Transverse Momentum Dependence of Semi-Inclusive Pion Production

PAC-34 Proposal PR12-09-017Spokespersons Peter Bosted, Rolf Ent, and Hamlet Mkrtchyan

PR12-09-017: Map the pT dependence (pT ~ < 0.5 GeV) of + and - production off proton and deuteron targets to study the kT dependence of (unpolarized) up and down quarks.

• Not much is known about the orbital motion of partons• Significant net orbital angular momentum of valence quarks implies significant transverse momentum of quarks

pT ~ <0.5 GeV chosen as theoretical framework for Semi-Inclusive Deep Inelastic Scattering has been well developed at small transverse momentum [A. Bacchetta et al., JHEP 0702 (2007) 093].

PR12-09-017 Collaboration

Semi-Inclusive Deep-Inelastic ScatteringPotentially rich physics arena for flavor decomposition, kT-dependent parton distribution functions, fragmentation, etc., but also many potential issues…

Multi-hall approach seems best, combining the large acceptance potential of CLAS12:

E12-06-112 Azimuthal distributions of final-state particlesE12-06-109 Flavor decomposition at large-x (SIDIS part)E12-07-107 Spin-Orbit Correlations w. Long. Pol. TargetE12-09-0xx 3 similar experiments emphasizing kaons

and the precision of the Hall C magnetic-spectrometer setup:

E12-06-104 Measurement of R = L/T in SIDIS (PAC-34) Precision +/- ratios in SIDIS:E12-09-002 I. Charge-Symmetry Violating PDFsE12-09-004 II. Flavor Dependence of the EMC EffectE12-09-017 Transverse Momentum Dependence of

Semi-Inclusive Pion production

(third advantage: reaching important corners of phase space, is not well enough established yet)

Solution: Detect a final state hadron in addition to scattered electron Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’

DIS probes only the sum of quarks and anti-quarks requires assumptions on the role of sea quarks

Measure inclusive (e,e’) at same time as (e,e’h)

SIDIS

SIDIS – Flavor Decomposition

• Leading-Order (LO) QCD • after integration over pT and • NLO: gluon radiation mixes x and z dependences

qqq

q

hqqq

(e,e') (x)(x)fe

(z)(x)Dfe

hX)(epdz

dσ

σ 2

2

1

: parton distribution function

: fragmentation function

)(xfq

)(zDhq

Closed (open) symbols reflect data after (before) events from coherent production are subtracted

GRV & CTEQ,@ LO or NLO

(Note: z = 0.65 ~ Mx

2 = 2.5 GeV2)

E00-108: Applicability of Parton Model

Good description for p and d targets for 0.4 < z < 0.65

PR12-09-017:

2.9 < M x

2 < 7.8 G

eV2

Pt = pt + z kt

+ O(kt2/Q2)

p

m

xTMD

TMDu(x,kT)

f1,g1,f1T ,g1T

h1, h1T ,h1L ,h1

Final transverse momentum of the detected pion Pt arises from convolution of the struck quark transverse momentum kt with the transverse momentum generated during the fragmentation pt.

Linked to framework of Transverse Momentum Dependent Parton Distributions

SIDIS – kT Dependence

General formalism for (e,e’h) coincidence reaction w. polarized beam:

Transverse momentum dependence of SIDIS

( = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction)

Unpolarized kT-dependent SIDIS: in framework of Anselmino et al. described in terms of convolution of quark distributions fq and (one or more) fragmentation functions Dq

h, each with own characteristic (Gaussian) width.

[A. Bacchetta et al., JHEP 0702 (2007) 093]

LUUTUU

thh

FFx

y

xyQdPdzddxdyd

d,,

22

2

2

2,

{2

1)1(2

}sin)2cos(cos sin)1(2)2cos(cos)1(2 hhhLUheUUhUUh FFF

Transverse momentum dependence of SIDISGeneral formalism for (e,e’h) coincidence reaction w. polarized beam:

( = azimuthal angle of e’ around the electron beam axis w.r.t. an arbitrary fixed direction)

Azimuthal h dependence crucial to separate out kinematic effects (Cahn effect) from twist-2 correlations and higher twist effects.

data fit on EMC (1987) and Fermilab (1993) data assuming

Cahn effect → <02> = 0.25

GeV2

(assuming 0,u =

0,d)

