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Title: Direct CP violation and the ΔI=1/2 rule in K→ππ decay from the standard model

Journal Article · · Physical Review D
 [1];  [2];  [3]; ;  [1];  [2];  [4]; ORCiD logo [4];  [5];  [1];  [6];  [7];  [4];  [8];  [1]
  1. Columbia Univ., New York, NY (United States)
  2. Univ. of Connecticut, Storrs, CT (United States); Brookhaven National Lab. (BNL), Upton, NY (United States). RIKEN Research Center
  3. Brookhaven National Lab. (BNL), Upton, NY (United States); Univ. of Edinburgh, Scotland (United Kingdom)
  4. Brookhaven National Lab. (BNL), Upton, NY (United States)
  5. Brookhaven National Lab. (BNL), Upton, NY (United States); Univ. Regensburg (Germany)
  6. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  7. Univ. of Southampton (United Kingdom)
  8. Univ. of Connecticut, Storrs, CT (United States)

We present a lattice QCD calculation of the ΔI=1/2 , Kππ decay amplitude A 0 and ϵ' , the measure of direct CP violation in Kππ decay, improving our 2015 calculation [1] of these quantities. Both calculations were performed with physical kinematics on a 323×64 lattice with an inverse lattice spacing of a - 1 =1.3784(68) GeV . However, the current calculation includes nearly 4 times the statistics and numerous technical improvements allowing us to more reliably isolate the ππ ground state and more accurately relate the lattice operators to those defined in the standard model. We find Re( A 0 )=2.99(0.32)(0.59)×10 - 7 GeV and Im( A 0 )=-6.98(0.62)(1.44)×10 - 11 GeV , where the errors are statistical and systematic, respectively. The former agrees well with the experimental result Re( A 0 )=3.3201(18)×10 - 7 GeV . These results for A 0 can be combined with our earlier lattice calculation of A 2 [2] to obtain Re(ϵ'/ϵ)=21.7(2.6)(6.2)(5.0)×10 - 4 , where the third error represents omitted isospin breaking effects, and Re( A 0 )/Re( A 2 )=19.9(2.3)(4.4) . The first agrees well with the experimental result of Re(ϵ'/ϵ)=16.6(2.3)×10 - 4 . A comparison of the second with the observed ratio Re( A 0 )/Re( A 2 )=22.45(6) , demonstrates the standard model origin of this “ ΔI=1/2 rule” enhancement.

Research Organization:
Brookhaven National Laboratory (BNL), Upton, NY (United States)
Sponsoring Organization:
USDOE Office of Science (SC), High Energy Physics (HEP); STFC
Contributing Organization:
RBC and UKQCD Collaborations
Grant/Contract Number:
SC0012704; ST/R00238X/1; ST/S002537/1; ST/R001006/1; SC0010339; SC0011090
OSTI ID:
1679957
Report Number(s):
BNL-219971-2020-JAAM; TRN: US2204027
Journal Information:
Physical Review D, Vol. 102, Issue 5; ISSN 2470-0010
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

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Figures / Tables (39)