Looking for chiral anomaly in K K reactions Phys. Rev. D93 , 094029 - PowerPoint PPT Presentation

Looking for chiral anomaly in Kγ → Kπ reactions Phys. Rev. D93 , 094029 (2016); 1512.04438 M. I. Vysotsky, E. V. Zhemchugov A. I. Alikhanov Institute for Theoretical and Experimental Physics Moscow, Russia 14th International Workshop on Meson Production, Properties and Interaction June 2–7, 2016 Krak´ ow, Poland

Institute for High-Energy Physics Protvino, Russia OKA Detector Current experiment E K = 17 . 7 GeV. K + ( K 0 ) K + γ π 0 ( π + ) Cu Cu E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 1/13

Institute for High-Energy Physics Protvino, Russia OKA Detector Current experiment [Yu. M. Antipov et. al. , Phys. Rev. D36 , 21 (1987)] E K = 17 . 7 GeV. E π = 40 GeV. K + ( K 0 ) K + π − π − π 0 γ γ π 0 ( π + ) C , Al , Fe Fe , Al , C Cu Cu E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 1/13

A ( π − γ → π − π 0 ) = h ( s, t, u ) · ε µαβγ A µ ∂ α π − ∂ β π + ∂ γ π 0 Sutherland-Veltman (chiral symmetry): h (0 , 0 , 0) ≡ h (0) = 0 Relation to the π 0 → γγ process 1   e  Wess-Zumino anomaly 2 = 9 . 8 GeV − 3 h (0) = 4 π 2 F 3 π  Direct calculation of the box  ( F π = 92 . 2 MeV from π → ℓν decay) h (0) � = 0 ⇒ chiral anomaly D π − π − γ U π 0 U U U γ U γ π 0 U 1 [Terent’ev, JETP Letters 14 , 94 (1971)] 2 [Wess, Zumino, Phys. Lett. 37B , 95 (1971)] E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 2/13

π − π − π − π − ρ − ρ 0 γ π 0 γ π 0 ( s ) ( t ) π 0 π − π − π − ρ − ω q γ γ π 0 π − ( u ) A ( π − γ → π − π 0 ) = h ( s, t, u ) · ε µαβγ A µ ∂ α π − ∂ β π + ∂ γ π 0 q 2 � 1 + 2 f ρππ f ρπγ � s t u � + f ωγ f ω 3 π � h ( s, t, u ) = h (0) ρ − s + ρ − t + m 2 ρ h (0) m 2 m 2 m 2 ρ − u m 2 ω h (0) m 2 ω − q 2 [Terent’ev, Phys. Lett. 38B , 419 (1972)] E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 3/13

A ( π − γ → π − π 0 ) = h ( s, t, u ) · ε µαβγ A µ ∂ α π − ∂ β π + ∂ γ π 0 q 2 � 1 + 2 f ρππ f ρπγ � � � s t u + f ωγ f ω 3 π h ( s, t, u ) = h (0) ρ − s + ρ − t + m 2 ρ h (0) m 2 m 2 m 2 ρ − u m 2 ω h (0) m 2 ω − q 2 h (0) values 9 . 8 GeV − 3 Theory 12 . 9 ± 0 . 9 ± 0 . 5 ± 1 . 0 GeV − 3 Experiment at LO (1987) 10 . 7 ± 1 . 2 GeV − 3 Experiment at NNLO + EMC (2001) Update from the COMPASS Collaboration? E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 4/13

π + γ → π + π 0 U U U γ π + π 0 π 0 π + π 0 D U U U D U γ π + π + π + γ π + D D U π 0 U π + U D π + − 1 3 + 2 3 + 2 3 = 1 E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 5/13

π + γ → π + π 0 π 0 π + U U π + π + U D π + π 0 D D − 1 3 + 2 3 + 2 − 1 3 + 2 3 − 1 3 = 1 3 = 0 K + γ → K + π 0 K + γ → K 0 π + U π 0 U π + K + U K + D S K + S K 0 − 1 3 + 2 3 + 2 − 1 3 + 2 3 − 1 3 = 1 3 = 0 neutral pion production charged pion production E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 6/13

K + K + K + γ → K + π 0 p k 1 q k 2 γ π 0 anomaly K + K + K + K + π 0 ρ 0 , ω , φ K ∗ + K ∗ + K + K + γ γ γ π 0 π 0 s channel u channel t channels K + K 0 K + γ → K 0 π + K + K 0 π + ρ + K ∗ + K ∗ 0 K + K 0 γ γ γ π + π + s channel u channel t channel E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 7/13

K + K + k 1 K ∗ + k 2 q p γ π 0 s -channel amplitude: 2 f K ∗ + K + γ f K ∗ + K + π 0 A (0) s ( K + γ → K + π 0 ) = − K ∗ + + i √ s Γ K ∗ + ( s ) ε αβγδ ǫ α p β k 1 γ k 2 δ s − m 2 A s ( K + γ → K + π 0 ) = A (0) s ( K + γ → K + π 0 ) − A (0) s ( K + γ → K + π 0 ) | s =0 Cross section: t + ( st − m 2 K + m 2 π 0 )( t − m 2 dσ ( K + γ → K + π 0 ) 1 � π 0 ) � = ( s − m 2 dt 2 7 π K + ) 2 � 2 f K ∗ + K + γ f K ∗ + K + π 0 e s � K ∗ + − s − i √ s Γ K ∗ + ( s ) · × + � 4 π 2 F 3 m 2 m 2 � π K ∗ + + 2 f K ∗ + K + γ f K ∗ + K + π 0 + 2 f ρ 0 π 0 γ f ρ 0 K + K + u t · · m 2 m 2 m 2 m 2 K ∗ + − u ρ 0 − t K ∗ + ρ 0 2 + 2 f ωπ 0 γ f ωK + K + + 2 f φπ 0 γ f φK + K + � t t � · · � m 2 m 2 m 2 ω − t m 2 φ − t ω � φ E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 8/13

