<p>We employ an equal-velocity quark combination model to study anisotropic flows <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub><mo>,</mo><mo> </mo><msub><mi>v</mi><mn>3</mn></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>4</mn></msub></math> of identified hadrons at midrapidity in heavy-ion collisions at Relativistic Heavy Ion Collider energies. Under the equal-velocity combination mechanism of constituent quarks at hadronization, we build analytical formulas of anisotropic flows of hadrons in terms of those of quarks just before hadronization. We systematically analyze the contribution of higher-order flows of quarks, and show how simple formulas of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub><mo>,</mo><mo> </mo><msub><mi>v</mi><mn>3</mn></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>4</mn></msub></math> of identified hadrons with the desired precision can be obtained by neglecting the small contribution of higher-order flows of quarks. We systematically test these simple formulas of hadronic flows by the experimental data of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub><mo>,</mo><mo> </mo><msub><mi>v</mi><mn>3</mn></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>4</mn></msub></math> of identified hadrons <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ϕ</mi><mo>,</mo><mo> </mo><mi mathvariant="normal">Λ</mi><mo>,</mo><mo> </mo><msup><mi mathvariant="normal">Ξ</mi><mo>−</mo></msup><mo>,</mo><mo> </mo><msup><mi mathvariant="normal">Ω</mi><mo>−</mo></msup><mo>,</mo><mo> </mo><mover accent="true"><mi mathvariant="normal">Λ</mi><mo>¯</mo></mover><mo>,</mo><mo> </mo><msup><mover accent="true"><mi mathvariant="normal">Ξ</mi><mo>¯</mo></mover><mo>+</mo></msup><mo>,</mo><mo> </mo><msup><mover accent="true"><mi mathvariant="normal">Ω</mi><mo>¯</mo></mover><mo>+</mo></msup><mo>,</mo><mo> </mo><mi>p</mi></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><mover accent="true"><mi>p</mi><mo>¯</mo></mover></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Au</mi><mo>+</mo><mi>Au</mi></mrow></math> collisions at <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>19.6</mn></mrow></math>, 54.4, and 200 GeV, and we find that the equal-velocity quark combination model can well describe the measured <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub><mo>,</mo><mo> </mo><msub><mi>v</mi><mn>3</mn></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>4</mn></msub></math> of identified hadrons in <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>Au</mi><mo>+</mo><mi>Au</mi></mrow></math> collisions at those collision energies. We further study the obtained anisotropic flows of quarks and find two scaling properties which can be qualitatively understood by the hydrodynamic evolution of the thermal quark medium produced in relativistic heavy-ion collisions.</p>

China

Yan-ting Feng

Rui-qin Wang

Feng-lan Shao

Jun Song

Anisotropic flows of identified hadrons in the equal-velocity quark combination model at energies available at the BNL Relativistic Heavy Ion Collider

We study the production of light nuclei in the coalescence mechanism of Au-Au collisions at midrapidity at   $ \sqrt{s_{NN}}=3 $  GeV. We derive analytic formulas of the momentum distributions of two bodies, three bodies, and four nucleons coalescing into light nuclei and naturally explain the transverse momentum spectra of the deuteron (d), triton (t), helium-3 ($^{3}$He), and helium-4 ($^{4}$He). We reproduce data on the yield rapidity densities, yield ratios, and averaged transverse momenta of d, t, $^{3}$He, and $^{4}$He and provide the proportions of contributions from different coalescence sources for t, $^{3}$He, and $^{4}$He in their production. We find that besides nucleon coalescence, nucleon+nucleus coalescence and nucleus+nucleus coalescence may play requisite roles in light nucleus production in Au-Au collisions at   $ \sqrt{s_{NN}}=3 $   GeV.

