Quark Mass Research Articles

Lambda _brightarrow p transition form factors in perturbative QCD

We reanalyze the Lambda _brightarrow p transition form factors in the perturbative QCD (PQCD) approach by including higher-twist light-cone distribution amplitudes (LCDAs) of a Lambda _b baryon and a proton. The previous PQCD evaluation performed decades ago with only the leading-twist Lambda _b baryon and proton LCDAs gave the form factors, which are two orders of magnitude smaller than indicated by experimental data. We find that the twist-4 Lambda _b baryon LCDAs and the twist-4 and -5 proton LCDAs contribute dominantly, and the enhanced form factors become consistent with those from lattice QCD and other nonperturbative methods. The estimated branching ratios of the semileptonic decays Lambda _brightarrow pell {bar{nu }}_ell and the hadronic decay Lambda _brightarrow ppi are also close to the data. It implies that the b quark mass is not really heavy enough, and higher-power contributions play a crucial role, similar to the observation made in analyses of B meson transition form factors. With the formalism established in this work, we are ready to study various exclusive heavy baryon decays systematically in the PQCD approach.

Baryonic form factors of the pion and kaon in a chiral quark model

The baryonic form factor of charged pions is studied in detail in the Nambu--Jona-Lasinio model with constituent quarks, where the spontaneously broken chiral symmetry is the key dynamical ingredient guaranteeing the would-be Goldstone boson nature of the pseudoscalar mesons octet. In general, this form factor arises when the isospin symmetry is broken, which is the case if the $u$ and $d$ quark masses are split, as in the real world, or if the electromagnetic effects were taken into account. We obtain estimates for this basic property of the pion resulting from the quark mass splitting for a range of model parameters, and importantly, for different pion masses, going up to the values used in lattice QCD. We find very stable model results, with the mean square radius of $\pi^+$ in the range $(0.05-0.07~{\rm fm})^2$. From charge conjugation, the baryonic form factor of $\pi^+$ and $\pi^-$ are equal and opposite. We also obtain the transverse-coordinate, relativistically invariant baryonic density of the charged pion. In $\pi^+$, the inner region carries a negative, and the outside -- a positive baryon number density, both cancelling to zero, as obviously the pion carries no net baryon charge. We also carry out an analogous analysis for the kaon, where the effect is much larger due to the sizable $s$ and $u/d$ quark mass splitting. We discuss the prospects of lattice QCD measurements of the baryonic form factors of charged pions and kaons.

Lepton and quark mixing patterns with generalized CP transformations

In this study, we modify a scenario, originally proposed by Grimus and Lavoura, in order to obtain maximal values for the atmospheric mixing angle and , violating the Dirac phase of the lepton sector. To achieve this, we employ and some discrete symmetries in a type II seesaw model. To make predictions about the neutrino mass ordering and smallness of the reactor angle, we establish some conditions on the elements of the neutrino mass matrix of our model. Finally, we study the quark masses and mixing pattern within the framework of our model.

Minimizing the phase structure of quark mass matrices

Fritzsch–Xing matrices are a particular class of texture 4 zero hermitian quark mass matrices, known to be successful in accommodating the quark mixing data. In the present work, it is shown that these texture 4-zero matrices with only one phase parameter, unlike the usually considered two phase parameters, are not only consistent with the latest experimental quark mixing data, but also predict the CP violation parameters, J and corresponding phase delta , in agreement with the recent global analyses. We also show that the mass matrix elements do not exhibit a strong hierarchy and there is a strong correlation between some of the mass matrix elements of up and down sector. A precision measurement of delta as well as small quark masses would have the potential to constrain the phase structure of the matrices further.

