An evolution equation for diffractive production with a definite rapidity gap is given. Coherent <italic>&#947;</italic>* <italic>A</italic> collisions in the unitarity (saturation) region are studied with the conclusion that the diffractive mass is always on the order of the <italic>&#947;</italic>* virtuality, <italic>Q</italic>, when the scattering is strong. Deep in the saturation region diffractive masses significantly greater than <italic>Q</italic> are strongly suppressed by a Levin-Tuchin mechanism.

United States

A.H. Mueller

Limits on the diffractive mass in strong coherent <italic>&#947;</italic>*-nucleus scattering

<p>Using the color dipole picture of deep inelastic scattering (DIS) and the color glass condensate effective theory, we study semi-inclusive jet production in DIS at small <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>x</mi></mrow></math> in the limit where the photon virtuality <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></mrow></math> is much larger than the transverse momentum squared <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msubsup><mrow><mi>P</mi></mrow><mrow><mo>⊥</mo></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></math> of the produced jet. In this limit, the cross section is dominated by aligned jet configurations, that is, quark–antiquark pairs in which one of the fermions—the would-be struck quark in the Breit frame—carries most of the longitudinal momentum of the virtual photon. We show that physically meaningful jet definitions in DIS are such that the effective axis of the jet sourced by the struck quark is controlled by its virtuality rather than by its transverse momentum. For such jet definitions, we show that the next-to-leading order cross section admits factorization in terms of the (sea) quark transverse momentum dependent distribution, which in turn satisfies a universal Dokshitzer-Gribov-Lipatov-Altarelli-Parisi and Sudakov evolution.</p>

France

Paul Caucal

Edmond Iancu

Germany

Feng Yuan

Jet Definition and Transverse-Momentum–Dependent Factorization in Semi-inclusive Deep-Inelastic Scattering

This paper presents a new set of multijet event shape variables introduced to further understand the Mueller-Navelet jet topology. This topology consists of having at least one pair of jets with a very large rapidity separation between them, treating additional jet activity inclusively. This multijet topology is expected to shed light on the radiation pattern that is expected in the high-energy limit of the strong interaction. The paper relies on a Monte Carlo event generator analysis. One set of predictions uses the bfklex event generator, which is based on Balitsky-Fadin-Kuraev-Lipatov (BFKL) perturbative quantum chromodynamics (pQCD) evolution with a resummation of large logarithms of energy at leading-logarithmic accuracy. The bfklex predictions are compared with a fixed-order next-to-leading order pQCD calculation using powheg matched to the parton shower of pythia8 (<math><mrow><mi>NLO</mi><mo>+</mo><mi>PS</mi></mrow></math>), which is the standard for NLO generator predictions at the LHC. We find that both approaches lead to compatible results at current LHC energies, assuming the current experimental constraints for the reconstruction of low transverse momentum jets in ATLAS and CMS. This shows the reliability of the BFKL approach at describing the behavior of the strong interaction in the preasymptotic limit of high center-of-mass energies. Differences between the <math><mrow><mi>NLO</mi><mo>+</mo><mi>PS</mi></mrow></math> and the BFKL-based approaches are found when the jet multiplicity is increased or when the minimum transverse momentum of the jets is decreased.