[A. Bacchetta et al., JHEP 0702 (2007) 093]

LUUTUU

thh

FFx

y

xyQdPdzddxdyd

d,,

22

2

2

2,

{2

1)1(2

}sin)2cos(cos sin)1(2)2cos(cos)1(2 hhhLUheUUhUUh FFF

Transverse momentum dependence of SIDISConstrain kT dependence of up and down quarks separately

1) Probe + and - final states

2) Use both proton and neutron (deuteron) targets

3) Combination allows, in principle, separation of

quark width from fragmentation widths(if sea quark contributions small)Spectrometers a must for such %-type (!) measurements:

acceptance is a common factor to all measurements(and can use identical H and D cells)

First example from JLab at 6 GeV on next slide(E00-108 experiment in Hall C,

H. Mkrtchyan, P. Bosted et al.,Phys. Lett. B665 (2008) 20)

Transverse momentum dependence of SIDIS

Pt dependence very similar for proton and deuterium targets, but deuterium slopes systematically smaller?

E00-108

Pt dependence very similar for proton and deuterium targets

Many authors believe these widths to be of order 0.25 GeV2 these numbers are close!

Transverse momentum dependence of SIDISSimple model, host of assumptions (factorization valid,

fragmentation functions do not depend on quark flavor, transverse momentum widths of quark and fragmentation functions are gaussian and can be added in quadrature, sea quarks are negligible, assume Cahn effect, etc.)

(+)2 ~ width of D+(z,pt), ()2 ~ width of D-

(z,pt), (u)2 ~ width of u(x,kt), (d)2 ~ width of d(x,kt)

Many authors believe these widths to be of order 0.25 GeV2 these numbers are close! But … is (u)2 < (d)2?? Expected from diquark models… Or, is there something wrong in our simple model or the used SIDIS framework?

Transverse Momentum Dependence: E00-108 Summary

E00-108 results can only be considered suggestive at best:• limited kinematic coverage

- assume (PT,) dependency ~ Cahn effect • very simple model assumptions

but PT dependence off D seems shallower than Hand intriguing explanation in terms of flavor/kT

deconvolutionMany limitations could be removed with 12 GeV:• wider range in Q2

• improved/full coverage in (at low pT)• larger range in PT

• wider range in x and z (to separate quark from fragmentation widths)

• possibility to check various model assumptions- Power of (1-z) for D-/D+

- quantitative contribution of Cahn term- Du

+ = Dd-

- Higher-twist contributions- consistency of various kinematics (global fit vs. single-point fits)

HMS + SHMS Accessible Phase Space for Deep Exclusive Scattering

For semi-inclusive, less Q2 phase space at fixed x due to:i) MX

2 > 2.5 GeV2; and ii) need to measure at both sides of

Choice of E12-09-017 Kinematics

6 GeV phase space

11 GeV phase space

E00-108

PR12-09-017Scan in (x,z,pT)+ scan in Q2

at fixed x

Choice of Kinematics – cont.Kin x Q2

(GeV2

)

z P (GeV)

(deg)

I 0.2 2.0 0.3 -0.6 1.7 – 3.3 8.0 – 23.0

II 0.3 3.0 0.3 -0.6 1.7 – 3.4 5.5 – 25.5

III 0.4 4.0 0.3 -0.6 1.7 – 3.4 5.5 – 25.5

IV 0.5 5.0 0.3 -0.6 1.7 – 3.5 8.0 – 28.0

V 0.3 1.8 0.3 -0.6 1.1 – 2.1 8.0 – 30.5

VI 0.3 4.5 0.3 -0.6 2.5 – 5.0 5.5 – 20.5

Kinematics I, II, III, and IV are identical to those where this collaboration also plans to map R (= L/T) in SIDIS in E12-06-104. This saves a total of five days, as follows:

1) three days of data taking2) one day of dedicated checkout3) one day for pass/kinematics changes and beam energy

meas.

Map of pT dependence in x and z, in Q2 to check (pT/Q) and (pT

2/Q2) behavior

PR12-09-017: PT coverage

• Excellent coverage up to pT = 0.2 GeV• Sufficient coverage up to pT = 0.4 GeV (compared to the E00-108 case below, now also good coverage at ~ 0o)• Limited coverage up to pT = 0.5 GeV

PT ~ 0.5 GeV: use dependencies measured in CLAS12 experiments (E12-06-112, LOI12-09-005)

= 0o

= 90o

= 180o

= 270o

pT = 0.4

pT = 0.6

Can do meaningful measurements at low pT (down to 0.05 GeV) due to excellent momentum and angle resolutions!