Transverse momentum distributions of valence quarks in light and heavy vector mesons

We study the leading-twist time-reversal even transverse momentum-dependent parton distribution functions (TMDs) of light and heavy vector mesons, i.e., the $\ensuremath{\rho}$, $J/\ensuremath{\psi}$ and $\mathrm{\ensuremath{\Upsilon}}$. We employ the leading Fock-state light front wave functions (LF-LFWFs) of $\ensuremath{\rho}$ and $J/\ensuremath{\psi}$ from our recent study, and supplement with $\mathrm{\ensuremath{\Upsilon}}$'s LF-LFWFs. These LF-LFWFs are extracted from dynamically solved Bethe-Salpeter wave functions. The vector meson TMDs are then studied with the light front overlap representation at leading Fock-state. All the obtained TMDs are nonvanishing and evolve with current quark mass, in particular the tensor polarized TMDs ${f}_{1LT}$ and ${f}_{1TT}$ which undergo a sign flip. The $\ensuremath{\rho}$ TMDs are compared with other model studies and agreement is found, aside from ${f}_{1LT}$ and ${f}_{1TT}$. Finally, the collinear PDFs of vector mesons are studied. The $\ensuremath{\rho}$'s valence PDFs ${f}_{1,v}(x)$ and ${g}_{1L,v}(x)$ are evolved to the scale of 2.4 GeV, with their first three moments compared to the lattice QCD prediction. The qualitative behavior of tensor polarized PDF ${f}_{1LL}(x)$ in $\ensuremath{\rho}$ at large $x$ is also discussed.

Toward the chiral phase transition in the Roberge-Weiss plane

We discuss the interplay between chiral and center sector phase transitions that occur in QCD with an imaginary quark chemical potential $\ensuremath{\mu}=i(2n+1)\ensuremath{\pi}T/3$. Based on a finite size scaling analysis in ($2+1$)-flavor QCD using highly improved staggered quark fermions with a physical strange quark mass and a range of light quark masses, we show that the endpoint of the line of first-order Roberge-Weiss (RW) transitions between center sectors is second order for light quark masses ${m}_{l}\ensuremath{\ge}{m}_{s}/320$, and that it belongs to the 3-d, $Z(2)$ universality class. The operator for the chiral condensate behaves like an energylike operator in an effective spin model for the RW phase transition. As a consequence, for any nonzero value of the quark mass, the chiral condensate will have an infinite slope at the RW phase transition temperature, ${T}_{\mathrm{RW}}$. Its fluctuation, the disconnected chiral susceptibility, behaves like the specific heat in $Z(2)$ symmetric models and diverges in the infinite volume limit at the RW phase transition temperature ${T}_{\mathrm{RW}}$ for any nonzero value of the light quark masses. Our analysis suggests the critical temperatures for the RW phase transition and the chiral phase transition coincide in the RW plane. On lattices with temporal extent ${N}_{\ensuremath{\tau}}=4$, we find in the chiral limit ${T}_{\ensuremath{\chi}}={T}_{\mathrm{RW}}=195(1)\text{ }\text{ }\mathrm{MeV}$.

Analysis of Identified Particle Transverse Momentum Spectra Produced in pp, p–Pb and Pb–Pb Collisions at the LHC Using TP-like Function

In the framework of a multi-source thermal model at the partonic level, we have analyzed transverse momentum spectra of hadrons measured by the ALICE Collaboration in proton–proton (pp or p–p) collisions at the center-of-mass energy of s=7 and 13 TeV, proton–lead (p–Pb) collisions at sNN=5.02 TeV, and lead–lead (Pb–Pb) collisions at sNN=2.76 TeV. For mesons (baryons), the contributions of two (three) constituent quarks are considered, in which each quark contributes to hadron transverse momentum to obey the revised phenomenological Tsallis transverse momentum distribution for Maxwell–Boltzmann particles (the TP-like function, in short) with isotropic random azimuthal angles. Three main parameters, namely, the revised index a0, effective temperature T, and entropy-related index n, are obtained, showing the same tendency for both small and large systems with respect to the centrality (or multiplicity) of events, the rest mass of hadrons, and the constituent mass of quarks.

