Production rates and branching fractions of heavy hadrons & quarkonia at LHC experiments

TL;DR

This paper reviews recent measurements of production cross-sections and branching fractions of heavy hadrons and quarkonia at LHC, providing insights into their production mechanisms and decay processes.

Contribution

It presents new experimental results on production rates and branching fractions of heavy hadrons and quarkonia at LHC, including a search for intermediate states in meson decay.

Findings

Measured production cross-sections of b-hadrons and quarkonia.

Reported branching fractions of bottom baryons and mesons.

Presented a new search for intermediate states in meson decay.

Abstract

Measurements of production cross-sections of inclusive $b$-hadrons pairs, bottom mesons and baryons, and quarkonia at LHC will be shown. Recent measurements of branching fractions of bottom baryons, bottom mesons with baryons in the final state, and a new result about a search for intermediate states in meson decay will also be shown.

Equations

$$\sigma (B(\to J/\psi [\to {\mu }^{+}{\mu }^{-}]+X)B(\to \mu +X)))=$$

$$(17.7\pm 0.1(\mathrm{stat})\pm 2.0(\mathrm{syst}))\mathrm{nb}\text{makebox}[0.0pt][l].$$

$$\sigma (pp\to B^{\pm }X(\sqrt{s}=7\mathrm{TeV})=$$

$$(43.0\pm 0.2(\mathrm{stat})\pm 2.5(\mathrm{syst})\pm 1.7(b.r.))\mu \mathrm{b}$$

$$\sigma (pp\to B^{\pm }X(\sqrt{s}=13\mathrm{TeV})=$$

$$(86.6\pm 0.5(\mathrm{stat})\pm 5.4(\mathrm{syst})\pm 3.4(b.r.))\mu \mathrm{b}$$

$$R=\frac{f_{{\Xi }_b^{-}}}{f_{{\Lambda }_b^0}}\cdot \frac{\Gamma ({\Xi }_b^{-}\to J/\psi {\Xi }^{-})}{\Gamma ({\Lambda }_b^0\to J/\psi {\Lambda }^0)}\cdot \frac{{\tau }_{{\Xi }_b^{-}}}{{\tau }_{{\Lambda }_b^0}}\text{makebox}[0.0pt][l]$$

$$=\frac{N({\Xi }_b^{-}\to J/\psi {\Xi }^{-})}{N({\Lambda }_b^0\to J/\psi {\Lambda }^0)}\cdot \frac{{ϵ}_{{\Lambda }_b^0}}{{ϵ}_{{\Xi }_b^{-}}}\text{makebox}[0.0pt][l].$$

$$m_{{\Xi }_b^{-}}=$$

$$(5796.70\pm 0.39(\mathrm{stat})\pm 0.15(\mathrm{syst})\pm 0.17(m_{{\Lambda }_b^0}))\mathrm{MeV}$$

$$\frac{f_{{\Xi }_b^{-}}}{f_{{\Lambda }_b^0}}=(6.7\pm 0.5(\mathrm{stat})\pm 0.5(\mathrm{syst})\pm 2.0(f.s.))\times 10^{-2}$$

$$\displaystyle{[}\makebox[0.0pt][l]{$\sqrt{s}=7,8~{}\mathrm{TeV}$}{]}$$

$$\frac{f_{{\Xi }_b^{-}}}{f_{{\Lambda }_b^0}}=(8.2\pm 0.7(\mathrm{stat})\pm 0.6(\mathrm{syst})\pm 2.5(f.s.))\times 10^{-2}$$

$$\displaystyle{[}\makebox[0.0pt][l]{$\sqrt{s}=\makebox[0.0pt][r]{$13~{}\mathrm{TeV}$}$}{]}$$

$$\displaystyle\sigma_{\mathrm{Fid}}(\makebox[0.0pt][r]{$\left|y_{{J/\psi}}\right|<\makebox[0.0pt][l]{$1.05$}$})=$$

$$(15.6\pm 1.3(\mathrm{stat})\pm 1.2(\mathrm{syst})\pm 0.2(b.r.)\pm 0.3(\mathrm{lum}))\mathrm{pb}$$

$$\displaystyle\sigma_{\mathrm{Fid}}(\makebox[0.0pt][r]{$1.05<\left|y_{{J/\psi}}\right|<\makebox[0.0pt][l]{$2.1$}$})=$$

$$(13.5\pm 1.3(\mathrm{stat})\pm 1.1(\mathrm{syst})\pm 0.2(b.r.)\pm 0.3(\mathrm{lum}))\mathrm{pb}$$

