo-Martin-Schwinger weight

A dedicated search is presented for new phenomena in inclusive 8- and 10-jet final states with low missing transverse momentum, with and without identification of jets originating from b quarks. The analysis is based on data from proton–proton collisions corresponding to an integrated luminosity of 19.7fb−1 collected with the CMS detector at the LHC at s=8TeV . The dominant multijet background expectations are obtained from low jet multiplicity control samples. Data agree well with the standard model background predictions, and limits are set in several benchmark models. Colorons (axigluons) with masses between 0.6 and 0.75 (up to 1.15) TeV are excluded at 95% confidence level. Similar exclusion limits for gluinos in R -parity violating supersymmetric scenarios are from 0.6 up to 1.1 TeV. These results comprise the first experimental probe of the coloron and axigluon models in multijet final states.

Armenia

Vardan Khachatryan

Albert M Sirunyan

Armen Tumasyan

Austria

Wolfgang Adam

Ece Aşılar

Thomas Bergauer

Johannes Brandstetter

Erica Brondolin

Marko Dragicevic

Janos Erö

Martin Flechl

Markus Friedl

Rudolf Fruehwirth

Vasile Mihai Ghete

Christian Hartl

Natascha Hörmann

Josef Hrubec

Manfred Jeitler

Axel König

Ilse Krätschmer

Dietrich Liko

Takashi Matsushita

Ivan Mikulec

Dinyar Rabady

Navid Rad

Babak Rahbaran

Herbert Rohringer

Jochen Schieck

Josef Strauss

Wolfgang Treberer-Treberspurg

Wolfgang Waltenberger

Claudia-Elisabeth Wulz

Belarus

Vladimir Mossolov

Nikolai Shumeiko

Juan Suarez Gonzalez

Belgium

Sara Alderweireldt

Eddi A De Wolf

Xavier Janssen

Jasper Lauwers

Merijn Van De Klundert

Hans Van Haevermaet

Pierre Van Mechelen

Nick Van Remortel

Alex Van Spilbeeck

Shimaa Abu Zeid

Freya Blekman

Jorgen D'Hondt

Nadir Daci

Isabelle De Bruyn

Kevin Deroover

Natalie Heracleous

Steven Lowette

Seth Moortgat

Lieselotte Moreels

Annik Olbrechts

Quentin Python

Stefaan Tavernier

Walter Van Doninck

Petra Van Mulders

Isis Van Parijs

Hugues Brun

Cécile Caillol

Barbara Clerbaux

Gilles De Lentdecker

Hugo Delannoy

Giuseppe Fasanella

Laurent Favart

Reza Goldouzian

Anastasia Grebenyuk

Georgia Karapostoli

Thomas Lenzi

Alexandre Léonard

Jelena Luetic

Thierry Maerschalk

Andrey Marinov

Aidan Randle-conde

Tomislav Seva

Catherine Vander Velde

Pascal Vanlaer

Ryo Yonamine

Florian Zenoni

China

Fengwangdong Zhang

Anna Cimmino

Tom Cornelis

Didar Dobur

Alexis Fagot

Guillaume Garcia

Muhammad Gul

Deniz Poyraz

Sinem Salva Diblen

Robert Schöfbeck

Michael Tytgat

Ward Van Driessche

Efe Yazgan

Nicolas Zaganidis

Hamed Bakhshiansohi

Camille Beluffi

Olivier Bondu

Sébastien Brochet

Giacomo Bruno

Search for new phenomena in events with high jet multiplicity and low missing transverse momentum in proton–proton collisions at s=8TeV