Transverse spin transfer to $\Lambda$ and $\bar{\Lambda}$ hyperons in polarized proton-proton collisions at $\sqrt{s}=200\,\mathrm{GeV}$

The transverse spin transfer from polarized protons to $\Lambda$ and $\bar{\Lambda}$ hyperons is expected to provide sensitivity to the transversity distribution of the nucleon and to the transversely polarized fragmentation functions. We report the first measurement of the transverse spin transfer to $\Lambda$ and $\bar{\Lambda}$ along the polarization direction of the fragmenting quark, $D_\mathrm{TT}$, in transversely polarized proton-proton collisions at $\sqrt{s}=200\,\mathrm{GeV}$ with the STAR detector at RHIC. The data correspond to an integrated luminosity of $18\,\mathrm{pb}^{-1}$ and cover the pseudorapidity range $\left|\eta\right|<1.2$ and transverse momenta $p_{\mathrm{T}}$ up to $8\,\mathrm{GeV}/c$. The dependence on $p_\mathrm{T}$ and $\eta$ are presented. The $D_\mathrm{TT}$ results are found to be comparable with a model prediction, and are also consistent with zero within uncertainties.

The transverse spin transfer from polarized protons to Λ andΛ hyperons is expected to provide sensitivity to the transversity distribution of the nucleon and to the transversely polarized fragmentation functions. We report the first measurement of the transverse spin transfer to Λ andΛ along the polarization direction of the fragmenting quark, DTT, in transversely polarized proton-proton collisions at √ s = 200 GeV with the STAR detector at RHIC. The data correspond to an integrated luminosity of 18 pb −1 and cover the pseudorapidity range |η| < 1.2 and transverse momenta pT up to The polarizations of Λ andΛ hyperons have been studied extensively in various aspects of spin effects in high energy reactions due to the self spin-analyzing parity violating decay [1]. Many of them have been found to be quite surprising, for example, the induced transverse polarization with respect to the production plane in unpolarized hadron-hadron reactions [2], and the global polarization with respect to the reaction plane observed recently in heavy ion collisions [3]. On the other hand, Λ polarization transferred from polarized lepton or hadron beams (usually referred to as "spin transfer") in different reactions provides a natural connection to polarized fragmentation functions and the polarized parton densities of the nucleon. A number of measurements have been made in polarized lepton-nucleon deep inelastic scattering (DIS), for example, E665 [4], HERMES [5] and COM-PASS [6], and in polarized hadron-hadron collisions in the STAR experiment at RHIC [7,8]. In particular, among the polarized parton distributions, the transversity distribution remains much less known than the helicity distribution due to its chiral-odd nature [9,10]. The transversity distribution describes the probability of finding a transversely polarized quark in a transversely polarized proton. Interestingly, the transverse spin transfer to Λ in lepton-hadron and/or hadron-hadron collisions provides a natural connection to transversity through polarized fragmentation functions [11][12][13][14][15][16]. Previously, sizable spin transfer along the normal direction of the Λ production plane, D NN , was observed at large x F with fixed target proton-proton collisions by the E704 Collaboration at Fermilab [17] and also in exclusive production in protonproton reactions at low energy [18].
We report the first measurement of transverse spin transfer to Λ andΛ hyperons in transversely polarized proton-proton collisions at √ s = 200 GeV with the STAR experiment at RHIC at Brookhaven National Laboratory. The transverse spin transfer, D TT , to the Λ in protonproton collisions is defined as: where ↑ (↓) denotes the positive (negative) transverse polarization direction of the particles and δσ Λ is the transversely polarized cross section. Within the factorization framework, δσ Λ can be factorized into the convolution of parton transversity, polarized partonic cross section and the polarized fragmentation function [13]. As the s(s) quark plays a dominant role in Λ (Λ) hyperon's spin content, the measurements of D TT for Λ (Λ) hyperon provide a natural connection to the transversity distribution of strange and anti-strange quarks [13,15,16]. Experimentally, the transverse spin transfer, D TT , can be measured along the transverse polarization direction of the outgoing quark after the hard scattering.