$$f_{\mathrm{DPS}}=(9.2\pm 2.1(\mathrm{stat})\pm 0.5(\mathrm{syst}))\%\text{makebox}[0.0pt][l].$$

$$\sigma =(15.2\pm 1.0(\mathrm{stat})\pm 0.9(\mathrm{syst}))\mathrm{nb}\text{makebox}[0.0pt][l].$$

$$f_{\mathrm{DPS}}=((42\pm 25)÷(86\pm 55))\%\text{makebox}[0.0pt][l].$$

$$\frac{\mathcal{B}({\Lambda }_b^0\to \psi (2\mathrm{S}){\Lambda }^0)}{\mathcal{B}({\Lambda }_b^0\to J/\psi {\Lambda }^0)}=$$

$$0.513\pm 0.023(\mathrm{stat})\pm 0.016(\mathrm{syst})\pm 0.011(b.r.)$$

$$\mathcal{B}(B_d^0\to J/\psi p\bar{p})=$$

$$\frac{N_{B_d^0\to J/\psi p\bar{p}}}{N_{B_s^0\to J/\psi \varphi }}\cdot \mathcal{B}(B_s^0\to J/\psi \varphi )\cdot \mathcal{B}(\varphi \to K^{+}{K}^{-})\cdot \frac{f_s}{f_d}$$

$$\mathcal{B}(B_s^0\to J/\psi p\bar{p})=$$

$$\frac{N_{B_s^0\to J/\psi p\bar{p}}}{N_{B_s^0\to J/\psi \varphi }}\cdot \mathcal{B}(B_s^0\to J/\psi \varphi )\cdot \mathcal{B}(\varphi \to K^{+}{K}^{-})\text{makebox}[0.0pt][l].$$

$$\mathcal{B}(B_d^0\to J/\psi p\bar{p})=$$

$$(4.51\pm 0.40(\mathrm{stat})\pm 0.44(\mathrm{syst}))\times 10^{-7}$$

$$\mathcal{B}(B_s^0\to J/\psi p\bar{p})=$$

$$(3.58\pm 0.19(\mathrm{stat})\pm 0.33(\mathrm{syst}))\times 10^{-6}\text{makebox}[0.0pt][l].$$

$$m_{B_d^0}=(5279.74\pm 0.30(\mathrm{stat})\pm 0.10(\mathrm{syst}))\mathrm{MeV}$$

$$m_{B_s^0}=(5366.85\pm 0.19(\mathrm{stat})\pm 0.13(\mathrm{syst}))\mathrm{MeV}\text{makebox}[0.0pt][l].$$

$$\frac{\mathcal{B}(B^{+}\to J/\psi {\bar{\Lambda }}^{0}p)}{\mathcal{B}(B^{+}\to J/\psi K^{\ast +})}=$$

$$1.054\pm 0.057(\mathrm{stat})\pm 0.028(\mathrm{syst})\pm 0.011(b.r.)$$

$$\mathcal{B}(B^{+}\to J/\psi {\bar{\Lambda }}^{0}p)=$$

$$(15.07\pm 0.81(\mathrm{stat})\pm 0.40(\mathrm{syst})\pm 0.86(b.r.))\times 10^{-6}$$

Full text

I Introduction

Measurements of heavy hadron and quarkonia cross sections at LHC allow probing QCD processes; they are also reference or ingredient for searches and measurements of rarer or new processes, as well as the baseline for associated production of heavy flavour and other objects.

The study of decay properties and branching fractions does allow a test of form-factor models as well as the search for new and exotic states that can be produced in the decay.

Results from ATLAS ref:aExper , CMS ref:cExper and LHCb ref:lExper will be shown in the following.

II Production cross-sections

II.1 Inclusive $b$-hadrons

An inclusive $b$-hadron pair production cross section measurement was obtained by ATLAS ref:aBBinc at an energy $\sqrt{s}=8~{}\mathrm{TeV}$; final states were selected looking for a ${J/\psi}$ coming from the first hadron and decaying to ${\mu^{+}\mu^{-}}$, and a muon coming from the second hadron. The fiducial volume was defined requiring the two muons from the ${J/\psi}$ to have $\left|\eta_{\mu,{J/\psi}}\right|<2.3$ and the third muon to have $\left|\eta_{\mu}\right|<2.5$; a minimum transverse momentum was also required: $p_{T,\mu}>6\mathrm{GeV}$. The total cross section in the fiducial volume was found:

[TABLE]