Spectrum of light nuclei in a finite volume

Lattice quantum chromodynamics calculations of multi-baryon systems with physical quark masses would start a new age of ab initio predictions in nuclear physics. Performed on a finite grid, such calculations demand extrapolation of their finite volume numerical results to free-space physical quantities. Such extraction of the physical information can be carried out fitting effective field theories (EFTs) directly to the finite-volume results or utilizing the L\"uscher free-space formula or its generalizations for extrapolating the lattice data to infinite volume. To understand better the effect of periodic boundary conditions on the binding energy of few nucleon systems we explore here light nuclei with physical masses in a finite box and in free space. The stochastic variational method is used to solve the few-body systems. Substantial optimizations of the method are introduced to enable efficient calculations in a periodic box. With the optimized code, we perform accurate calculations of light nuclei $A \le 4$ within leading order pionless EFT. Using L\"uscher formula for the two-body system, and its generalization for 3- and 4-body systems, we examine the box effect and explore possible limitations of these formulas for the considered nuclear systems.

Electromagnetic and strong isospin breaking in light meson masses

We study electromagnetic as well as strong isospin breaking effects in the isospin mass splittings of light pseudoscalar and vector mesons. To this end we employ a coupled system of quark Dyson-Schwinger and meson Bethe-Salpeter equations whose interaction kernels contain gluon, pion and photon exchange interactions. In bound states, QCD-induced isospin breaking is manifest on different levels. On the one hand, a different explicit up- and down-quark mass directly affects the propagators of the constituent quarks. On the other hand, it leads to different interaction kernels within the isospin multiplets. In addition, electromagnetic isospin breaking is induced via a photon exchange diagram. Using the kaon iso-doublet and the charged pion masses as input to determine the up, down and strange quark masses we find for the pion, kaon and rho meson mass splittings different patterns each. In particular, our results provide evidence that the effects from two sources of mass splittings, the different quark masses and the different quark charges, do not add up linearly.

Recent results on top quark mass and properties and rare/anomalous top quarks interactions in CMS

The amount of data collected by the CMS experiment at the CERN LHC in the second data taking period provides the possibility to study absolute and differential cross sections of top quark interaction processes with high precision. Utilizing these results, fundamental standard model parameters such as the top quark mass are extracted. Moreover, given standard model measurements are interpreted in the context of beyond the standard model theories. Recent results on top quark properties and rare or anomalous top quark interactions by CMS are presented in these proceedings. Furthermore, the implications of experimental results to effective field theory are discussed.

Signature of a Doubly Charm Tetraquark Pole in DD^{*} Scattering on the Lattice.

The doubly charm tetraquark with flavor ccu[over ¯]d[over ¯] and isospin I=0 is investigated by calculating the DD^{*} scattering amplitude with lattice QCD. The simulation is done on CLS ensembles with dynamical u/d, s quarks and m_{π}≃280 MeV for two charm quark masses, one slightly larger and one slightly lower than the physical value. The scattering amplitudes for partial waves l=0, 1 are extracted near threshold via the Lüscher method by considering systems with total momenta PL/(2π)=0,1,sqrt[2],2 on two spatial volumes. A virtual bound state pole in the DD^{*} scattering amplitude with l=0 is found 9.9_{-7.1}^{+3.6} MeV below the DD^{*} threshold for the charm quark mass closer to the physical value. This pole is likely related to the doubly charm tetraquark discovered by LHCb less than 1MeV below the D^{0}D^{*+} threshold. Future lattice simulations closer to the continuum limit and physical quark masses would be valuable to establish this connection systematically.

Photon production rate calculation from quark-gluon plasma using MEQM in heavy-ion collision

It is widely accepted that a huge and intense magnetic field is created along with the exotic state of matter in heavy-ion collision. The photon yield from quark-gluon plasma created in a magnetic environment is studied using a thermal quasi-particle mass. The quarks acquire this mass depending on the temperature and nonzero value of quark chemical potential which gets modified as magnetized effective quark mass (MEQM) in the presence of magnetic field. The total photon rate is shown for one loop process incorporating MEQM. It is found that the emission rate to lowest order increases strongly with increasing of the quark chemical potential and temperature. The enhanced yield in photon is also compared with the recently reported theoretical results.

