Measurement of global spin alignment of K ∗0 and ϕ vector mesons using the STAR detector at RHIC
NNuclear Physics A 00 (2020) 1–4
NuclearPhysics A / locate / procedia XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions(Quark Matter 2019)
Measurement of global spin alignment of K ∗ and φ vectormesons using the STAR detector at RHIC Subhash Singha (for the STAR Collaboration)
Institute of Modern Physics Chinese Academy of Sciences, Lanzhou, Gansu, China [email protected]
Abstract
We report the transverse momentum ( p T ) and centrality dependence of global spin alignment ( ρ ) of K ∗ vector mesonat midrapidity ( | y | < .
5) in Au + Au collisions at √ s NN = K ∗ results are compared to that of φ meson. At low- p T region and midcentral collisions, the K ∗ ρ is found tobe smaller than 1 / σ significance, while that of φ meson is observed to be larger than 1 / σ significance. The ρ results are compared between RHIC and LHC energies. The physics implication of our results isalso discussed. Keywords: relativistic heavy-ion collisions, vector meson, spin alignment
1. Introduction
In non-central heavy-ion collisions, a large initial global angular momentum ( ∼ (cid:125) ) is expected [1].This can induce a non-vanishing polarization for hadrons with non-zero spin via spin-orbit coupling. Themeasurement of spin polarization can o ff er new insight into the initial conditions and dynamics of the Quark-Gluon Plasma (QGP) [2, 3]. The STAR Collaboration reported significant non-zero Λ polarization at RHICenergies [4, 5]. This provides the first experimental evidence of the vorticity of the QGP medium inducedby the initial angular momentum. The spin alignment of vector mesons can also be used to probe thevorticity [6]. The vector meson global spin alignment is quantified by the diagonal element of the spindensity matrix ( ρ ) [7]. It is measured from the angular distribution of the decay daughter of the vectormeson: dNd cos θ ∗ ∝ (cid:104) (1 − ρ ) + (3 ρ − θ ∗ (cid:105) , (1)where θ ∗ is the angle between the polarization axis and momentum direction of the daughter particle inthe rest frame of parent particle. For global spin alignment, the polarization axis is chosen as the directionperpendicular to the reaction plane which is correlated with the direction of the angular momentum of thecolliding system. In the absence of spin alignment, the value of ρ is expected to be 1 /
3. Any deviation a r X i v : . [ nu c l - e x ] F e b Subhash Singha (for STAR Collaboration) / Nuclear Physics A 00 (2020) 1–4 of ρ from 1 / ρ due to vorticity of the medium is expected to be smaller than 1 /
3, while that induced by the initialmagnetic field can be larger or smaller than 1 / ff erent hadronization scenarios, such as the fragmentation and coalescencemechanisms can cause ρ to be larger and smaller than 1 / K ∗ and φ , are expectedto be produced predominantly from primordial production, unlike hyperons which are expected to have largeresonance decay contribution. Another advantage is that the spin alignment of vector mesons are generallyadditive, whereas hyperons polarization are subject to local cancellation e ff ects. Moreover, the lifetime ofthese vector mesons di ff er by a factor of ten, so they can carry informations of the medium from di ff erenttime scale during its evolution.
2. Analysis method
This proceedings report the measurement of K ∗ ρ at midrapidity ( | y | < .
5) in Au + Au collisionsat √ s NN = | η | < ffi ciency using a Monte Carlo Glauber simulation [11]. The 2 nd -order eventplane (experimental approximate of reaction plane) is reconstructed using tracks inside the TPC. The particleidentification is done using the specific ionization energy loss in TPC gas volume and the velocity of particles(1 /β ) measured by the Time-of-Flight (TOF) detector [12]. The K ∗ ( K ∗ ) is reconstructed via hadronicdecay channel: K ∗ ( K ∗ ) → K + π − ( K − π + ) (branching ratio: 66%) [13]. Measurement of K ∗ and K ∗ areaveraged and they are collectively referred to as K ∗ . The combinatorial background is estimated from apair rotation technique. The invariant mass signal is obtained after the subtraction of the combinatorialbackground. The signal is fitted with a Breit-Wigner distribution and a second-order polynomial functionto take care of residual background. The yield is estimated by integrating signal histogram bins within therange: ( m − Γ , m + Γ ), where m and Γ are the invariant mass peak position and width of K ∗ . The K ∗ yield is obtained in five cos θ ∗ bins, where the θ ∗ is the angle between the direction perpendicular to the2 nd -order event plane and the momentum direction of daughter kaon in the rest frame of K ∗ . The yield ineach cos θ ∗ bin is then corrected for detector acceptance and e ffi ciency using a Monte Carlo embedding. Weextract the observed ρ (denoted as ρ obs00 ) by fitting the yield vs. cos θ ∗ distribution using Eq. 1. The ρ obs00 isthen corrected for event plane resolution, following method detailed in [14], to obtain ρ : ρ − = + R ( ρ obs −
13 ) , (2)where R is the TPC 2 nd -order event plane resolution, estimated from the correlation of two sub-events [15].
