Regular Series

Vol. 49 (2018), No. 6, pp. 1007 – 1400

Cracow Epiphany Conference On Advances in Heavy Flavour Physics

Future Contributions to \(\phi _{s}\) Measurements

Acta Phys. Pol. B 49, 1015 (2018)

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The most recent results on the CP-violating phase \(\phi _{s}\) measurements in the \(B^{0}_{s}\)–\(\bar {B}^{0}_{s}\) system obtained by the LHCb Collaboration with Run 1 data are presented. Thanks to the precise prediction of the \(\phi _{s}\) value in the frame of the Standard Model, it represents an excellent probe to search for new physics. Current results are compatible with the Standard Model predictions, and their precision will be increased with larger data sets. Further improvement is expected from the inclusion of results obtained using decay modes with smaller branching fractions.

The Dynamics of Beauty & Charm Hadrons and Top Quarks in the Era of the LHCb & Belle II and ATLAS & CMS — Motto: Non-perturbative QCD & Many-body Final States

Acta Phys. Pol. B 49, 1021 (2018)

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Our community has to apply non-perturbative QCD on different levels of flavor dynamics in strange, charm and beauty hadrons and even for top quarks. We need consistent parameterization of the CKM matrix and describe weak decays of beauty hadrons with many-body final states. It is crucial to use the Wilsonian OPE and discuss “duality” in the worlds of quarks vs. hadrons. The pole mass of heavy quarks is not well-defined on the non-perturbative level: it is not Borel summable in total QCD. We need a novel team to combine the strengths of our tools from MEP and HEP.

The Return of Kaon Flavour Physics

Acta Phys. Pol. B 49, 1043 (2018)

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Kaon flavour physics has played in the 1960s and 1970s a very important role in the construction of the Standard Model (SM) and in the 1980s and 1990s in SM tests with the help of CP violation in \(K_{\rm L}\to \pi \pi \) decays represented by \(\varepsilon _K\) and the ratio \(\varepsilon '/\varepsilon \). In this millennium, this role has been taken over by \(B_{s,d}\) and \(D\) mesons. However, there is no doubt that in the coming years, we will witness the return of kaon flavour physics with the highlights being the measurements of the theoretically clean branching ratios for the rare decays \(K^+\rightarrow \pi ^+\nu \bar \nu \) and \(K_{\rm L}\rightarrow \pi ^0\nu \bar \nu \), and the improved SM predictions for the ratio \(\varepsilon '/\varepsilon \), for \(\varepsilon _K\) and the \(K^0\)–\(\bar K^0\) mixing mass difference \(\Delta M_K\). Theoretical progress on the decays \(K_{\rm L,S}\to \mu ^+\mu ^-\) and \(K_{\rm L}\to \pi ^0\ell ^+\ell ^-\) is also expected. They are all very sensitive to new physics (NP) contributions and the correlations between them should help us to identify new dynamics at very short distance scales. These studies will be enriched when theory on the \(K\to \pi \pi \) isospin amplitudes \({\rm Re} A_0\) and \({\rm Re} A_2\) improves. This paper summarizes several aspects of this exciting field. In particular, we emphasize the role of the Dual QCD approach in getting the insight in the numerical Lattice QCD results on \(K^0\)–\(\bar K^0\) mixing and \(K\to \pi \pi \) decays.

Review and Outlook on Kaon Physics

Acta Phys. Pol. B 49, 1079 (2018)

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The status of kaon physics and its prospects are reviewed. A new round of experiment is taking data with the potential of making a significant step in sensitivity on many fronts by the end of the decade.

NNLO QCD Contributions to \(\varepsilon ^\prime /\varepsilon \)

Acta Phys. Pol. B 49, 1087 (2018)

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Recent progress in Lattice QCD and subsequent Next-to-Leading Order analysis of the ratio \(\varepsilon ^\prime /\varepsilon \) resulted in a \(2.9\sigma \) discrepancy between the Standard Model predictions and experimental data. This inconsistency could have several sources, one of which could be the missing contribution of new particles in the theory predictions. However, a reliable Standard Model prediction is essential to disentangle possible new physics effects from the Standard Model background. Indeed, possible higher order corrections could significantly alter the theory prediction. This is particularly true for \(\varepsilon ^\prime /\varepsilon \) where the Next-to-Leading Order corrections have been found to be large. To close this gap, we aim to calculate the relevant matching corrections at Next-to-Next-to-Leading Order for this physical quantity and present a more accurate theoretical prediction within the Standard Model.