Open charm mesons and charmonia in magnetized strange hadronic matter * *A.J.C.S acknowledges the support towards this work from the Department of Science and Technology, Government of India, via an INSPIRE fellowship (INSPIRE Code IF170745). AM acknowledges financial support from Department of Science and Technology (DST), Government of India (CRG/2018/002226)

We investigate the in-medium masses of open charm mesons (D( , ), ( , ), ( , )) and charmonium states ( , , , , ) in strongly magnetized isospin asymmetric strange hadronic matter using a chiral effective model. In the presence of a magnetic field, the number and scalar densities of charged baryons have contributions from Landau energy levels. The mass modifications of open charm mesons result from their interactions with nucleons, hyperons, and the scalar fields (the non-strange field σ, strange field ζ, and isovector field δ) in the presence of a magnetic field. The mass modifications of the charmonium states result from the modification of gluon condensates in a medium simulated by the variation in the dilaton field (χ) in the chiral effective model. The effects of finite quark masses are also incorporated in the trace of the energy-momentum tensor in quantum chromodynamics to investigate the mass shifts of charmonium states. The in-medium masses of open charm mesons and charmonia are observed to decrease with an increase in baryon density. The charged , , , and mesons have additional positive mass shifts due to Landau quantization in the presence of a magnetic field. The effects of the strangeness fraction are observed to be more dominant for mesons compared with D mesons. The mass shifts of charmonia are observed to be larger in hyperonic media compared with nuclear media when the effect of the finite quark mass term is neglected. These medium mass modifications can have observable consequences on the production of the open charm mesons and charmonia in high-energy asymmetric heavy-ion collision experiments.

O(αs) perturbative and nonperturbative corrections to polarized semileptonic Λb decay distributions

In this paper we calculate first order radiative QCD corrections to the decay process $b\to cW^-(\to\ell^-\bar\nu_\ell)$ of a polarized bottom quark. Taking into account both the bottom and charm quark masses, the analytical expressions given in this paper allow for a detailed analysis of the differential decay rate of the polarized quark in dependence on the polar and azimuthal angles of the lepton pair and the angle of the polarization vector of the quark relative to the momentum direction of the $W$ boson. The results are given for different polarization states of the charged lepton. In addition, we calculated nonperturbative corrections and estimated their contribution.

Understanding mass hierarchy in collisional energy loss through heavy flavor data

While experimental observations, such as the mass hierarchy effect, are attributed and analyzed within radiative models, their interpretation crucially depends on collisional energy loss contribution, which is often neglected in such analyses. To our knowledge, neither a (direct) simple relation between collisional energy loss and heavy quark mass is established, nor an observable that quantifies this effect. On the other hand, the upcoming high-luminosity measurements at RHIC and LHC will generate heavy flavor data with unprecedented precision, providing an opportunity to utilize high-pT heavy flavor data to analyze the interaction mechanisms in the quark-gluon plasma. To this end, we employ a recently developed DREENA framework based on our dynamical energy loss formalism to study the mass hierarchy in heavy flavor suppression. We present i) Analytical derivation of a direct relation between collisional suppression/energy loss and heavy quark mass. ii) A novel observable sensitive only to the collisional energy loss mechanism to be tested by future high-precision experiments. iii) Analytical and numerical extraction of the mass hierarchy in collisional energy losses through this observable.