II.2 Bottom mesons and baryons

II.2.1 ${B^{+}}$ production

The differential $pp\rightarrow{B^{+}}+X$ cross-section versus transverse momentum or rapidity was measured by CMS ref:cBPdif at an energy $\sqrt{s}=13~{}\mathrm{TeV}$ in the region $\left|y_{B}\right|<1.45$ or $\left|y_{B}\right|<2.1$ and $10~{}\mathrm{GeV}<p_{T,B}<100~{}\mathrm{GeV}$ or $17~{}\mathrm{GeV}<p_{T,B}<100~{}\mathrm{GeV}$; the ratio with the corresponding cross-section at $\sqrt{s}=7~{}\mathrm{TeV}$ was measured and compared with FONLL ref:fonll1 ; ref:fonll2 ; ref:fonll3 and PYTHIA ref:pythia predictions. Results are shown in Fig. 1.

An analogous study was done by LHCb ref:lBPdif , that measured the double differential cross-section versus transverse momentum and rapidity in the region $2.0<\left|y_{B}\right|<4.5$ , $p_{T,B}<40~{}\mathrm{GeV}$. Again the ratio with the corresponding cross-section at $\sqrt{s}=7~{}\mathrm{TeV}$ was measured and compared with FONLL ref:fonllf predictions. Differential cross-sections are shown in Fig. 2; the integrated cross sections were found:

[TABLE]

where the last uncertainty comes from the ${{B^{\pm}}\rightarrow{J/\psi}{K^{\pm}}}$ branching fraction.

II.2.2 ${\Xi_{b}^{-}}$ production

Recently LHCb measured the ratio $f_{\Xi_{b}^{-}}/f_{\Lambda^{0}_{b}}$ of the fragmentation fractions to ${\Xi_{b}^{-}}$ and ${\Lambda^{0}_{b}}$ ref:lFFRxl . The decay of the ${\Xi_{b}^{-}}$ baryon has been studied since some time and a measurement of a branching fraction was done ref:lXbbrm , but its absolute determination requires knowing the fragmentation ratio.

The quantity that is directly accessible is the ratio $R$ of the number of reconstructed decays in the channel ${\Xi_{b}^{-}}\rightarrow{J/\psi}\Xi^{-}$, and a normalization one, with ${\Lambda^{0}_{b}}\rightarrow{J/\psi}{\Lambda^{0}}$, but the ratio $R$ can be expressed also as the ratio of the products of fragmentation and branching fractions; the latter can be expressed as the products of the ratios of partial widths and lifetimes:

[TABLE]

The ratio of widths can be assumed to be $2/3$ from $SU(3)$ flavor symmetry ref:su3fs1 ; ref:su3fs2 ; ref:su3fs3 and the ratio of lifetimes can be taken from PDG ref:pdgPRD so that the fragmentation ratio can be obtained. The decay has been reconstructed pairing a ${J/\psi}\rightarrow{\mu^{+}\mu^{-}}$ with a ${\Lambda^{0}}\rightarrow p\pi^{-}$ or a $\Xi^{-}\rightarrow{\Lambda^{0}}\pi^{-}$. For the reconstruction of the $\Xi^{-}$ or ${\Lambda^{0}}$ tracks have been classified as “long” or “downstream”, depending on the track originating before or after the vertex detector. For ${\Lambda^{0}}$ downstream tracks have been used, due to the long lifetime, while a long track was used as candidate for the pion coming from the $\Xi^{-}$ decay. The signal yields were estimated from fits to the mass distributions, as shown in Fig. 3.

Using the mass difference $m_{\Xi_{b}^{-}}-m_{\Lambda^{0}_{b}}$ as free parameter in the fit and using the ${\Lambda^{0}_{b}}$ mass from the PDG ref:pdgPRD the most precise measurement of ${\Xi_{b}^{-}}$ mass was obtained:

[TABLE]

where the last uncertainty comes from the ${\Lambda^{0}_{b}}$ mass.

With the signal yields from the fits and the efficiencies from simulation the ratio $R$ was obtained, and in the end the fragmentation fraction was extracted:

[TABLE]

where the last uncertainty is due to the flavor symmetry assumption and taken to be 30%.

II.3 Quarkonia

Several measurements of the production cross-section for quarkonia have been done at LHC experiments; a special interest can be found in the production of quarkonia pairs. Quarkonia pairs can be produced in single parton scattering (SPS), that’s assumed to dominate and lead to strongly correlated pairs with small rapidity differences, but, in the high parton densities in proton-proton collisions, also double parton scattering (DPS) can occur producing multiple heavy flavour particles with large $\Delta y$ ref:qqpBar ; ref:qqpKom .

