QCD with axial hemial p otential and p ola rization of - PowerPoint PPT Presentation

QCD with axial hemi al p otential and p ola rization of dilepton p ro du tion in heavy-ion ollisions Alexander A. Andrianov Saint-P etersburg State Universit y HSQCD 2014 Axial hemi al p otential 1

Outline Phenomenology of lo al pa rit y b reaking (LPB) Axial ba ry on ha rge T axial hemi al p otential µ 5 ⇔ 5 E�e tive meson theo ry in a medium with LPB V e to r Meson Dominan e (VMD) app roa h to LPB: Massive Maxw ell-Chern-Simons ele tro dynami s (CFJ mo del) A.Andrianov, V.Andrianov, D. Esp riu & X. Planells, Phys. Lett. B 710:230 (2012) E�e tive s ala r/pseudos ala r meson theo ry with µ 5 ◮ A. A. Andrianov, D. Esp riu & X. Planells, Eur. Phys. J. C , 73:2294 (2013) Phase stru ture of the NJL qua rk mo del with µ ◮ 5 A. A. Andrianov, D. Esp riu & X. Planells, Eur. Phys. J. C , 74:2776 (2014) ◮ Manifestation of LPB in heavy ion ollisions (HIC): dilepton p ola rization asymmetry A. A. Andrianov, V. A. Andrianov, D. Esp riu & X. Planells, a rXiv:1402.2147 HSQCD 2014 Axial hemi al p otential 2 ◮

Phenomenology of lo al pa rit y b reaking P a rit y: w ell established global symmetry of strong intera tions. Reasons to b elieve it ma y b e b rok en in a �nite volume?! quantum �u tuations of θ pa rameter ( P -o dd bubbles [ T. D. Lee and G. C. Wi k . . . ℄: their manifestation in Chiral Magneti E�e t (CME))[ D. E. Kha rzeev, A.Zhitnitsky , L. D. M Lerran, K.F ukushima, H. J. W a rringa (an ea rlier p rop osal: A.Vilenkin , 1980)℄ New QCD phase ha ra terized b y a sp ontaneous pa rit y b reaking due to fo rmation of neutral pion-lik e ba kground [ A.A.Anselm . . . . . . A. A., V. A. Andrianov & D. Esp riu ℄ High energy p ro du tion of pseudos ala r gluelumps ⇔ pa rit y-o dd bun hes of gluon jets ⇒ then a PB ba kground remains inside a hot dense nu lea r �reball in HIC !? HSQCD 2014 Axial hemi al p otential 3

Phenomenology of lo al pa rit y b reaking P a rit y: w ell established global symmetry of strong intera tions. Reasons to b elieve it ma y b e b rok en in a �nite volume?! quantum �u tuations of θ pa rameter ( P -o dd bubbles [ T. D. Lee and G. C. Wi k . . . ℄: their manifestation in Chiral Magneti E�e t (CME))[ D. E. Kha rzeev, A.Zhitnitsky , L. D. M Lerran, K.F ukushima, H. J. W a rringa (an ea rlier p rop osal: A.Vilenkin , 1980)℄ New QCD phase ha ra terized b y a sp ontaneous pa rit y b reaking due to fo rmation of neutral pion-lik e ba kground [ A.A.Anselm . . . . . . A. A., V. A. Andrianov & D. Esp riu ℄ High energy p ro du tion of pseudos ala r gluelumps ⇔ pa rit y-o dd bun hes of gluon jets ⇒ then a PB ba kground remains inside a hot dense nu lea r �reball in HIC !? HSQCD 2014 Axial hemi al p otential 3

Phenomenology of lo al pa rit y b reaking P a rit y: w ell established global symmetry of strong intera tions. Reasons to b elieve it ma y b e b rok en in a �nite volume?! quantum �u tuations of θ pa rameter ( P -o dd bubbles [ T. D. Lee and G. C. Wi k . . . ℄: their manifestation in Chiral Magneti E�e t (CME))[ D. E. Kha rzeev, A.Zhitnitsky , L. D. M Lerran, K.F ukushima, H. J. W a rringa (an ea rlier p rop osal: A.Vilenkin , 1980)℄ New QCD phase ha ra terized b y a sp ontaneous pa rit y b reaking due to fo rmation of neutral pion-lik e ba kground [ A.A.Anselm . . . . . . A. A., V. A. Andrianov & D. Esp riu ℄ High energy p ro du tion of pseudos ala r gluelumps ⇔ pa rit y-o dd bun hes of gluon jets ⇒ then a PB ba kground remains inside a hot dense nu lea r �reball in HIC !? HSQCD 2014 Axial hemi al p otential 3

Phenomenology of lo al pa rit y b reaking P a rit y: w ell established global symmetry of strong intera tions. Reasons to b elieve it ma y b e b rok en in a �nite volume?! quantum �u tuations of θ pa rameter ( P -o dd bubbles [ T. D. Lee and G. C. Wi k . . . ℄: their manifestation in Chiral Magneti E�e t (CME))[ D. E. Kha rzeev, A.Zhitnitsky , L. D. M Lerran, K.F ukushima, H. J. W a rringa (an ea rlier p rop osal: A.Vilenkin , 1980)℄ New QCD phase ha ra terized b y a sp ontaneous pa rit y b reaking due to fo rmation of neutral pion-lik e ba kground [ A.A.Anselm . . . . . . A. A., V. A. Andrianov & D. Esp riu ℄ High energy p ro du tion of pseudos ala r gluelumps ⇔ pa rit y-o dd bun hes of gluon jets ⇒ then a PB ba kground remains inside a hot dense nu lea r �reball in HIC !? HSQCD 2014 Axial hemi al p otential 3