Italy

C. Baldenegro

Spain

Portugal

G. Chachamis

M. Kampshoff

M. Klasen

J.G. Milhano

C. Royon

A. Sabio Vera

J. G. Milhano

Multijet event shape variables for Mueller-Navelet jet topologies

The GLR-MQ equation is a nonlinear evolution equation that takes into account the shadowing effect, which tames the growth of the gluon at small-x. In this study, we analytically solve for the first time the nonlinear GLR-MQ equation using the homogeneous balance method. The definite solution of the GLR-MQ equation is obtained by fitting the MSTW2008LO gluon distribution data. We find that the geometric scaling is an inherent property of our analytical solution. Furthermore, the gluon distribution functions derived from our solution are capable of accurately reproducing the MSTW2008LO data across most regions. These results indicate that our analytical solution from the homogeneous balance method is valid to describe the gluon behavior at small-x and moderate <math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></math> regions. Moreover, the saturation scale <math><msub><mrow><mi>Q</mi></mrow><mrow><mi>s</mi></mrow></msub></math> has been extracted from our analytical solution, we find that the energy-dependent saturation scale obeys the exponential law <math><msubsup><mrow><mi>Q</mi></mrow><mrow><mi>s</mi></mrow><mrow><mn>2</mn></mrow></msubsup><mspace width="0.2em"></mspace><mo>∝</mo><mspace width="0.2em"></mspace><msubsup><mrow><mi>Q</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup><msup><mrow><mi>e</mi></mrow><mrow><mi>λ</mi><mi>Y</mi></mrow></msup></math>. We also perform a numerical simulation using the analytical results at <math><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>5</mn><mspace width="0.25em"></mspace><msup><mrow><mtext>GeV</mtext></mrow><mrow><mn>2</mn></mrow></msup></math> as the initial condition. We find that our analytical results are consistent with the numerical results in small-x.

China

Yanbing Cai

Xiaopeng Wang

Xurong Chen

New analytical solution of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu equation

We present the full next-to-leading order (NLO) prediction for the jet-gap-jet cross section at the LHC within the BFKL approach. We implement, for the first time, the NLO impact factors in the calculation of the cross section. We provide results for differential cross sections as a function of the difference in rapidity and azimuthal angle betwen the two jets and the second leading jet transverse momentum. The NLO corrections of the impact factors induce an overall reduction of the cross section with respect to the corresponding predictions with only LO impact factors.

Dimitri Colferai

Federico Deganutti

Timothy Raben

Christophe Royon

First computation of Mueller Tang processes using a full NLL BFKL approach

We numerically study for the first time the nonlinear GLR-MQ evolution equations for nuclear parton distribution function (nPDFs) to next-to-leading order accuracy and quantify the impact of gluon recombination at small <math><mi>x</mi></math>. Using the nCTEQ15 nPDFs as input, we confirm the importance of the nonlinear corrections for small <math><mi>x</mi><mo>≲</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math>, whose magnitude increases with a decrease of <math><mi>x</mi></math> and an increase of the atomic number <math><mi>A</mi></math>. We find that at <math><mi>x</mi><mo>=</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>5</mn></mrow></msup></math> and for heavy nuclei, after the upward evolution from <math><msub><mi>Q</mi><mn>0</mn></msub><mo>=</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> to <math><mi>Q</mi><mo>=</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, the quark singlet <math><mi>Ω</mi><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> and the gluon <math><mi>G</mi><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> distributions become reduced by 9%–15%, respectively. The relative effect is much stronger for the downward evolution from <math><msub><mi>Q</mi><mn>0</mn></msub><mo>=</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> to <math><mi>Q</mi><mo>=</mo><mn>2</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>, where we find that <math><mi>Ω</mi><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> is suppressed by 40%, while <math><mi>G</mi><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> is enhanced by 140%. These trends propagate into the <math><msubsup><mi>F</mi><mn>2</mn><mi>A</mi></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> nuclear structure function and the <math><msubsup><mi>F</mi><mi>L</mi><mi>A</mi></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> longitudinal structure function, which after the downward evolution become reduced by 45% and enhanced by 80%, respectively. Our analysis indicates that the nonlinear effects are most pronounced in <math><msubsup><mi>F</mi><mi>L</mi><mi>A</mi></msubsup><mo>(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo>)</mo></math> and are already quite sizable at <math><mi>x</mi><mo>∼</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> for heavy nuclei. We have checked that our conclusions very weakly depend on the choice of input nPDFs. In particular, using the EPPS21 nPDFs as input, we obtain quantitatively similar results.