A measurement of the DPS contribution in double ${J/\psi}$ production was done by ATLAS ref:aDJPsi at $\sqrt{s}=8~{}\mathrm{TeV}$. In the analysis ${J/\psi}$ pairs coming from different $pp$ interactions were removed with a cut on the distance along the beam direction between the reconstructed vertices, while the residual pile-up contamination was estimated looking at the kinematic variables distributions in sidebands. In double parton scattering ${J/\psi}$ candidates are assumed to be produced independently, so a template $\Delta y\Delta\phi$ distribution has been built with ${J/\psi}$ pairs from different events and has been normalized to data at large rapidity difference. Then event weights in each $\Delta y\Delta\phi$ bin have been computed from the ratio of the normalized template and full data; this weight can be used as an estimate of the DPS fraction, that can be compared to prediction from NLO versus rapidity difference and transverse momentum as shown in Fig. 4.

The total cross-section, in two fiducial regions $\left|y_{{J/\psi}}\right|<1.05$ , $1.05<\left|y_{{J/\psi}}\right|<2.1$ with $p_{T,{J/\psi}}>8.5~{}\mathrm{GeV}$, $p_{T,\mu}>2.5~{}\mathrm{GeV}$ and $\left|\eta_{\mu}\right|<2.3$, were found to be:

[TABLE]

with a DPS fraction

[TABLE]

A similar measurement at $\sqrt{s}=13~{}\mathrm{TeV}$ has been done from LHCb ref:lDJPsi ; ref:lDJPse ; the measured total cross-section for the production in the region $2.0<\left|y\right|<4.5$ , $p_{T}<10~{}\mathrm{GeV}$ was:

[TABLE]

The DPS component prediction was obtained from a large number of pseudoexperiments, where two uncorrelated ${J/\psi}$ mesons were produced according to the measured differential cross-sections, and SPS predictions from theoretical calculations using several approaches (LO, NLO, color singlet or color octet). Several data distributions were fitted with a two-component model to obtain the DPS fraction giving results in the range:

[TABLE]

As an example, the comparison between the measured and predicted differential cross-section vs. $p_{T,{J/\psi}{J/\psi}}$ is shown in Fig. 5.

III Branching fractions

III.1 Bottom baryon decay

Ratios of branching fractions of $b$-hadrons with a ${J/\psi}$ or a ${\psi(2\mathrm{S})}$ in the final state allow testing the factorization of amplitudes; some recent result of such ratios involve baryons. A measurement of the ratio of branching fractions of ${\Lambda^{0}_{b}}\rightarrow{\psi(2\mathrm{S})}{\Lambda^{0}}$ and ${\Lambda^{0}_{b}}\rightarrow{J/\psi}{\Lambda^{0}}$ was done by ATLAS ref:aBRLbr a few years ago giving a result that shows a discrepancy from covariant quark model prediction ref:brLBr1 ; ref:brLBr2 . Another measurement has just been done by LHCb ref:lBRLbr that reconstructed $\psi$ from non-prompt muons, a ${\Lambda^{0}}$ with two tracks of the same type, “long” or “downstream”, built a common vertex and applied a constrained fit with the masses of the $\psi$ and the ${\Lambda^{0}}$.

Events have been weighted with the inverse of efficiency; the latter was estimated in the simulation as well as the background from decays of ${B^{0}}\rightarrow\psi({K^{0}_{S}}\rightarrow\pi^{+}\pi^{-})$ or ${\Xi_{b}^{-}}\rightarrow\psi(\Xi^{-}\rightarrow{\Lambda^{0}}\pi^{-})$: the invariant mass distributions are shown in Fig. 6.

Taking the signal yields from the mass distributions fit and branching fractions of the $\psi$ from PDG ref:pdgPRD the branching fractions ratio was obtained:

[TABLE]

where the last uncertainty comes from the $\psi$ branching fraction.

III.2 Baryon production in meson decays

III.2.1 ${B^{0}_{d,s}}$ decay

Some special interest related to baryons can be found in heavy hadron decays not only when baryon themselves are decaying, but also when they are present in the final state. Their presence can be used to look for possible pentaquark intermediate states; an evidence was claimed by LHCb ref:lLBpk1 ; ref:lLBpk2 in the decay of ${\Lambda^{0}_{b}}\rightarrow{J/\psi}pK^{-}$. The presence of a baryon and an antibaryon can also test possible glueball states ref:gball1 ; ref:gball2 . LHCb then studied the decays ${B^{0}_{d,s}}\rightarrow{J/\psi}p\bar{p}$ ref:lBJPpp ; both the decays are suppressed: the ${B^{0}_{d}}$ decay in this channel is suppressed by Cabibbo while the ${B^{0}_{s}}$ decay in the same channel is suppressed by OZI. A branching fraction at the level of $10^{-9}$ would be expected, with some enhancement via a resonant contribution from $f_{J}(2220)\rightarrow p\bar{p}$.