3. Results and discussions T ) dependence The solid star and circle markers in the left panel of Fig. 1 present the K ∗ ρ measured using the 2 nd -order event plane as a function of p T for 10-60% central Au + Au collisions at √ s NN = ρ with respect to a three-dimensional (3D) random plane which is not expectedto be correlated with the angular momentum direction. We observe that the ρ for p T < / c issmaller than 1 / σ significance, while for higher p T region the ρ is consistent with 1 / ρ with respect to the 3D random plane is found to be consistent with 1 / K ∗ ρ in low- p T region can be qualitatively explained by models that considerthe hadronization of polarized quarks via coalescence mechanism [6]. But to date, there is no quantitativeestimate of K ∗ ρ available from such models. The ρ of φ meson for p T = / c in midcentralAu + Au collisions at √ s NN =
200 GeV (presented in QM2018) [16] is observed to be larger than 1 /
3. The φρ measurement does not fit into the naive quark coalescence or fragmentation model. ubhash Singha (for STAR Collaboration) / Nuclear Physics A 00 (2020) 1–4 (GeV/c) T p r * K Au+Au, 10-60%TPC EP TPC EP3D random 3D random STAR Preliminary54.4 GeV 200 GeV æ part N Æ r * K < 1.5 GeV/c T Au+Au, 1.0 < p 54.4 GeV200 GeVSTAR Preliminary TPC-EP
Fig. 1. Left panel: The solid circles and star markers present the K ∗ ρ using the 2 nd -order event plane as function of p T for 10-60%central Au + Au collisions at √ s NN = K ∗ ρ using the 2 nd -order event plane as function of (cid:104) N part (cid:105) for 1 . < p T < . / c. The vertical bars and caps denote statistical and systematic uncertainties, respectively. (cid:104) N part (cid:105) ) dependence The right panel in Fig. 1 shows the K ∗ ρ as function of average number of participating nucleons( (cid:104) N part (cid:105) ) for 1 . < p T < . / c in Au + Au collisions at √ s NN = ρ from 1 / K ∗ ρ is consistent with 1 / /
3. The ρ of φ mesons (presented in QM2018) [16] shows similar centrality dependence, but with an opposite trend and the ρ is larger than 1 / ρ of K ∗ and φ mesons. (GeV) NN s r * K < 5.0 GeV/c T STAR Preliminary, 10-60%, 1.2 < pAu+Au < 1.2 GeV/c T ALICE, 10-50%, 0.8 < pPb+Pb (GeV) NN s r f > 1.2 GeV/c T STAR Preliminary, 20-60%, pAu+Au < 1.2 GeV/c T ALICE, 10-50%, 0.8 < pPb+Pb
Fig. 2. Left panel: beam-energy dependence of K ∗ ρ in midcentral collisions. Right panel: beam-energy dependence of φ ρ inmidcentral collisions. In both panels, the vertical bars and caps denote statistical and systematic uncertainties, respectively. √ s NN ) dependence The left panel in Fig. 2 presents the beam-energy dependence of K ∗ ρ in midcentral collisions. Thenew measurements for Au + Au collisions at √ s NN = + Aucollisions at √ s NN = + Pb collisions at √ s NN = K ∗ ρ for low p T and midcentral collisions is found to be smaller than 1 / φ ρ . The STAR results [16] from Au + Au collisions at √ s NN = φ ρ in midcentral collisions at RHIC energies Subhash Singha (for STAR Collaboration) / Nuclear Physics A 00 (2020) 1–4
Table 1. Sumary of ρ and P H measurements at RHIC and LHC Species Quark content J P ρ / P H at top-RHIC ρ / P H at LHC K ∗ d ¯ s − ρ < / ∼ σ ) ρ < / ∼ σ ) φ s ¯ s − ρ > / ∼ σ ) ρ < / ∼ σ ) Λ uds / + P H >
0; ( ∼ σ ) P H ∼ ∼ σ )is observed to be larger than 1 / σ significance at 39 and 200 GeV), it is found to be smaller than1 / σ significance). The trend of φ ρ at RHIC energies can be explainedby a recent model calculation that considers the existence of coherent mesonic field [18]. Note that thecalculation mentioned above does not exist for the K ∗ meson.