J. Rausch

Finland

V. Guzey

Australia

Numerical evaluation of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu evolution equations for nuclear parton distribution functions

By making use of the hybrid collinear and high-energy factorization, where the Balitsky-Fadin-Kuraev-Lipatov (BFKL) resummation of leading and next-to-leading energy logarithms is combined with the standard description in terms of collinear parton densities, we compare predictions for Mueller-Navelet jet rapidity and angular differential rates with data collected by CMS at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>7</mn><mtext> </mtext><mtext> </mtext><mi>TeV</mi></math>. We provide an evidence that the study of azimuthal distributions, calculated as a Fourier sum of correlation moments and embodying the high-energy signal coming from all conformal-spin modes, permits us to overcome the well-known issues emerging in the description of Mueller-Navelet final states at natural values of the renormalization scale. We come out with a clear indication that the next-to-leading BFKL description of these observables at natural scales is valid when the rapidity interval between the two jets is large, and it allows us to catch the core high-energy dynamics emerging from data.

Francesco Giovanni Celiberto

Alessandro Papa

Mueller-Navelet jets at the LHC: Hunting data with azimuthal distributions

We investigate different final state features in Mueller–Navelet jets events at hadron colliders. The focus lies on the average rapidity ratio between subsequent minijet emissions which has been investigated in previous works but now is modified to also incorporate the transverse momenta together with the rapidities of the emitted jets. We study the dependence of this observable on a lower transverse momentum veto which does affect the typical minijet multiplicity of the events under scrutiny. We find that this observable is stable when including higher order quantum corrections, also when collinear terms are resummed to all orders.

N. Bethencourt de León

Average minijet rapidity ratios in Mueller–Navelet jets

In this paper we derived in QCD the Balitsky-Fadin-Kuraev-Lipatov (BFKL) linear, inhomogeneous equation for the factorial moments of multiplicity distribution (<math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>k</mi></mrow></msub></mrow></math>) from Le-Mueller-Munier equation. In particular, the equation for the average multiplicity of the color-singlet dipoles (<math><mi>N</mi></math>) turns out to be the homogeneous BFKL while <math><mrow><msub><mrow><mi>M</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>∝</mo><msup><mrow><mi>N</mi></mrow><mrow><mi>k</mi></mrow></msup></mrow></math> at small <math><mi>x</mi></math>. Second, using the diffusion approximation for the BFKL kernel we show that the factorial moments are equal to <math><msub><mi>M</mi><mi>k</mi></msub><mo>=</mo><mi>k</mi><mo>!</mo><mi>N</mi><msup><mrow><mo>(</mo><mi>N</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></msup></math> which leads to the multiplicity distribution <math><mfrac><msub><mi>σ</mi><mi>n</mi></msub><msub><mi>σ</mi><mtext>in</mtext></msub></mfrac><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><msup><mrow><mo>(</mo><mfrac><mrow><mi>N</mi><mo>−</mo><mn>1</mn></mrow><mi>N</mi></mfrac><mo>)</mo></mrow><mrow><mi>n</mi><mo>−</mo><mn>1</mn></mrow></msup></math>. We also suggest a procedure for finding corrections to this multiplicity distribution which will be useful for descriptions of the experimental data.

Chile

Eugene Levin

Multiplicity distribution of dipoles in QCD from the Le-Mueller-Munier equation

We study the dijet azimuthal de-correlation in relativistic heavy ion collisions as an important probe of the transverse momentum broadening effects of a high energy jet traversing the quark–gluon plasma. We take into account both the soft gluon radiation in vacuum associated with the Sudakov logarithms and the jet <math><msub><mrow><mi>P</mi></mrow><mrow><mi>T</mi></mrow></msub></math>-broadening effects in the QCD medium. We find that the Sudakov effects are dominant at the LHC, while the medium effects can play an important role at RHIC energies. This explains why the LHC experiments have not yet observed sizable <math><msub><mrow><mi>P</mi></mrow><mrow><mi>T</mi></mrow></msub></math>-broadening effects in the measurement of dijet azimuthal correlations in heavy ion collisions. Future investigations at RHIC will provide a unique opportunity to study the <math><msub><mrow><mi>P</mi></mrow><mrow><mi>T</mi></mrow></msub></math>-broadening effects and help to pin down the underlying mechanism for jet energy loss in a hot and dense medium.

Bin Wu

Bo-Wen Xiao

Probing transverse momentum broadening in heavy ion collisions