E00-108

Choice of Kinematics – cont.Kin E

(GeV)

E’ (GeV

)

e’ (deg

)

W2 (GeV2)

(deg

)

q (GeV

)

I 11.0 5.67 10.27 8.88 10.57 5.51

II 11.0 5.67 12.59 7.88 12.75 5.60

III 11.0 5.67 14.55 6.88 14.49 5.69

IV 11.0 5.67 16.28 5.88 15.96 5.78

V 8.8 5.60 10.96 5.08 17.90 3.47

VI 11.0 5.67 21.26 11.38 7.57 8.27• Keep HMS momentum (~E’) constant for all kinematics• Dedicated measurements (within requested beam time) will be added with E’ increased by 25% and possibly

50% for radiative correction modeling.(HMS goes to 7.3 GeV momentum need to swap HMS-SHMS roles for

50%)

• E12-06-104 includes beam time at E = 6.6 GeV.We plan to dedicate part of that time also for

radiative correction modeling.

Systematic Uncertainties in +/- Ratios

Project Source HMS(*) SHMS

Spectrometer Acceptance(**) 0.1% 0.4%

Tracking Efficiency(**) 0.1% 0.4%

Detection Efficiency(**) 0.1% 0.4%

Pion Absorption Correction 0.1%

Radiative Corrections(***) 0.5%

Added in Quadrature 0.9%

Anticipated systematic uncertainties in ratios of transverse momentum dependences. The combined use of the CLAS12 experiments is assumed to fully constrain the (pT,)

dependency.

(*) HMS is kept at constant momentum of 5.67 GeV, at forward scattering angles (<22 degrees, hence viewing a 3.7 cm effective target length), at singles rates < 100 kHz, and at /e ratios < 13.

(**) The main uncertainties are due to spectrometer polarity changes.The SHMS total rate is kept <700 kHz to constrain the tracking eff.

(***) Assuming dedicated measurements to constrain therequired radiative correction model input.

Radiation contributions, including from exclusive

Contributions from

Non-trivial contributions to (e,e’) Cross Section

Further data from CLAS12 () and Hall C (F -12, CT-12) will constrain!

Non-trivial contributions to (e,e’) Cross Section

Radiative Corrections - Typical corrections are <10% for z < 0.7. - Checked with SIMC and POLRAD 2.0. - Good agreement between both methods.

Exclusive Pions - Interpolated low-W2, low-Q2 of MAID with high-W2, high-Q2 of Brauel/Bebek. - Introduces large uncertainty at low z, but contributions there are small. - Tail agreed to 10-15% with “HARPRAD”. - Further constraints with F-12 and CT-12.

Pions from Diffractive - Used PYTHIA with modifications as implemented by HERMES (Liebing,Tytgat). - Used this to guide cross section in SIMC. - simulated results agree to 10-15% with CLAS data (Harut Avagian). - In all cases, quote results with/without diffractive subtraction.

PR12-09-017 Projected Results - I

III

II

I

IV

VI

V

Kaon IdentificationParticle identification in SHMS:0) TOF at low momentum (~1.5 GeV)1)Heavy (C4F8O) Gas Cherenkov

to select + (> 3 GeV)2)60 cm of empty space could be

used for two aerogel detectors:- n = 1.015 to select + (> 1 GeV)

select K+ (> 3 GeV)- n = 1.055 to select K+ (>1.5 GeV)

Heavy Gas Cherenkov and 60 cm of empty space

PR12-09-017 Projected Results - Kaons

III

II

I

IV

VI

V

Transverse Momentum Dependence of Semi-Inclusive Pion Production

PR12-09-017: Map the pT dependence (pT ~ < 0.5 GeV) of + and - production off proton and deuteron targets to measure the kT dependence of up and down quarks

• Not much is known about the orbital motion of partons• Significant net orbital angular momentum of valence quarks implies significant transverse momentum of quarks

Can only be done using spectrometer setup capable of %-

type measurements (an essential ingredient of the global SIDIS program!)