Rui-Qin Wang

Ji-Peng Lv

Yan-Hao Li

Feng-Lan Shao

Different coalescence sources of light nucleus production in Au-Au collisions at GeV  

We apply an equal-velocity quark combination model to study the  $$\varLambda _{c}^{+}/D^{0}$$  <math> <mrow> <msubsup> <mi>Λ</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mo>/</mo> <msup> <mi>D</mi> <mn>0</mn> </msup> </mrow> </math>   ratio in the range  $$p_{T}\lesssim 10$$  <math> <mrow> <msub> <mi>p</mi> <mi>T</mi> </msub> <mo>≲</mo> <mn>10</mn> </mrow> </math>   GeV/c in pp collisions at  $$\sqrt{s}=13$$  <math> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>13</mn> </mrow> </math>   TeV. We decompose the ratio into four parts which are related to quark numbers, light-flavor quark  $$p_{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>   spectrum, charm quark  $$p_{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>   spectrum, momentum correlation between light and charm quarks, respectively. Their influence on  $$\varLambda _{c}^{+}/D^{0}$$  <math> <mrow> <msubsup> <mi>Λ</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mo>/</mo> <msup> <mi>D</mi> <mn>0</mn> </msup> </mrow> </math>   ratio is individually studied. The curvature property of light-flavor quark  $$p_{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>   spectrum is the main reason of the non-monotonic  $$p_{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>   dependence of  $$\varLambda _{c}^{+}/D^{0}$$  <math> <mrow> <msubsup> <mi>Λ</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mo>/</mo> <msup> <mi>D</mi> <mn>0</mn> </msup> </mrow> </math>   ratio exhibited in high multiplicity events. Moreover, the multiplicity dependence of  $$\varLambda _{c}^{+}/D^{0}$$  <math> <mrow> <msubsup> <mi>Λ</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mo>/</mo> <msup> <mi>D</mi> <mn>0</mn> </msup> </mrow> </math>   ratio as the function of  $$p_{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>   is mainly because of the multiplicity dependence of light-flavor quark  $$p_{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>   spectrum. Using the light-flavor quark  $$p_{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>   spectrum obtained from experimental data of light-flavor hadrons and charm quark  $$p_{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>   spectrum obtained from FONLL and/or PYTHIA calculations, the  $$p_{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>   dependence of experimental data of  $$\varLambda _{c}^{+}/D^{0}$$  <math> <mrow> <msubsup> <mi>Λ</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mo>/</mo> <msup> <mi>D</mi> <mn>0</mn> </msup> </mrow> </math>   ratio in high multiplicity events and that in low multiplicity events in pp collisions at  $$\sqrt{s}=13$$  <math> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>13</mn> </mrow> </math>   TeV are reasonably understood.

Hai-hong Li

Transverse momentum and multiplicity dependence of  $$\varLambda _{c}^{+}/D^{0}$$  <math> <mrow> <msubsup> <mi>Λ</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> <mo>/</mo> <msup> <mi>D</mi> <mn>0</mn> </msup> </mrow> </math>   ratio in pp collisions at  $$\sqrt{s}=13$$  <math> <mrow> <msqrt> <mi>s</mi> </msqrt> <mo>=</mo> <mn>13</mn> </mrow> </math>   TeV

We apply an equal-velocity quark combination model to systematically study the transverse momentum (<math><msub><mi>p</mi><mi>T</mi></msub></math>) spectra of identified hadrons <math><msubsup><mi>K</mi><mrow><mi>S</mi></mrow><mn>0</mn></msubsup><mo>,</mo><mo> </mo><mi>ϕ</mi><mo>,</mo><mo> </mo><mi>Λ</mi><mo>,</mo><mo> </mo><msup><mi>Ξ</mi><mo>−</mo></msup><mo>,</mo><mo> </mo><msup><mi>Ω</mi><mo>−</mo></msup><mo>,</mo><mo> </mo><mover><mi>Λ</mi><mo>¯</mo></mover><mo>,</mo><mo> </mo><msup><mover><mi>Ξ</mi><mo>¯</mo></mover><mo>+</mo></msup><mo>,</mo><mo> </mo><msup><mover><mi>Ω</mi><mo>¯</mo></mover><mo>+</mo></msup><mo>,</mo><mo> </mo><mi>p</mi><mo>,</mo><mo> </mo><mover><mi>p</mi><mo>¯</mo></mover><mo>,</mo><mo> </mo><msup><mi>π</mi><mo>+</mo></msup></math>, and <math><msup><mi>π</mi><mo>−</mo></msup></math> at midrapidity in <math><mrow><mi>Au</mi><mo>+</mo><mi>Au</mi></mrow></math> collisions at <math><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>7.7</mn></mrow></math>, 11.5, 19.6, 27, 39, 54.4 GeV. The relative deviation between model calculations and experimental data of these 12 hadrons is generally about 10% in central collisions even at low collision energies and is weakly increased in peripheral collisions. We systematically explain the dependence of two baryon-to-meson ratios <math><mrow><mover><mi>Λ</mi><mo>¯</mo></mover><mo>/</mo><msubsup><mi>K</mi><mrow><mi>S</mi></mrow><mn>0</mn></msubsup></mrow></math> and <math><mrow><mi>Ω</mi><mo>/</mo><mi>ϕ</mi></mrow></math> on <math><msub><mi>p</mi><mi>T</mi></msub></math>, collision centrality, and collision energy by the property of quark <math><msub><mi>p</mi><mi>T</mi></msub></math> spectra at hadronization. We derive the analytic relations between <math><msub><mi>R</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math> of hadrons and those of quarks, and we use them to naturally explain the species and <math><msub><mi>p</mi><mi>T</mi></msub></math> dependence of <math><msub><mi>R</mi><mrow><mi>C</mi><mi>P</mi></mrow></msub></math> of those strange hadrons.

