with IMC Hao Liu Institute of High Energy Physics, CAS UCLA collaboration with Mei Huang and Lang Yu

Transcription

1 Charged condensation with IMC Hao Liu Institute of High Energy Physics, CAS collaboration with Mei Huang and Lang Yu UCLA !1

2 Outline Introduction & Motivation Charge condensation with MC NJL model and Formalism! Numerical Results and Discussion! Charged condensation with IMC Three different approaches to introduce IMC! Numerical results and Discussion! Summary!2

3 Strong Magnetic Fields in QCD Early Universe: up to Gauss Magnetars: about Gauss Heavy ion collisions: to Gauss!3

4 QCD Phase Diagram under Strong Magnetic Field CME CVE Inverse Magnetic Catalysis Vacuum SC (Inverse) Magnetic Catalysis? B B Magnetar!4

5 Vacuum Superconductor M. N. Chernodub, Phys. Rev. Lett. 106 (2011) [arxiv: [hep-ph]]! -Energy of relativistic particle in the external magnetic field B: E 2 n,s z (p z )=p 2 z +(2n 2sgn(q)s z + 1)eB + m 2 nonnegative integer number the momentum along the external projection of spin on the magnetic field direction of magnetic field -Masses of mesons and in magnetic field: m 2 ± (B) = m 2 ± +eb becomes larger where m 2 ± (B) = m 2 ± eb becomes lighter m ± = 768MeV, m ± = 140 MeV!5

6 Vacuum Superconductor The charged rho becomes massless and condensates at a critical magnetic field : eb c =m 2 ± M. N. Chernodub, Phys. Rev. Lett. 106 (2011) [arxiv: [hep-ph]] The pions become heavier while the charged vector mesons become lighter in the external magnetic field. The ±! ± 0 decay stops at a critical eb.!6

7 Vacuum Superconductor? A point particle model for the charged rho : eb c =m 2 ± NJL Model (LLL):!! eb c > 1GeV 2 M. N. Chernodub, Phys. Rev. Lett. 106 (2011) [arxiv: [hep-ph]] NJL Model: eb c =0.978 m 2 q M. Frasca, JHEP 1311, 099 (2013) [arxiv: [hep-ph]] Holographic approach: eb c 1.08m 2 (B = 0) N. Callebaut, D. Dudal and H. Verschelde, PoS FACESQCD, 046 (2010) [arxiv: [hep-ph]]!7

8 Vacuum Superconductor? DSE and BSE: Kunlun Wang PhD thesis Quark-antiquark Green Function and effective Hamiltonian (LLL) M. A. Andreichikov, B. O. Kerbikov, V. D. Orlovsky and Y.. A. Simonov, Phys. Rev. D 87, no. 9, (2013) [arxiv: [hep-ph]] The masses of the systems in GeV as a functions of eb!8

9 Our work H. Liu, L. Yu and M. Huang, Phys. Rev. D 91 (2015) 1, [arxiv: [hep-ph]]! We explore the character of rho meson in magnetic field in NJL Model!9

10 NJL Model and Analysis Result L = (i 6D m 0 ) + G 1 ( ) 2 +( i 5 ) 2 G 2 ( µ ) 2 +( µ 5 ) 2 = 2G 1 < > and M = m Σ GeV eb GeV 2!10

11 NJL Model and Analysis Result µ ab = i 1 X p,k=0 Z D p D k Z d 4 xe i( p k q) x µ pk,ab ( p, k, x 1 ) where µ pk,ab ( p, k, x 1 )=tr sfc µ a P p (x 1 )D 1 Q ( p)p p(0) b K k (0)D 1 Q ( k)k k (x 1 )!11

12 NJL Model and Analysis Result Ritus fermion propagator: Z1X S Q (x, y) =i p=0 D p e i p (x y) P p (x 1 )D 1 Q ( p) P p(y 1 ) V. I. Ritus, Annals Phys. 69, 555 (1972) K. Fukushima, D. E. Kharzeev and H. J.Warringa, Nucl.Phys. A 836, 311 (2010) [arxiv: [hep-ph] Sh. Fayazbakhsh and N. Sadooghi, Phys. Rev. D 88, no.6, (2013) [arxiv: [hep-ph]] P p (x 1 )= 1 2 [f +s p (x 1 )+ p fp s (x 1 )] f +s p (x 1 )= p x 1 s Q p 2`2B f s p (x 1 )= p 1 x 1 s Q p 2`2B p(x) =a p exp x 2 2`2B H p x `B,D Q ( p) = p Q m a p =(2 p p! p `B) 1/2 `B = QeB 1/2!12