RooMCMarkovChain a Metropolis–Hastings Algorithm for the Root Framework

Acta Phys. Pol. B 49, 1097 (2018)

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This paper reports work done during an internship at the LHCb experiment at CERN. The task was to implement a Metropolis algorithm as a minimizer for negative log likelihood (nnl) fits into the ROOT Data analysis framework. The Metropolis algorithm is based on a MCMC which w.r.t. previously broadly used algorithm called Minuit can easily be scaled to multidimensional parameter space. Moreover, such kind of algorithms can easily be parallelized.

Searching for New Physics with \(b\to s \tau \tau \) Processes

Acta Phys. Pol. B 49, 1105 (2018)

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In recent years, intriguing hints for the violation of Lepton Flavour Universality (LFU) have been accumulated in semileptonic \(B\) decays, both in the charged-current transitions \(b\to c\ell ^-\bar \nu _\ell \) (i.e. , \(R_D\), \(R_{D^*}\) and \(R_{J/\psi }\)) and the neutral-current transitions \(b\to s\ell ^+\ell ^-\) (i.e. , \(R_K\) and \(R_{K^*}\)). Hints for LFU violation in \(R_{D^{(*)}}\) and \(R_{J/\psi }\) point at large deviations from the SM in processes involving tau leptons. Moreover, LHCb has reported deviations from the Standard Model (SM) expectations in \(b\to s\mu ^+\mu ^-\) processes as well as in the ratios \(R_K\) and \(R_{K^*}\), which together point at new physics (NP) affecting muons with a high significance. These hints for NP suggest the possibility of huge LFU-violating effects in \(b\to s\tau ^+\tau ^-\) transitions. We report recent works, where we predicted the branching ratios of \(B\to K\tau ^+\tau ^-\), \(B\to K^{*}\tau ^+\tau ^-\) and \(B_s\to \phi \tau ^+\tau ^-\) taking into account NP effects in the Wilson coefficients \(C_{9(')}^{\tau \tau }\)and \(C_{10(')}^{\tau \tau }\). Assuming a common NP explanation of \(R_{D}\), \(R_{D^{(*)}}\) and \(R_{J/\psi }\), we showed that a very large enhancement of \(b\to s\tau ^+\tau ^-\) processes, of around three orders of magnitude compared to the SM, can be expected under fairly general assumptions. We found that the branching ratios of \(B_s\to \tau ^+\tau ^-\), \(B_s\to \phi \tau ^+\tau ^-\) and \(B\to K^{(*)}\tau ^+\tau ^-\) under these assumptions are in the observable range for the LHCb and Belle II.

Search for the Rare Decay \(B^+ \to \ell ^+ \nu _{\ell } \gamma \) at Belle and Belle II

Acta Phys. Pol. B 49, 1121 (2018)

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The Belle Collaboration reported an upper limit on the partial branching fraction on the rare decay \(B^+ \to \ell ^+ \nu _{\ell } \gamma \) using the full dataset recorded at the \({\mit \Upsilon }(4S)\) resonance. The decay allows for the extraction of the first inverse momentum of the light-cone distribution amplitude, an important parameter for QCD factorization for non-leptonic \(B\) decays. We present a Monte Carlo study applying an improved tagging algorithm developed for the Belle II experiment. We observe an increase in the signal reconstruction efficiency by a factor of three, improving the expected sensitivity to \( 3.8\sigma \). Furthermore, we give an outlook for the sensitivity of measuring \(B^+ \to \ell ^+ \nu _{\ell } \gamma \) with the Belle II experiment.

Measurement of the \(t\bar {t}\gamma \) Production Cross Section in Proton–Proton Collisions at \(\sqrt {s}=8\) TeV with the ATLAS Detector

Acta Phys. Pol. B 49, 1127 (2018)

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The cross section of top-quark pair production in association with a photon in proton–proton collisions at a center-of-mass energy of \(\sqrt {s} = 8~\mathrm {TeV}\) is measured. The data with a total integrated luminosity of \(20.2~\mathrm {fb}^{-1}\) collected by the ATLAS detector at the Large Hadron Collider in 2012 is used. The measurement is performed in the single lepton decay channel. The signal region is defined by the final state of exactly one high-\(p_{\mathrm {T}}\) lepton, large missing transverse momentum, at least four jets where at least one is being \(b\)-tagged and exactly one photon with \(p_{\mathrm {T}}\gt 15~\mathrm {GeV}\). The cross section times the branching ratio is determined in a fiducial region defined in terms of the detector acceptance. In addition, the first differential cross-section measurements as a function of photon \(p_{\mathrm {T}}\) and \(\eta \) are presented. The measured fiducial inclusive and differential cross sections are in a good agreement with the next-to-leading order (NLO) prediction.