Zi-yao Song

Collision centrality and energy dependence of strange hadron production in Au <math><mo>+</mo></math> Au collisions at <math><mrow><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt><mo>=</mo><mn>7.7</mn></mrow></math>–54.4 GeV

With the kinetic freeze-out nucleons and antinucleons obtained from the quark combination model, we study the production of light nuclei and antinuclei in the (anti-)nucleon coalescence mechanism in relativistic heavy ion collisions. We derive analytic formulas of the momentum distributions of different light nuclei and apply them to compute transverse momentum <math><mo>(</mo><msub><mi>p</mi><mi>T</mi></msub><mo>)</mo></math> spectra of (anti-)deuterons <math><mo>(</mo><mi>d</mi></math>, <math><mover><mi>d</mi><mo>¯</mo></mover><mo>)</mo></math> and (anti-)tritons <math><mo>(</mo><mi>t</mi><mo>,</mo></math> <math><mover><mi>t</mi><mo>¯</mo></mover><mo>)</mo></math> in Au-Au collisions at <math><mrow><msqrt><msub><mi>s</mi><mi>NN</mi></msub></msqrt><mo>=</mo><mn>7.7</mn><mo>,</mo><mo> </mo><mn>11.5</mn><mo>,</mo><mo> </mo><mn>19.6</mn><mo>,</mo><mo> </mo><mn>27</mn><mo>,</mo><mo> </mo><mn>39</mn><mo>,</mo><mo> </mo><mn>54.4</mn><mo> </mo><mi>GeV</mi></mrow></math>. We find that the experimental data available for these <math><msub><mi>p</mi><mi>T</mi></msub></math> spectra can be well reproduced. We further study the yields and yield ratios of different light (anti-)nuclei and naturally explain their interesting behaviors as a function of the collision energy. We especially point out that the multiparticle yield ratio <math><mrow><mi>t</mi><mi>p</mi><mo>/</mo><msup><mi>d</mi><mn>2</mn></msup></mrow></math> should be carefully corrected from hyperon weak decays for protons to probe the production characteristics of light nuclei. All of our results show that the coalescence mechanism for (anti-)nucleons plays a dominant role for the production of light nuclei and antinuclei at the BNL Relativistic Heavy Ion Collider beam energy scan energies.

Xiang-Yu Zhao

Yan-Ting Feng

Production characteristics of light (anti-)nuclei from (anti-)nucleon coalescence in heavy ion collisions at energies employed at the RHIC beam energy scan

