Spin polarization of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi mathvariant="normal">Λ</mml:mi> </mml:math> hyperons along the beam direction in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>p</mml:mi> <mml:mo>+</mml:mo> <mml:mi>Pb</mml:mi> </mml:mrow> </mml:math> collisions at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:msub> <mml:mi>s</mml:mi> <mml:mrow> <mml:mi>N</mml:mi> <mml:mi>N</mml:mi> </mml:mrow> </mml:msub> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>8.16</mml:mn> </mml:mrow> </mml:math> TeV using hydrodynamic approaches
Bibliographic record
Abstract
We have implemented the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>3</a:mn> <a:mo>+</a:mo> <a:mn>1</a:mn> </a:mrow> </a:math> dimensional CLVisc hydrodynamics model with TENTo-3D initial conditions to investigate the spin polarization of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mi mathvariant="normal">Λ</b:mi> </b:math> hyperons along the beam direction in <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mi mathvariant="normal">p</d:mi> <d:mo>+</d:mo> <d:mi>Pb</d:mi> </d:mrow> </d:math> collisions at <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"> <f:mrow> <f:msqrt> <f:msub> <f:mi>s</f:mi> <f:mrow> <f:mi>N</f:mi> <f:mi>N</f:mi> </f:mrow> </f:msub> </f:msqrt> <f:mo>=</f:mo> <f:mn>8.16</f:mn> </f:mrow> </f:math> TeV. Following our previous theoretical framework based on quantum kinetic theory, we consider three different scenarios: <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mi mathvariant="normal">Λ</g:mi> </g:math> equilibrium, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mi>s</i:mi> </i:math> quark equilibrium, and isothermal equilibrium scenarios. We have computed the second Fourier sine coefficients of spin polarization along the beam direction, denoted as <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mrow> <j:mo>〈</j:mo> <j:msub> <j:mi>P</j:mi> <j:mi>z</j:mi> </j:msub> <j:mo form="prefix">sin</j:mo> <j:mn>2</j:mn> <j:mrow> <j:mo>(</j:mo> <j:msub> <j:mi>ϕ</j:mi> <j:mi>p</j:mi> </j:msub> <j:mo>−</j:mo> <j:msub> <j:mi mathvariant="normal">Ψ</j:mi> <j:mn>2</j:mn> </j:msub> <j:mo>)</j:mo> </j:mrow> <j:mo>〉</j:mo> </j:mrow> </j:math> , with <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:msub> <m:mi>ϕ</m:mi> <m:mi>p</m:mi> </m:msub> <m:mo>−</m:mo> <m:msub> <m:mi mathvariant="normal">Ψ</m:mi> <m:mn>2</m:mn> </m:msub> </m:mrow> </m:math> being the azimuthal angle relative to the second-order event plane <o:math xmlns:o="http://www.w3.org/1998/Math/MathML"> <o:msub> <o:mi mathvariant="normal">Ψ</o:mi> <o:mn>2</o:mn> </o:msub> </o:math> , as functions of multiplicity, transverse momentum, and pseudorapidity in the three scenarios. Additionally, we have also computed the spin polarization along the beam direction, <q:math xmlns:q="http://www.w3.org/1998/Math/MathML"> <q:msub> <q:mi>P</q:mi> <q:mi>z</q:mi> </q:msub> </q:math> , as a function of the azimuthal angle. We find that the spin polarization induced by thermal vorticity always provides an opposite contribution compared to the shear-induced polarization in <r:math xmlns:r="http://www.w3.org/1998/Math/MathML"> <r:mrow> <r:mi mathvariant="normal">p</r:mi> <r:mo>+</r:mo> <r:mi>Pb</r:mi> </r:mrow> </r:math> collisions. The total spin polarization computed by the current hydrodynamic model disagrees with the data measured by LHC-CMS experiments.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.006 |
| Meta-epidemiology (narrow) | 0.004 | 0.007 |
| Meta-epidemiology (broad) | 0.002 | 0.008 |
| Bibliometrics | 0.002 | 0.007 |
| Science and technology studies | 0.008 | 0.007 |
| Scholarly communication | 0.005 | 0.006 |
| Open science | 0.009 | 0.009 |
| Research integrity | 0.007 | 0.008 |
| Insufficient payload (model declined to judge) | 0.090 | 0.008 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; both teacher heads agree on what is shown here.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".