Phenomenology of lo al pa rit y b reaking Lo al la rge �u tuations in the top ologi al ha rge p resumably exist in a hot environment. F o r p eripheral heavy ion ollisions they lead to the Chiral Magneti E�e t (CME): La rge � B ⇒ la rge � E ⇒ ha rge sepa ration. D. Kha rzeev, R. D. Pisa rski & M. H. G. T ytgat, Phys. Rev. Lett. 81, 512 (1998) K. Bu kley , T. F ugleb erg, & A. Zhitnitsky , Phys. Rev. Lett. 84 (2000) 4814 D. E. Kha rzeev, L. D. M Lerran and H. J. W a rringa, Nu l. Phys. A 803, 227 (2008) F o r entral ollisions (and light qua rks) they o rresp ond to an ephemeral phase with axial hemi al p otential µ 0 lo ated in 5 � = "�u tons" of few-F ermi size. A. A. Andrianov, V. A. Andrianov, D. Esp riu & X. Planells, Phys. Lett. B 710 (2012) 230. HSQCD 2014 Axial hemi al p otential 4

Axial ba ry on ha rge and axial hemi al p otential QCD has a non-trivial va uum stru ture with di�erent top ologi al se to rs. T op ologi al ha rge T ma y 5 a rise in a �nite volume due to quantum �u tuations in a hot medium due to sphaleron transitions [Manton, M Lerran, Rubak ov, Shap oshnik ov℄ 1 2 3 j ∂ k l − j k l T d x ε T r G G i G G G 5 = jkl 2 8 π 3 vol. and survive fo r a sizeable lifetime in a heavy-ion �reball T 0 fo r t ≃ τ 5 ÷ 10 fm . 5 � � = �reball ≃ HSQCD 2014 Axial hemi al p otential 5 � � � � ∆ ∆

Axial ba ry on ha rge and axial hemi al p otential Latti e simulation of lo al �u tuations of the top ologi al ha rge in the QCD va uum [Leinw eb er℄. HSQCD 2014 Axial hemi al p otential 6

Axial ba ry on ha rge and axial hemi al p otential F o r the �reball lifetime one an ontrol the value of � ∆ T intro du ing 5 � into the QCD Lagrangian a top ologi al hemi al p otential µ θ in a gauge inva riant w a y via ∆ L T , where top = µ θ ∆ 5 t f 1 3 T T t T 0 ) = dt d x T r G µν � G µν 5 = 5 ( f ) − 5 ( 2 8 π 0 vol. The pa rtial onservation of axial urrent (b rok en b y gluon anomaly) N f J µ 2 im J T r G µν � G µν q 5 = 5 − 2 8 π p redi ts the indu ed axial ha rge (in the hiral limit m 0) q ≃ � � d � � q q 3 Q 2 N T 0 , Q d x ¯ q γ q = � N N f 5 ) ≃ 0 γ 5 L − R � 5 − 5 = ∆ . dt ( vol. to b e onserved during τ . �reball � � ∂ µ HSQCD 2014 Axial hemi al p otential 7 �

Axial ba ry on ha rge and axial hemi al p otential The ha ra teristi left-right os illation time is governed b y inverse qua rk masses. V − 1 ∼ F o r u , d qua rks 1 / m 1 / 5 Me 40 fm ≫ τ and the q ∼ �reball left-right qua rk mixing an b e negle ted. V − 1 ∼ s F o r s qua rk 1 / m 1 / 150 Me 1 fm ≪ τ and � Q 0 s ∼ 5 � ≃ �reball due to left-right os illations. F o r u , d qua rks QCD with a top ologi al ha rge � ∆ T 0 an b e equally 5 � � = des rib ed at the Lagrangian level b y top ologi al hemi al p otential µ θ o r b y axial hemi al p otential µ 5 1 1 q T Q 5 � ≃ 5 ≃ 5 � ⇐ 2 N 2 N f f q T Q top = µ θ ∆ 5 ⇐ q = µ 5 5 HSQCD 2014 Axial hemi al p otential 8 � ∆ � ⇒ µ µ θ , ∆ L ⇒ ∆ L

Axial ba ry on ha rge and axial hemi al p otential LPB is investigated in e.m. intera tions of leptons and photons with hot/dense nu lea r matter via heavy ion ollisions. e.m. intera tion implies N q q em em 3 j ∂ k ˆ l � Q Q Q T T d x ε T r A A 5 = jkl 5 → ˜ 5 − 5 , 5 2 8 π vol. is onjugated to (nea rly) onserved ˜ Q 5 5 Bosonization of ˜ Q with hiral Lagrangian, VMD... 5 � ∆ T 5 � 5 � � The ⇐ sense means that if one is able to �t µ from phenomenology , 5 ˆ = . T an b e found using kno wn te hniques on the latti e. 5 � Ho w do es ˜ Q a�e t the hadroni phenomenology? 5 µ HSQCD 2014 Axial hemi al p otential 9 ⇐ ⇒ µ = � ∆