We find signals of quark combination at hadronization from the experimental data of <math><msub><mi>p</mi><mi>T</mi></msub></math> spectra of hadrons at midrapidity in <math><mi>p</mi><mi>p</mi></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>. The first is the constituent quark number scaling property for <math><msub><mi>p</mi><mi>T</mi></msub></math> spectra of <math><msup><mi>Ω</mi><mo>−</mo></msup></math> and <math><mi>ϕ</mi></math> and that for <math><msub><mi>p</mi><mi>T</mi></msub></math> spectra of <math><mi>p</mi></math> and <math><msup><mi>ρ</mi><mn>0</mn></msup></math>. The second is that <math><msub><mi>p</mi><mi>T</mi></msub></math> spectra of <math><mi>Λ</mi></math>, <math><msup><mi>Ξ</mi><mo>−</mo></msup></math>, and <math><msup><mi>K</mi><mrow><mo>*</mo><mn>0</mn></mrow></msup></math> can be self-consistently described using the spectrum of strange quarks from <math><mi>ϕ</mi></math> data and that of up/down quarks from <math><mi>p</mi></math> data in the equal-velocity combination mechanism. The third is that experimental data for <math><msub><mi>p</mi><mi>T</mi></msub></math> spectrum of <math><msup><mi>D</mi><mrow><mo>*</mo><mo>+</mo></mrow></msup></math> are also well described by the spectrum of up/down quarks from <math><mi>p</mi></math> data and a spectrum of charm quarks which is consistent with theoretical calculations of the fixed-order next-to-leading-logarithmic approach. These results indicate a similarity between hadron production in <math><mi>p</mi><mi>p</mi></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> and that at LHC energies. We predict <math><msub><mi>p</mi><mi>T</mi></msub></math> spectra of single-charm hadrons and their spectrum ratios. We suggest systematic measurements in <math><mi>p</mi><mi>p</mi></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math> in the future so as to better understand the property of the small parton system created in <math><mi>p</mi><mi>p</mi></math> collisions at different collision energies.

Signals of quark combination at hadronization in <math><mi>p</mi><mi>p</mi></math> collisions at <math><msqrt><mi>s</mi></msqrt><mo>=</mo><mn>200</mn><mtext> </mtext><mtext> </mtext><mi>GeV</mi></math>

We apply an equal-velocity quark combination model to study the production of light-flavor hadrons and single-charmed hadrons at midrapidity in the   $ pp $   collisions at   $ pp $   TeV. We find that the experimental data for the   $ pp $   spectra of   $ pp $   and   $ pp $   exhibit the quark number scaling property, which clearly indicates the quark combination mechanism at hadronization. Experimental data for the   $ pp $   spectra of   $ pp $  ,   $ pp $  ,   $ pp $  ,   $ pp $  ,   $ pp $  , and   $ pp $   are systematically described by the model. The non-monotonic   $ pp $   dependence of the   $ pp $   ratio is naturally explained, and we find that it is closely related to the shape of the logarithm of the strange quark   $ pp $   distribution. Using the   $ pp $   spectra of light-flavor quarks obtained from light-flavor hadrons and the   $ pp $   spectrum of charm quarks, which is consistent with perturbative QCD calculations, the experimental data for differential cross-sections of   $ pp $  ,   $ pp $  , and   $ pp $   as functions of   $ pp $   are systematically described. We predict the differential cross-sections of   $ pp $   and   $ pp $  . The ratio   $ pp $   in our model is approximately 0.16, and   $ pp $   is approximately 0.012, owing to the cascade suppression of strangeness. In addition, the predicted   $ pp $   and   $ pp $   ratios exhibit the non-monotonic dependence on   $ pp $   in the low   $ pp $   range.

Production of light-flavor and single-charmed hadrons in Collisions at TeV in an equal-velocity quark combination model  

We study the defect groups of   <math> <msubsup> <mi>D</mi> <mi>p</mi> <mi>b</mi> </msubsup> </math>  $$ {D}_p^b $$ (G) theories using geometric engineering and BPS quivers. In the simple case when b = h ∨(G), we use the BPS quivers of the theory to see that the defect group is compatible with a known Maruyoshi-Song flow. To extend to the case where b ≠ h ∨(G), we use a similar Maruyoshi-Song flow to conjecture that the defect groups of   <math> <msubsup> <mi>D</mi> <mi>p</mi> <mi>b</mi> </msubsup> </math>  $$ {D}_p^b $$ (G) theories are given by those of G (b)[k] theories. In the cases of G = A  n , E 6, E 8 we cross check our result by calculating the BPS quivers of the G (b)[k] theories and looking at the cokernel of their intersection matrix.