Central Exclusive Production Measurements in the LHCb

Acta Phys. Pol. B 49, 1135 (2018)

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Central Exclusive Production (CEP) is a class of diffractive processes studied at the Large Hadron Collider, that offers a very clean experimental environment for probing the low-energy regime of Quantum Chromodynamics and testing the Standard Model predictions. The paper summarizes the CEP analyses conducted by the LHCb Collaboration. The latest measurements of \(J/\psi \) and \(\psi (2S)\) photoproduction are discussed, along with the impact of the HeRSCheL detector on dissociation background reduction. Finally, a novel Monte Carlo event generator for diffractive physics is presented as a work-in-progress project.

Subleading Shape Functions in \(\bar {B} \to X_{s,d} \ell \ell \)

Acta Phys. Pol. B 49, 1141 (2018)

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We analyse the resolved power corrections to the inclusive decays \(\bar B \to X_{s} \ell ^+ \ell ^-\) and also \(\bar B \to X_{d} \ell ^+ \ell ^-\). As a distinctive feature, the resolved contributions remain non-local when the hadronic mass cut is released. Therefore, they reflect an irreducible uncertainty not dependent on the hadronic mass cut. They factorize in hard functions describing physics at the high scale \(m_b\), in so-called jet functions characterizing the physics at the hadronic final state \(X_s\) which corresponds to an invariant mass of the order of \(\sqrt {m_b {\mit \Lambda }_{\rm QCD}}\), and in soft functions, so-called shape functions, parametrizing the hadronic physics at the scale \({\mit \Lambda }_{\rm QCD}\). Knowing the explicit form of the latter, one can derive general properties of such shape functions which allow for precise estimates of the corresponding uncertainties.

The Muon \(g-2\) in Progress

Acta Phys. Pol. B 49, 1157 (2018)

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Two next generation muon \(g-2\) experiments at Fermilab in the USA and at J-PARC in Japan have been designed to reach a four times better precision from 0.54 ppm to 0.14 ppm and the challenge for the theory side is to keep up in precision as far as possible. This has triggered a lot of new research activities. The main motivation is the persisting 3 to 4\(\sigma \) deviation between standard theory and experiment. As the Standard Model predictions almost without exception match perfectly all other experimental information, the deviation in one of the most precisely measured quantities in particle physics remains a mystery and inspires the imagination of model builders. Plenty of speculations are aiming to explain what beyond the Standard Model effects could fill what seems to be missing. Here, very high precision experiments are competing with searches for new physics at the high-energy frontier lead by the Large Hadron Collider at CERN. Actually, the tension is increasing steadily as no new states are found which could accommodate the \(g_\mu -2\) discrepancy. With the new muon \(g-2\) experiments, this discrepancy would go up at least to 6\(\sigma \), in the case the central values do not move, up to 10\(\sigma \) could be reached if the present theory error could be reduced by a factor of two.

Analysis of Multibody Beauty to Open-charm Decays at LHCb

Acta Phys. Pol. B 49, 1177 (2018)

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The LHCb detector is designed for precise measurements of beauty and charm quark decays and searching for new physics beyond the Standard Model. Its precise tracking, excellent particle identification and high trigger efficiency allow to measure the CKM matrix parameters with unprecedented accuracy. Selected results regarding decays of beauty mesons to final states containing open charm particles as well as the description of data analysis techniques applied for such complicated multibody decays are presented.

Impact of LHC Heavy-Flavour Data on Nuclear Gluon PDF

Acta Phys. Pol. B 49, 1185 (2018)

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We use for the first time experimental data for the inclusive heavy-quark production in proton–lead collisions at the LHC in order to improve our knowledge of the gluon distribution in nuclei. We first check that the two most recent global nuclear parton distribution analyses (nCTEQ15 and EPPS16) provide a good overall description of the data, and then use these data in a PDF reweighing analysis. We find a first clear confirmation of gluon shadowing at small \(x\). Additionally, it demonstrates that the inclusion of such heavy-flavour data in a global fit would significantly reduce the uncertainty on the gluon density down to \(x \simeq 7\times 10^{-6}\) while keeping an agreement with the other data of the global fits. Our study accounts for the factorisation scale uncertainties which become the largest for the charm(onium) sector.