4. Summary and conclusion
We presented p T and centrality dependence of ρ of K ∗ meson for Au + Au collisions at √ s NN = p T and midcentral collisions, the K ∗ ρ is observed to be smaller than 1 / σ significance for both beam energies. This is an indication of K ∗ spin alignment for both beam energies.For midcentral collisions, while the K ∗ ρ is found to be smaller than 1 /
3, the φ ρ is observed to belarger than 1 /
3. It could be due to the di ff erent lifetime of these vector mesons and di ff erent responses to thevorticity of the medium at di ff erent time scales. No current theoretical model can explain simultaneouslythe trend of K ∗ and φ ρ . Within the current precision, no significant beam-energy dependence is observedfor K ∗ ρ . The data from the 2 nd phase of the Beam Energy Scan in RHIC will improve the precision ofthe low energy data. The p T and centrality dependence of ρ of K ∗ is qualitatively similar between RHICand LHC energies.From the current theoretical understanding, the global hyperon polarization ( P H ) is proportional to thequark polarization ( P q ): P H ∝ P q , while the spin alignment, ρ ∝ P q . Based on the above assumptions andthe input of P q from Λ polarization measurement, the expected ρ is close to 1 /
3. Hence, the current largedeviation of ρ is surprising and poses challenges to theoretical understanding. Given the ρ can dependon multiple physics mechanisms, e.g. the vorticity, magnetic field, hadronization scenarios and mesonicfields, more theoretical e ff orts are required for understanding of the data. References [1] F. Becattini, F. Piccinini, J. Rizzo, Phys. Rev.
C77 (2008) 024906.[2] Z.-T. Liang, X.-N. Wang, Phys. Rev. Lett. (2005) 102301, [Erratum: Phys. Rev. Lett.96,039901(2006)].[3] B. Betz, M. Gyulassy, G. Torrieri, Phys. Rev. C76 (2007) 044901.[4] L. Adamczyk, et al. , [STAR Collaboration], Nature (2017) 6265[5] J. Adam, et al. , [STAR Collaboration], Phys. Rev.
C98 (2018) 014910.[6] Z.-T. Liang, X.-N. Wang, Phys. Lett.
B629 (2005) 2026.[7] K. Schilling, P. Seyboth, G. E. Wolf, Nucl. Phys.
B15 (1970) 397412, [Erratum: Nucl. Phys.B18,332(1970)].[8] Y.-G. Yang, R.-H. Fang, Q. Wang, X.-N. Wang
C97 (3) (2018) 034917[9] W. J. Llope, et al. , [STAR Collaboration], Nucl. Instrum. Meth.
A522 (2004) 252273.[10] M. Anderson, et al. , [STAR Collaboration], Nucl. Instrum. Meth.
A499 (2003) 659678.[11] B. I. Abelev, et al. , [STAR Collaboration], Phys. Rev.
C79 (2009) 034909.[12] B. Bonner et al. , Nucl. Instrum. Meth.
A508 (2003) 181184.[13] M. Tanabashi, et al. ,, Review of Particle Physics, Phys. Rev.
D98 (3) (2018) 030001.[14] A. H. Tang, B. Tu, C. S. Zhou, Phys. Rev.
C98 (4) (2018) 044907[15] A. M. Poskanzer, S. A. Voloshin, Phys. Rev.
C58 (1998) 16711678.[16] C. Zhou, [for STAR Collaboration], Nucl. Phys.
A982 (2019) 559562.[17] S. Acharya, et al.et al.