hadronic interaction and beyond standard model from lattice gauge - PowerPoint PPT Presentation

hadronic interaction and beyond standard model from lattice gauge theory Takeshi Yamazaki University of Tsukuba 素粒子物理学の進展 2014 @ 京都大学基礎物理学研究所 , July 28–August 1, 2014

hadron interaction from lattice QCD and search for walking technicolor from lattice gauge theory Takeshi Yamazaki University of Tsukuba 素粒子物理学の進展 2014 @ 京都大学基礎物理学研究所 , July 28–August 1, 2014

Hadron interaction from lattice QCD — Review — • L¨ uscher’s finite volume method • Scattering lengths • Scattering phase shifts (Resonances) • Bound states (Light nuclei)

Hadronic interactions One of ultimate goals of Lattice QCD quantitatively understand properties of hadrons Current status of lattice QCD very close to reproduce mass for stable hadrons Experiment Many hadrons decay through hadronic interaction, originating from strong interaction Next task: hadronic interactions Decay and scattering Cannot be treated separately to understand properties of unstable hadrons finial states of unstable particle = scattering states More di ffi cult to calculate, but important for the ultimate goal 1

Hadron masses from Lattice QCD N f = 2 + 1( m u = m d ̸ = m s ) N f = 2 + 1 + 1( m u ∼ m d ̸ = m s ̸ = m d ) ’10 PACS-CS ’14 Alexandrou et al. Light hadrons Charmed baryons: spin 3 / 2 5 ETMC N f =2+1+1 PACS-CS N f =2+1 (m h /m Ω ) lat / (m h /m Ω ) exp − 1 0.20 Na et al. N f =2+1 4.5 Briceno et al. N f =2+1+1 4 0.10 M (GeV) 3.5 0.00 3 original target -0.10 2.5 η ss ρ π K K* φ N Λ Σ Ξ ∆ Σ∗ Ξ∗ Ω * * * * * � ccc � c � c � c � cc � cc 0 target = physical pion mass Light hadrons consistent within a few% Predictions in some charmed baryons, also in Ω cc , B c and B ∗ c 1-a

Hadronic interactions One of ultimate goals of Lattice QCD quantitatively understand properties of hadrons Current status of lattice QCD very close to reproduce mass for stable hadrons Experiment Many hadrons decay through hadronic interaction, originating from strong interaction Next task: hadronic interactions Decay and scattering Cannot be treated separately to understand properties of unstable hadrons finial states of unstable particle = scattering states More di ffi cult to calculate, but important for the ultimate goal 1-b

Hadronic interactions One of ultimate goals of Lattice QCD quantitatively understand properties of hadrons Famous hadronic interaction nuclear force : bind nucleons into nucleus originate from strong interaction ← well known in experiment Another ultimate goal of lattice QCD quantitatively understand formation of nuclei from first principle of strong interaction http://www.jicfus.jp/jp/promotion/pr/mj/2014-1/ c.f. Nuclear force from lattice QCD, see slide of PPP2013 by S. Aoki Review recent results related to scatterings, decays, and light nuclei 2

L¨ uscher’s finite volume method L¨ uscher, CMP105:153(1986),NPB354;531(1991) spinless two-particle elastic scattering in center of mass frame on L 3 Important assumption V(r)=0 1. Two-particle interaction is localized. V(r)=0 → Interaction range R exists. � ̸ = 0 ( ∼ e − cr )( r ≤ R ) R V ( r ) = 0 ( ∼ e − cr )( r > R ) 2. V ( r ) is not a ff ected by boundary. → R < L/ 2 L Two-particle wave function φ p ( ⃗ r ) satisfies Helmholtz equation ∇ 2 + p 2 � � φ p ( ⃗ r ) = 0 in r > R ( R < L/ 2) ← Klein-Gordon eq. of free two particles � 2 � 2 π � m 2 + p 2 , p 2 ̸ = E = 2 in general L · ⃗ n 3