Beam time request: 32 days of beam time in Hall CBeam time request: 32 days of beam time in Hall C

Spin-off: Radiative correction modeling for (e,e’)Single-spin asymmetries at low pT (< 0.2

GeV)Low-energy (x,z) factorization for kaons

Appendix

PR12-09-017: Beam Time Request• Map yields as function of z and pT at x = 0.2 and Q2 = 2.0 GeV2

4.5 Days (incl. overhead)• Map yields as function of z and pT at x = 0.3 and Q2 = 3.0 GeV2

5.8 Days• Map yields as function of z and pT at x = 0.4 and Q2 = 4.0 GeV2

5.3 Days• Map yields as function of z and pT at x = 0.5 and Q2 = 5.0 GeV2

5.3 Days• Map yields as function of z and pT at x = 0.3 and Q2 = 1.8 GeV2

6.9 Days• Map yields as function of z and pT at x = 0.3 and Q2 = 4.5 GeV2

4.0 Days

Total: 32 Days (incl. overhead)

* Overhead consists of spectrometer polarity, momentum, and angle, and target changes

PR12-09-017 Projected Results - IISimulated data use (u)2 = (d)2 = 0.2, and then fit using statistical errors.Step 1: Kinematics I-VI fitted separately, (pT,) dependency ~ Cahn

Step 2: Add eight parameters to mimic possible HT, but assume Cahn uncertainties grow with about factor of two

Step 3: Simulate with and without Cahn term results remain similar as in step 2

Step 1: Kinematics I-VI fitted separately, (pT,) dependency ~ Cahn(if all six fitted together, diameter < 0.01 GeV2)

Step 2: Add eight parameters to mimic possible HT, but assume Cahn uncertainties grow with about factor of two(if all six fitted together, diameter remains < 0.01 GeV2)

Step 3: Simulate with and without Cahn term results remain similar as in step 2(if all six fitted together, diameter grows to < 0.02 GeV2)

PR12-09-017 Projected Results - II

Step 1: Kinematics I-VI fitted separately, (pT,) dependency ~ Cahn

Step 2: Add eight parameters to mimic possible HT, but assume Cahn uncertainties grow with about factor of two

Step 3: Simulate with and without Cahn term results remain similar as in step 2

Simulated data use (u)2 = (d)2 = 0.2, and then fit using statistical errors.

Choice of PR12-09-017 Kinematics

• W2 = 5.08 GeV2 and larger (up to 11.38 GeV2)

• Use SHMS angle down to 5.5 degrees (for detection) HMS angle down to 10.5 degrees (e- detection) separation HMS-SHMS > 17.5 degrees

• MX2 = Mp

2 + Q2(1/x – 1)(1 – z) > 2.9 GeV2 (up to 7.8

GeV2)

• Choice to keep Q2/x fixed q ~ constant• exception are data scanning Q2 at fixed x

• All kinematics both for + (and K+) and - (and K-), both for LH2 and LD2 (and Al

dummy)

• Choose z > 0.3 (p > 1.7 GeV) to be able to neglect differences in (+N) and (-N)

• not possible for x = 0.3, Q2 = 1.80: p > 1.1 GeV

Experimental Details• Beam current is varied to keep the total SHMS rate below 700 kHz

• 10-80 A beam currents (with 10 cm LH2/LD2)• rate limitation to guarantee precision +/- ratios• Anticipated syst. uncertainty in ratio 0.9%• Real : Accidental ratio typically ~ 2 : 1

Experimental Details and Spin-Off

• Syst. uncertainty has four roughly equal ingredients: spectrometer acceptance, tracking + detector efficiencies, radiative corrections

• to model latter, include dedicated runs at lower E and E’• Collaboration did similar (published) modeling efforts on JLab inclusive 1H(e,e’) and 2H(e,e’) scattering results

• While this measurement is not ideally suited to measurement of Single-Spin Asymmetries (lack of full coverage), we expect to map such SSA’s well up to pT ~ 0.2 GeV (with errors of typ. 0.003-0.008), further facilitating kT-dependence model checking

• Hence, we request 80% long. polarized beam• Kaon identification would be facilitated by the addition of an aerogel detector to the SHMS base detector package

• study the low-energy (x,z) factorization for charged kaons• Collaboration built HMS aerogel detector (NIM A548, 364)

PR12-09-017 TAC Report1. The proposal assumes that the experiment will be scheduled so

that its run plan can be combined with E12-06-104. Therefore, the time request does not include time for checkout, pass changes and beam energy measurements.

