Understanding the Effect of Conserved Charges on the Coalescence Sum Rule of Directed Flow
Recently, the rapidity-odd directed flow (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>v</mi><mn>1</mn></msub></semantics></math></inline-formula>) of...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-03-01
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| Series: | Universe |
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| Online Access: | https://www.mdpi.com/2218-1997/10/3/112 |
| _version_ | 1797239185999921152 |
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| author | Kishora Nayak Shu-Su Shi Zi-Wei Lin |
| author_facet | Kishora Nayak Shu-Su Shi Zi-Wei Lin |
| author_sort | Kishora Nayak |
| collection | DOAJ |
| description | Recently, the rapidity-odd directed flow (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>v</mi><mn>1</mn></msub></semantics></math></inline-formula>) of produced hadrons (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>K</mi><mo>−</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>p</mi><mo>¯</mo></mover></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mo>Λ</mo><mo>¯</mo></mover></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover><mo>Ξ</mo><mo>¯</mo></mover><mo>+</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mo>Ω</mo><mo>−</mo></msup></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover><mo>Ω</mo><mo>¯</mo></mover><mo>+</mo></msup></semantics></math></inline-formula>) has been studied. Several combinations of these produced hadrons, with very small mass differences but differences in the net electric charge (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>q</mi></mrow></semantics></math></inline-formula>) and net strangeness (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>S</mi></mrow></semantics></math></inline-formula>) on the two sides, have been considered. A difference in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>v</mi><mn>1</mn></msub></semantics></math></inline-formula> between the two sides of these combinations (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>) has been proposed as a consequence of the electromagnetic field produced in relativistic heavy-ion collisions, especially if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> increases with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi mathvariant="normal">q</mi></mrow></semantics></math></inline-formula>. Our study is performed to understand the effect of the coalescence sum rule (CSR) on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>. We point out that the CSR leads to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub><mo>=</mo><msub><mi>c</mi><mi>q</mi></msub><mo>Δ</mo><mi>q</mi><mo>+</mo><msub><mi>c</mi><mi>S</mi></msub><mo>Δ</mo><mi>S</mi></mrow></semantics></math></inline-formula>, where the coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>c</mi><mi>q</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>c</mi><mi>S</mi></msub></semantics></math></inline-formula> reflect the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> of produced quarks. Equivalently, one can write <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub><mo>=</mo><msub><mi>c</mi><mi>q</mi></msub><mo>Δ</mo><mi>q</mi><mo>+</mo><msub><mi>c</mi><mi>B</mi></msub><mo>Δ</mo><mi>B</mi></mrow></semantics></math></inline-formula>, involving the difference in the net baryon number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>B</mi></mrow></semantics></math></inline-formula>, where the CSR gives <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>c</mi><mi>B</mi></msub><mo>=</mo><mo>−</mo><mn>3</mn><msub><mi>c</mi><mi>S</mi></msub></mrow></semantics></math></inline-formula>. We then propose two methods to extract the coefficients for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>q</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>S</mi></mrow></semantics></math></inline-formula> dependences of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-04-24T17:47:32Z |
| format | Article |
| id | doaj.art-a96ef91bbedb42fc85c22ce56f2cf6e1 |
| institution | Directory Open Access Journal |
| issn | 2218-1997 |
| language | English |
| last_indexed | 2024-04-24T17:47:32Z |
| publishDate | 2024-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Universe |
| spelling | doaj.art-a96ef91bbedb42fc85c22ce56f2cf6e12024-03-27T14:06:37ZengMDPI AGUniverse2218-19972024-03-0110311210.3390/universe10030112Understanding the Effect of Conserved Charges on the Coalescence Sum Rule of Directed FlowKishora Nayak0Shu-Su Shi1Zi-Wei Lin2Department of Physics, Panchayat College, Sambalpur University, Bargarh 768028, IndiaKey Laboratory of Quark & Lepton Physics (MOE) and Institute of Particle Physics, Central China Normal University, Wuhan 430079, ChinaDepartment of Physics, East Carolina University, Greenville, NC 27858, USARecently, the rapidity-odd directed flow (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>v</mi><mn>1</mn></msub></semantics></math></inline-formula>) of produced hadrons (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>K</mi><mo>−</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ϕ</mi></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mi>p</mi><mo>¯</mo></mover></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover><mo>Λ</mo><mo>¯</mo></mover></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover><mo>Ξ</mo><mo>¯</mo></mover><mo>+</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mo>Ω</mo><mo>−</mo></msup></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mover><mo>Ω</mo><mo>¯</mo></mover><mo>+</mo></msup></semantics></math></inline-formula>) has been studied. Several combinations of these produced hadrons, with very small mass differences but differences in the net electric charge (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>q</mi></mrow></semantics></math></inline-formula>) and net strangeness (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>S</mi></mrow></semantics></math></inline-formula>) on the two sides, have been considered. A difference in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>v</mi><mn>1</mn></msub></semantics></math></inline-formula> between the two sides of these combinations (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>) has been proposed as a consequence of the electromagnetic field produced in relativistic heavy-ion collisions, especially if <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> increases with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi mathvariant="normal">q</mi></mrow></semantics></math></inline-formula>. Our study is performed to understand the effect of the coalescence sum rule (CSR) on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>. We point out that the CSR leads to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub><mo>=</mo><msub><mi>c</mi><mi>q</mi></msub><mo>Δ</mo><mi>q</mi><mo>+</mo><msub><mi>c</mi><mi>S</mi></msub><mo>Δ</mo><mi>S</mi></mrow></semantics></math></inline-formula>, where the coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>c</mi><mi>q</mi></msub></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>c</mi><mi>S</mi></msub></semantics></math></inline-formula> reflect the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> of produced quarks. Equivalently, one can write <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub><mo>=</mo><msub><mi>c</mi><mi>q</mi></msub><mo>Δ</mo><mi>q</mi><mo>+</mo><msub><mi>c</mi><mi>B</mi></msub><mo>Δ</mo><mi>B</mi></mrow></semantics></math></inline-formula>, involving the difference in the net baryon number <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>B</mi></mrow></semantics></math></inline-formula>, where the CSR gives <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>c</mi><mi>B</mi></msub><mo>=</mo><mo>−</mo><mn>3</mn><msub><mi>c</mi><mi>S</mi></msub></mrow></semantics></math></inline-formula>. We then propose two methods to extract the coefficients for the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>q</mi></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>S</mi></mrow></semantics></math></inline-formula> dependences of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><msub><mi>v</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2218-1997/10/3/112directed flowcoalescence sum rule |
| spellingShingle | Kishora Nayak Shu-Su Shi Zi-Wei Lin Understanding the Effect of Conserved Charges on the Coalescence Sum Rule of Directed Flow Universe directed flow coalescence sum rule |
| title | Understanding the Effect of Conserved Charges on the Coalescence Sum Rule of Directed Flow |
| title_full | Understanding the Effect of Conserved Charges on the Coalescence Sum Rule of Directed Flow |
| title_fullStr | Understanding the Effect of Conserved Charges on the Coalescence Sum Rule of Directed Flow |
| title_full_unstemmed | Understanding the Effect of Conserved Charges on the Coalescence Sum Rule of Directed Flow |
| title_short | Understanding the Effect of Conserved Charges on the Coalescence Sum Rule of Directed Flow |
| title_sort | understanding the effect of conserved charges on the coalescence sum rule of directed flow |
| topic | directed flow coalescence sum rule |
| url | https://www.mdpi.com/2218-1997/10/3/112 |
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