Recent Heavy Flavour Results from CMS

Acta Phys. Pol. B 49, 1199 (2018)

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Recent results on \(b\)-flavour physics obtained by the CMS Collaboration will be presented. The flexible and powerful CMS trigger system allows the experiment to be sensitive to \(b\)-physics phenomena of different kinds, mostly in channels with muons in the final state. In this paper, some of these results will be reported, namely single quarkonia production, \(J/\psi \), \(\psi (2S)\), \({\mit \Upsilon }(1S,2S,3S)\), as well as the observation of double prompt \({\mit \Upsilon }\) production. The lifetimes of different states, \(B^0\to J/\psi K^\star \), \(B^0 \to J/\psi K_{\rm S}\), \(B^0_s \to J/\psi \pi \pi \), \(B^0_s \to J/\psi \phi \), \({\mit \Lambda }_b \to J/\psi {\mit \Lambda }\), and \(B_c^+ \to J/\psi \pi \) will be described. Other measurements include \({\mit \Lambda }_b\) polarization, search for \(X^+(5568)\to B^0_s \pi ^+\), and the rare decay \(B^0_s \to \mu \mu \). Finally, the recent measurements of some angular parameters of the \(B^0 \to K^\star \mu \mu \) decay will be reviewed.

Current and Future Neutrino Experiments

Acta Phys. Pol. B 49, 1213 (2018)

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The article presents a review of selected results from neutrino experiments, concerning the mass measurements and studies of neutrino oscillations with various neutrino sources. Some of the projects planned to start in the near future are also presented.

Belle II Prospects for CP-violation Measurements

Acta Phys. Pol. B 49, 1229 (2018)

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The Belle II Collaboration operates a substantially upgraded Belle detector at the SuperKEKB energy-asymmetric \(e^{+}e^{-}\) collider. Belle II will start recording collisions at the \({\mit \Upsilon }\)(4S) energy in 2018, aiming to collect by 2025 50 ab\(^{-1}\) of data, 50 times more than the Belle experiment. We report prospects for measuring quantities associated with charge-parity violation, with special emphasis on the Cabibbo–Kobayashi–Maskawa angle \(\phi _3\)(\(\gamma \)) and observables in semileptonic \(B\)-meson decays associated with the quark-mixing matrix element \(V_{ub}\).

Flavour Physics at the FCC-ee

Acta Phys. Pol. B 49, 1241 (2018)

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The perspectives of flavour physics studies at the future FCC-ee collider are briefly discussed. The latter comprises a project of giant circular electron–positron collider which is under consideration at CERN. The following three specific issues will be addressed: studies of the decay \(B \to K^{*0}(892)\tau ^+\tau ^-\), searches for charged lepton flavour violation in \(Z^0\) boson and \(\tau \) lepton decays, together with the detection prospects of heavy, long-living sterile neutrinos.

Muon \(g-2\), Current Experimental Status and Future Prospects

Acta Phys. Pol. B 49, 1247 (2018)

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The muon gyromagnetic anomaly \(a_\mu \) has been measured with a precision \(\delta a_\mu /a_\mu = 540\) ppb using magic-momentum muon decays recorded up to 2001 by the E821 BNL experiment. Two projects aim at significantly improving that experimental precision: the E989 Collaboration at Fermilab plans to collect 21 times the BNL statistics and to improve by a factor four the uncertainty, the E34 Collaboration is designing a new experiment at J-PARC with a novel approach based on the production, injection and storage of ultra-cold low-energy muons. E34 aims at matching the BNL precision in a first phase, and to provide a significantly higher precision measurement in a second phase.