This is correct. Including this time would require an additional five (three DAQ and two overhead) days. In the proposal we stated eight days, which is incorrect: E12-06-104 required higher statistics runs.

2. In the early years of 12 GeV operation, the practical limit on beam current for 11 GeV running will be 75 A.

In about half of the kinematics beam currents of 75 A or less are used to limit the hadron singles rates in SHMS to less than 700 kHz. The impact from Table IX is then ((80-75)/75*260) = 17.5 hours.

3. Comments on measurements of SIDIS observables: The adequate coverage at small (!) pT is shown in the

proposal. This experiment only addresses the pT dependence of + and - off LH2 and LD2. Pions from diffractively produced mesons are simulated taking into account HERMES input and checked vs. CLAS data.

4. Comments on measurements involving kaons/strange quarks: PR12-09-017 kaon measurements affect factorization tests

only.

Backup Slides (not printed)

Total point-to-point Total point-to-point systematic systematic uncertainty for E94-uncertainty for E94-110 is 1.6%.110 is 1.6%.

Compare with SLAC E140X (DIS)

1 x 10-3 0.3%1 x 10-3 0.2%0.1 mr 0.3%0.3% 0.3%0.2% 0.2%0.3% 0.3%0.1% 0.1%0.2% 0.2%0.5% 0.5%

1.0% 1.0%1.3%

Systematic Uncertainties – the (e,e’) Case

Projected SystematicUncertainty

Source

Pt-Ptε-randomt-random

ε-uncorrelate

dcommon to all t-bins

Scaleε-globalt-global

Spectrometer Acceptance 0.4% 0.4% 1.0%

Target Thickness 0.2% 0.8%

Beam Charge - 0.2% 0.5%

HMS+SHMS Tracking 0.1% 0.4% 1.5%

Coincidence Blocking 0.2%

PID 0.4%

Pion Decay Correction 0.03% - 0.5%

Pion Absorption Correction

- 0.1% 1.5%

MC Model Dependence 0.2% 1.0% 0.5%

Radiative Corrections 0.1% 0.4% 2.0%

Kinematic Offsets 0.4% 1.0% -Added in quadrature: 1.8%

Systematic Uncertainties – the z 1 LimitFrom: G. Huber’s presentation on PR12-06-101 “Measurement of the Charged Pion Form Factor to High Q2”

SHMS Tracking Efficiency ConsiderationsSeveral approved experiments (E12-06-101, E12-06-104, E12-07-105) require good tracking efficiency knowledge at ~1 MHz rate.HMS tracking efficiency is robust, but we typically still restrict rates to < 0.5 MHz:

Rate dependence well understood on basis of Poisson statistics:- DC TDC’s have wider window than hodoscope TDC’s (difference fit with 77 ns)- varying width of DC TDC window find same corrected yield!- 2 electron tracks tracking efficiency 70 +/- 3% (can’t find track for two electrons close-by): agrees well with number found from TDC window study- Important to have device with well-defined rates and aperture

SHMS Design incorporates well-shielded detector hut, well-defined apertures, 3X and 3Y measurements per chamber, and multi-hit TDCs Good knowledge @ 1 MHz probable (but lot of work)

So what about R = L/T for pion electroproduction?

quark

“Semi-inclusive DIS”

RSIDIS RDIS disappears with Q2!

“Deep exclusive scattering” is the z 1 limit of this “semi-inclusive DIS” process

Here, R = L/T ~ Q2

Not clear what R will behave like at large pT

Example of 12-GeV

projected data

assuming R

SIDIS =

RDIS

How Can We Verify Factorization?Neglect sea quarks and assume no pt dependence to parton distribution functions

Fragmentation function dependence drops out in Leading Order

[p(+) + p(-)]/[d(+) + d(-)]

= [4u(x) + d(x)]/[5(u(x) + d(x))]

~ p/d independent of z and pt

[p(+) - p(-)]/[d(+) - d(-)]