The polarization of Λ (Λ) hyperons, P Λ (Λ) , can be measured from the angular distribution of the final state particles via their weak decay channel Λ → pπ − (Λ →pπ + ), where A is the detector acceptance varying with θ * as well as other observables, α Λ (Λ) is the weak decay parameter, and θ * is the angle between the Λ (Λ) polarization direction and the (anti-) proton momentum in the Λ (Λ) rest frame. For the D TT measurements in this analysis, the transverse polarization direction of the outgoing fragmenting parton is used to obtain θ * . Since there is a rotation along the normal direction of the scattering plane between the transverse polarization directions of incoming and outgoing quarks [19], the direction of the momentum of the outgoing parton is required and the reconstructed jet axis adjacent to the Λ (Λ) is used as the substitute for the direction of the outgoing fragmenting quark. The data were collected at RHIC with the STAR experiment in the year 2012. An integrated luminosity of 18 pb −1 was sampled with transverse proton beam polarization. The proton polarization was measured for each beam and per fill using Coulomb-Nuclear Interference (CNI) proton-Carbon polarimeters [20], which were calibrated using a polarized atomic hydrogen gas-jet target [21]. The average transverse polarizations for the two beams were 58% and 64% for the analyzed data. Polarization up and down bunch patterns were changed between beam fills to minimize systematic uncertainties.
The primary detector sub-system used in this analysis is the Time Projection Chamber (TPC) [22], which provides tracking for charged particles in the 0.5 T magnetic field in the pseudo-rapidity range of |η| < 1.2 with full azimuthal coverage. The measurement of specific energy loss, dE/dx, in the TPC gas provided information for particle identification. The Barrel Electromagnetic Calorimeter (BEMC) [23] and Endcap Electromagnetic Calorimeter (EEMC) [24] were used in generating the primary jet trigger information at STAR. The total BEMC coverage was |η| < 1 with full azimuth in 2012, and the EEMC extends the pseudo-rapidity coverage up to η ∼ 2. The data samples used in this analysis were recorded with jet-patch (JP) trigger conditions which required a transverse energy deposit E T in BEMC or EEMC patches (each covering a range of ∆η × ∆φ = 1 × 1 in pseudo-rapidity and azimuthal angle) exceeding certain thresholds. The thresholds were E T ∼ 3.5 GeV for JP0, or E T ∼ 5.4 GeV for JP1, or E T ∼ 7.3 GeV for JP2, or two adjacent jet patches (AJP) with each exceeding the threshold of E T ∼ 3.5 GeV for the AJP trigger.  The Λ andΛ candidates were reconstructed from their dominant weak decay channels, Λ → pπ − andΛ →pπ + , with a branching ratio of 63.9% [25]. The location of the primary vertex (PV) was required to be within 60 cm of the center of the TPC along the beam axis to ensure uniform acceptance. The selection procedure of Λ andΛ candidates in this analysis is based on the topology of the weak decay using a method that is very similar to the one used in the previous longitudinal spin transfer measurement reported in Ref. [7]. (Anti-) proton and pion tracks were first identified based on dE/dx in the TPC. They were paired to form a Λ (Λ) candidate, and topological selections were used to further reduce the background. The selection cuts were tuned in each hyperon p T bin to keep the residual background fraction below 10%; these cuts are summarized in Table I. As mentioned earlier, reconstructed jets were employed to obtain the momentum direction of the fragmenting quark and thus the transverse polarization direction of hyperons for the D TT measurement. In this analysis, jets were reconstructed using the anti-k T algorithm [26] with a resolution parameter R = 0.6 and jet p T > 5 GeV/c. In STAR, the TPC tracks and tower energies from the BEMC and EEMC are used for the jet reconstruction [27,28]. Then the association between Λ (Λ) candidates and the adjacent reconstructed jet was made by constraining the radius, ∆R = (∆η) 2 + (∆φ) 2 , between the Λ (Λ) momentum direction and the jet axis in η − φ space. The Λ (Λ) candidates that have a jet with ∆R < 0.6 were used in the following D TT determination. The fraction of Λ (Λ) candidates that have a matching jet increases from about 30% to 90% from the lowest hyperon p T bin to the highest.