Simultaneous Production of \(D\) and \(B\) Mesons

Acta Phys. Pol. B 49, 1257 (2018)

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We present results of our studies of double-parton scattering (DPS) effects in simultaneous production of heavy flavour mesons (charm and bottom). We discuss production of charm–bottom and bottom–bottom meson–meson pairs in proton–proton collisions at the LHC. The calculation of DPS mechanism is performed within factorized Ansatz where each parton scattering is calculated within \(k_{\rm T}\)-factorization approach. The hadronization is done with the help of fragmentation functions. For completeness, we compare results for double- and single-parton scattering (SPS). The SPS components are also calculated in the \(k_{\rm T}\)-factorization with the help of KaTie Monte Carlo generator. As in the case of double charm production, also here the DPS dominates over the SPS, especially for small transverse momenta. We present several distributions and integrated cross sections with realistic cuts for simultaneous production of \(D^0 B^+\) and \(B^+ B^+\), suggesting future experimental studies at the LHC.

Updated Fits to the Present \(b \to s \ell ^+\ell ^-\) Data

Acta Phys. Pol. B 49, 1267 (2018)

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We discuss the observed deviations in \(b \to s \ell ^+ \ell ^-\) processes from the Standard Model predictions and present global fits for both hadronic effects and the new physics description of these anomalies. We investigate whether the different anomalies can be described by a consistent new physics effect. We consider all the possible relevant new physics contributions to the semileptonic \(b \to s\) transitions. Moreover, we study the prospects of future LHCb upgrade for establishing new physics with the theoretically clean observables.

Combined Interpretation of \(B\)-physics Anomalies and Model Building

Acta Phys. Pol. B 49, 1279 (2018)

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The observed anomalies in semileptonic \(B\)-meson decays represent the most significant deviation from the SM observed to date in particle physics. In this paper, I discuss how these can be consistently combined in a coherent and simple EFT setup. The complete set of heavy states which can generate the required operators when integrated out is then presented: colourless vectors, vector leptoquarks and scalar leptoquarks. Among these, the leptoquarks offer the most compelling case and their most interesting signatures in high-\(p_{\rm T}\) searches are explored.

Radiative Decays of the \(B\) Meson: a Progress Report

Acta Phys. Pol. B 49, 1291 (2018)

page 1291 •


Bounds on new physics from \(\bar B\to X_s\,\gamma \) depend on precise calculations of the Standard Model contributions. The expected experimental accuracy at Belle II implies that both the non-perturbative and perturbative effects need to be evaluated more precisely. Here, the status and progress of such calculations is summarized.

Majorana Neutrino Searches at the LHCb Experiment

Acta Phys. Pol. B 49, 1301 (2018)

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These proceedings present a set of searches for Majorana neutrinos, performed using decays of \(B\) and \(D\) mesons to final states with a pair of the same-sign leptons, using data collected by the LHCb experiment. No signal of Majorana neutrinos is observed for any of these decays and upper limits on the branching fractions are set.

cLFV Searches at LHCb

Acta Phys. Pol. B 49, 1309 (2018)

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The Large Hadron Collider beauty (LHCb) detector is an experiment designed for the study of heavy-flavour physics. These proceedings describe a set of searches for charged Lepton Flavour Violating (cLFV) decays at the LHCb detector. Analyses are performed with 1 fb\(^{-1}\) and 2 fb\(^{-1}\) of proton–proton collision data collected at center-of-mass energies of 7 and 8 TeV, respectively.

all authors

A. Ali, L. Maiani, A.V. Borisov, I. Ahmed, M.J. Aslam, A.Ya. Parkhomenko, A.D. Polosa, A. Rehman

New Look at Hidden Charm Tetra and Pentaquark States

Acta Phys. Pol. B 49, 1315 (2018)

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The work presents the analysis of the hidden charm \(P\)-wave tetraquarks in the diquark model, using an effective Hamiltonian incorporating the dominant spin–spin, spin–orbit and tensor interactions. We compare them with other \(P\)-wave systems such as \(P\)-wave charmonia and the newly discovered \({\mit \Omega }_c\) baryons, analyzed recently in this framework. The experimental situation on the \(Y\)-states is not certain, therefore, by using different spectra a detailed discussion of the parameters related to the diquark model is presented. Using the parameters from the currently preferred \(Y\)-states pattern, we work out the spin-parity, \(J^{PC}\), and mass spectrum for many states in the hidden charm \(P\)-wave supermultiplet. We hope in future when there will be an experimental consensus on different \(Y\)-states, an observation of these new resonances would be a decisive footprint of the underlying diquark dynamics.