NLO JIMWLK evolution with massive quarks

NLO evolution of the Jalilian-Marian-Iancu-McLerran-Weigert-Leonidov-Kovner (JIMWLK) equation with massless quarks was derived a few years ago. We make a step further to compute the evolution kernels focusing on the effects due to finite quark masses. To this goal, the light-cone wave function of a fast moving dilute hadronic projectile is computed up to mathcal{O} (g3) in QCD coupling constant. Compared with the massless case, a new IR divergence emerges, which is eventually canceled by a mass dependent counter term. Our results extend the theoretical tools used in physics of gluon saturation and aim at improving precision in future phenomenological applications.

Gluon fusion production at NLO: merging the transverse momentum and the high-energy expansions

The virtual corrections to gg → HH and gg → ZH are analytically evaluated combining an expansion in the small transverse momentum of the final particles with an expansion valid at high energies. The two expansion methods describe complementary regions of the phase space and we merge their results, extending the range of validity of both expansions using Padé approximants. We show that this approach can reproduce the available numerical results retaining the exact top quark mass dependence with an accuracy below the 1% level. Our results allow a fast and flexible evaluation of the virtual corrections of the considered processes. Furthermore, they are available in different renormalisation schemes of the top quark mass.

Dynamical mass generation in Minkowski space at QCD scale

We undertake the challenging task to reveal the properties of dressed light-quarks in the space- and time-like regions. For that aim, we solved the Dyson-Schwinger equation (DSE) in Minkowski space for the quark propagator in a QCD inspired model, focusing on the realization of dynamical chiral symmetry breaking (DCSB) in the large coupling regime. The DSE is considered in the quenched approximation within the rainbow-ladder truncation with a massive gluon and a Pauli-Villars term, which is used to tune the infrared (IR) physics of the model. The solution of the DSE in Minkowski space is performed by resorting to the integral representation of the quark self-energy and propagator, which leads to a coupled set of closed self-consistent equations for the spectral densities, taking into account finite on-mass-shell renormalization. The parameters of the model are chosen such that the gluon mass scale is consistent with recent lattice QCD (LQCD) calculations, the Pauli-Villars mass is lowered down to about 1 GeV to concentrate strength in the infrared momentum region, and the coupling constant and renormalized mass are tuned to reproduce LQCD results for the quark mass function in the Landau gauge. Future application to study the pion consistently with DCSB within the Bethe-Salpeter framework with self-energies in Minkowski space is also delineated.

The 3d O(4) model as an effective approach to the QCD phase diagram

The QCD phase diagram is one of the most prominent outstanding puzzles within the Standard Model. Various experiments, which aim at its exploration beyond small baryon density, are operating or in preparation. From the theoretical side, this is an issue of non-perturbative QCD, and therefore of lattice simulations. However, a finite baryon density entails a technical problem (known as the “sign problem”), which has not been overcome so far. Here we present a study of an effective theory, the O(4) non-linear sigma model. It performs spontaneous symmetry breaking with the same Lie group structure as 2-flavor QCD in the chiral limit, which strongly suggests that they belong to the same universality class. Since we are interested in high temperature, we further assume dimensional reduction to the 3d O(4) model, which implies topological sectors. As pointed out by Skyrme, Wilczek and others, its topological charge takes the role of the baryon number. Hence the baryon chemical potential µB appears as an imaginary vacuum angle, which can be included in the lattice simulation without any sign problem. We present numerical results for the critical line in the chiral limit, and for the crossover in the presence of light quark masses. Their shapes are compatible with other predictions, but up to the value of about µB ≈ 300 MeV we do not find the notorious Critical Endpoint (CEP).

Flavourful axion and the Peccei-Quinn symmetry

A model is presented, where the Froggatt-Nielsen and Peccei-Quinn symmetries are identified. This provides a solution to the strong CP problem and an explanation to the fermion mass hierarchy. At leading order, the quark mass matrix possess a Nearest-Neighbour-Interaction structure, while the neutrino mass matrix has a Majorana A2 texture. From a thorough numerical analysis the viability of this model is asserted, by comparing against current measurements. The data obtained from this analysis is then used to study properties from the axion.