The branching fraction is measured by a comparison with a normalization channel, so that the ratio of branching fractions is measured, using the well known ${{B^{0}_{s}}\rightarrow{J/\psi}\phi}$ decay as reference. The branching fraction of the studied channel is given by the ratio of reconstructed decays, multiplied by the branching fractions of ${{B^{0}_{s}}\rightarrow{J/\psi}\phi}$, $\phi\rightarrow{K^{+}K^{-}}$ and, only for ${B^{0}_{d}}$, the ratio of fragmentation fractions:

[TABLE]

The number of events was obtained by an extended maximum likelihood fit to the mass distributions, as shown in Fig. 7; the product ${\cal B}({{B^{0}_{s}}\rightarrow{J/\psi}\phi})\cdot{\cal B}(\phi\rightarrow{K^{+}K^{-}})\cdot f_{s}/f_{d}$ was measured ref:brProd at $\sqrt{s}=7~{}\mathrm{TeV}$ as well as the fragmentation ratio $f_{s}/f_{d}$ ref:lfsfdr ; ref:lfsfdu and scaled to $\sqrt{s}=13~{}\mathrm{TeV}$ ref:lfsfds .

The ${{B^{0}_{d,s}}\rightarrow{J/\psi}{p\bar{p}}}$ decay branching ratios have finally been extracted:

[TABLE]

Due to the very low phase space available the momentum uncertainty is negligible; that does allow as a side results the most precise single measurements of ${B^{0}_{d}}$ and ${B^{0}_{s}}$ masses:

[TABLE]

III.2.2 ${B^{+}}$ decay

Another study including the look for intermediate states has been done by CMS about the decay ${{B^{+}}\rightarrow{J/\psi}\bar{\Lambda}^{0}p}$ ref:cBpJLp : that decay was first seen at $B$-factories ref:bBaBar ; ref:bBelle ; in this new study new exotic states were searched in the ${J/\psi}\bar{\Lambda}^{0}$ or ${J/\psi}p$ systems.

As in the previous study of ${B^{0}_{d,s}}$ decay branching fraction has been measured as ratio with the normalization channel ${B^{+}}\rightarrow{J/\psi}K^{*+}$ ($K^{*+}\rightarrow{K^{0}_{S}}\pi^{+}$ , ${K^{0}_{S}}\rightarrow\pi^{+}\pi^{-}$).

The ratio and the absolute vaule of branching fractions were measured as:

[TABLE]

where the last uncertainty comes from the involved cascade decays branching fractions.

The distributions of invariant masses of the ${J/\psi}\bar{\Lambda}^{0}$ and ${J/\psi}p$ systems have then been studied and compared with expectations, from pure phase space or phase space corrected for reflections from $K^{*+}\rightarrow\bar{\Lambda}^{0}p$ resonances. To do that the event sample has been divided in $M(\bar{\Lambda}^{0}p)$ invariant mass bins and in each bin the first 8 Legendre polynomials and momenta have been computed using the $\bar{\Lambda}^{0}p$ helicity angle to describe the angular distributon. Simulated events have then be reweighted using the $\bar{\Lambda}^{0}p$ mass distribution ratio as reference, or the weights given by Legendre polynomials and moments. The distributions obtained in this way have been fitted to data.

The ${J/\psi}p$ and ${J/\psi}\bar{\Lambda}^{0}$ invariant mass distributions are shown in Fig. 8, compared with the simulation using pure phase space, the simulation reweighted with the Legendre polynomials or a function fitted to the $\cos\theta_{K^{*}}$ distribution in data.

The quality of the data description from the different hypotheses has been estimated generating a large number of pseudoexperiments according to the PDF for the pure phase space or the reweighted angular distributions; a log-likelihood ratio has then been computed, to extract a compatibility, or incompatibility, significance. The significance of the incompatibility of data with the pure phase space was found to be much larger than the incompatibility with the phase space corrected by the Legendre polynomials:

[TABLE]

IV Conclusions

ATLAS, CMS and LHCb have produced many measurements of heavy hadron production cross-sections and decay branching fractions:

• •

cross-sections have been compared to predictions and simulations and are input for other measurements,

• •

branching fractions allow test model predictions,

• •

in the study of decays the possible presence of intermediate exotic states has been investigated.

All those measurements allow important tests of QCD.