United Kingdom

Saghar Hosseini

Sweden

Robert Moscrop

Maruyoshi-Song flows and defect groups of   <math> <msubsup> <mi>D</mi> <mi>p</mi> <mi>b</mi> </msubsup> </math>  $$ {\mathrm{D}}_{\mathrm{p}}^{\mathrm{b}} $$ (G) theories

We study the momentum dependence of the production of light nuclei in high-energy collisions in the nucleon coalescence mechanism. We derive formulas of the momentum distributions of deuterons <math><mi>d</mi></math> and helions <math><mmultiscripts><mi>He</mi><mprescripts></mprescripts><none></none><mn>3</mn></mmultiscripts></math>. We obtain the analytic expressions of the coalescence factor <math><msub><mi>B</mi><mi>A</mi></msub></math> (<math><msub><mi>B</mi><mn>2</mn></msub></math> for <math><mi>d</mi></math> and <math><msub><mi>B</mi><mn>3</mn></msub></math> for <math><mmultiscripts><mi>He</mi><mprescripts></mprescripts><none></none><mn>3</mn></mmultiscripts></math>) as functions of the collision system size and the momentum. We apply the deduced results to <math><mi>p</mi><mo>−</mo><mi>p</mi></math>, <math><mi>p</mi></math>-Pb and Pb-Pb collisions to explain naturally the interesting behavior of <math><msub><mi>B</mi><mi>A</mi></msub></math> observed in experiments at the CERN Large Hadron Collider.

Momentum dependence of light nuclei production in <math><mi>p</mi><mo>−</mo><mi>p</mi></math>, <math><mi>p</mi><mtext>−</mtext><mi>Pb</mi></math>, and Pb-Pb collisions at energies available at the CERN Large Hadron Collider

We apply a quark combination model with equal-velocity combination (EVC) approximation to study the elliptic flow ( $$v_{2}$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>  ) of hadrons in heavy-ion collisions in a wide collision energy range ( $$\sqrt{s_{NN}}=$$  <math> <mrow> <msqrt> <msub> <mi>s</mi> <mrow> <mi>NN</mi> </mrow> </msub> </msqrt> <mo>=</mo> </mrow> </math>   27–5020 GeV). Utilizing the simple relationship between  $$v_{2}$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   of hadrons and those of quarks under EVC, we find that  $$v_{2}$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   of up/down quarks obtained by experimental data of proton is consistent with that obtained by data of  $$\varLambda $$  <math> <mi>Λ</mi> </math>   and  $$\varXi $$  <math> <mi>Ξ</mi> </math>  .  $$v_{2}$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   of strange quarks obtained by data of  $$\varOmega $$  <math> <mi>Ω</mi> </math>   is consistent with that obtained by data of  $$\varLambda $$  <math> <mi>Λ</mi> </math>   and  $$\varXi $$  <math> <mi>Ξ</mi> </math>  , and at RHIC energies it is also consistent with that obtained by data of  $$\phi $$  <math> <mi>ϕ</mi> </math>  . This means that  $$v_{2}$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   of these hadrons have a common quark-level source. Using data of  $$D^0$$  <math> <msup> <mi>D</mi> <mn>0</mn> </msup> </math>  , we obtain  $$v_{2}$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   of charm quarks with  $$p_T\lesssim 6$$  <math> <mrow> <msub> <mi>p</mi> <mi>T</mi> </msub> <mo>≲</mo> <mn>6</mn> </mrow> </math>   GeV/c. We find that under EVC charm quark dominates  $$v_{2}$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   of D mesons at low  $$p_{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>   but light-flavor quarks significantly contribute to  $$v_{2}$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   of D mesons in the range  $$3\lesssim p_{T}\lesssim 8$$  <math> <mrow> <mn>3</mn> <mo>≲</mo> <msub> <mi>p</mi> <mi>T</mi> </msub> <mo>≲</mo> <mn>8</mn> </mrow> </math>   GeV/c. We predict  $$v_{2}$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   of charmed baryons  $$\varLambda _{c}^{+}$$  <math> <msubsup> <mi>Λ</mi> <mrow> <mi>c</mi> </mrow> <mo>+</mo> </msubsup> </math>   and  $$\varXi _{c}^{0}$$  <math> <msubsup> <mi>Ξ</mi> <mrow> <mi>c</mi> </mrow> <mn>0</mn> </msubsup> </math>   which show a significant enhancement at intermediate  $$p_{T}$$  <math> <msub> <mi>p</mi> <mi>T</mi> </msub> </math>   due to the double contribution of light-flavor quarks. The properties of the obtained quark  $$v_{2}$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   under EVC are studied and a regularity for  $$v_{2}$$  <math> <msub> <mi>v</mi> <mn>2</mn> </msub> </math>   of quarks as the function of  $$p_{T}/m$$  <math> <mrow> <msub> <mi>p</mi> <mi>T</mi> </msub> <mo>/</mo> <mi>m</mi> </mrow> </math>   is found.