f K ∗ + K + π 0 = 3 . 10 Decay widths: f K ∗ + K 0 π + = 4 . 38 Γ( K ∗ → Kπ ) = f K ∗ 0 K + π + = 4 . 41 ⇒ | f K ∗ Kπ | Γ( K ∗ → Kγ ) = f ρ 0 K + K + = 3 . 16 ⇒ | f K ∗ Kγ | f ρ + K + K 0 = − 4 . 47 Γ( φ → K + K − ) = ⇒ | f φK + K + | f ωK + K + = 3 . 16 Γ( ρ + → π + γ ) = ⇒ | f ρ + π + γ | f φK + K + = − 4 . 47 0 . 240 GeV − 1 = Γ( ρ 0 → π 0 γ ) = f K ∗ + K + γ ⇒ | f ρ 0 π 0 γ | = − 0 . 385 GeV − 1 f K ∗ 0 K 0 γ Γ( ω → π 0 γ ) = ⇒ | f ωπ 0 γ | 0 . 252 GeV − 1 = f ρ 0 π 0 γ 0 . 219 GeV − 1 Γ( φ → π 0 γ ) = = ⇒ | f φπ 0 γ | f ρ + π + γ 0 . 696 GeV − 1 = f ωπ 0 γ 0 . 040 GeV − 1 = f φπ 0 γ SU (3) symmetry: √ 2 f K ∗ + K + π 0 = f K ∗ + K 0 π + = f K ∗ 0 K + π + = − f ρ + K + K 0 √ √ = 2 f ρ 0 K + K + = 2 f ωK + K + = − f φK + K + f K ∗ + K + γ = f ρ + π + γ = f ρ 0 π 0 γ = 1 3 f ωπ 0 γ = − 1 2 f K ∗ 0 K 0 γ The sign of the anomaly term is unknown. E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 9/13

K + K γ � q π N N Weizsacker-Williams equivalent photons approximation: dσ ( K + N → KπN ) Z 2 α q 2 dσ ( K + γ → Kπ ) ⊥ q 2 ) | 2 = | F ( � dt ds dq 2 π ( s − m 2 K + ) � s − m 2 � 2 � 2 dt � ⊥ q 2 ⊥ + K + 2 E K � � � r 2 � q 2 � q 2 ) = exp F ( � − 6 dσ ( K + N → KπN ) = Z 2 α E 1 ( a ) − 1 dσ ( K + γ → Kπ ) s − m 2 dt ds π dt K + ∞ � 2 e − z � s − m 2 z dz, a = 1 � 0 A 2 / 3 K + 3 r 2 E 1 ( a ) = 2 E K a E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 10/13

✂ ✁ 250 K ✄ N ☎ K ✄ ✆ ✝ N K ✄ N ☎ K ✄ ✆ ✝ N (anomaly only) K ✄ N ☎ K ✄ ✆ ✝ N (no anomaly) 200 16 14 b/GeV² 12 150 10 8 /ds, 6 100 4 d 2 50 0 0.4 0.45 0.5 0.55 0 0.4 0.5 0.6 0.7 0.8 0.9 1 s, GeV² E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 11/13

✂ ✁ 400 K ✄ N ☎ K ✄ ✆ ✝ N K ✄ N ☎ K ✄ ✆ ✝ N (anomaly only) 350 K ✄ N ☎ K ✝ ✆ ✄ N 16 300 14 b/GeV² 12 250 10 200 8 /ds, 6 150 4 d 2 100 0 0.4 0.45 0.5 0.55 50 0 0.4 0.5 0.6 0.7 0.8 0.9 1 s, GeV² E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 12/13

Conclusions ◮ A theoretical prediction has been made for the cross sections of K + γ → K + π 0 and K + γ → K 0 π + reactions at low energies. For the anomalous reaction, we predict two possible values depending on the a priori unknown sign of the interference term, which should be resolved by the experiment. ◮ It is possible to observe the chiral anomaly through comparison of cross section of K + Cu → K + π 0 Cu reaction with that of K + Cu → K 0 π + Cu reaction at √ s � 0 . 6 GeV 2 . The point is that only the first one has the anomaly which manifests itself as an increase in the cross section at low √ s . ◮ Luminosity of 60 µ b − 1 at 0 . 4 < s < 0 . 6 GeV 2 is planned to be collected in the Protvino experiment. In this case expected observations are ≈ 10 events of K 0 π + production and either ≈ 20 or ≈ 70 events of K + π 0 production, depending on the sign of the interference term. E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 13/13

π + γ → π + π 0 U D U π + π 0 π + π + π + π 0 D U U U D U γ γ γ π + π 0 π + D U U − 1 + 2 + 2 3 3 3 U D U π + π + π + π 0 π + π + D D U D D D γ γ γ π 0 π + π 0 D U D − 1 + 2 − 1 3 3 3 Total: 1 E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 1/2

K + γ → K + π 0 U S U K + π 0 K + K + K + π 0 S U U U S U γ γ γ K + π 0 K + S U U − 1 + 2 + 2 3 3 3 Total: 1 K + γ → K 0 π + U S U K + π + K + K 0 K + π + S D U D S D γ γ γ K 0 π + K 0 S U D − 1 + 2 − 1 3 3 3 Total: 0 E. V. Zhemchugov Chiral anomaly in Kγ → Kπ PRD 93, 094029; 1512.04438 2/2