L¨ uscher’s finite volume method (cont’d) L¨ uscher, CMP105:153(1986),NPB354;531(1991) Helmholtz equation on L 3 1. Solution of ( ∇ 2 + p 2 ) φ p ( ⃗ r ) = 0 in r > R e i ⃗ r · ⃗ n (2 π /L ) � 2 � Lp q 2 = � φ p ( ⃗ r ) = C · n 2 − q 2 , ̸ = integer 2 π ⃗ n ∈ Z 3 ⃗ 2. Expansion by spherical Bessel j l ( pr ) and Noeman n l ( pr ) functions φ p ( ⃗ r ) = β 0 ( p ) n 0 ( pr ) + α 0 ( p ) j 0 ( pr ) + ( l ≥ 4) 3. S -wave Scattering phase shift δ 0 ( p ) in infinite volume π 3 / 2 q β 0 ( p ) 1 1 q = 2 π � Z 00 ( s ; q 2 ) = α 0 ( p ) = tan δ 0 ( p ) = √ n 2 − q 2 ) s , L p Z 00 (1; q 2 ) ( ⃗ 4 π ⃗ n ∈ Z 3 Scattering amplitude = E 1 � e 2 i δ ( p ) − 1 � 2 p 2 i � � � m 2 + p 2 Relation between δ ( p ) and p E = 2 Wave function: CP-PACS, PRD70:094504(2005), Sasaki and Ishizuka, PRD78:014511(2008) Potential: Ishii, Aoki, and Hatsuda, PRL99:022001(2007), · · · Applications K → ππ : Lellouch and L¨ uscher, CMP219:31(2001), M K L − M K S : RBC+UKQCD, arXiv:1406.0916 4

Scattering length a I 0 tan δ ( p ) a 0 = lim p p → 0 0 and I = 1 / 2 K π a 1 / 2 I = 2 ππ a 2 0

Scattering length I I = 2 ππ Simplest scattering system Comparison of dynamical calculations 0 Exp E865(2010) 2 m π -0.6 Exp NA48/2(2010) a 0 N f =2 CP-PACS(2004) N f =2+1 MA NPLQCD(2006) -0.1 -0.8 N f =2+1 MA NPLQCD(2008) N f =2+1 RBC-UKQCD(2009) -1 N f =2 ETMC(2010) N f =2 JLQCD(2011) 2 m π -0.2 a 0 -1.2 N f =2+1 NPLQCD(2012) Exp E865(2010) N f =2+1 Had Spec(2012) Exp NA48/2(2010) N f =2+1 PQ Fu(2012) N f =2 CP-PACS(2004) -1.4 |LO ChPT| N f =2+1 Fu(2013) N f =2+1 MA NPLQCD(2006) -0.3 N f =2+1 PACS-CS(2014) N f =2+1 MA NPLQCD(2008) -1.6 N f =2+1 RBC-UKQCD(2009) N f =2 ETMC(2010) -1.8 -0.4 N f =2 JLQCD(2011) N f =2+1 PQ Fu(2012) N f =2+1 Fu(2013) -2 N f =2+1 PACS-CS(2014) -0.5 LO ChPT -2.2 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 1 2 3 4 2 [GeV 2 ] m π m π /f π � Wilson type; � ASQTAD; △ DWF; � Twisted; ▽ overlap MA:DWF on ASQTAD; PQ:partial quenched N f = 2 + 1 Twisted m π = 0 . 32–0.40[GeV] [Talk:Knippschild Mon 1B 14:35] m 2 � π L ππ + analytic + log �� − 1 + 32 NLO ChPT: a 2 π m 2 � 0 m π = 8 π f 2 f 2 π π 5

Scattering length I I = 2 ππ Simplest scattering system Comparison of dynamical calculations at physical m π N f =2 CP-PACS(2004) N f =2+1 MA NPLQCD(2006) N f =2+1 MA NPLQCD(2008) N f =2 ETMC(2010) N f =2 JLQCD(2011) N f =2+1 NPLQCD(2012) N f =2+1 PQ Fu(2012) N f =2+1 Fu(2013) N f =2+1 PACS-CS(2014) CGL(2001) E865(2010) w/ ChPT E865(2010) NA48/2(2010) w/ ChPT NA48/2(2010) -0.05 -0.045 -0.04 -0.035 -0.03 2 m π a 0 NPLQCD(2012): m π /f π from MA calc. � Wilson type; � ASQTAD; △ DWF; � Twisted; ▽ overlap MA:DWF on ASQTAD; PQ:partial quenched Sources of systematic error: finite volume e ff ects, ∆ MA , ∆ Wilson , · · · high precision measurements era more precise calculation under way 6