Discrimination of Effective Radiative and Collisional In-medium Energy-loss Models by Their Effects on Angular Jet Structure

Acta Phys. Pol. B 49, 1325 (2018)

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Energy-loss studies of hard particle probes produced in heavy-ion collisions have often been used to get information on the interactions within the medium of a quark–gluon plasma (QGP). However, with the study of in-medium energy-loss of individual particles alone, it remains still ambiguous, whether the occurred decrease in particle energy is caused by predominantly radiative or collisional energy-loss mechanisms. Focusing on the in-medium energy-loss of hard jet partons, we propose additional studies of the angular jet structure as a means to further constrain the energy-loss mechanisms.

Charm Physics: Another Route Towards New Physics

Acta Phys. Pol. B 49, 1335 (2018)

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We summarize recent results for charm physics. These results span several categories: charm mixing, indirect (time-dependent) CP violation, direct (time-integrated) CP violation, \(T\) violation, semileptonic and leptonic decays, and decays of charm baryons.

Top-quark Differential Cross-section Measurements with the ATLAS Detector

Acta Phys. Pol. B 49, 1353 (2018)

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The most recent results on top-quark pairs and single top-quark differential cross-section measurements in proton–proton (\(pp\)) collisions with the ATLAS detector at the Large Hadron Collider (LHC) at \(\sqrt {s}=8\) and 13 TeV are presented. The results are compared to the latest QCD theoretical calculations.

Overview of ATLAS Heavy Flavor Measurements

Acta Phys. Pol. B 49, 1359 (2018)

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The ATLAS Experiment presents four recent measurements in the field of \(B\)-physics using data recorded at the center-of-mass energy of 8 TeV at the LHC. All are compared to contemporary models. These measurements involve differential cross sections for \(b\)-hadron pair production; prompt \(J/\psi \) pair production differential cross sections; differential production cross sections for \(\psi (2S)\) and \(X(3872)\), both observed in decays to \(J/\psi \pi ^+ \pi ^-\); and an angular analysis of \(B_d^0 \rightarrow K^* \mu ^+ \mu ^-\) decays.

Searching New Physics with Beauty Mesons

Acta Phys. Pol. B 49, 1371 (2018)

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The rare decay \(B\to K^{\!*}\ell ^+\ell ^-\) is an important mode for indirect search of new physics due to the measurement of large number of observables in experiments. Using the most general parametric form of the amplitude in the Standard Model (SM), we probe the physics beyond Standard Model in a theoretically clean approach. The model-independent framework has been implemented in the maximum \(q^2\) limit to highlight strong evidence of right-handed currents, which are absent in the SM. The conclusions derived are free from hadronic corrections. Next, we explain, in terms of a simple and compelling new physics scenario with only two new parameters, the discrepancies between the SM expectations and the data for the neutral-current observables \(R_{K^{(*)}}\), as well as the charged-current observables \(R(D^{(*)})\) while being consistent with all other data.

\(D \bar D\) Asymmetry at Low and High Energies and Possible Consequences for Prompt Atmospheric Neutrinos

Acta Phys. Pol. B 49, 1383 (2018)

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We discuss the role of unfavoured light quark/antiquark into \(D\) meson fragmentation. The unknown parameters of fragmentation process are adjusted to describe the asymmetry for \(D^+\) and \(D^-\) production measured by the LHCb. Predictions for similar asymmetry for neutral \(D\) mesons are presented. The predicted asymmetry at large rapidity (or \(x_{\rm F}\)) are very large which is related to the valence-quark contribution. As a result, prompt atmospheric neutrino flux at high neutrino energies can be much larger than for the conventional \(c \to D\) fragmentation. We predict large rapidity-dependent \(D^+/D^-\) and \(D^0/{\bar D}^0\) asymmetries for low (\(\sqrt {s} =20\)–100 GeV) energies. The \(q/\bar q \to D\) fragmentation leads to enhanced production of \(D\) mesons at low energies. Predictions for \(p+^{4}\!\textrm {He}\) collisions relevant for a fixed target LHCb experiment are discussed.

Reparametrization Invariance and Partial Resummation of the Heavy-quark Expansion

Acta Phys. Pol. B 49, 1393 (2018)

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Reparametrization invariance (RPI) relates different orders in the heavy-quark expansion. We discuss the implications of RPI for total rates of inclusive decays. The obtained results are manifestly RPI, allowing for a re-summation of higher-order terms in the heavy-quark expansion, which reduces the number of independent parameters.


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