= [4u(x) - d(x)]/[3(u(x) + d(x))]

independent of z and pt,

but more sensitive to assumptions

E00-108: Leading-Order x-z factorization

1R*4

R4

D

D

π

π

N

NR

(Resonances cancel (in SU(6)) in D-/D+ ratioextracted from deuterium data)

region

(Deuterium data)

Should not depend on x

But should depend on z

Solid lines: simple Quark Parton Model prescription assuming

factorization

quark

Collinear Fragmentation

factorization

E00-108 (6 GeV): PT coverage

E00-108 measured up to PT2 ~ 0.2 GeV2, but coverage was not

complete needed to make assumptions on (PT,) dependencies: ~ Cahn effect

General formalism for (e,e’h) coincidence reaction:

Factorized formalism for SIDIS (e,e’h):

In general, A and B are functions of (x,Q2,z,pT,).

e.g., “Cahn

effect”:

Transverse momentum dependence of SIDIS

Model PT dependence of SIDISGaussian distributions for PT dependence, no sea quarks, and leading order in (kT/q)

Inverse of total width for each combination of quark flavor and fragmentation function given by:

And take Cahn effect into account, with e.g. (similar for c2, c3, and c4):

Duality in Meson Electroproduction

hadronic description quark-gluon description

TransitionForm Factor

DecayAmplitude

Fragmentation Function

Requires non-trivial cancellations of decay angular distributions If duality is not observed, factorization is

questionableDuality and factorization possible for Q2,W2 3

GeV2 (Close and Isgur, Phys. Lett. B509, 81 (2001))

p┴ = PT – z k┴ + O(k┴

2/Q2)

kT-dependent SIDIS

data fit assuming Cahn effect → <0

2> = 0.25 GeV2

EMC (1987) and Fermilab (1993) data(assuming 0

u = 0

d)

Anselmino et al

Factorization of kT-dependent PDFs proven at low PT of hadrons (Ji et al) Universality of kT-dependent distribution and fragmentation functions

proven (Collins,Metz, …)

Transverse Momentum Dependence of Semi-Inclusive Pion Production

Outline:• SIDIS: framework and general remarks • Results from E00-108

- Low-energy (x,z) factorization for charged pions- Transverse momentum dependence of charged pions

• PR12-09-017- Choice of kinematics- Experimental details

• Spin-off relevant for the general SIDIS program- Radiative correction modeling: linking to z = 1- Single-spin asymmetries- Low-energy (x,z) factorization for charged kaons

• PR12-09-07 Beam Time Request and Projected Results

PAC-34 Proposal PR12-09-017

Solution: Detect a final state hadron in addition to scattered electron Can ‘tag’ the flavor of the struck quark by measuring the hadrons produced: ‘flavor tagging’

DIS probes only the sum of quarks and anti-quarks requires assumptions on the role of sea quarks

SIDIS

SIDIS – Flavor Decomposition

(e,e’)

(e,e’m)

Mx2 = W2 = M2 + Q2 (1/x – 1)

Mx2 = W’2 = M2 + Q2 (1/x – 1)(1 - z)

z = Em/

(For Mm small, pm collinear with , and Q2/2 << 1)

(M,0)

Low-Energy x-z Factorization

P.J. Mulders, hep-ph/0010199 (EPIC Workshop, MIT, 2000)

At large z-values easier to separate current and target fragmentation region for fast hadrons factorization (Berger Criterion) “works” at lower energies

At W = 2.5 GeV: z > 0.4 At W = 5 GeV: z > 0.2(Typical JLab-6 GeV) (Typical HERMES)

(after integration over pT and )

Final transverse momentum of the detected pion Pt arises from convolution of the struck quark transverse momentum kt with the transverse momentum generated during the fragmentation pt.

SIDIS – kT Dependence

PR12-09-017: Map the pT dependence (pT ~ < 0.5 GeV) of + and - production off proton and deuteron targets to study the kT dependence of (unpolarized) up and down quarks

Pt = pt + z kt

+ O(kt2/Q2)

Spin-off: study x-z Factorization for kaons

P.J. Mulders, hep-ph/0010199 (EPIC Workshop, MIT, 2000)

At large z-values easier to separate current and target fragmentation region for fast hadrons factorization (Berger Criterion) “works” at lower energies

At W = 2.5 GeV: z > 0.6If same arguments as validated for apply to K:

(but, z < 0.65 limit may not apply for kaons!)