After topological selections and jet correlation, the invariant mass distributions for the Λ andΛ candidates with 1 < p T < 8 GeV/c and |η| < 1.2 are shown in The invariant mass distribution versus cos θ * for Λ candidates with 1 < pT < 8 GeV/c in this analysis as an example.  [25]. The 2-dimensional distribution of invariant mass versus cos θ * as defined in Eq. 2 is shown in Fig. 2 for Λ candidates. A similar distribution was also obtained forΛ candidates. The bin counting method was used to obtain the raw yields of Λ andΛ candidates. The signal mass windows were chosen to be about 3σ of the mass width. These range from 1.111 ∼ 1.119 GeV/c 2 in the lowest p T bin to 1.104 ∼ 1.128 GeV/c 2 in the highest p T bin. About 1.02 × 10 6 Λ and 1.17 × 10 6Λ candidates in the selected signal mass windows were kept as the signal. The residual background fractions were estimated by the side-band method and found to be 7% ∼ 10%. The yields, background fractions and signal mass windows are listed in Table I. TheΛ signal is larger than that of the Λ because of the effects of anti-proton annihilation in the BEMC and EEMC, which provides additional energy to the JP trigger conditions for theΛ.
The observed cos θ * spectra are affected by detector efficiency and acceptance as seen in Eq. 2. To minimize the systematics associated with acceptance and relative luminosity, D TT has been extracted from the asymmetry in small cos θ * intervals using I. Summary of selection cuts and the Λ andΛ candidate counts and the residual background fractions in each pT bin. Here "DCA" denotes distance of closest approach, and N (σ) quantitatively measures the distance of a particle track to a certain particle band in dE/dx vs. rigidity space [29]. l is representative of the vector from the PV to the Λ decay point and p is the reconstructed momentum of Λ.  where α Λ = 0.642 ± 0.013 [25], αΛ = −α Λ , P beam is the beam polarization and cos θ * denotes the average value in the cos θ * interval. N ↑(↓) is the Λ yield in the corresponding cos θ * bin when the proton beam is upward (downward) polarized. The relative luminosity between N ↑ and N ↓ is cancelled in this cross-ratio asymmetry.
The acceptance is also cancelled as the acceptance in a small cos θ * interval is expected to remain the same when flipping the beam polarization [7], and the effect from limited cos θ * bin width is negligible. At RHIC both proton beams are polarized, and the single spin hyperon yield N ↑(↓) was obtained by summing over the spin states of the other beam, as the beam fill patterns are nearly balanced with opposite polarizations. The yields N ↑ and N ↓ were first determined in each cos θ * interval from the observed Λ orΛ candidate yields in the chosen mass interval, and the raw spin transfer, D raw TT , was extracted using Eq. 3 in each cos θ * bin. Then the D raw TT values were averaged over the entire cos θ * range in each hyperon p T bin. Since single spin yields can be obtained with either beam polarized, we have two independent measurements for the same physics η range, but with different detector coverage, by treating one beam as polarized and summing over the polarization states of the other beam. After confirming their consistency, the final D raw TT results are determined from the weighted mean. Figure 3(a) shows the beam combined D raw TT versus cos θ * for Λ hyperons in the positive and negative η regions, respectively, with 2 < p T < 3 GeV/c provided as an example. The results forΛ hyperon are shown in Fig. 3(b). Positive η is defined along the direction of the incident polarized beam. The extracted D raw TT is constant with cos θ * as expected and confirmed by the quality of the fit. A null-measurement was performed with the spin transfer for the spinless K 0 S , δ TT , as a cross check, which has a similar event topology. The δ TT obtained with an artificial weak decay parameter α K 0 S = 1 are shown in Fig. 3(c). As expected, the results were found to be consistent with no spin transfer.
D raw TT values and their statistical uncertainties were then corrected for residual background dilution according to where r is the background fraction in each p T bin estimated by the side-band method [8], and D bkg TT was obtained from the left and right side-band mass intervals as shown in last two rows of Table I using the same procedure as D raw TT following Eq. 3 and was consistent with zero within the statistical uncertainty.
The systematic uncertainties of D TT include contributions from the decay parameter α, from the measurement of the beam polarizations as well as uncertainty caused by the residual background fraction, event pile-up effects and trigger bias due to trigger conditions. The total systematic uncertainties in D TT range from 0.0003 to 0.009 in different p T bins, while the corresponding statistical uncertainties vary from 0.006 to 0.040. The above contributions are considered to be independent and their sizes have been estimated as described below. The trigger bias is the dominant contribution to the systematic uncertainty.