Scattering length II I = 1 / 2 K π needs rectangle diagram 3 BDM(2004) N f =2+1 PQ Fu(2012) N f =2 Lang et al.(2012) N f =2+1 MA NPLQCD(2008) 2.5 N f =2+1 PACS-CS(2014) N f =2+1 PQ Fu(2012) 2 1/2 m π a 0 N f =2+1 PACS-CS(2014) 1.5 1 BDM(2004) 0.5 0 0 0.05 0.1 0.15 0.2 0.25 0.1 0.15 0.2 0.25 0.3 0.35 0.4 2 [GeV 2 ] 1/2 m π m π a 0 � Wilson type; � ASQTAD PQ:partial quenched Fu, PRD85:074501(2012), Lang et al. , PRD86:054508(2012), PACS-CS, PRD89:054502(2014) other works: NPLQCD, PRD74:114503(2006)(indirect), Nagata et al. , PRC80:045203(2009) , m phys N f = 2 + 1 DWF m phys on L = 5 . 5fm [Talk:Janowski Mon 1B 15:15] π K µ π K = µ 2 m π m K L ′ + m 2 π + m 2 � � �� 2 + 32 NLO ChPT: a 1 / 2 π K K L 5 + analytic + log 0 4 π f 2 f 2 2 π π µ π K = m π m K / ( m π + m K ) I = 0 ππ needs disconnected diagram → much more di ffi cult 7

Scattering phase shift δ ( p ) I = 2 ππ , I = 1 ππ → ρ , I = 1 / 2 K π → K ∗

Phase shift I I = 2 S-wave ππ Simplest scattering system 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 0 -5 - 10 -10 -15 d H degrees L - 20 -20 -25 CP - PACS '04 ‡ -30 - 30 GKPRY '11 ‡ -35 CGL '01 ‡ NPLQCD '11 ‡ -40 - 40 0.05 0.10 0.15 0.20 k 2 H GeV 2 L NPLQCD, PRD85:034505(2012) Hadron Spectrum, PRD86:034031(2012) NLO ChPT in p ̸ = 0 → physical m π S- and D-wave ( l = 0 and 2) from m π = 0 . 39 GeV, m π /f π from MA calc. calc. at m π = 0 . 39 GeV other works: CP-PACS, PRD67:014502(2003), Kim, NPB(Proc.Suppl.)129:197(2004), CP-PACS, PRD70:074513(2004), CLQCD, JHEP06:053(2007), Sasaki and Ishizuka, PRD78:014511(2008), Kim and Sachrajda, PRD81:114506(2010), Hadron Spectrum, PRD83:071504(R)(2011) 8

Phase shift II I = 1 P-wave ππ → ρ 1. 2. 3. 4. 5. 6. √ √ √ √ √ 0,1 2 , 0 ∗ 0,1 2 , 2 3 , 3 2 ,2 L | P | / 2 π 1 0,1, 2 0,1, 2 2 N mom 2 5–6 5 6 6 29 m π [MeV] 320 290-480 270 410, 300 300 390 4.2 ≥ 3.7 2.7 6.0, 4.4 ≥ 4 . 6 ≥ 3.8 m π L ∗ asymmetric lattice L 2 × η L , η = 1 , 1 . 25 , 2 1. CP-PACS, PRD76:094506(2007), 2. ETMC, PRD83:094505(2011), 3. Lang et al. , PRD84:054503(2011), 4. PACS-CS, PRD84:094505(2011), 5. Pelissier et al. , PRD87:014503(2013), 6. Hadron Spectrum, PRD87:034505(2013) other works:QCDSF, PoS(LATTICE 2008)136, BMW, PoS(Lattice 2010)139 180 Breit-Wigner form fit 160 p 3 √ s cot δ ( p ) = 6 π 140 ( m 2 ρ − s ) g 2 120 ρππ 100 s = E 2 cm 80 60 Γ ρ = p 3 g 2 ρ = m 2 40 ρ ρππ ρ p 2 4 − m 2 6 π , π 20 m 2 ρ 0 800 850 900 950 1000 1050 Hadron Spectrum, PRD87:034505(2013) 9