13 NJL Model and Analysis Result -In the rest frame of charged µ = B A = meson: B0 a ib 0 0 ib a 0A c -In the rest frame of neutral meson: µ = B A = B0 d d 0A e!13

14 NJL Model and Analysis Result µ ab = 1 P µ + 2 P µ L µ + 4 u µ u ab with P µ + = µ 1 1,P µ = µ 2 2,L µ = b µ b b µ =(0, 0, 0, 1),u µ =(1, 0, 0, 0) µ 1, µ 2 are right-and left-handed helicities. 1 : the projection of spin is -1 2 : the projection of spin is 1 3 : the projection of spin is 0 The Gap equation for vector meson: 1 + 2G 2 i =0!14

15 NJL Model and Analysis Result -For charged rho : Condensation: where 1+2G 2 2 =0 1+2G 2 1 =0, 1 = (a + b), 2 = b a, Mass square of + decrease with eb -For neutral rho : Mass square of decrease with eb 1 = 2 = d, 3 = e!15

16 Parameters f = 95MeV,m = 140MeV,M = 768MeV m = 458MeV,m 0 =5MeV Soft cut off = 582MeV,G 1 2 =2.388,G 2 2 =1.73!16

17 !17 Vacuum Superconductor H. Liu, L. Yu and M. Huang, Phys. Rev. D 91 (2015) 1, [arxiv: [hep-ph]] M r ± 2 D eb@gev 2 D The masses of ± decrease and become massless at eb c 0.2 GeV 2!

18 Nonzero temperature and nonzero density (arxiv: , accepted by CPC)!18

19 Numerical Results and Discussion MΡ ±2 GeV 2 MΡ ±2 GeV T 0 GeV Μ 0.1 GeV Μ 0.3 GeV Μ 0.34 GeV eb GeV 2 Μ 0 GeV T 0.1 GeV T 0.2 GeV T 0.25 GeV eb GeV 2 ebc GeV Μ 0 GeV Μ 0.3 GeV Μ 0.46 GeV T GeV Both temperature and chemical potential suppress condensation. condensation can survive at very high temperature!!19

20 Introduce the IMC (In preparation)!20

21 Fitting the Lattice data G. S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S. D. Katz, S. Krieg, A. Schafer and K. K. Szabo, JHEP 1202, 044 (2012); G. S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S. D. Katz and A. Schafer, Phys. Rev. D 86, (2012); u u d d 2 GeV T 0 MeV T 130 MeV T 142 MeV T 148 MeV T 153 MeV T 163 MeV eb GeV 2

22 Running coupling constant G S (eb) = 2 4G S (eb) + B2 2 n E q +ln 1+e 3 X q f 2{ 2 3, 1 3 } (E q +µ) +ln q f eb +1 X p=0 1+e p Z +1 1 (E q µ) o, dp G S ( ) G S (0) = 1+a 2 + b 3 1+c 2 + d 4 where G S (0) = G S, = eb 2 QCD, QCD = 300 MeV.

23 Running coupling constant G S (eb) a = ,b = ,c = ,d = G S eb GeV eb GeV 2 u u d d 2 GeV T 0 MeV T 100 MeV T 170 MeV T 200 MeV T 250 MeV eb GeV 2

24 Chiral chemical potential µ 5 J. Chao, P. Chu and M. Huang, Phys. Rev. D 88, (2013) doi: /physrevd [arxiv: [hep-ph]]. µ 5 (eb) =0.5 p eb u u d d 2 GeV T 0 MeV T 130 MeV T 170 MeV T 200 MeV T 220 MeV eb GeV 2

25 Numerical Results and Discussion ebc GeV T GeV 0.22 Fitting Lattice data ebc GeV T GeV Chiral chemical potential ebc GeV Comparing with case in MC, the IMC phenomenon affects the appearance of charged condensation T GeV Running coupling constant Charged around the can condensate easier T C.

26 Summary Charged rho meson condensates at eb c 0.2 GeV 2 < 0.6 GeV 2! Both temperature and chemical potential suppress the condensation when we consider the MC. Comparing with case in MC, the IMC phenomenon affects the appearance of charged condensation. When we consider the IMC, charged can condensate easier around the T C.!26

27 Thanks for your attention!!27