The uncertainty in α Λ = −αΛ = 0.642 ± 0.013 corresponds to a 2% scale uncertainty in D TT . The uncertainty in the RHIC beam polarization measurements contribute an additional 3.4% scale uncertainty in D TT . The pile-up effect due to possible overlapping events recorded in the TPC was studied by examining the hyperon yield per event versus the STAR collision rate. A comparison between the yields per collision event found by fitting with a constant and a linear extrapolation to very low collision rates was used to estimate the pile up contribution for different spin states, and the corresponding uncertainty to D TT was found to be small (< 0.005). The residual background fractions were estimated by the sideband method and D TT was corrected accordingly. The corresponding uncertainty was quantified from the difference in the results when the background fractions were estimated instead by fitting the mass spectra. This part is found to be also very small (< 0.003). The data samples used in this analysis were recorded with jet-patch trigger conditions, which help to reach high transverse momenta of hyperons. However, these trigger conditions may bias the D TT measurements by changing the natural composition of hyperon events with respect to the distributions of the hyperon momentum fraction in its associated jet, the hard production subprocesses, the flavor of the associated jet, the decay contribution, etc. The uncertainties caused by the above mentioned jet trigger conditions were studied with a Monte Carlo simulation of events generated using PYTHIA 6.4 [30] with the Perugia 2012 tune [31] and the STAR detector response package based on GEANT 3 [32]. The uncertainties from trigger bias were then estimated by comparing the D TT values obtained from a theoretical model [16] before and after applying the trigger conditions. This yields uncertainties up to 0.008 with increasing p T . The STAR results for D TT versus hyperon p T are shown in Fig. 4 for Λ andΛ at both positive and negative η regions relative to the polarized beam in protonproton collisions at √ s = 200 GeV. About 60% of Λ orΛ are not primary particles, but stem from decay of heavier hyperons. No corrections have been applied for decay contributions from heavier baryonic states. Several of the models do take into account the decay contribution [13,15,16]. The statistical and systematic uncertainties are shown with vertical bars and open boxes, respectively. The systematic uncertainties in the positive η range are larger than those in the negative η range, owing to the larger trigger bias in the positive η range. These results provide the first measurements on transverse spin transfer of hyperons at a high energy of √ s = 200 GeV.
The D TT results for Λ andΛ are consistent with zero within uncertainties. The data cover p T up to 7 GeV/c, where D TT = 0.031 ± 0.033(stat.) ± 0.008(sys.) for Λ and D TT = −0.034 ± 0.040(stat.) ± 0.009(sys.) forΛ at η = 0.5 and p T = 6.7 GeV/c. Strange quarks and anti-strange quarks are expected to carry a significant part of the spins of Λ andΛ; therefore the measurements of transverse spin transfer to them can provide insights into the transversity distribution of strange quarks. Knowledge of transversity of valence quarks has been learned mostly from DIS experiments. But the transversity distribution of strange quarks is not yet constrained experimentally [33][34][35].
A few model predictions exist of hyperon transverse spin transfer in hadron-hadron collisions, based on different assumptions on the transversity distribution and transversely polarized fragmentation functions [13,15,16]. In Fig. 4, the D TT data are compared with a model estimation calculated at η = ±0.5, which is available for RHIC energy, with simple assumptions of the transversity (using the DSSV helicity distribution as input) and the SU6 picture of fragmentation functions [15,16]. The data are in general consistent with the model predictions. The D TT of Λ andΛ are not in disagreement with each other, with a χ 2 /ndf of 9.5/6. A possible difference between them could come, for example, from different frag-mentation contributions from the non-strange quarks.
In summary, we report the first measurement of the transverse spin transfer, D TT , to Λ andΛ in transversely polarized proton-proton collisions at √ s = 200 GeV at RHIC. The data correspond to an integrated luminosity of 18 pb −1 taken by the STAR experiment in 2012, and cover mid-rapidity, |η| < 1.2, and p T up to 8 GeV/c. The D TT value and precision in the highest p T bin, where the effects are expected to be largest, are found to be D TT = 0.031 ± 0.033(stat.) ± 0.008(sys.) for Λ and D TT = −0.034 ± 0.040(stat.) ± 0.009(sys.) forΛ at η = 0.5 and p T = 6.7 GeV/c. The results for D TT are found to be consistent with zero for Λ andΛ within uncertainties, and are also consistent with model predictions.